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1403 | 1403.2771_arXiv.txt | Improvement in telescope detection limits, % technical evolution of detectors and emergence of huge databases of observational data resulted in more careful spectral classification of objects, and provision of new spectral subclasses. % In 2010, \citet{WalbornOIfc} proposed to introduce a new subclass ${\rm Ofc}$ to denote O-stars with comparable intensity of C{\scriptsize III}~$\lambda\lambda 4647, 4650, 4652$ and N{\scriptsize III}~$\lambda\lambda4634, 4640, 4642$ lines. This phenomenon is often observed at spectral type O5 at all luminosity classes, but preferentially in some associations or clusters and not the others \citep{WalbornOIfc}. % For today, eighteen Galactic O-stars are classified as ${\rm Ofc}$. % Although ${\rm Ofc}$ class was introduced recently, CNO dichotomy is well known among O-stars (\citet{WalbornCNO,Walborn03,Walborn76} and references therein). Anticorrelations of N versus C and O and correlations with He/H % have encouraged interpretations in terms of mixing of CNO-cycled material into the atmospheres and winds of massive stars. The mixing depends on the rotation rate and increases at low metallicity \citep{MaederMeynet}. But whether ${\rm Ofc}$ stars are related to CNO dichotomy only? With the advent of the ${\rm Ofc}$ class of stars the following questions arose: \begin{itemize} \item[-] Whether it is related only to the CNO-cycle and mixing processes in the star itself or it arises under the influence of a general dynamical evolution of clusters or associations? \item[-] How does multiplicity of objects influence the excess of carbon? \item[-] Are there differences between the physical parameters of ${\rm Ofc}$ stars and ${\rm Of}$ stars? \item[-] How should an $ {\rm Ofc} $ star evolve further? % \end{itemize} To obtain more data and to estimate more parameters of ${\rm Ofc}$ stars are important steps for better understanding of the nature of these objects. \objeleven\footnote{$\alpha$=20:34:08.52 $\delta$=+41:36:59.36 according to SIMBAD {http://simbad.u-strasbg.fr/simbad/}} \ is one of the Galactic supergiants % located near the northern border of the Cyg~OB2 (VI Cygni) association. This association was first noticed more than half a century ago by \citet{MunchMorgan}. It still attracts the attention of researchers due to the large number of O-stars and extremely high, heterogeneous interstellar reddening. Star \#11 was immediately recognized as a member of the association \citep{MunchMorgan}. The first spectroscopy of the brightest stars belonging to Cyg~OB2 (including \#11) was performed by \citet{JohnsonMorgan}. They classified \objeleven \ as O6f. Later \citet{Walborn73} classified the star as ${\rm O5~If_+}$ using spectrograms obtained at Kitt Peak National Observatory. \citet{MT91} performed its CCD photometry in three (U, B, V) bands. \objeleven \ is included in their catalog under number 734 (MT91 734). Stellar magnitude in $V$ band is $V=10.03~{\rm mag}$ \citep{MT91}. % As of now, \objeleven \ is classified as $ {\rm O5.5~Ifc}$ \citep{WalbornOIfc,Sota}. \citet{binaryO11} found that \objeleven \ is a single-lined spectroscopic binary (SB1 type). The spectrum of \objeleven \ was modeled previously by several groups. Initially, by means of numerical modeling \citet{Herrero1999} determined the parameters of \objeleven \ (effective temperature, luminosity, ${\log{g}}$ and helium abundance). They compared the spectral line profiles of H, He I and He II with the line profiles synthesized for a large set of NLTE plane-parallel, hydrostatic model atmospheres. \citet{HerreroUV} measured terminal velocity of the wind employing resonance lines in the ultraviolet range. Then \objeleven \ was modeled by \citet{Herrero2002} using the {\sc fastwind} \citep{fastwind, Puls} code. In that work the mass-loss rate and velocity law in the stellar wind have been determined. Finally, \citet{MokiemObj7} for the first time applied the automated fitting method and clarified the physical parameters of \objeleven. It is worth noting that the mass-loss rate was determined by \citet{Herrero2002} and \citet{MokiemObj7} without taking clumping into account. Inhomogeneities in the winds of the stars were studied in the article \citet{PulsMarkova}. Based on a simultaneous modeling of H$\alpha$, infrared, millimeter and radio observations authors concluded that clumping is three to six times stronger in the lower wind, where H$\alpha$ forms, compared with the outer wind, where the radio continuum originates. In the next section, we describe the observational data and their processing. In Section~\ref{sec:model} we will tell about the construction of the model, discuss the results and compare them with previous works. Section~\ref{sec:chemical} is devoted to determination of chemical composition of the atmosphere of \objeleven, while Section~\ref{sec:diagram} shows locations of \objeleven \ on the different diagrams. The search for companions of \objeleven \ is described in Section~\ref{sec:binary}. The conclusions are presented in Section~\ref{sec:results}. | 14 | 3 | 1403.2771 |
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1403 | 1403.3893_arXiv.txt | $B$$V$$R_{\rm C}$$I_{\rm C}$ photometry and low-, medium- and high-resolution Echelle fluxed spectroscopy is presented and discussed for three faint, heavily reddened novae of the FeII-type which erupted in 2013. V1830 Nova Aql 2013 reached a peak $V$=15.2 mag on 2013 Oct 30.3 UT and suffered from a huge $E_{B-V}$$\sim$2.6 mag reddening. After a rapid decline, when the nova was $\Delta V$=1.7 mag below maximum, it entered a flat plateau where it remained for a month until Solar conjunction prevented further observations. Similar values were observed for V556 Nova Ser 2013, that peaked near $R_{\rm C}$$\sim$12.3 around 2013 Nov 25 and soon went lost in the glare of sunset sky. A lot more observations were obtained for V809 Nova Cep 2013, that peaked at $V$=11.18 on 2013 Feb 3.6. The reddening is $E_{B-V}$$\sim$1.7 and the nova is located within or immediately behind the spiral Outer Arm, at a distance of $\sim$6.5 kpc as constrained by the velocity of interstellar atomic lines and the rate of decline from maximum. While passing at $t_3$, the nova begun to form a thick dust layer that caused a peak extinction of $\Delta V$$>$5 mag, and took 125 days to completely dissolve. The dust extinction turned from neutral to selective around 6000 \AA. Monitoring the time evolution of the integrated flux of emission lines allowed to constrain the region of dust formation in the ejecta to be above the region of formation of OI 7774 \AA\ and below that of CaII triplet. Along the decline from maximum and before the dust obscuration, the emission line profiles of Nova Cep 2013 developed a narrow component (FWHM=210 km/sec) superimposed onto the much larger normal profile, making it a member of the so far exclusive but growing club of novae displaying this peculiar feature. Constrains based on the optical thickness of the innermost part of the ejecta and on the radiated flux, place the origin of the narrow feature within highly structured internal ejecta and well away from the central binary. | Several Galactic novae are regularly missed because of yearly Sun conjunction with the Galactic central regions, where most of them appear, or because the heavy interstellar absorption low on the Galactic plane dims them below the observability threshold. Others are so fast that remains above the detection threshold of equipment used by amateur astronomers (who discover the near totality of Galactic novae), for too short a time to get a fair chance to be discovered (Warner 1989, 2008; Munari 2012). Finally, a significant fraction of those discovered and catalogued lack published data necessary to properly document and characterized them (Duerbeck 1988). All these deficiencies reflect into still debated statistics about the basic properties of the Galactic novae, like their average number per year or their fractional partnership to Galactic populations like the Bulge, and the Thin Disk and the Thick Disk (della Valle and Livio 1998; della Valle 2002; Shafter 2002, 2008). The latter has long reaching implications about the origin, birth-rate and evolution of binary systems leading to nova eruption, the amount and type of nuclearly-processed material returned to the interstellar medium, the viability of recurrent novae as possible precursors of type Ia supernovae. Three heavily reddened and faint novae appeared in 2013. V1830~Aql and V556~Ser were rapidly lost in the glare of sunset sky, and the spectroscopic observations here presented could possibly be the only multi-epoch available. V809~Cep was more favourably placed on the sky, but its peak brightnes of just $V$=11.18, the fast decline and the very thick dust cocoon it rapidly developped one month into the decline required a highly motivated effort to conduct a thorough monitoring at optical wavelengths. As a result of our effort to contribute to the documentation of as many as possible of the less observed novae, in this paper we present the results and analysis of our $B$$V$$R_{\rm C}$$I_{\rm C}$ photometry and low-, medium- and high-resolution fluxed spectroscopy of these three novae. | 14 | 3 | 1403.3893 |
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1403 | 1403.6708_arXiv.txt | {We investigate iPTF13bvn, a core-collapse (CC) supernova (SN) in the nearby spiral galaxy NGC 5806. This object was discovered by the intermediate Palomar Transient Factory (iPTF) very close to the estimated explosion date and was classified as a stripped-envelope CC~SN, likely of Type Ib. Furthermore, a possible progenitor detection in pre-explosion \textit{Hubble Space Telescope (HST)} images was reported, making this the only SN~Ib with such an identification. Based on the luminosity and color of the progenitor candidate, as well as on early-time spectra and photometry of the SN, it was argued that the progenitor candidate is consistent with a single, massive Wolf-Rayet (WR) star.} {We aim to confirm the progenitor detection, to robustly classify the SN using additional spectroscopy, and to investigate if our follow-up photometric and spectroscopic data on iPTF13bvn are consistent with a single-star WR progenitor scenario.} {We present a large set of observational data, consisting of multi-band light curves (\textit{UBVRI}, $g^{\prime} r^{\prime} i^{\prime} z^{\prime}$) and optical spectra. We perform standard spectral line analysis to track the evolution of the SN ejecta. We also construct a bolometric light curve and perform hydrodynamical calculations to model this light curve to constrain the synthesized radioactive nickel mass and the total ejecta mass of the SN. Late-time photometry is analyzed to constrain the amount of oxygen. Furthermore, image registration of pre- and post-explosion \textit{HST} images is performed.} {Our \textit{HST} astrometry confirms the location of the progenitor candidate of iPTF13bvn, and follow-up spectra securely classify this as a SN~Ib. We use our hydrodynamical model to fit the observed bolometric light curve, estimating the total ejecta mass to be 1.9~\msun\ and the radioactive nickel mass to be 0.05~\msun. The model fit requires the nickel synthesized in the explosion to be highly mixed out in the ejecta. We also find that the late-time nebular $r^{\prime}$-band luminosity is not consistent with predictions based on the expected oxygen nucleosynthesis in very massive stars.} {We find that our bolometric light curve of iPTF13bvn is not consistent with the previously proposed single massive WR-star progenitor scenario. The total ejecta mass and, in particular, the late-time oxygen emission are both significantly lower than what would be expected from a single WR progenitor with a main-sequence mass of at least 30~\msun.} | \label{sec:intro} Type Ibc core-collapse supernovae (CC~SNe) have either had their envelopes stripped of hydrogen (SNe~Ib) or stripped of both hydrogen and helium in the case of SNe~Ic \citep[e.g.,][]{1997ARA&A..35..309F}. The mass loss could either be due to an extensive wind in a single massive star \citep{2014A&A...564A..30G}, or due to binary interaction \citep{Yoon:2010aa}. The discovery of iPTF13bvn was made by the intermediate Palomar Transient Factory (iPTF) \citep{Law:2009aa} in the nearby\footnote{$d = 22.5$~Mpc, $\mu = 31.76$~mag \citep{Tully:2009}.} galaxy NGC 5806 on 2013 June 16.24 (UT), just 0.57 days past the estimated explosion date \citep[JD 2456459.17;][]{2013ApJ...775L...7C}. Early-time spectra indicated a likely Type Ib classification. Furthermore, \cite{2013ApJ...775L...7C} used adaptive optics (AO) images and {\it Hubble Space Telescope (HST)} pre-explosion archival images to show that there is a possible progenitor within 80 milliarcsec (mas) of the estimated location of the explosion. The luminosity and colors of this progenitor candidate are consistent with those of a single Wolf-Rayet (WR) star. \cite{2013ApJ...775L...7C} further argue that the early-time light curves (LCs) and spectra in the optical and near-infrared, along with the mass-loss rate estimated from radio observations, are all consistent with a WR star as the progenitor. WR stars are very massive, with zero-age main-sequence masses ($M_{\mathrm{ZAMS}}$) easily surpassing 30~\msun~\citep{1981A&A....99...97M,2007ARA&A..45..177C}. These stars have very strong winds, resulting in high mass-loss rates ($\dot{{M}}$) sometimes even exceeding $\dot{{M}}$~$\approx$~$10^{-5}$~\msun~yr$^{-1}$. It is believed that the high mass-loss rate can cause the entire hydrogen envelope to be expelled before the star undergoes core collapse \citep{Groh:2013ab,2014A&A...564A..30G}. The result of this would then be a stripped-envelope Type Ib supernova. Following the discovery and the possible progenitor detection, \cite{Groh:2013aa} used their Geneva stellar evolution models \citep{Groh:2013ab,2014A&A...564A..30G} in combination with the radiative transfer code \emph{CMFGEN} \citep{1998ApJ...496..407H} to model iPTF13bvn. They conclude that the possible progenitor candidate detection and the early-time photometry and spectroscopy are compatible with a model where the progenitor of iPTF13bvn is a single WR star with a main-sequence mass of 32 \msun. In this paper, we expand on the discussion of iPTF13bvn. In Sect.~\ref{sec:Observations and Data Reduction} we describe our follow-up observations and give details of the data reduction. Section~\ref{sec:prog_13bvn} provides a confirmation of the astrometric identification of the {\it HST} progenitor candidate. In Sect.~\ref{sec:Photometry} we present the filtered LCs and describe the construction of the bolometric LC of iPTF13bvn. We use semi-analytic arguments based on the model of \cite{1982ApJ...253..785A} and the methodology developed by \cite{Cano:2013aa} to show that the bolometric properties of the SN are not consistent with the progenitor being very massive (i.e., $M_{\rm ZAMS} > 30$~\msun). In Sect.~\ref{sec:Spectroscopy} we report our follow-up spectroscopy, confirm the classification of iPTF13bvn as a SN~Ib and provide velocity measurements of the SN ejecta. The latter are used in Sect.~\ref{sec:hydro} together with the hydrodynamical model \emph{HYDE} (Ergon et al. 2014b, in prep.) to further constrain the synthesized nickel and ejecta masses of the explosion and the helium-core mass of the progenitor. In Sect.~\ref{sec:Spectroscopy} we also use late-time photometry ($> 200$ days past the explosion) to constrain the amount of oxygen in the ejecta by comparing our data to the detailed nebular modeling by \cite{jerkstrand2014}. These results are also inconsistent with a very massive progenitor. | We have confirmed the classification of iPTF13bvn as a Type Ib SN, and also that the pre-explosion {\it HST} progenitor identification suggested by \cite{2013ApJ...775L...7C} is very likely correct (Sect.~\ref{sec:prog_13bvn}). While the color and luminosity of the progenitor in the {\it HST} images are consistent with those of a WR star, we have shown that the later-time photometry (Sect.~\ref{sec:Photometry}) of iPTF13bvn is not consistent with a single, very massive WR progenitor scenario. Our hydrodynamical model can fit the observed bolometric light curve to constrain the total ejecta mass to be $\sim1.9$~\msun. The corresponding mass of the He core of the progenitor is $\sim 3.4$~\msun\ immediately prior to the explosion. The synthesized nickel mass is constrained to be $\sim0.05$~\msun. The model also requires the synthesized nickel to be highly mixed out in the ejecta, consistent with the high average mixing found for the sample of SNe~Ibc by \cite{taddia2014}. The total ejecta mass and our limits on the late-time oxygen emission are both inconsistent with what would be expected from a single massive WR progenitor with $M_{\mathrm{ZAMS}} \approx 30$~\msun\ as suggested by \cite{Groh:2013aa}. We note that while it could be argued that a significant part of the He core could fall back onto the central compact object, such a scenario that still produces an apparently nickel-powered LC, normal observed photospheric velocities, and the measured oxygen emission appears unlikely. We also note that while the deduced high mass-loss rate was interpreted by \cite{Groh:2013aa} as favoring a massive WR star, the mass-loss estimate depends on an assumed high stellar wind velocity. A lower wind velocity in combination with the radio measurements of \cite{2013ApJ...775L...7C} can also be consistent with a less massive star. To date, the SN~Ibc showing the largest deviation in LC shape compared to the typical SN~Ibc LC \citep[e.g.,][]{2011ApJ...741...97D,taddia2014} is the bolometric LC of SN~Ic~2011bm presented by \cite{Valenti:2012aa}. SN~2011bm has a very high peak luminosity and (most importantly) a very slow evolution of the bolometric LC and a broad peak, which is difficult to explain without assuming a very high ($> 30$~\msun) main-sequence mass for the progenitor. This is the kind of SN LC we would expect from a scenario including the very massive progenitor star suggested by \cite{Groh:2013aa}. It is clear that the bolometric LC of iPTF13bvn is very different from that of SN~2011bm. If the progenitor is less massive, a binary system for the progenitor is perhaps the most natural conclusion. Using the progenitor constraints from our hydrodynamical model, the evolutionary models for binary systems by \cite{Yoon:2010aa} predict values for the radius, mass-loss rate, and hydrogen content in the progenitor that are all consistent with what can be derived from the early-time observations by \cite{2013ApJ...775L...7C}. In contrast, current single-star evolutionary synthesis models \citep[e.g.,][]{Groh:2013ab} have a harder time producing a progenitor with a sufficiently low mass to match the observed properties; stars with low enough ZAMS masses to explain the low ejecta mass, as well as the observed nebular oxygen emission constraints, are not predicted to produce SNe~Ibc in this context. The ultimate test to assess the nature of the progenitor will be to reobserve the location of iPTF13bvn with {\it HST} after the SN has faded. A single massive WR progenitor scenario predicts that the progenitor candidate would completely disappear, while a less massive progenitor in a binary system would lead to a smaller decrease in the luminosity at the location of the progenitor. Finally, we emphasize that the use of the new \cite{jerkstrand2014} nebular modeling in conjunction with photometry during the nebular phase could be an efficient way to constrain the ZAMS masses for a larger sample of stripped-envelope CC~SNe. Future studies of nebular spectra of iPTF13bvn are planned, and we are also performing a detailed investigation of the host environment of the SN (Fremling et al. 2014b, in prep.). | 14 | 3 | 1403.6708 |
1403 | 1403.6825_arXiv.txt | Supernovae provide a backdrop from which we can probe the end state of stellar evolution in the final years before the progenitor star explodes. As the shock from the supernova expands, the timespan of mass loss history we are able to probe also extends, providing insight to rapid time-scale processes that govern the end state of massive stars. While supernovae transition into remnants on timescales of decades to centuries, observations of this phase are currently limited. Here we present observations of SN\,1970G, serendipitously observed during the monitoring campaign of SN\,2011fe that shares the same host galaxy. Utilizing the new Jansky Very Large Array upgrade and a deep X-ray exposure taken by the Chandra Space Telescope, we are able to recover this middle-aged supernova and distinctly resolve it from the HII cloud with which it is associated. We find that the flux density of SN\,1970G has changed significantly since it was last observed - the X-ray luminosity has increased by a factor of $\sim 3$, while we observe a significantly lower radio flux of only $27.5 \mu$Jy at 6.75 GHz, a level only detectable through the upgrades now in operation at the Jansky Very Large Array. These changes suggest that SN\,1970G has entered a new stage of evolution towards a supernova remnant, and we may be detecting the turn-on of the pulsar wind nebula. Deep radio observations of additional middle-aged supernovae with the improved radio facilities will provide a statistical census of the delicate transition period between supernova and remnant. | Middle-aged radio supernovae span the gap in which the non-thermal radio emission is attributed to shock interaction with the circumstellar material (CSM) as shaped by the evolution of the progenitor star, and the interstellar material (ISM). This transition occurs on a time-scale of decades and radio studies probe the final stages of stellar evolution including the progenitor star mass loss rate. Several middle-aged radio supernovae have shown strong time evolution in their radio fluxes indicating variable densitiy profiles. For example, historical supernovae in M83 show a wide range of radio emission properties \citep{historical_sne} and observations of SN 1980K from 1994-1995 show a rapid decline in flux (a factor of two below the expected flux from the previous measured power-law decline), which is believed to be due to a decline in the circumstellar density \citep{98k_dropoff}. Similarly, \citet{57D_dropoff} measured a steep decline in radio flux from SN 1957D ($F_{\nu}\propto t^{\alpha}$; $\alpha = -2.9 \pm 0.3$), steeper than other intermediate aged supernovae. The detection of radio emission from nearby Type IIb supernovae (hydrogen and helium dominate the optical spectra; e.g., \citealt{matheson}) has occurred more frequently with detections of SNe 2001ig \citep{Ryder04}, 2003bg \citep{S06}, 2001gd \citep{gd07}, 1993J \citep{93J_longterm}, 2008ax \citep{roming09}, and 2011dh (\citealt{krauss12,soderberg11dh}), among others, yielding information on the SN shockwave as well as the final stages of massive star evolution. In the future, these objects will illuminate the physical processes that govern the transition from supernova to remnant. Today, however, there are only a handful of known radio supernovae old enough to probe this intermediate regime. The early radio emission is typically characterized by a synchrotron spectrum and is generated by interaction of the shock with the CSM ejected by the star prior to the explosion (\citealt{C82,Chev98}, \citet{CandF06}). In some cases the inferred circumstellar density follows a simple $\rho \propto r^{-2}$ wind profile; however, there is a growing number of radio supernovae that show modulations in their radio light curves. These are usually interpreted to be variations in the circumstellar density (\citet{93J_massloss}, \citet{Ryder04}, \citet{S06}, \citet{Kotak_and_Vink}, \citet{gd07}, \citet{Wellons12}). While it is currently unclear what causes the sudden changes in mass-loss rate, the simplest solution is that the mass loss rate and wind velocity of the progenitor star are not uniform on the timescales we see the radio emission changing, typically representing decades to centuries before the death of the star. Other possible solutions include dynamic instabilities, such as those seen in luminous blue variables like $\eta$ Carinae \citep{etacar_chin} and other instabilities observed in nearby S Doradus type stars \citep{S-Dor_Groot}. Interestingly, some of the mass loss rates inferred from the measured radio emission are larger than the saturation strength for line driven winds, which is around $\dot M \approx 10^{-5} M_\sun$ yr$^{-1}$ \citep{Crow07}. This limit, however, may not apply to lower mass progenitors; standard stellar models prefer smaller mass loss rates \citep{standard_mass_loss_model}, although there is some evidence that the mass loss rates of red supergiants may be larger than these models imply \citep{redgiant_evolution_mass_loss}. SNe 1993J, 2001gd, and 2004C show evidence for a large mass loss rate and a circumstellar density profile morphologically similar to a uniform shell of material or a power law falling off more shallow than $r^{-2}$, instead of a wind profile (\citet{93J_massloss}, \citet{93J_longterm}, \citet{gd07}). While the wealth of recent detections of supernovae in the radio have provided insight into the final stages of stellar evolution, there are relatively few studied for more than a couple decades and providing information on the final chapter of stellar evolution. Recovering historical supernovae at radio wavelengths is therefore a rewarding endeavor. Here we focus on middle-aged SN 1970G, serendipitously observed as part of our Target-of-Opportunity program for Type Ia SN 20011fe in the same host galaxy, M101 (D = $7.4^{+1.0}_{-1.5}$ Mpc \citet{m101_distance}). SN 1970G was the first supernova detected in the radio, by \citet{Nature_Original_Detection}. After this initial detection, attempts at continuously monitoring SN 1970G were made with the Westerbork Synthesis Radio Telescope (WSRT), and a compilation of these efforts is presented by \citet{Supernova_Last_70s}. Extracting the supernova flux from the flux of the galaxy and the nearby HII region was impaired due to the low resolution of the available radio telescopes \citep{Supernova_Last_70s}. They found that the flux density of SN 1970G was likely below the threshold for detection at 11 cm and 21 cm wavelengths for the first 0.4 years since the optical supernova explosion \citep{Supernova_Last_70s} before ultimately being detected by \citet{Nature_Original_Detection}. SN 1970G remained detectable at approximately $5$ mJy through 1973 when the last marginal detection occurred \citep{Supernova_Last_70s}. Throughout this period, SN 1970G remained undetectable at 6 cm wavelengths below a limit of 1.5 mJy \citep{Supernova_Last_70s}. In this paper, we present a new detection of SN 1970G using the VLA and the Chandra X-ray Observatory. We detect a point source at the same location of SN 1970G robustly at 6 cm and marginally at 4.5 cm. We demonstrate the increased precision of the Jansky Very Large Array after its recent upgrade that will create new opportunities for studying radio supernovae to late time. We show that a new emission mechanism in the X-ray regime is now dominating the evolution of the supernova/supernova remnant and attribute it to the likely turn-on of a pulsar wind nebula. We suggest future observations that can confirm the nature of this emission and offer a unique perspective into the formation of pulsar wind nebulae from an observational standpoint. | We present new observations of the middle-aged supernova SN\,1970G in the radio with the Very Large Array and in the X-rays with the Chandra X-ray Observatory. We find that the radio flux has decreased significantly since 2000 to a level of $\approx 33 $ $\mu$Jy. This is approximately a factor of 3 smaller than expected from the study of \citet{70g_2000}. Indeed, in the near future, SN\,1970G will again become undetectable even by the Jansky Very Large Array, if the present decay rate continues. This detection represents one of the faintest objects observed by the Jansky Very Large Array and underscores how valuable this instrument will be in future years in understanding the supernova - supernova remnant transition. Additionally, we have found an enhancement of the X-ray flux from SN\,1970G over the past 5 years, which we believe is unlikely to result from the reverse shock region, previously shown to be decaying. We find that the X-ray luminosity of SN\,1970G is not atypical for pulsar wind nebula and suggests that we may be witnessing the birth of a pulsar wind nebula from a middle-aged supernova. In the future, we expect SN\,1970G to begin brightening in the radio, as the supernova finally evolves to a remnant. Studying this process is now possible with the improved sensitivity of the Very Large Array, and regular monitoring should help record when this process begins. Additionally, SN\,1957D in M83 has recently been reported to show similar behavior to SN\,1970G, with a steepening of the time-domain behavior of the radio flux density to an index of $\alpha \approx -4.0$, as well as a similar X-Ray luminosity of $\approx 10^{37}$ ergs/s \citep{roger_57d_aas}. This indicates that the physical processes producing this behavior may be common to middle-aged type IIL supernovae. With RMS noise of $\sim$ few $\mu$Jy, studying radio supernova for many decades can become a routine occurrence. With this ability, new insights into the end stages of massive star evolution (up to centuries before the progenitor exploded) can be obtained. This is a new regime of studying the end states of massive stars, for which SN 1970G represents a unique case. | 14 | 3 | 1403.6825 |
1403 | 1403.5420_arXiv.txt | We study the cosmology of K-mouflage theories at the background level. We show that the effects of the scalar field are suppressed at high matter density in the early Universe and only play a role in the late time Universe where the deviations of the Hubble rate from its $\Lambda$-CDM counterpart can be of the order five percent for redshifts $1 \lesssim z \lesssim 5$. Similarly, we find that the equation of state can cross the phantom divide in the recent past and even diverge when the effective scalar energy density goes negative and subdominant compared to matter, preserving the positivity of the squared Hubble rate. These features are present in models for which Big Bang Nucleosynthesis is not affected. We analyze the fate of K-mouflage when the nonlinear kinetic terms give rise to ghosts, particle excitations with negative energy. In this case, we find that the K-mouflage theories can only be considered as an effective description of the Universe at low energy below $1$ keV. In the safe ghost-free models, we find that the equation of state always diverges in the past and changes significantly by a few percent since $z\lesssim 1$. | \label{Introduction} Scalar fields could be playing a role in late time cosmology and have something to do with the recent acceleration of the expansion of the Universe\cite{Copeland:2006wr}. They could also induce modifications of gravity on large scales \cite{Khoury:2010xi} which may be within the reach of the forthcoming EUCLID mission \cite{Amendola:2012ys}. For instance one always expects at least one scalar field to be present in massive extensions of General Relativity (GR) which could lead to such deviations\cite{deRham:2012az}. In both cases, the mass of the scalar field is very small, implying the possibility of the existence of a scalar fifth force. All in all, scalar fields with low masses acting on very large scales of the Universe are ubiquitous. Nevertheless, such scalars have never manifested themselves in the Solar System or the laboratory where deviations from General Relativity have been painstakingly sought for\cite{Will:2004nx}. It has been recently advocated that this could be the result of the screening of these scalar fields in dense environments\cite{Brax:2012yi,Brax:2013ida}. As a result, they would be nearly invisible locally while acting as full fledged modifications of the dynamics of the Universe on large scales. In this paper, we shall focus on one particular type of screening: K-mouflage\cite{Babichev:2009ee,Brax:2012jr}. More precisely, we focus on models that have the simplest K-essence form \cite{Armendariz-Picon:1999aa}, where the nonstandard kinetic term is only a nonlinear function of $(\pl\varphi)^2$. This is a subclass of the possible models that one can build with nonstandard kinetic terms, that may also depend on the field $\varphi$ or higher derivatives $\pl^2\varphi$ \cite{Babichev:2009ee}. These models partake in the three types of screening mechanisms which are compatible with second order equations of motion for higher order scalar field theories. In K-mouflage theories, the equations of motion are always second order but the Hamiltonian corresponding to the scalar energy density may be negative for large values of the field's time derivative, depending on the form of the kinetic term. However, even in such cases, the cosmological screening of the scalar field in high cosmological densities implies that the Hubble rate squared is always positive. Another issue comes from the fact that, when the Hamiltonian becomes negative, the kinetic energy of K-mouflage excitations seen as particles may destabilize the vacuum and lead to a large background of gamma rays. For canonical ghosts, it is known that one cannot extend the validity of the models for energies larger than a few MeV \cite{Cline:2003gs}. Here we revisit this issue for K-mouflage models and find that the validity range of these theories is even more restricted to energies always less than 1 keV when ghosts are present. Models where the kinetic term keeps the standard positive sign do not have ghosts and do not suffer from this problem. A first type of screening which differs from K-mouflage is the chameleon \cite{Khoury:2003aq,Khoury:2003rn}(and also the Damour-Polyakov \cite{Damour:1994zq}) mechanism. In these models, screened regions are such that the Newtonian potential of dense objects is larger than the value of the scalar field outside the object. A second type of screening is the Vainshtein mechanism \cite{Vainshtein:1972sx} which only occurs for noncanonical scalar fields, and where screened regions correspond to a spatial curvature larger than a critical value. The K-mouflage mechanism is also present for noncanonical theories and is effective in regions where the gravitational acceleration is larger than a critical value, in a way reminiscent of the MOND hypothesis \cite{Babichev:2011kq}. For this reason, K-mouflage models differ from General Relativity on large scales and are well suited to be tested cosmologically. The absence of convergence towards GR in the large distance regime differs drastically from what happens for chameleons. The same lack of convergence is also there for models with the Vainshtein property. On the other hand, the K-mouflage and Vainshtein mechanisms differ locally in the vicinity of a dense object of mass $m$ where the distance below which General Relativity is recovered scales like $m^{1/2}$ and $m^{1/3}$, respectively. They also differ drastically cosmologically as the latter (Vainshtein) allows for screening of cosmological overdensities like galaxy clusters while the former (K-mouflage) does not screen such large-scale structures. Consequently the theories with the K-mouflage property essentially behave like linear theory with a time dependent Newton constant up to quasilinear scales. In this paper, we will focus on the background evolution and leave the properties of structure formation on large scales for a companion paper \cite{Brax:2014ab}. We will concentrate on the cosmology of K-mouflage models and leave their gravitational properties for further work. At the background level and for K-mouflage models leading to the late time acceleration of the expansion of the Universe, we find that the Hubble rate can differ significantly from the one of $\Lambda$-CDM for moderate redshifts. This fact corresponds to the cosmological screening at high cosmological densities of the scalar field whose dynamics play a role only when the density of matter is sufficiently small. In the very recent past, the models converge to a $\Lambda$-CDM behavior. This implies that the deviations from $\Lambda$-CDM are maximal for intermediate redshifts of the order $1\lesssim z \lesssim 5$. For these redshifts, the effective energy density of the scalar can become positive after being negative in the distant past. This implies in particular that the equation of state is not bounded from below, can be less than $-1$ and can even diverge. This is an artefact of the the definition of the equation of state with no consequence on the dynamics of the models as the total matter density is always positive. It is remarkable that this result, i.e. the divergence of the equation of state, stands for all models even when the Big Bang Nucleosynthesis constraints \cite{Uzan:2010pm} on the variation of masses are applied. Moreover, when excluding the possibility of ghosts, the K-mouflage models always cross the phantom divide. A feature which is strikingly different from chameleonlike models \cite{Brax:2004qh} and Galileons \cite{Li:2013tda,Barreira:2013eea}. In section II, we recall the physical classification of screening models for theories with second order equations of motions. K-mouflage models are particular as screening only occurs when the gravitational acceleration is large enough. In part III, we introduce the K-mouflage models. In section IV, we study the tracking properties of the cosmological background and apply the BBN bounds to K-mouflage. In part V, we study the expansion history of the models and we confirm it numerically in section VI. Finally we study the constraints provided by the gamma ray flux due to ghosts in section VII. We then conclude in section VIII. | We have presented a cosmological analysis of K-mouflage models, one of the three types of theories with screening properties for a long range scalar interaction on cosmological scales. In this paper, we have focused on the background cosmology. K-mouflage models are characterized by a nonlinear Lagrangian in the kinetic terms of a scalar field. In dense environments, such as the early Universe, the effects of the scalar field are screened and deviations from the Einstein-de Sitter cosmology characterizing the matter-dominated era become negligible. At late time, the background cosmology for small redshifts can be taken to be close to the one of an accelerated universe with a cosmological constant. In between these two epochs, the cosmology of K-mouflage models is rich and differs from the ones of chameleonlike and Galileon models, the other two archetypical models with screening properties. More precisely, in the early Universe, the screening of the scalar field does not imply that the dark sector of the model converges to the $\Lambda$-CDM model. Indeed, the equation of state of the scalar field converges in the far past to a negative constant, which is not equal to $-1$. At late time and for $z\lesssim 1$, the equation of state is not constant and can evolve by a few percent while other constraints such as the absence of disruption for Big Bang Nucleosynthesis are applied. For moderate redshifts, $1\lesssim z\lesssim 5$, the Hubble rate is significantly different from the $\Lambda$-CDM case. Moreover, in the case where no quantum ghosts and therefore no vacuum instability are present, the equation of state always crosses the phantom divide and even diverges for moderate redshifts. This follows from the change of sign of the effective energy density of the scalar field which goes from negative in the distant past to positive in the recent past. The fact that the scalar energy density becomes negative does not jeopardize the soundness of the models, indeed the scalar becomes more and more screened in the past and the total energy density is always positive. At the background level and for small redshifts, the K-mouflage models could be tested by observations of the time evolution of the equation of state. At the perturbation level, and as shown in a companion paper \cite{Brax:2014ab}, the K-mouflage models are such that large-scale structures are still in the linear regime of the scalar sector. Therefore, deviations from $\Lambda$-CDM on the growth of large-scale structure and on the Integrated Sachs Wolfe effects are present. K-mouflage models are also very different from models like Galileons in the small-scale and large-density regime. The study of the behavior of K-mouflage models in this nonlinear regime is left for future work. | 14 | 3 | 1403.5420 |
1403 | 1403.0343_arXiv.txt | {} {Since asymptotic giant branch (AGB) stars are bright and extended infrared objects, most Galactic AGB stars saturate the Wide-field Infrared Survey Explorer (WISE) detectors and therefore the WISE magnitudes that are restored by applying point-spread-function fitting need to be verified. Statistical properties of circumstellar envelopes around AGB stars are discussed on the basis of a WISE AGB catalog verified in this way.} {We cross-matched an AGB star sample with the WISE All-Sky Source Catalog and the Two Mircon All Sky Survey catalog. Infrared Space Observatory (ISO) spectra of a subsample of WISE AGB stars were also exploited. The dust radiation transfer code DUSTY was used to help predict the magnitudes in the W1 and W2 bands, the two WISE bands most affected by saturation, for calibration purpose, and to provide physical parameters of the AGB sample stars for analysis.} {DUSTY is verified against the ISO spectra to be a good tool to reproduce the spectral energy distributions of these AGB stars. Systematic magnitude-dependent offsets have been identified in WISE W1 and W2 magnitudes of the saturated AGB stars, and empirical calibration formulas are obtained for them on the basis of 1877 (W1) and 1558 (W2) AGB stars that are successfully fit with DUSTY. According to the calibration formulae, the corrections for W1 at 5 mag and W2 at 4 mag are $-0.383$ and 0.217 mag, respectively. In total, we calibrated the W1/W2 magnitudes of 2390/2021 AGB stars. The model parameters from the DUSTY and the calibrated WISE W1 and W2 magnitudes are used to discuss the behavior of the WISE color-color diagrams of AGB stars. The model parameters also reveal that O-rich AGB stars with opaque circumstellar envelopes are much rarer than opaque C-rich AGB stars toward the anti-Galactic center direction, which we attribute to the metallicity gradient of our Galaxy.} {} | The asymptotic giant branch (AGB) phase is the final stellar evolutionary stage of intermediate-mass (1 -- 8 $M_{\odot}$) stars driven by nuclear burning. Stars in this stage have low surface effective temperatures (below 3000 K) and experience intense mass loss (from $10^{-7}$ to $10^{-4}$ ${M}_{\odot}{\rm yr}^{-1}$) \citep{Habing1996}. Heavy elements in the mass outflow from a central star will condense to form dust when the gas temperature drops to the sublimation temperature of the dust grains. Dusty circumstellar envelopes will form at the distance of several stellar radii. Dust grains in the envelopes absorb stellar radiation and re-emit in the infrared. Thus, AGB stars are important infrared sources. The mass-loss process plays an important role in the evolution of AGB stars because it affects the lifetime of the AGB phase and the core-mass of the subsequent post-AGB stars. Statistics of a large sample of AGB stars would help to constrain the evolution of dust envelope. Due to the relative over-abundance between carbon and oxygen, there are two main types of AGB stars: (1) the O-rich with C/O $<1$ and mainly silicate-type grains in the outflow, and (2) C-rich with C/O $>1$ and mainly carbonaceous grains in the envelopes. The different dust compositions of these two types of AGB stars result in different infrared spectral features, which can be used to distinguish the two groups of the stellar objects. The first-generation infrared space-telescope, the Infrared Astronomical Satellite ({\sl IRAS}; \citealt{Neugebauer1984}), mapped the sky in two mid-infrared and two far-infrared bands (12, 25 $\mu$m and 60, 100 $\mu$m, respectively) in the 1980s. It discovered many mass-losing AGB stars in the Milky Way and the Magellanic Clouds. Several dozen AGB stars were observed spectroscopically by the Infrared Space Observatory \citep[ISO;][]{Kessler1996} with the Short-Wave Spectrometer (SWS) onboard, which works in the range of 2.4 $\mu$m to 45 $\mu$m. These infrared spectra provide tremendous information about dusty circumstellar envelopes around the AGB stars, but they are limited by the sample size. The Galactic Plane Survey of the Spitzer Space Telescope \citep{werner2004} provides high-resolution and sensitive infrared images of Galactic plane at the 3.6, 4.5, 5.8, 8.0, 24, and 70 $\mu$m bands. However, it cannot adequately separate the two types of AGB stars in mid-infrared color-color diagrams without filters between 8 $\mu$m and 24 $\mu$m. Launched on 2009 December 14, the Wide-field Infrared Survey Explorer (WISE) completed an entire sky survey in the 3.4, 4.6, 12 and 22 $\mu$m bands (hereafter named W1, W2, W3, and W4, respectively) in 2010. The FWHMs of the point spread functions (PSF) are $6.''1$, $6.''4$, $6.''5$, and $12.''0$ for the four WISE bands, and the sensitivities ($5 \sigma$) of the point sources are 0.08, 0.11, 1, and 6 mJy \citep{Wright2010}. The Two Micron All Sky Survey (2MASS; \citealt{Skrutskie2006}) also mapped the entire sky in three near-infrared, J (1.25 $\mu$m), H (1.65 $\mu$m) and $\mathrm{K}_{\rm s}$ (2.17 $\mu$m) bands. They are an important supplement to the mid-infrared WISE data to complete the infrared spectral energy distribution (SED) of AGB stars. Recently, galaxy-wide AGB populations have been identified and studied in nearby galaxies using ground- and space-based near- and mid-infrared data (\citealt{riebel2012}, \citealt{boyer2012} in the Magellanic Clouds and \citealt{javadi2013} in M33). While similar research in our galaxy is hindered by foreground extinction, there are some studies on large datasets of Galactic AGB stars, such as the work of \citet{jura1989} in the solar neighborhood. \citet{Suh2009,Suh2011} composed a large verified AGB catalog in our galaxy from the literature and investigated infrared colors of AGB stars and their distribution in color-color diagrams. To study an AGB star population, a more time-saving way is constructing a set of model grids to simulate the infrared SED of AGB stars and acquire their physical parameters, such as mass-loss rate and optical depth. Many model grids have been developed to study the evolved-star populations in the local group galaxies \citep{groenewegen2006,sargent2011,srinivasan2011}. All of the models are publicly available. However, the model set of \citet{groenewegen2006} does not have WISE synthetic photometry. The Magellanic Clouds have a lower metallicity than our Galaxy, and \citet{sargent2011} and \citet{srinivasan2011} chose a stellar photosphere model with subsolar metallicity as input of a radiative transfer model, which is not the case in our galaxy. Therefore, we used DUSTY \citep{ivezic1997} to generate a new grid of radiative transfer models to simulate the infrared SEDs of Galactic AGB stars. As AGB stars typically are bright IR objects, most of our AGB samples are brighter than the WISE detector saturation limits and only photometry of unsaturated pixels are available, therefore their WISE magnitudes need to be verified. The main goal of this paper is to study the properties of AGB stars in WISE bands and recalibrate the WISE photometry for sources saturated in WISE bands. We describe our AGB sample, DUSTY algorithm and calibration method in \textsection2. A possible calibrating solution is presented in \textsection3.1. We present our results about the distinct location of the two types of AGB stars in a color-color diagram in \textsection3.2, the model parameter effects on WISE colors in \textsection3.3, and the Galactic longitude distribution in \textsection3.4. Our summary is presented in \textsection4. All the magnitudes mentioned in this paper are Vega magnitudes. | We reported our findings on AGB star colors in the WISE bands. We found that the WISE W1 and W2 magnitudes of AGB stars do not agree with the spectroscopic measurements from ISO when we compared our sample of ISO simulated W1--W4 magnitudes with WISE observations, which we attribute to the residual bias in the PSF-fit photometry of saturated objects in these two bands. The WISE saturated W3 and W4 magnitudes are directly calibrated based on ISO synthetic photometry. To calibrate the WISE W1 and W2 bands, we resorted to ISO spectra of a subsample of our AGB stars and proved that the radiation transfer code DUSTY can be used to reproduce unbiased W1 and W2 magnitudes of bright stars. Using DUSTY, we successfully developed a calibration method for the observed WISE W1 and W2 bands to lift the residual bias of the PSF-fit photometry. The calibration procedure revealed that WISE may in general have underestimated W1 flux and overestimated W2 flux, and these deviations seem to be magnitude-dependent. Combining the model-calibrated W1 and W2 data with the directly calibrated WISE W3 and W4 magnitudes, we analyzed the W1$-$W2 vs W3$-$W4 color-color diagram and found that the two main types of AGB stars, O-rich AGB and C-rich AGB, can be effectively distinguished by their WISE colors. The division is mainly caused by the different extinction efficiencies between silicate-type and carbonaceous grains. The spatial distribution of the AGB sample is consistent with previous work. We also found that O-rich AGB stars with an opaque circumstellar envelope are much rarer toward the anti-Galactic Center direction than C-rich AGB stars, which we attribute to the metallicity gradient of our Galaxy. | 14 | 3 | 1403.0343 |
1403 | 1403.5566_arXiv.txt | We use three-dimensional numerical hydrodynamic simulations of the turbulent, multiphase atomic interstellar medium (ISM) to construct and analyze synthetic \ion{H}{1} 21~cm emission and absorption lines. Our analysis provides detailed tests of 21~cm observables as physical diagnostics of the atomic ISM. In particular, we construct (1) the ``observed'' spin temperature, $\Tsobs\equiv T_B(\vch)/[1-e^{-\tau(\vch)}]$, and its optical-depth weighted mean $\Tsyn$; (2) the absorption-corrected ``observed'' column density, $\Nsyn \propto \int d\vch T_B(\vch) \tau(\vch)/[1-e^{-\tau(\vch)}]$; and (3) the ``observed'' fraction of cold neutral medium (CNM), $\fcsyn\equiv T_c/\Tsyn$ for $T_c$ the CNM temperature; we compare each observed parameter with true values obtained from line-of-sight (LOS) averages in the simulation. Within individual velocity channels, $\Tsobs$ is within a factor 1.5 of the true value up to $\tau(\vch)\sim 10$. As a consequence, $\Nsyn$ and $\Tsyn$ are respectively within 5\% and 12\% of the true values for 90\% and 99\% of LOSs. The optically thin approximation significantly underestimates $\Nsim$ for $\tau>1$. Provided that $T_c$ is constrained, an accurate observational estimate of the CNM mass fraction can be obtained down to 20\%. We show that $\Tsyn$ cannot be used to distinguish the relative proportions of warm and thermally-unstable atomic gas, although the presence of thermally-unstable gas can be discerned from 21~cm lines with $200\Kel\simlt\Tsobs\simlt1000\Kel$. Our mock observations successfully reproduce and explain the observed distribution of the brightness temperature, optical depth, and spin temperature in \citet{2013MNRAS.436.2352R}. The threshold column density for CNM seen in observations is also reproduced by our mock observations. We explain this observed threshold behavior in terms of vertical equilibrium in the local Milky Way's ISM disk. | \label{sec:intro} The \ion{H}{1} 21~cm line is a powerful tool for studying the atomic interstellar medium (ISM). The first detections of emission and absorption at 21~cm date back to the 1950s (\citealt{1951Natur.168..356E,1951Natur.168..357M} for emission, and \citealt{1955ApJ...122..361H} for absorption). The \ion{H}{1} 21~cm line has been observed extensively since then, and proved extremely valuable in revealing many properties of the Milky Way Galaxy, including the vertical and radial distribution and warp of the atomic disk, the galactic rotation curve and dark matter distribution, and spiral structure. In addition to large-scale properties of the Milky Way, \ion{H}{1} 21~cm observations provide a wealth of knowledge regarding the detailed physical state of the interstellar medium (see reviews including \citealt{1976ARA&A..14..275B,1990ARA&A..28..215D,2009ARA&A..47...27K} and references therein). Recently, the combined Leiden-Argentine-Bonn survey (LAB survey, \citealt{2005A&A...440..775K}) produced a high-sensitivity 21~cm emission map over the entire sky with 36 arcmin resolution by merging the Leiden-Dwingeloo survey \citep{1997agnh.book.....H} with the Instituto Argentino de Radioastronom\'ia survey \citep{2005A&A...440..767B}. This high-sensitivity, single-dish survey with stray radiation correction enables highly detailed investigation of \ion{H}{1} in the Milky Way \citep{2006Sci...312.1773L,2006ApJ...643..881L,2007A&A...469..511K,2008A&A...487..951K}. Information about the thermodynamic state of hydrogen can be obtained from emission/absorption line pairs, which yield the excitation temperature (a.k.a. spin temperature) of the 21~cm line. Since the available radio continuum background sources are generally weak at 21~cm, the line profile toward a continuum source gives a mixture of emission and absorption by \ion{H}{1}. In order to separate emission and absorption, \ion{H}{1} emission contributions must be estimated from off-source measurements with sufficient spatial resolution. Using the largest single dish telescope, the Arecibo telescope (beamwidth of 3.2 arcmin), \citet{2003ApJS..145..329H} have investigated the emission/absorption line pairs toward continuum sources at high and intermediate latitudes, but the resolution from a single dish is not sufficient for accurate interpolated emission at latitudes below $10^\circ$. Interferometric surveys including the Canadian Galactic Plane Survey (CGPS, \citealt{2003AJ....125.3145T}), the Southern Galactic Plane Survey (SGPS, \citealt{2005ApJS..158..178M}), and the VLA Galactic Plane Survey (VGPS, \citealt{2006AJ....132.1158S}) achieve angular resolution about $\sim$1 arcmin. In order to overcome inherent low sensitivity of interferometric observations to extended structures (zero-spacing), these new surveys apply short-spacing corrections from single dish observations, allowing accurate measurement of the expected emission and hence absorption spectra \citep{2006AJ....132.1158S}. The resulting emission/absorption line pairs in these Galactic plane surveys reveal a pervasive multiphase structure in the atomic ISM out to a galactocentric radius of $25\kpc$ \citep{2009ApJ...693.1250D}. Using emission/absorption line pairs, the total atomic column density and the harmonic mean spin temperature on a given line-of-sight (LOS) can be derived with a simple radiative transfer calculation \citep[][see Section~\ref{sec:syn} below]{1978ppim.book.....S,2011piim.book.....D}. In classical models of the neutral ISM, two distinct phases are expected: the cold neutral medium (CNM; $T\sim 100\Kel$) and the warm neutral medium (WNM; $T\sim 8000\Kel$), in pressure equilibrium with each other \citep[e.g.,][]{1969ApJ...155L.149F,1995ApJ...443..152W,2003ApJ...587..278W}. Since the WNM is optically thin at 21~cm due to its low density and high temperature, a simple single temperature approximation for radiative transfer would be satisfied if there is no overlap between CNM clouds within narrow velocity channels. However, recent dynamical models that simulate the atomic ISM \citep[e.g.,][]{2000ApJ...540..271V,2005A&A...433....1A,2005ApJ...626..864M,2007A&A...465..431H,2007ApJ...663..183P,2008ApJ...681.1148K,2011A&A...526A..14S,2013arXiv1301.3446S}, along with detailed observations \citep[e.g.,][]{2003ApJ...586.1067H,2003MNRAS.346L..57K,2013MNRAS.436.2366R} have shown a broad distribution over a wide temperature range and a significant amount of gas in the thermally unstable temperature range $T=500-5000\Kel$ \citep{1995ApJ...443..152W}. Moreover, the velocity field is complex, with turbulence dominated by large scales but potential for velocity overlap at distinct locations along LOSs. Under realistic circumstances of complex velocity fields and broad temperature distributions, validity of the standard assumptions adopted in interpreting \ion{H}{1} observations are open to question. To address some of these questions, \citet{2013MNRAS.432.3074C} have performed Monte Carlo simulations assigning varying mass fractions of each component along each LOS, showing that the isothermal estimator of the \ion{H}{1} column density agrees well with the true column density within a factor of 2. However, to date there have been no corresponding studies that construct and analyze synthetic emission/absorption lines using results from realistic hydrodynamic simulations of the ISM. In this paper, we utilize our recent three dimensional hydrodynamic simulations \citep[][hereafter Paper~I]{2013ApJ...776....1K} to create and analyze detailed synthetic \ion{H}{1} 21~cm lines. Our simulations enable us to investigate fundamental questions related to use of \ion{H}{1} 21~cm lines as ISM diagnostics. In addition, we can address a puzzle that has emerged from recent deep, high-resolution interferometric observations toward radio loud quasars \citep{2013MNRAS.436.2352R}, in combination with the LAB survey. These observations have sufficient sensitivity to detect absorption by the WNM, as in \citet{2003MNRAS.346L..57K}. Using emission/absorption line pairs, \citet{2011ApJ...737L..33K} reported a threshold \ion{H}{1} column density at $\Nth\equiv2\times10^{20}\psc$, below which the mean spin temperature exceeds $T_s>1000\Kel$. They speculated that this apparent threshold might represent a minimum column density for CNM to develop due to self-shielding against ultraviolet photons. However, detailed modeling of interstellar radiation sources have suggested that the ionization fraction remains small for the hydrogen density of $n>10\pcc$ when the absorbing WNM column density exceeds $10^{18}\psc$ for solar neighborhood condition (see Figure~3(c) in \citealt{1995ApJ...443..152W}). In addition, absorption lines with a low optical depth and a narrow line width have been detected, implying a very low CNM column density of $\Nsim\sim5\times10^{18}\psc$ \citep{2010ApJ...722..395B}. Furthermore, \citet{2009ApJ...693.1250D} have shown that the ratio of (integrated) emission to absorption is nearly constant over the radial distance range of 10 to 25 kpc, whereas the emission and absorption alone decrease by two orders of magnitude. This implies that the mass fraction of the CNM is unchanged, while the total column density drops by more than an order of magnitude, lower than $\Nth$. Here, we shall propose an alternative explanation for the \ion{H}{1} threshold behavior observed in the solar neighborhood. This proposal is based on the concept of the warm/cold ISM representing a self-regulated thermal and dynamical equilibrium system that is heated and dynamically stirred by energy injection from star formation \citep{2010ApJ...721..975O,2011ApJ...743...25K}. In dynamical equilibrium, a given midplane pressure implies a minimum column of gas; here, we shall show that this can give rise to a threshold column behavior similar to that seen in observations. The plan of this paper is as follows. Section~\ref{sec:method} briefly reviews the numerical models and explains how we extract LOS simulated data and produce synthetic lines, including our procedure for spin temperature calculation. In Section~\ref{sec:comp_sim}, we compare true values of column density, spin temperature, and CNM mass fraction to those that would be deduced using standard observational methods applied to our synthetic 21~cm lines. Section~\ref{sec:comp_obs} presents mock observations for brightness temperature, optical depth, and spin temperature for each velocity channel and for column density distributions. We shall show that the mock observations reproduce \ion{H}{1} 21~cm line observations very well for individual velocity channels \citep{2013MNRAS.436.2352R} as well as integrated over velocity \citep{2011ApJ...737L..33K}. In addition, we show that the threshold column density is well reproduced, and consistent with the expectation of the thermal/dynamical model. | The very first step to deduce the \ion{H}{1} column density from 21~cm line observations is to convert the observed brightness temperature $T_B(l,b,\vch)$ to channel column density using Equation (\ref{eq:Nsyn}) or (\ref{eq:Nthin}). Despite the importance of this first conversion step, the validity and uncertainty of the conversion methods have not previously been tested and quantified with realistic ISM models. At a minimum, a realistic ISM model should include multi-scale turbulence, as well as self-consistent density and temperature structure responding to the heating and cooling of the dynamic ISM. Our recent ISM simulations in Paper~I include these ingredients, and thus provide a valuable testbed for evaluating 21~cm diagnostic techniques. Since our simulations are local, we limit our analysis to latitudes larger than $|b|>5^\circ$ in which horizontal variations of the ISM play a lesser role. Our main findings are summarized as follows. \begin{enumerate} \item By conducting mock observations toward random LOSs, we find that the observed spin temperature $\Tsobs$ deduced from the brightness temperature and the optical depth (see Equation (\ref{eq:Tsobs})) agrees very well with the true harmonic mean spin temperature $\Tsavg$ (see Equation (\ref{eq:Tsavg})). The agreement is within a factor of 1.5 even for the channel optical depths as large as $\tau(\vch)\sim10$. Since $\Tsobs$ effectively assumes a single component along the LOS, this agreement implies that for the adopted velocity channel width of $1\kms$, there is limited LOS overlap of opaque CNM clouds. The agreement $\Tsavg\approx\Tsobs$ in individual velocity channels also leads to good agreement between ``observed'' and ``true'' velocity-integrated properties, including $\Nsyn\approx\Nsim$ and $\Tsyn\approx\Tsim$ (see Figure~\ref{fig:NHcomp}). $\Nsyn$ (see Equation \ref{eq:Nsyn}) is also known as the ``isothermal'' estimator of the \ion{H}{1} column density and widely used in observations \citep{1982AJ.....87..278D,2013MNRAS.432.3074C}. The ``thin'' column density is within a factor of $\sim0.7$ of the ``true'' column density for $\tauint<10$, comparable to the observed ratio of ``thin'' to opacity-corrected column density $\sim 0.6-0.8$ \citep{2003ApJ...585..801D}. \item In our analysis, we calculate the spin temperature with and without the WF effect via the Ly-$\alpha$ resonant scattering, which provide upper and lower limits for the spin temperature of the WNM, respectively. As a consequence, we find the harmonic mean spin temperature (Equation \ref{eq:Tsyn}) is limited to $\Tsyn\simlt2000\Kel$ without the WF effect (see Figure~\ref{fig:fcnm}) and $\Tsyn\simlt4000\Kel$ with the WF effect (see Figure~\ref{fig:fcnm_WF}). There are a few absorption line observations of the WNM that have reported spin temperature up to $\sim 6000\Kel$ \citep{1998ApJ...502L..79C,2003MNRAS.346L..57K}. The possible underestimation of the WNM spin temperature in our analysis (we omit collisional transitions due to electrons) might lead to higher optical depth of the WNM than in the real ISM. However, the optical depth is already quite small in the WNM, and we find a similar distribution in the space of $T_B(\vch)$-$\tau(\vch)$-$\Tsobs$ to observations irrespective of the method for the spin temperature calculation (see Figures~\ref{fig:TBtau} and \ref{fig:TBtau_WF}). \item Our analysis shows that thermally-unstable and true warm gases appear in comparable proportions along all LOSs for most values of $\Tsyn$ (Figures~\ref{fig:fcnm} and \ref{fig:fcnm_WF}). However, we do find that for $\Tsyn$ in the range $\sim 500\Kel-1000\Kel$, UNM dominates over WNM. The detection of absorption with spin temperature in a range of $\Tsyn\sim 500-5000\Kel$ \citep[e.g.,][]{1998ApJ...502L..79C,2002ApJ...567..940D,2003MNRAS.346L..57K,2010ApJ...725.1779B} may imply the possible existence of thermally unstable gas. More definitive evidence for the UNM is given by a distribution of observational data in the space of $T_B(\vch)$-$\tau(\vch)$-$\Tsobs$ (Figures~\ref{fig:TBtau} and \ref{fig:TBtau_WF}). We show that the UNM alone populates the regime with $200\Kel\simlt\Tsobs\simlt1000\Kel$ (near point ``C'' in Figure~\ref{fig:TBtau}(b)) without the WF effect. With the WF effect, this regime can be extended to $200\Kel\simlt\Tsobs\simlt2000\Kel$ (see Figure~\ref{fig:TBtau_WF}(b)). This is because the one-to-one correspondence between $\Tsobs$ and $\Tkavg$ persists up to at least $\Tsobs\simlt1000\Kel$ and at best $\Tsobs\simlt2000\Kel$ without and with WF effect, respectively. The presence of observational data points in this region strongly suggest that the presence of thermally unstable gas. Since the majority of the UNM and WNM occupy the low optical depth regime $\tau(\vch)\simlt10^{-2}$, with high spin temperature $\Tsobs\simgt1000\Kel$ where their distributions are completely mixed, however, the exact mass fractions of the UNM and WNM are difficult to derive from \ion{H}{1} 21~cm observations. \item While the spin temperature provides only limited ability to differentiate UNM and WNM, it is a very good probe of the CNM mass fraction. From Equation (\ref{eq:fcnm}), the CNM mass fraction for moderate $\Tsyn$ is $\fcsyn\approx T_c/\Tsyn$. In our simulations, the median CNM temperature is $80\Kel$, and Figure~\ref{fig:fcnm}(a) shows that for LOSs with low spin temperature $\Tsyn\simlt400\Kel$, $\fcsyn\approx 80\Kel/\Tsyn$ fits quite well. Because CNM temperature is not a single constant, however, there is an inherent uncertainty of about a factor of 2 in this result. Using Gaussian decomposition of emission/absorption lines, \citet{2003ApJ...585..801D} have found the CNM temperature are in range of $40\Kel\simlt T_c\simlt100\Kel$ with median value of $\sim65\Kel$. \citet{2003ApJ...586.1067H} also have reported similar distributions with median and mass-weighted CNM temperatures of $48\Kel$ and $70\Kel$, respectively. Interesting results for the CNM mass fraction have recently been derived by emission/absorption line pairs from galactic plane surveys \citep{2003AJ....125.3145T,2005ApJS..158..178M,2006AJ....132.1158S}. \citet{2009ApJ...693.1250D} have shown that the radial dependence of harmonic mean spin temperature in the Milky Way is nearly flat, implying that nearly constant CNM mass fraction out to $25\kpc$. Our numerical models (Paper~I; see also \citealt{2011ApJ...743...25K}) indeed find that mean CNM mass fraction varies only from $\sim0.2$ to $0.4$ for a wide range of conditions. \item For a given equilibrium disk condition with midplane thermal pressure $\Pth$ and scale height of the WNM $H_w$, there is a maximum WNM-only vertical column density $\Nwnm$ (Equation (\ref{eq:Nwnm})). This is comparable to the observed column density where a transition in $\Tsyn$ occurs, $\Nth\sim2\times10^{20}\psc$ \citep{2011ApJ...737L..33K}. The detailed distributions of our mock observations shows that LOSs with projected column density $\Nsim\sin|b|$ smaller than $\Nwnm$ are highly likely to consist only of the WNM. $\Nwnm$ therefore represents well the transition column density from warm-dominated LOSs to LOSs with a two-phase mixture, for a wide range of model parameters (Figure~\ref{fig:ntau_ext}). \end{enumerate} | 14 | 3 | 1403.5566 |
1403 | 1403.4610_arXiv.txt | This paper is the first in a series in which we perform an extensive comparison of various galaxy-based cluster mass estimation techniques that utilise the positions, velocities and colours of galaxies. Our primary aim is to test the performance of these cluster mass estimation techniques on a diverse set of models that will increase in complexity. We begin by providing participating methods with data from a simple model that delivers idealised clusters, enabling us to quantify the underlying scatter intrinsic to these mass estimation techniques. The mock catalogue is based on a Halo Occupation Distribution (HOD) model that assumes spherical Navarro, Frenk and White (NFW) haloes truncated at $R_{\rm 200}$, with no substructure nor colour segregation, and with isotropic, isothermal Maxwellian velocities. We find that, above $\rm 10^{14} M_{\odot}$, recovered cluster masses are correlated with the true underlying cluster mass with an intrinsic scatter of typically a factor of two. Below $\rm 10^{14} M_{\odot}$, the scatter rises as the number of member galaxies drops and rapidly approaches an order of magnitude. We find that richness-based methods deliver the lowest scatter, but it is not clear whether such accuracy may simply be the result of using an over-simplistic model to populate the galaxies in their haloes. Even when given the true cluster membership, large scatter is observed for the majority non-richness-based approaches, suggesting that mass reconstruction with a low number of dynamical tracers is inherently problematic. | Deducing the masses of the largest gravitationally bound structures in the Universe, galaxy clusters, remains a complex problem that is at the focus of current and future cosmological studies. The characteristics of the galaxy cluster population provide crucial information for studies of large scale-structure (e.g., \citealt{1988ARA&A..26..631B}; \citealt{2001AJ....122.2222E}; \citealt{2005MNRAS.357..608Y}; \citealt{2008ApJ...676..206P}; \citealt{2013MNRAS.430..134W}), constraining cosmological model parameters (see \citealt{2011ARA&A..49..409A} for a review) and galaxy evolution studies (e.g., \citealt{2003MNRAS.346..601G}; \citealt{2005ApJ...623..721P}; \citealt{2008MNRAS.391..585M}). Despite the wealth of information clusters can provide, deriving strong constraints from cluster surveys is a non-trivial problem due to the complexity of estimating accurate cluster masses. The use of cluster surveys as a dark energy probe provides greater statistical power than other techniques (Dark Energy Task Force; \citealt{2006astro.ph..9591A}). However, enabling this statistical precision requires significant advances in treating the systematic uncertainties between survey observables and cluster masses.\\ \indent Clusters can be detected across several different wavelength regimes using various techniques. They are identified in optical and infrared light as over-densities in the number counts of galaxies (e.g., \citealt{1958ApJS....3..211A}, \citealt{1968cgcg.book.....Z}), while colour information improves the contrast by selecting the red galaxies that dominate in these systems (e.g., \citealt{2005yCat..21570001G}, \citealt{2007ApJ...660..221K}, \citealt{2011ApJ...736...21S}, \citealt{2012MNRAS.420.1167A}). At X-ray wavelengths, the hot intra-cluster medium produces bright extended sources (e.g., \citealt{1972ApJ...178..309F}, \citealt{2000ApJS..129..435B}, \citealt{2002ARA&A..40..539R}, \citealt{2009ApJ...692.1033V}), while at millimeter wavelengths, inverse Compton scattering of photons from this gas results in characteristic distortions in the cosmic microwave background (e.g., \citealt{1972CoASP...4..173S}, \citealt{2002ARA&A..40..643C}, \citealt{2013arXiv1303.5089P}, \citealt{2010ApJ...722.1180V}, \citealt{2013JCAP...07..008H}). Finally, distortions of images of faint background galaxies through weak gravitational lensing offers perhaps the most direct measure of the huge masses of these systems (e.g., \citealt{2012arXiv1208.0605A}). \indent Despite these diverse methods of detecting clusters, no cluster observable \emph{directly} delivers a mass. The cluster mass function is one key method to constrain the dark energy parameter. Ongoing and future dark energy missions plan to consider cluster counts in their analyses. Hence, it is crucial to be able to measure cluster masses as accurately as possible. Follow-up spectroscopy is of great importance to all group/cluster surveys, providing the kinematics of cluster galaxies, which is one of a few mass proxies that is directly related to cluster mass (by providing a direct measure of the dark matter potential well). This series of papers examines various observable - mass relations by testing an extensive range of galaxy-based cluster mass estimation techniques with the aim of calibrating follow-up mass proxies. \indent Galaxy-based mass estimation techniques commonly follow three general steps: first identify the cluster overdensity, second deduce cluster membership, and finally, using this membership, estimate a cluster mass. Common optical cluster finding methods include using the \citet{1982ApJ...257..423H} Friends-Of-Friends (FOF) group-finding algorithm (e.g., \citealt{2006ApJS..167....1B}; \citealt{2008AJ....135..809L}; \citealt{2012A&A...540A.106T}; \citealt{2013arXiv1305.1891J}) and methods based upon Voronoi tessellation (e.g., \citealt{2002ApJ...580..122M}; \citealt{2004AJ....128.1017L}; \citealt{2009MNRAS.395.1845V}; \citealt{2011ApJ...727...45S}). Also widely used are red-sequence filtering techniques (e.g., \citealt{2000AJ....120.2148G}; \citealt{2012MNRAS.420.1861M}; \citealt{2013arXiv1303.3562R}) and methods that rely on the bright central galaxy (BCG) to identify the presence of a cluster (e.g., \citealt{2005MNRAS.356.1293Y}; \citealt{2007ApJ...660..221K}). Cluster catalogues are also constructed using the positions and magnitudes of galaxies to search for over-densities via the matched filter algorithm (e.g., \citealt{1996AJ....111..615P}; \citealt{1999A&A...345..681O}; \citealt{1999ApJ...517...78K}; \citealt{2009ApJ...698.1221M}).\\ \indent Once the over-densities are identified, many methods select an initial cluster membership using the groups obtained via the FOF algorithm (e.g., \citealt{2012MNRAS.423.1583M}; Pearson et al. in preparation; \citealt{2012A&A...540A.106T}), whilst others select galaxies within a specified volume in phase space (e.g., \citealt{2007MNRAS.379..867V}; \citealt{2009MNRAS.399..812W}; \citealt{2013MNRAS.429.3079M}; \citealt{2013ApJ...768L..32G}; \citealt{2013ApJ...772...25S}; Pearson et al. in preparation) or within a certain region of colour--magnitude space where cluster galaxies are known to reside (e.g., \citealt{2013ApJ...772...47S}). Once the initial set of member galaxies is chosen, it is common to iteratively refine membership using either the estimated velocity dispersion, radius and colour information, or even a combination of these properties. Deducing which galaxies are members of a cluster is non-trivial, and unfortunately the inclusion of even quite small fractions of interloper galaxies that are not gravitationally bound to the cluster can lead to a strong bias in velocity dispersion-based mass estimates (e.g., \citealt{1983MNRAS.204...33L}; \citealt{1997NewA....2..119B}; \citealt{1997ApJ...485...39C}; \citealt{2006A&A...456...23B}; \citealt{2007A&A...466..437W}). For this reason, methods often employ careful interloper removal techniques, for example, by modelling interloper contamination when performing density fitting, by using the Gapper technique or via iterative clipping as described above.\\ \indent Many methods then follow the classical approach of applying the virial theorem to the projected phase space distribution of member galaxies (e.g., \citealt{1937ApJ....86..217Z}; \citealt{1977ApJ...214..347Y}; \citealt{Evrard:2008vo}), assuming that the system is in equilibrium. Other methods utilise the distribution of galaxies in projected phase space, assuming a Navarro, Frenk and White (NFW) density profile (\citealt{1996ApJ...462..563N}; \citealt{1997ApJ...490..493N}) to obtain an estimate of cluster mass. The number of galaxies associated with a cluster above a given magnitude limit (the richness) is also used as a proxy for mass (e.g., \citealt{2003ApJ...585..215Y}). In addition, the more-recently developed caustic method identifies the projected escape velocity profile of a cluster in radius-velocity phase space, delivering a measure of cluster mass (e.g., \citealt{1997ApJ...481..633D}; \citealt{1999MNRAS.309..610D}; \citealt{2013ApJ...768L..32G}).\\ \indent The aim of this paper is to perform a comprehensive comparison of 23 different methods that employ variations of the techniques described above by deducing both the mass and membership of galaxy clusters from a mock galaxy catalogue. In order to simplify the problem, the clusters are populated with galaxies in a somewhat idealised manner, with cluster locations that are specified {\it a priori}; in this way, the basic workings of the various algorithms can be tested under optimal conditions, without the potential for confusion from more complex geometries or misidentified clusters.\\ \indent The paper is organised as follows. We describe the mock galaxy catalogue in Section~2, and the mass reconstruction methods applied to this catalogue are described in Section~3. In Sections~4 and 5, we present our results on cluster mass and membership comparisons. We end with a discussion of our results and conclusions in Section 6. Throughout the paper we adopt a Lambda cold dark matter ($\Lambda$CDM) cosmology with $\Omega_{\rm 0}=0.25$, $\Omega_{\rm \Lambda}=0.75$, and a Hubble constant of $H_{\rm 0} = 73\,\rm{km\,s^{-1}}\,\rm{Mpc^{-1}}$, although none of the conclusions depend strongly on these parameters. | \label{sec:Discussion} \begin{figure*} \centering \includegraphics[trim = -5mm 14mm 0mm 25mm, clip, width=1.02\textwidth]{phase_1_ngaltrue_ngalrec_unknown_final.eps} \caption{Recovered number of galaxies associated with each group/cluster versus the true number of galaxies when the group/cluster membership is not known. The black dotted line represents the 1:1 relation and the black ticks represent the true minimum and maximum number of galaxies associated with the input groups/clusters. `NR' in the legend represents groups/clusters that are not recovered because they are found to have very low ($\rm < 10^{10} \rm M_{\odot}$) or zero mass.} \label{fig:phase_1_ngaltrue_nalcat} \end{figure*} \begin{figure*} \centering \includegraphics[trim = 0mm 15mm 0mm 26mm, clip, width=1.0\textwidth]{phase_1_mass_vs_ngal_unknown_final.eps} \caption{Recovered richness versus recovered mass for each halo, when the group/cluster membership is not known. The black dotted line represents the true mass versus the true number of galaxies associated with each halo and the black ticks represent the true minimum and maximum number of galaxies associated with the input groups/clusters. `NR' in the legend represents groups/clusters that are not recovered because they are found to have very low ($\rm < 10^{10} \rm M_{\odot}$) or zero mass. The bottom right panel displays the input HOD mass-richness distribution.} \label{fig:phase_1_mass_ngal} \end{figure*} The initial set-up used for this project was kept deliberately simple. We began with a simulated dark matter halo catalogue, and a model that inserts galaxies via smooth, spherically-symmetric NFW distributions centred at the centre of the dark matter potential well and scaled by the mass of the halo. Within the $z=0$ snapshot, haloes of mass above $\rm 10^{11.5}M_\odot$ (Figure~\ref{fig:phase_1_mass_functions}) are populated and a light-cone is then drawn through this distribution to create the ``observations'' used for this test. Once this baseline study has quantified and minimised the uncertainties intrinsic in mass estimation, we will move on to a more sophisticated cluster model to identify the additional levels of uncertainty that such complexity introduces. Due to the simplicity of the model used for this initial phase and the use of a single cosmology, we cannot comment on the absolute calibration of each model, other than noting that the values have been calibrated to at least approximate reality. The main focus of this paper is to quantify the underlying scatter inherent in cluster mass estimation techniques that use the positions, velocities, and colours of galaxies. \indent There are three general stages involved in galaxy-based cluster mass estimation. The first stage is the identification of a group/cluster overdensity, the second is the selection of galaxies deemed to be group/cluster members, and the third is the estimation of cluster properties based on this membership. These steps are not, in practice, independent from each other. For instance, a cluster mass estimation method based on dynamical properties might be very sensitive to contamination by unrelated field galaxies. As such, it is perhaps better in such a method to be very conservative with the membership selection at the expense of completeness and then recalibrate the mass estimate based on this incomplete galaxy sample. Conversely, a method based on the volume covered might not be sensitive to interlopers but highly reliant on obtaining a nearly complete galaxy sample. \indent Following the philosophy of this study of making things as simple as possible, and to aid the inter-comparison of the results of different methods, we supplied the participants with a list of initial centres (i.e. the first stage of this process) about which to look for structures. We further note that not all methods taking part in this study include this step. The centres of the group/cluster sample correspond with the location of the brightest cluster galaxy in all cases and are the ``true'' location of the halo centre in the DM simulation (the HOD model used places the brightest galaxy at the location of the most bound DM particle in the halo). Some methods (indicated by an asterisk in Table~1) chose not to use this information, and instead used the full galaxy catalogue detecting initial centres themselves. After calculating the properties of the identified groups/clusters, these methods then matched to our supplied coordinates. This is admirable and a more stringent test of these methods. We aim to investigate the issue of initial search location further in subsequent work. We conclude from this study that, for clusters with masses above $10^{14}\,M_\odot$, the uncertainty in the methods seems to be around a factor of two. Richness-based methods have the smallest uncertainties, but this reliability may be due to the underlying simplicity of the HOD model, which includes no a-sphericity, dynamical substructure or large scale velocity distortions. However, we note that low scatter in the richness--mass relation has been observed for photometric samples (e.g., \citealt{2014arXiv1401.7716R}). Below $\rm 10^{14}\,M_\odot$, the scatter rises as the number of member galaxies drops, and the uncertainty rapidly approaches an order of magnitude. This level of error has severe implications for studies of cosmology based on cluster masses given the steeply-falling cluster mass function: there are many more $\rm 10^{13}\,M_\odot$ clusters than $\rm 10^{14}\,M_\odot$ clusters such that a large scatter in mass estimates will introduce very unpleasant Malmquist-like biases that will render the answers meaningless unless the biases can be very well modelled and controlled. \indent In order to pinpoint the primary source of the errors, we also supplied the participants with the ``true'' galaxy cluster membership, as the halo has been initially populated by the HOD model. We then asked the participants to return the group/cluster properties based on this galaxy list rather than the one they had calculated. This simplification did not improve mass estimates; for the majority of methods, the level of scatter was increased. The key factor here is the way in which methods have been calibrated. Those which have been tuned to return unbiased results on the basis of galaxies lying within the 3D `virial' radius will naturally perform best when provided with such data, whilst methods attuned to the more practical situation in which interlopers cannot be avoided have adopted a variety of approaches to deal with this (aperture selection, background subtraction etc.) and are likely to perform worse in the absence of the expected interlopers. We note that the masses of the cluster sample used for this `known' membership test are, on average, slightly lower than the `unknown' membership test. This may deliver a small contribution to the higher levels of scatter, as we have seen previously, that the level of scatter is higher for the lower mass clusters. \indent The bottom line is that, with the exception of the richness-based methods whose accuracy is unlikely to be realised in a more realistic scenario, the limited number of cluster tracers for the lower-mass systems (typically only $\sim 10-20$) results in an irreducible large uncertainty in the cluster mass estimate. We stress that this experiment has been carried out on the most unchallenging possible test case of spherical systems with known locations and no imposed substructure. Observational challenges such as spectroscopic target selection, incompleteness, and slit/fibre collisions are also not considered. With a more realistic model for the galaxy population and a more observationally challenging set-up, it is likely that accurate group/cluster mass reconstruction will be even more problematic. | 14 | 3 | 1403.4610 |
1403 | 1403.7205_arXiv.txt | We use A-type stars selected from Sloan Digital Sky Survey data release 9 photometry to measure the outer slope of the Milky Way stellar halo density profile beyond $50$ kpc. A likelihood-based analysis is employed that models the $ugr$ photometry distribution of blue horizontal branch (BHB) and blue straggler (BS) stars. In the magnitude range, $18.5 < g < 20.5$, these stellar populations span a heliocentric distance range of: $10 \lesssim D_{\rm BS}/\mathrm{kpc} \lesssim 75$, $40 \lesssim D_{\rm BHB}/\mathrm{kpc} \lesssim 100$. Contributions from contaminants, such as QSOs, and the effect of photometric uncertainties, are also included in our modeling procedure. We find evidence for a very steep outer halo profile, with power-law index $\alpha \sim 6$ beyond Galactocentric radii $r=50$ kpc, and even steeper slopes favored ($\alpha \sim 6-10$) at larger radii. This result holds true when stars belonging to known overdensities, such as the Sagittarius stream, are included or excluded. We show that, by comparison to numerical simulations, stellar halos with shallower slopes at large distances tend to have more recent accretion activity. Thus, it is likely that the Milky Way has undergone a relatively quiet accretion history over the past several Gyr. Our measurement of the outer stellar halo profile may have important implications for dynamical mass models of the Milky Way, where the tracer density profile is strongly degenerate with total mass-estimates. | In our model Universe, the balance between expansion and collapse stipulates that the size and the mass of a galaxy are set by its formation epoch (see e.g. \citealt{press74}). Once most of the galactic contents are in place, subsequent matter infall adds little to the final mass budget (see e.g. \citealt{zemp13}). The total mass is dominated by dark matter; even though gas and stars might extend as far, their densities drop faster with radius and therefore contribute little to the integral over the virial volume. However, despite amounting to only $1$ per cent of the total galaxy luminosity or $<0.01$ per cent of the total mass, the stellar halo allows us to gauge the details of the mass distribution beyond the edge of the disk. The stars in the halo are more than mere tracers of the potential. The dark matter radial density profiles are universal (and hence featureless beyond the scale radius), or at least they appear to be so for a considerable range of distances explored in numerical simulations (e.g. \citealt{nfw97}). However, due to the plummeting star-formation efficiency in low-mass sub-halos (e.g. \citealt{bullock00}; \citealt{somerville02}), the stellar halo formation is a much more stochastic process. The lumpier accretion, combined with extremely long mixing times ($>1$ Gyr) can lead to a greater variety of stellar halo radial density profiles (see e.g. \citealt{libeskind11}). Therefore, there is hope that by studying the phase-space and chemical properties of halo stars today, we can uncover the fossil record of the Milky Way's accretion history. In order to quantify the stellar halo distribution, we often fit model profiles, such as power-laws and Einasto profiles (\citealt{einasto89}), to the stellar number counts. This approach has been widely used in the literature, and although these models may not represent a truly physical representation of the stellar halo, they provide a useful framework that can be compared with predictions from numerical simulations. Early work limited to Galactocentric radii $r \sim 20-30$ kpc found that the Milky Way stellar halo follows an oblate, single power-law distribution with minor-to-major axis ratio $q \sim 0.5-0.8$, and power-law index $\alpha \sim 2-4$ (e.g., \citealt{preston91}; \citealt{robin00}; \citealt{yanny00}; \citealt{newberg06}; \citealt{juric08}). More recent work, probing to greater distances in the halo, found evidence for a ``break'' in the stellar density profile at $r \sim 20-30$ kpc\footnote{In fact, the first hint of a break in the stellar halo density profile at $r \sim 25$ kpc was reported by \cite{saha85}, using a sample of $N \sim 29$ RR lyrae stars}. These studies find a power-law slope of $\alpha \sim 2-3$ can describe the stellar halo within $r \sim 20-30$ kpc, but a steeper slope with $\alpha \sim 3.8-5$ is required at larger distances (\citealt{bell08}; \citealt{watkins09}; \citealt{sesar11}; \citealt{deason11}). \cite{deason13a} argued that this broken profile could be caused by the build-up of stars at their apocenters, either from the accretion of one massive dwarf, or from several dwarfs accreted at a similar epoch. On the other hand, \cite{beers12} claim that the change in power-law slope near the break radius is caused by a transition from an ``inner'' to an ``outer'' stellar halo population. Several groups have found evidence for correlations between metallicity and kinematics of halo stars, which perhaps suggest two distinct populations (e.g. \citealt{carollo07}; \citealt{carollo10}; \citealt{nissen10}; \citealt{deason11a}; \citealt{hattori13}; \citealt{kafle13}). However, at present it is not obvious whether these signatures can be produced purely from the accretion of dwarf galaxies, or if some of these findings are biased by distance uncertainites and/or contamination (e.g. \citealp{schonrich11, schonrich14}; \citealt{fermani13}). It is clear that from a relatively ``simple'' measure of star counts, we can learn a great deal about the formation mechanism and/or past accretion history of the stellar halo. This bodes well for studies of stellar halos beyond the local group, where we are already able to measure the surface brightness profiles of these incredibly diffuse halos out to projected radii of $R \sim 50-70$ kpc (e.g. \citealt{radburn11}; \citealt{monachesi13}; \citealt{greggio14}; \citealt{vandokkum14}). The surface brightness profile of our nearest neighbor, M31, has now been mapped out to an impressive $R \sim 200$ kpc (e.g. \citealt{gilbert12}; \citealt{ibata14}). In contrast to our own Galaxy, these studies find no evidence for a break in the stellar density profile, and the star counts can be well-described by a single power-law with slope $\alpha \sim 3-3.5$. The differences between the stellar halo density profiles can give us an important insight into the contrasting accretion histories of the Milky Way and M31 (see \citealt{deason13a}). Superimposed on the ``field'' (or phase-mixed) stellar halo distribution is a wealth of un-relaxed substructure in the form of streams, clouds and other overdensities (e.g. \citealt{ibata95}; \citealt{newberg02}; \citealt{belokurov06}; \citealt{belokurov07}; \citealt{juric08}). Most striking is the vast stream of tidal debris associated with the disrupting Sagittarius dwarf (\citealt{belokurov06}), where we are privy to a front-seat view of accretion in action. The presence of these recent accretion relics can significantly bias stellar halo number counts. Several studies have attempted to excise these known substructures, and only model the relatively phase-mixed halo component. However, it is important to understand the affect that these structures have on density profile measurements, especially when making comparisons with numerical simulations or stellar halos of external galaxies. For the latter, it is generally unfeasible to isolate the sort of substructures that we are able to identify in our own Galaxy. Halo stars provide one of the best tracers of the Milky Way mass at large radii. \cite{deason12} compiled a sample of stellar halo stars with measured line-of-sight (LOS) velocities out to $r \sim 150$ kpc, and found a dramatic drop in LOS velocity dispersion beyond 50 kpc (see also \citealt{battaglia05}). If this drop reflects a fall in the circular velocity of the halo, then the Milky Way mass is likely below $\sim 10^{12}M_\odot$. This result agrees with several other stellar dynamical studies, which favor relatively low halo masses (e.g. \citealt{xue08}; \citealt{bovy12}). By contrast, other methods for estimating the Milky Way mass give larger values. For example, \cite{sohn13} recently used multi-epoch Hubble Space Telescope (\textit{HST}) images to measure the proper motion of the distant Milky Way satellite galaxy Leo I. Comparison of the large observed velocity to numerical simulations implies that the Milky Way mass is likely well above $10^{12} M_\odot$ (\citealt{boylan13}) . More generally, attempts to measure the total mass of the Milky Way using satellite galaxies (e.g. \citealt{wilkinson99}; \citealt{watkins10}), the Magellanic Clouds (e.g. \citealt{kallivayalil13}), the local escape speed (e.g. \citealt{smith07}), the timing argument (e.g. \citealt{li08}; \citealt{vandermarel12}; \citealt{gonzalez13}), and the methods already mentioned, have been distressingly inconclusive with total masses in the range $0.5-3 \times 10^{12}M_\odot$. Halo stars have tremendous potential for constraining the Milky Way mass, since LOS velocities have been measured for many of them, but to make progress the \textit{mass-anisotropy-density} degeneracy must be addressed. Our mass measures based on halo star kinematics are limited by the uncertainty in the tracer density profile and velocity anisotropy. These systematic uncertainties are significant, and mass-measures can vary by up to factors of $\sim 5$ because of unknown tracer properties. Fortunately, the upcoming \textit{Gaia} mission and deep, multi-epoch \textit{HST} proper motion measurements (\citealt{deason13b}; \citealt{hstpromo}), will provide the missing transverse velocity information needed to measure the velocity ellipsoid of distant halo stars. However, we still have very little knowledge of the tracer density profile beyond 50 kpc. Thus, somewhat ironically, the ``simple'' task of counting stars will likely be the main bottleneck for dynamical mass measures of the Milky Way in the near future. In this study, we use A-type halo stars selected from Sloan Digital Sky Survey (SDSS) data release 9 (DR9) photometry to measure the stellar halo density slope beyond $\sim 50$ kpc. These A-type stars comprise of blue horizontal branch (BHB) and blue straggler (BS) populations. The former stellar population, constitute our prime halo tracers and can probe out to $\sim 100$ kpc in the magnitude range used in this work ($18.5 < g < 20.5$). Our method models both BHB and BS populations simultaneously using photometric data alone, and includes the contribution from contaminants, such as QSOs. The combination of the large SDSS sky coverage ($\sim 14,000$ deg$^2$) and the accurate distance estimates provided by the BHB stars, allows us, for the first time, to constrain the outer density profile slope of the Milky Way stellar halo. The paper is arranged as follows. In \S2.1 we describe the SDSS DR9 photometric data and our selection criteria for A-type stars. The remainder of \S2 describes our A-type star models and the absolute magnitude-color relations for the two populations. In \S3 we address the contribution of contaminants and the affects of photometric uncertainties on our modeling procedure. In \S4, we describe our likelihood-based method to determine the density profile of the stellar halo and in \S5 we present our results. Finally, we discuss the implications for the accretion history and the mass of the Milky Way in \S6, and summarize our main conclusions in \S7. | We model the density distribution of distant BHB and BS halo stars using SDSS DR9 photometry, with the aim of measuring the outer slope of the Milky Way stellar halo density profile beyond $r \sim 50$ kpc. We construct number density PDFs in $ugr, m_g$ space, and include contributions from QSO contaminants. Our PDF is convolved with the $ugr, m_g$ error distribution to take into account the significant photometric uncertainties at faint magnitudes. We fix the QSO number density using the QSO model developed by \cite{bovy11}, and allow the stellar halo profile within $r \sim 40-50$ kpc to lie within an observationally motivated parameter space. The outer halo model parameters are identified by modeling the stellar distribution in $u-g$, $g-r$, $m_g$, $\ell$, $b$ space. We test our method on simulated catalogs of BHBs, BSs and QSOs, and demonstrate that the properties of the distant halo can be recovered with sufficient accuracy. We apply our likelihood analysis to high latitude ($|b| > 30$ deg) SDSS DR9 stars in the color and magnitude range; $0.7 < u-g < 1.6$, $-0.25 < g-r < -0.1$ and $18.5 < g < 20.5$. With this selection, BHB and BS stars span a heliocentric distance range: $10 \lesssim D_{\rm BS}/\mathrm{kpc} \lesssim 75$, $40 \lesssim D_{\rm BHB}/\mathrm{kpc} \lesssim 100$. We identify stars coincident on the sky with the known substructures Virgo and SGR, and apply our analysis both including and excluding these stars. Our analysis assumes: 1) stellar halo sphericity at large radii, 2) an inner stellar halo ($r \lesssim 40$ kpc) density parametrization consistent with current constraints in the literature, and 3) BHB and BS intrinsic color distributions that remain the same throughout the halo. The relative contributions of A-type stars (BHB and BS) and QSOs are computed iteratively from the convolved PDFs for each set of model parameters. In our selection box $0.7 < u-g < 1.6$, $-0.25 < g-r < -0.1$, and magnitude range $18.5 < g < 20.5$, we find a QSO contamination fraction of $f_{Q} \sim 0.2$ and a BHB fraction of $f_{\rm BHB} \sim 0.2$; these fractions have a weak dependence on our model parameters. After excluding known substructures, we find that very steep outer halo profiles are preferred, with $\alpha_{\rm out} \sim 6$ beyond $r=50$ kpc. Even when SGR and Virgo stars are included in the analysis, we find very steep outer profiles. There is evidence for a break in the stellar density at $r_b \sim 50-60$ kpc, which is coincident with the apocenter of the SGR leading arm. We compare our results to the predictions of simulated stellar halos. The \cite{bullock05} suite of halos, built up purely from the accretion of dwarf galaxies, have outer profile slopes which depend on the accretion history of the halo; steeper outer slopes suggest earlier accretion epochs than shallow slopes. Thus, our finding of a very steep outer halo profile argues that, apart from the relatively recent accretion of SGR, the majority of the Milky Way stellar halo was built up from relatively early accretion events ($ T > 6$ Gyr ago). This is in contrast to the M31 stellar halo which has a much shallower density slope out to $r \sim 200$ kpc ($\alpha \sim 3-3.5$; \citealt{gilbert12}; \citealt{ibata14}), and thus presumably has had a more active late-time accretion history. The density profile of the Milky Way stellar halo is an important ingredient for dynamical mass estimates of the Galaxy. Until now, the unknown stellar density slope beyond $\sim 50$ kpc has proved to be a troublesome bottleneck in constraining the total mass out to large distances. Our finding of a very steep outer halo slope may have important implications for studies utilizing the kinematics of halo stars to estimate the total mass of the Milky Way. The measurement we report here, in combination with constraints on the halo star velocity anisotropy from upcoming surveys (such as \textit{Gaia}) will, undoubtedly, significantly reduce the uncertainty surrounding dynamical mass measurements of the Milky Way. | 14 | 3 | 1403.7205 |
1403 | 1403.4495_arXiv.txt | The astronomical dark matter is an essential component of the Universe and yet its nature is still unresolved. It could be made of neutral and massive elementary particles which are their own antimatter partners. These dark matter species undergo mutual annihilations whose effects are briefly reviewed in this article. Dark matter annihilation plays a key role at early times as it sets the relic abundance of the particles once they have decoupled from the primordial plasma. A weak annihilation cross section naturally leads to a cosmological abundance in agreement with observations. Dark matter species subsequently annihilate -- or decay -- during Big Bang nucleosynthesis and could play havoc with the light element abundances unless they offer a possible solution to the $^{7}$Li problem. They could also reionize the intergalactic medium after recombination and leave visible imprints in the cosmic microwave background. But one of the most exciting aspects of the question lies in the possibility to indirectly detect the dark matter species through the rare antimatter particles -- antiprotons, positrons and antideuterons -- which they produce as they currently annihilate inside the galactic halo. Finally, the effects of dark matter annihilation on stars is discussed. | Large amounts of invisible matter in the Universe have been discovered in 1933 when the Swiss astronomer Fritz Zwicky measured~\cite{1933AcHPh...6..110Z} the velocity dispersion of individual galaxies inside the Coma cluster. That self-gravitating system contains thousands of objects and has quite certainly virialized given its age and spherical shape. Because a steady state has been reached, the cluster mass and size can be related to the velocity dispersion of the galaxies which it shelters. Zwicky determined for the first time the dynamical mass of the Coma cluster and obtained a value more than a hundred times larger than the visible counterpart inferred from the luminosity of galaxies. The astronomical dark matter puzzle originates from this measurement. Since then, it has been continuously confirmed by an impressive series of refined observations performed with quite different methods. The analysis of the X-ray emission from the hot gas filling clusters allows to reconstruct their gravitational potential wells and to infer their dynamical mass. The weak and strong lensing of distant sources can also be used to derive the amount of material bending the light trajectories. The dynamical to visible mass ratio is always very large. Clusters can be pictured as icebergs with a tiny emerged visible part and a by far dominant hidden component made of dark matter (DM). The problem also exists on galactic scales as demonstrated by Vera Rubin~\cite{1980ApJ...238..471R} and Albert Bosma~\cite{1979A&A....79..281B} in 1979. The rotation curves of spirals are determined with the help of the Doppler effect through the 21 cm line emission from orbiting clouds of neutral atomic hydrogen HI. The rotation speed of the disk does not exhibit the Keplerian decrease which would be typical of a central and dominating mass. On the contrary, it is found to remain flat far beyond the optical radius. The dynamical mass of spirals does not lie therefore in their bulges but is spread over an extended halo of unseen material. More recently, the measurements of the cosmic microwave background (CMB) anisotropies by the Planck satellite in 2013 provide clear evidence~\cite{Ade:2013zuv} for a flat universe whose density $\Omega_{\rm tot} = 1$ is equal to the closure value. A fluid with negative pressure, dubbed dark energy or quintessence, coexists with non-relativistic matter. Dark energy contributes a fraction $\Omega_{\Lambda} = 0.6825$ to the total mass budget whereas matter amounts to $\Omega_{\rm M} = 0.3175$. Nucleons and electrons which make up the so-called baryonic matter contribute only a small fraction $\Omega_{\rm B} = 0.049$ in agreement with primordial nucleosynthesis. A dark component with density $\Omega_{\rm DM} = \Omega_{\rm M} - \Omega_{\rm B} = 0.2685$ appears on cosmological scales with the surprising property of being made of an unknown form of matter. Theoreticians have been imagining for the last three decades a plethora of candidates for this astronomical dark matter. In spite of the proliferation of more or less exotic models, the interest of the community has focused on the supersymmetric or Kaluza-Klein extensions of the standard model of particle physics. These theories are based on a new symmetry of Nature and naturally predict the existence of a weakly interacting and massive particle -- dubbed WIMP -- whose mass lies in the GeV to TeV range with typically weak interactions. This species is moreover stable because of the conservation of the quantum number associated to the new symmetry. It is electrically neutral and is its own anti-particle. A WIMP pair can annihilate to produce standard particles like fermions or gauge bosons. \beq {\chi} + {\chi} \rightleftharpoons f + \bar{f} \, , \, W^{+} \! + W^{-} \, , \, Z^{0} + Z^{0} \, , \, \cdots \label{annihil_reac} \eeq Dark matter annihilation plays a crucial role in the early Universe as it provides a natural mechanism through which WIMPs have been produced. Because reaction~(\ref{annihil_reac}) is in equilibrium during the Big Bang, DM species exist under the form of an ultra-relativistic radiation as long as the temperature of the primordial plasma exceeds their mass. For a 10~GeV particle, this happens before an age of a few ns. As soon as this condition stops to be fulfilled, WIMPs annihilate without being produced back from lighter particles. Their density drops significantly until they are so diluted that they stop interacting with each other. This chemical quenching leaves a steady population of particles whose density decreases as space expands. Because they are stable, WIMPs contribute today to the mass budget of the Universe. Actually, their cosmological relic abundance is found~\cite{PhysRevLett.39.165} to depend only on the annihilation cross section with \beq \Omega_{\chi} h^{2} \, = \, {\displaystyle \frac{3 \times 10^{-27} \; {\rm cm^{3}} \; {\rm s^{-1}}}{< \! \Sa v \! >}} \;\; , \eeq where $h$ is the Hubble constant. With a cross section $< \! \Sa v \! > \sim 3 \times 10^{-26} \; {\rm cm^{3}} \; {\rm s^{-1}}$ typical of weak interactions, the cosmological abundance $\Omega_{\chi}$ falls naturally close to the observed value of $\Omega_{\rm DM} \simeq 0.27$. This coincidence is called the WIMP miracle and is the reason why this type of particle is considered as the favoured candidate to the astronomical dark matter. | 14 | 3 | 1403.4495 |
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1403 | 1403.4947_arXiv.txt | {In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E- and B- mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a well-defined manner. Specifying General Relativity, we write down a complete set of equations for a GR$+\Lambda$CDM universe for computing all of the possible lensing terms from Newtonian N-body simulations. We illustrate this with the vector potential and show that, in a GR$+\Lambda$CDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a $\Lambda$CDM cosmology.} \begin{document} | It has been understood since the dawn of General Relativity that one of the consequences of a gravitational theory incorporating the equivalence principle is the bending of light by gravitating masses \citep{LorEinMin52}. An important consequence of this light bending is that galaxy images are distorted by gravitational influences along the line of sight. A statistical analysis of the shapes of galaxy images allows this weak gravitational lensing effect, known as cosmic shear, to be observed. Since the first measurements of cosmic shear \citep{Wittman:2000tc,Kaiser:2000if,Bacon:2000sy,vanWaerbeke:2000rm}, increasingly precise measurements have been made of the cosmic shear power spectra, leading up the the latest CHTLens results \citep{Kilbinger:2012qz}. Now, weak lensing is becoming an important tool for cosmology, with claims that it can place constraints on the equation of state of dark energy \citep{Albrecht:2006um} and modified gravity models \citep{euclid}. Current and future surveys include the Dark Energy Survey \citep{Abbott:2005bi}, LSST \citep{Ivezic:2008fe}, SKA \citep{ska} and the ESA satellite mission Euclid \citep{Refregier:2010ss}. These missions will yield a wealth of precise data, including tomographic weak lensing power spectra. However, these power spectra will largely come from non-linear scales in the universe, i.e. scales smaller than around 8-10 h$^{-1}$ Mpc, where the matter density contrast has gone non-linear. Broadly speaking, cosmologists study linear and non-linear scales in different ways. On larger, linear scales, fully relativistic perturbative schemes are used where the matter and metric perturbations in the universe are assumed to be small. On smaller scales in the universe, gravity is assumed to be Newtonian and N-body simulations are run to examine the evolution of the density field. Weak-lensing calculations have been carried out both in the Newtonian regime \citep{Bartelmann:1999yn} and with GR perturbation theory (see e.g. \citep{dodelson:2003,Dodelson:2005zj}). However, there are few studies that both apply on smaller, non-linear scales in cosmology and are fully relativistic, thus justifying the standard ray tracing approach to extracting lensing observables from N-body simulations. The post-Friedmann formalism, introduced in \citep{postf,thesis} and applied in \citep{Bruni:2013mua}, is a non-linear approximation scheme designed to study relativistic structure formation in the universe on all scales, including scales where the density contrast is large. It is based upon a post-Newtonian type expansion in inverse powers of the speed of light $c$, building the relativistic corrections on top of the Newtonian equations. The resulting equations are a non-linear approximation to the full Einstein equations that are valid on all scales. At leading order, the post-Friedmann formalism reproduces Newtonian cosmology \citep{postf,thesis}. In this paper, we use the post-Friedmann metric to compute the complete weak-lensing deflection angle up to order $c^{-4}$, including terms that are quadratic in the first order deflection, the first post-Newtonian corrections to the two scalar gravitational potentials and the effects of the vector and tensor contributions to the metric. This is the first time that the complete weak-lensing deflection angle on non-linear scales has been computed in a fully relativistic manner, including scalar, vector and tensor contributions to the metric. We then examine how the different terms in the deflection angle contribute to the E- and B-mode power spectra. The calculation of the deflection angle here is purely geometrical, i.e. does not assume the Einstein equations, thus it should be valid for any metric theory of gravity. The strength of this approach to weak lensing is that the metric components that contribute to the lensing can be consistently related to the matter inhomogeneities. We illustrate this with a set of equations demonstrating how each of the quantities that contributes to the deflection angle can be computed from N-body simulations for a $\Lambda$CDM cosmology and demonstrate that the contribution to the E-mode from the vector potential is negligible for such a cosmology. The equation for the deflection angle, equation (\ref{bend_final}), coupled with equations (\ref{complete_matter_eqns1})-(\ref{complete_matter_eqns8}) demonstrating how to relate the metric perturbations to the matter in a $\Lambda$CDM, comprise the main results of this paper. This paper is laid out as follows. In section \ref{sec_postf} we will briefly introduce the relevant parts of the post-Friedmann formalism, which will then be used to calculate the weak-lensing deflection angle in section \ref{sec_bend}. In section \ref{sec_power}, we will examine how the vector and tensor parts of the deflection angle contribute to the E- and B-mode power spectra of cosmic shear. Section \ref{sec_matter} will examine how to relate the matter inhomogeneities in the universe to the metric potentials, including the example of the post-Friedmann vector potential. We conclude in section \ref{sec_conc}. | \label{sec_conc} Weak gravitational lensing is rapidly becoming an important tool in cosmology and promises to constrain both the parameters composing the concordance model of cosmology and physics beyond the $\Lambda$CDM model. Weak-lensing calculations predominantly use relativistic perturbation theory, which works well for the largest scales. However, future surveys will yield the majority of their information on non-linear scales, requiring the use of ray tracing through N-body simulations. In this paper we have calculated the full weak-lensing deflection angle up to order $c^{-4}$ using the post-Friedmann formalism. Crucially, this formalism doesn't require the matter inhomogeneities to be small, so this calculation of the deflection angle can be used on fully non-linear scales in our universe. This deflection angle, equation (\ref{bend_final}), is the first main result of this paper and should hold for any metric theory of gravity. The main advantage of using the post-Friedmann formalism for lensing is that the metric potentials can be related to the matter perturbations in the universe on non-linear scales. The second main result of this paper is the set of equations (\ref{complete_matter_eqns1})-(\ref{complete_matter_eqns8}), derived from \citep{postf,thesis}, showing how the metric potentials contributing to the deflection angle can be computed from N-body simulations. These equations are valid for a $\Lambda$CDM cosmology. As an example, we have used the calculation of the post-Friedmann vector potential in \citep{Bruni:2013mua,longerpaper} to show that the vector contribution to the E-mode power spectrum is unlikely to be detected, even on fully non-linear scales. Thus far, we have been unable to extract the time derivative of the vector potential from the simulations. However, we have calculated a simple order of magnitude estimate of the B-mode power spectrum that this time derivative would generate, showing it to be very small. Thus, there are no significant sources of the B-mode spectrum on non-linear scales in a $\Lambda$CDM cosmology, allowing its use as one control of systematics as is often done in analysis of weak lensing data. We also have not yet extracted the post-Friedmann scalar potentials $U_P$ and $V_P$ or the tensor modes from the N-body simulations, however these are higher order than the vector potential and so cannot be significantly larger than the vector potential if using Newtonian simulations for $\Lambda$CDM cosmologies has any validity. Thus, their contributions to the E-mode should be equally negligible. We leave it to future work to verify by direct extraction from simulations using equations (\ref{complete_matter_eqns1})-(\ref{complete_matter_eqns8}) that these are indeed small. If this is the case then, for a $\Lambda$CDM cosmology, the use of ray tracing tracing through N-body simulations, taking into account only the Newtonian scalar gravitational potential, is valid on all scales. If these quantities are found to be not small then the use of Newtonian simulations for $\Lambda$CDM cosmologies requires serious scrutiny. In order to investigate lensing on fully non-linear scales for dark energy or modified gravity cosmologies, equivalent equations to (\ref{complete_matter_eqns1})-(\ref{complete_matter_eqns8}) would need to be derived. It is possible that the post-Friedmann vector potential, and/or its time derivative, are larger in modified gravity theories (such as f(R) gravity), due to both the modified behaviour of galaxies \citep{spinf(R)} and the intrinsically relativistic nature of a scalar field. We leave it to future work to develop the modified Einstein equations in dark energy and modified gravity cosmologies using the post-Friedmann formalism. Once the equations have been derived, they can be applied to modified N-body simulations in order to calculate the potentials contributing to the deflection angle (\ref{bend_final}). {\sl Acknowledgements.} MB and DW are supported by STFC grants ST/H002774/1,\\ ST/L005573/1 and ST/K00090X/1. We thank David Bacon for comments on the manuscript. \appendix | 14 | 3 | 1403.4947 |
1403 | 1403.1565_arXiv.txt | The helical kink instability \q{of a twisted magnetic flux tube} has been suggested as a trigger mechanism for solar filament eruptions and coronal mass ejections (CMEs). \q{In order to investigate if estimations of the pre-eruptive twist can be obtained from observations of writhe in such events, we} quantitatively analyze the conversion of twist into writhe in the course of the instability, using numerical simulations. We consider the line tied, cylindrically symmetric Gold--Hoyle flux rope model and measure the writhe using the formulae by Berger and Prior which express the quantity as a single integral in space. We find that the amount of twist converted into writhe does not simply scale with the initial flux rope twist, but depends mainly on the growth rates of the instability eigenmodes of higher longitudinal order than the basic mode. \q{The saturation levels of the writhe, as well as the shapes of the kinked flux ropes, are very similar for considerable ranges of initial flux rope twists, which essentially precludes estimations of pre-eruptive twist from measurements of writhe. However, our simulations suggest an upper twist limit of $\sim 6\pi$ for the majority of filaments prior to their eruption.} | \label{s:int} The $m=1$ kink mode or helical kink instability (hereafter KI) is a current-driven, ideal magnetohydrodynamic (MHD) instability. It occurs in a magnetic flux rope if the winding of the field lines about the rope axis (the twist) exceeds a critical value \citep[e.g.,][]{shafranov57,kruskal58,freidberg82,priest82}. The instability lowers the magnetic energy of the flux rope by reducing the bending of field lines, which leads to a characteristic helical deformation (writhe) of the rope axis. Such writhing is often observed in erupting filaments or prominences in the solar corona (Figure\,\ref{f:filaments}), which has led to the suggestion that the KI can trigger filament eruptions and CMEs \citep[e.g.,][]{sakurai76,sturrock01,torok05,fan05}. The KI has been studied extensively for laboratory plasmas \citep[see, e.g.,][and references therein]{bateman78,goedbloed10}. In applications relevant to the low-$\beta$ solar corona, typically force-free, cylindrically symmetric flux rope configurations of finite length are considered. The anchoring of coronal loops and prominences in the solar surface is modeled by imposing line tied boundary conditions at the flux rope ends. Properties of the KI such as the instability threshold and growth rate, as well as the formation of current sheets, have been investigated for various radial twist profiles in both straight and arched flux rope geometries \citep[e.g.,][]{hood81,mikic90,baty96,gerrard01,torok04}. MHD simulations of kink-unstable flux ropes have been employed to model coronal loop heating and \q{bright-point} emission \citep{galsgaard97,haynes07}, soft X-ray sigmoids \citep{kliem04}, energy release in compact flares \citep{gerrard03}, microwave sources in eruptive flares \citep{kliem10}, and rise profiles, rotation, and writhing of erupting filaments and CMEs \citep{torok05,williams05,fan05,kliem12}. In spite of this large body of work, the amount and evolution of the writhing in kink-unstable flux ropes was quantified only very rarely \citep{linton98,torok10}. Systematic investigations of the dependence of the writhe on parameters such as the initial flux rope twist or geometry have not yet been undertaken. The quantity \emph{writhe} measures the net \q{self-coiling} of a space curve. It is related to the total torsion along the curve: the sum of writhe and total torsion remains constant under deformations, unless the curve develops an inflexion point, where curvature vanishes \citep{moffatt92}. Twist and writhe of a thin flux rope are related to its magnetic helicity via $H=F^2(T+W)$, where $F$ is the axial magnetic flux, $T$ is the number of field line turns, and $W$ is the writhe of the rope axis \citep{calugareanu59,berger06}. The writhe for flux ropes with footpoints on a boundary (such as the photosphere) can be defined by the same formula, using relative helicity for $H$ \citep{berger84}. $W$ depends only on the shape of the axis of the rope; while $T$ measures the net twist of the field lines in the rope about the axis. Since magnetic helicity is conserved in ideal MHD, the KI converts twist into an equal amount of writhe. Here we quantify this process for the first time systematically for a range of initial flux rope twists, using MHD simulations. For our study we consider the straight, uniformly twisted, force-free flux rope equilibrium by \citet[][hereafter GH]{Gold60}, line tied at both ends. In the absence of knowledge about typical twist profiles in coronal flux ropes and due to its force freeness, the equilibrium serves as a convenient reference model. Mechanisms other than the KI that may cause writhing (see \citealt{kliem12} for a detailed discussion) are excluded. Furthermore, the KI of the GH model does not lead to the formation of a helical current sheet, which triggers reconnection in the nonlinear development of other flux rope equilibria \citep[e.g.,][]{baty96,gerrard03}. Therefore, the evolution of the axis deformation can be followed well into the saturation phase of the writhe, which makes this equilibrium particularly suited for our purpose. We measure the axis writhe using the formulae by \cite{berger06}, which express the quantity as a single integral in space, facilitating its calculation. Our motivation for this study is derived from the interest in obtaining estimates of the twist in pre-eruptive solar configurations from the amount of writhing observed during an eruption. At present, the twist cannot be obtained directly, since the magnetic field cannot be measured in the coronal volume and since extrapolations from photospheric vector magnetograms are not yet sufficiently reliable in practice, especially for volumes containing a filament \citep{mcclymont97,schrijver08a}. Twist estimations based on the observations of pre-eruptive coronal configurations are hampered with substantial uncertainties (see Section\,\ref{s:dis}). The writhe of erupting filaments, on the other hand, can be obtained with a reasonable accuracy if the filament displays a coherent shape (Figure\,\ref{f:filaments}) and if observations from more than one viewing angle are available \citep[for example from the {\it STEREO} mission;][]{kaiser08} or if the eruption is directed toward the observer \citep{torok10}. Although twist estimates from the writhe can only be obtained in retrospect, they may facilitate systematic studies of this possibly critical parameter for CME initiation and may be useful for comparison with other means of estimation. | \label{s:dis} We studied the conversion of twist into writhe in a simulation series of the KI in the GH model, considering initial flux rope twists in the range $3.0\,\pi \le \Phi_0 \le 10.6\,\pi$. We found in all cases a saturation of writhe in the nonlinear phase of the instability, after an initial exponential increase during the linear phase. However, the final writhe does not scale simply with the initial flux rope twist. Rather, the amount of twist converted into writhe seems to be determined predominantly by the number of helical turns the flux rope axis develops in the nonlinear phase. For $3.0\,\pi \lesssim \Phi_0 \lesssim 7.5\,\pi$, the rope axis develops a one-turn helix. For twists close to the upper end of this range, internal helical deformations of the one-turn helix develop, due to helical eigenmodes with wavelengths $\lambda < 2 L_y.$ However, the axis shape remains to be dominated by one turn in the nonlinear phase of the instability. The resulting writhe is close to unity for all cases, corresponding to a converted twist of $\sim 2\,\pi$ in the vicinity of the flux rope axis. If the twist is increased beyond this range, the rope axis develops more than one helical turn, and considerably more twist is converted into writhe ($\sim 3.5\,\pi$ in our simulations with $\Phi_0=9.0\,\pi$ and $\Phi_0=10.6\,\pi$). We attributed the relatively similar writhe values obtained in each respective range, as well as the pronounced increase of the writhe between them, to the action of the hoop force on line-tied, kink-unstable flux ropes of finite length. The basically discontinuous dependence of the final writhe upon the initial twist displayed in Figure~\ref{fig:gh_writhe} essentially precludes a reasonable estimation of the initial twist from observations of the writhe in solar filament eruptions and CMEs. The saturation levels of the writhe are \q{very} similar for initial twists up to $\Phi_0\approx8\pi$, requiring an accuracy of writhe determination for such an estimate that cannot be reached in solar observations. Moreover, the final writhe, as any other property of the KI, depends on the radial twist profile of the initial equilibrium. Therefore, a precise knowledge of this profile, combined with a parametric simulation study like the one in Figures~\ref{fig:gh_rope} and \ref{fig:gh_writhe} for a range of different profiles, would be required to permit a reliable estimate of twist. Further effects of importance for the final writhe enter when arched flux rope equilibria are considered \citep[see][]{torok10}, rendering a twist estimation from writhe observations even more difficult. In order to compare our results with the KI in force-free equilibria with non-uniform radial twist \q{profile}, we performed simulation series similar to the one presented here for the straight flux rope model termed ``Equilibrium 2'' in \cite{gerrard01} and the arched flux rope model by \cite{titov99}. Unfortunately, in all runs the flux rope axis was destroyed by reconnection at current sheets before the writhe would clearly saturate (see \citealt{amari99a}, \citealt{haynes08}, and \citealt{valori10} for examples of such reconnection), so that these simulations cannot be used for the purpose of this study. However, our writhe measurements for the KI in the GH equilibrium provide at least a rough upper limit for the initial twist of erupting filaments. It is observed that kinking filaments typically do not display more than one helical turn and hardly any significant internal helical deformation of their axis. Combined with our simulations, this suggests that the initial twist typically does not exceed values $\Phi_0\sim6\pi$. This is supported by simulations of the KI in the Titov-D\'emoulin model, which show strong internal helical deformations for twists above this value (see, e.g., Figure~1 in \citealt{kliem10} and Figure~12 in \citealt{torok10}). Occasionally, however, the Sun seems to succeed in building up higher twists. Several examples can be found in \cite{vrsnak91}, whose estimates of the end-to-end twist fall in the range $(3\mbox{--}15)\,\pi$ for a sample of prominences close to the time of eruption. A particularly clear indication of very high twist (of $\sim10\pi$) was obtained by \cite{romano03} for a filament eruption on 19 July 2000 (Figure\,\ref{f:filaments}c). These estimations are based on measurements of the pitch angle of selected helical prominence threads, which are then converted into twist assuming a uniform radial twist profile both along and across the axis of the underlying flux rope. The latter assumption may be a severe oversimplification, since force-free flux ropes embedded in potential field must generally have a nonuniform radial twist profile in order to match the field at the surface of the rope \citep[see, e.g., Figure~2 in][]{torok04}. Still, the simulations presented here support the existence of such a high twist at least for the case shown in Figure\,\ref{f:filaments}c, based on the strong bending in the lower part of the filament legs \citep[see also Figure 12b in][where a strongly nonuniform radial twist profile was used]{torok10}. A further observed case of very high twist may have been an apparently three-fold helix described in \cite{gary04}. While these estimations remain uncertain to a considerable degree, we can ask how such large twists, if present, may be produced in the solar corona. It is widely believed that twist is accumulated prior to an eruption by flux emergence \citep[e.g.,][]{leka96}, photospheric vortex flows \citep[e.g.,][]{romano05}, or the slow transformation of a sheared magnetic arcade into a flux rope \citep[e.g.,][]{moore01,aulanier10}. It has been argued that flux ropes that form by one or more of these mechanisms will become kink-unstable long before the large twists mentioned above can be reached. While this is likely true for the majority of cases, several scenarios for the build-up of large twists appear to plausible. First, the KI threshold can vary in a wide range as a function of the thickness of the rope \citep[e.g.,][]{hood79,baty01,torok04}, so sufficiently thin flux ropes may be able to harbor large twist in a stable state. Second, sufficiently flat highly twisted flux ropes may be stabilized by strong ambient shear fields \citep[][]{torok10}, or by gravity if they contain sufficient filament material. Third, significant twist may be added by reconnection to the rising flux in the course of an eruption \citep[e.g.,][]{qiu07}. Finally, flux ropes may reconnect and merge prior to an eruption, thereby adding up their respective twists \citep[e.g.,][]{pevtsov96,canfield98,schmieder04,vanballegooijen04}. | 14 | 3 | 1403.1565 |
1403 | 1403.3097_arXiv.txt | *{} \abstract{The chemical composition of the Sun is among the most important quantities in astrophysics. Solar abundances are needed for modelling stellar atmospheres, stellar structure and evolution, population synthesis, and galaxies as a whole. The solar abundance problem refers to the conflict of observed data from helioseismology and the predictions made by stellar interior models for the Sun, if these models use the newest solar chemical composition obtained with 3D and NLTE models of radiative transfer. Here we take a close look at the problem from observational and theoretical perspective. We also provide a list of possible solutions, which have yet to be tested.} | \label{sec:1} Until recently, we thought we understand the Sun very well: its surface temperature, surface pressure, age and mass, interior physical properties, abundances of different chemical elements. After all, most of these parameters can be determined by very precise direct methods: solar effective temperature is known to an astonishing accuracy of $0.01 \%$, as measured from the radiant bolometric flux; neutrino fluxes provide the temperature in the solar core; solar age is obtained from isotopic ratios in meteorites; helioseismolgy - the analysis of propagation of acoustic waves in the solar interior - gives accurately the depth of the convective zone and surface helium abundance. It turned out, however, that what is still not known exactly is the solar chemical composition. The main reasons for this gap in our knowledge of the Sun will be discussed in this lecture. The first paper giving a reference set of the solar abundances for many chemical elements - standard solar composition (SSC), appeared about a century ago \citep{1929ApJ....70...11R}. However, only a few decades later, when computer power increased enough to run complex numerical algorithms, this dataset acquired its main value. The abundances were rightly plugged into a variety of astrophysical models. The first major application of SSC was found in the standard solar models (SSM), which predict evolution of the Sun from its formation till present. SSC went into models of stellar evolution, stellar populations, and galaxies, becoming a ruler for measuring how dissimilar from {\it the Sun} are other cosmic objects. Highly accurate solar abundance distributions are nowadays needed for research into the physics of Galactic formation and evolution \citep[e.g.][]{2006A&A...451.1065G, 2013NewAR..57...80F}, to search for solar twins, i.e. stars very similar to the Sun and thus potentially hosting earth-like planets \citep{2012A&A...543A..29M}. The Sun has also traditionally been used as a laboratory for particle physics, particularly for setting constraints on the properties of dark matter candidates such as axions, using the sensitivity of helio-seismic probes of the solar structure \citep{1999APh....10..353S}. Also in this case, highly accurate chemical composition of the Sun is needed: abundances in the solar interior determine the radiative opacities and affect the interaction between dark matter and baryons. For example, for certain dark matter candidate particles, interaction with baryons depends strongly on the properties of nuclei -charge, spin- and a detailed knowledge of the chemical composition and profiles in the solar interior is necessary. Another example is that of non-annihilating dark matter particles, which can strongly modify the energy transport in the solar interior. \begin{figure}[b] \begin{center} \includegraphics[scale=.35]{fig1.pdf} \caption{Present-day solar abundances, taken from AGSS09, as a function of atomic number. \label{fig:agss09}} \end{center} \end{figure} Very recently, a revision of the SSC was proposed by \cite[][hereafter AGSS09]{2009ARA&A..47..481A}. The new dataset (Figure~\ref{fig:agss09}) immediately became a new standard in astronomy. But more than that, it led to a conflict with the theory of stellar evolution thus motivating a rapid increase of research efforts in the field. The predictions of standard solar models are now in conflict with the internal structure of the Sun, as measured by the helioseismology. This is known as \textit{the solar abundance problem} \citep{2009ApJ...705L.123S}. The problem has not been solved yet. Here we only review the methods, recent progress in the field, and provide our opinion on the problem. | 14 | 3 | 1403.3097 |
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1403 | 1403.2328_arXiv.txt | For the first time, we reveal large amounts of cold molecular gas in a ram pressure stripped tail, out to a large, ``intracluster'' distance from the galaxy. With the APEX telescope we have detected $^{12}$CO(2-1) emission corresponding to more than $10^9~M_\odot$ of H$_2$ in three H$\alpha$ bright regions along the tail of the Norma cluster galaxy ESO~137-001, out to a projected distance of 40~kpc from the disk. ESO~137-001 has an 80~kpc long and bright X-ray tail associated with a shorter (40~kpc) and broader tail of numerous star-forming \ion{H}{2} regions. The amount of $\sim 1.5\times 10^8~M_\odot$ of H$_2$ found in the most distant region is similar to molecular masses of tidal dwarf galaxies, though the standard Galactic CO-to-H$_2$ factor could overestimate the H$_2$ content. Along the tail, we find the amount of molecular gas to drop, while masses of the X-ray emitting and diffuse ionized components stay roughly constant. Moreover, the amounts of hot and cold gas are large and similar, and together nearly account for the missing gas from the disk. We find a very low star formation efficiency ($\tau_{\rm dep}> 10^{10}$~yr) in the stripped gas in ESO~137-001 and suggest that this is due to a low average gas density in the tail, or turbulent heating of the interstellar medium that is induced by a ram pressure shock. The unprecedented bulk of observed H$_2$ in the ESO~137-001 tail suggests that some stripped gas may survive ram pressure stripping in the molecular phase. | The dense environments of galaxy clusters and groups have been identified as places where transformations of galaxies from blue, star-forming to red, gas-poor systems happen. Late-type galaxies are rare in the cores of galaxy clusters although dominate in their outer parts and outside of clusters \citep[the morphology-density relation,][]{dressler1980,vanderwel2010}. Cluster galaxy populations evolve over cosmic time, as shown by the excess of optically blue galaxies in clusters at higher redshifts \citep[the Butcher-Oemler effect,][]{butcher1978, butcher1984}. Several mechanisms are active in clusters that could account for the observed evolution, such as mutual gravitational interactions of galaxies, including mergers and rapid galaxy encounters, alias harassment, the tidal influence of the cluster potential, and ram pressure of the intracluster medium (ICM) on the interstellar matter (ISM) of member galaxies \citep{gunn1972}, accompanied by numerous hydrodynamic effects. While there is a wealth of observational evidence of one-sided, clearly ram pressure stripped, gas tails in: (a) \ion{H}{1} in the Virgo cluster \citep[e.g.,][]{kenney2004, chung2007, chung2009, abramson2011, kenney2014} and more distant clusters \citep[A1367,][]{scott2010, scott2012}, (b) diffuse H$\alpha$ tails \citep{gavazzi2001, cortese2006, cortese2007, sun2007, yagi2007, yoshida2004, yoshida2008, kenney2008, fossati2012}, (c) young stars seen either in H$\alpha$ or UV \citep{cortese2006, sun2007, yoshida2008, smith2010, hester2010, yagi2013, ebeling2014}, and (d) X-rays \citep{wang2004, finoguenov2004, machacek2005, sun2005, sun2006, sun2010}, \textit{no example} of a prominent (cold) molecular one-sided tail is known up to now, except a few cases of extraplanar molecular gas located fairly close to the disk \citep[NGC~4438, NGC~4522,][]{vollmer2005, vollmer2008}. Recently, \citet{jachym2013} searched for cold molecular gas in the star-forming ram pressure stripped tail of the Virgo dwarf galaxy IC3418, that is (almost) completely stripped, but reached only sensitive upper limits. Presence of molecular gas has been known in some intracluster regions though, as revealed by Carbon monoxide (CO) emission, the most widely used tracer of the molecular interstellar medium. Observations of filaments near cluster cores have revealed anomalously strong H$_2$ emission that may extend to large distances from the cD galaxies \citep{johnstone2007, salome2011}. Also, in the off-disk locations of the Virgo cluster galaxy M86, \citet{dasyra2012} found CO emission in the long H$\alpha$ tidal trail that connects M86 with NGC~4438. One of the main issues in galaxy formation and evolution is to understand the star formation history, and in particular how star formation is triggered, and how it can be suddenly quenched. Environmental effects could play an important role in this matter, and in particular ram pressure stripping of the gas of spiral galaxies. Stars form from cold molecular interstellar gas gathered into giant molecular clouds \citep[GMCs, e.g.,][]{wong2002}. While \ion{H}{1} can be easily stripped from galaxies by the ICM wind, the GMCs are less efficiently removed since they are typically denser and distributed with a higher concentration to the galactic center. Very recently, \citet{boselli2014} found evidence that Virgo cluster galaxies that are \ion{H}{1} deficient have on average also somewhat less molecular gas than \ion{H}{1}-normal field galaxies. The effective H$_2$ ram pressure stripping in these galaxies may be a consequence of removal of diffuse \ion{H}{1} that normally feeds giant molecular clouds. Moreover, hydrodynamic ablation by the ICM wind is assumed to assist the effective H$_2$ stripping \citep{nulsen1982, quilis2000, kapferer2009, tonnesen2009}. Numerical simulations predict that in the gas-stripped tails, depending on the ICM ambient pressure, radiative cooling can form in situ new dense (molecular) clouds which might then form a population of new stars \citep{kapferer2009, tonnesen2009}. If their native gas clumps were accelerated by ram pressure to velocities exceeding the escape speed from the galaxy, such stars can contribute to the intracluster light (ICL) population. In extreme environments of massive or merging galaxy clusters it is possible that strong ram pressures could directly strip the dense molecular clouds. \subsection{The galaxy ESO~137-001} The Norma cluster (Abell 3627, $R_{\rm A}= 2$~Mpc, $M_{\rm dyn}\sim 1\times 10^{15}~M_\odot$, $\sigma= 925$~km\,s$^{-1}$) is the closest ($z= 0.0163$) rich cluster comparable in mass and number of galaxies to Coma or Perseus\footnote{Mean radial velocity of $4871\pm 54$~km\,s$^{-1}$ was measured for the A3627 cluster by \citet{woudt2008} from radial velocities of 296 member galaxies.}. It occurs close to the center of the Great Attractor, at the crossing of a web of filaments of galaxies \citep[dubbed the Norma wall;][]{woudt2008}. The Norma cluster is strongly elongated along the Norma wall indicating an ongoing merger at the cluster core (see the central part of the cluster in Fig.~\ref{FigNorma}). The spiral and irregular galaxy population appears far from relaxed \citep{woudt2008}. The center of the cluster is assumed to be at the position of the cD galaxy ESO~137-006. \begin{figure}[t] \centering \includegraphics[width=0.46\textwidth]{./f1.eps} \caption{ Central part of the A3627 cluster in a $0.5-2$~keV XMM image. The left circle marks position of ESO~137-008 and the right one of ESO~137-006, two galaxies in the central region of the cluster with the same 2MASS K$_{\rm s}$-band magnitude. Position of ESO~137-001 is marked with a rectangle. We zoom in into this region in Fig.~\ref{FigPoints}. }\label{FigNorma} \end{figure} \begin{table} \centering \caption[] {Parameters of the ESO~137-001 galaxy.} \label{TabPar} \begin{tabular}{ll} \hline \hline \noalign{\smallskip} ESO~137-001 (WKK6176): & \\ \noalign{\smallskip} \hline \noalign{\smallskip} RA, Dec (J2000) & $16^{\rm h}13^{\rm m}27^{\rm s}.24$, $-60^\circ45'50''.6$\\ type & SBc\\ radial velocity $\upsilon$ & $4661\pm 46$~km~s$^{-1}$\\ major/minor diameter & $1.26'$/$0.56'$\\ PA, inclination\tablenotemark{1} & $8.9^\circ$, $66.2^\circ$\\ total $B$ and $I$ magnitudes\tablenotemark{2} & $14.31\pm 0.08$, $13.20\pm 0.07$\\ stellar mass\tablenotemark{3} & $(0.5- 1.4)\times 10^{10}~M_\odot$\\ rotation velocity\tablenotemark{4} & $\sim 110$~km\,s$^{-1}$\\ luminosity distance\tablenotemark{3} & 69.6~Mpc\\ \noalign{\smallskip} \hline \noalign{\smallskip} \end{tabular} \tablecomments{ From HyperLeda catalogue \citep{paturel2003}.} \tablenotetext{1}{\citet{sun2007} give $i=61^\circ-64^\circ$} \tablenotetext{2}{from \citet{sun2007}, the correction for the intrinsic extinction is not applied} \tablenotetext{3}{from \citet{sun2010} and \citet{sivanandam2010}} \tablenotetext{4}{from $K$-band velocity-luminosity relation \citep{sivanandam2010}} \end{table} At a projected distance of $\sim 280$~kpc from the cluster center to the NW direction a blue galaxy ESO~137-001 is located (see Fig.~\ref{FigNorma} and Table~\ref{TabPar}). Its line-of-sight velocity is about -200~km~s$^{-1}$ w.r.t. the cluster mean which suggests that the main velocity component is in the plane of the sky. $Chandra$ and XMM-$Newton$ imaging revealed a long, narrow X-ray tail extending from the galaxy to $\sim 80$~kpc projected distance \citep{sun2006}, see the left panel of Fig.~\ref{FigPoints}. It points away from the direction to the cluster center. The total estimated X-ray gas mass is about $10^9 M_\odot$. Deeper $Chandra$ observation revealed even a fainter secondary X-ray tail that is well separated from the primary one \citep{sun2010}. The bright X-ray emission in the tails is presumably arising from mixing of cold stripped ISM with the surrounding hot ICM \citep{sun2010, tonnesen2011}. Currently, \citet{ruszkowski2014} suggested that the tail bifurcation may arise as a consequence of magnetized ram pressure wind that produces very filamentary morphology of the tail. Optical images of ESO~137-001 reveal a $\sim 40$~kpc long H$\alpha$ tail comprised of diffuse gas and discrete \ion{H}{2} regions roughly coincident with the X-ray tail. Moreover, a number of discrete \ion{H}{2} regions are occurring outside the visible X-ray tail, forming a broader tail \citep{sun2007}. A large amount of star formation corresponding to the total number of more than 30 \ion{H}{2} regions is thus occurring well outside the main body of the galaxy. The total mass of starbursts in the \ion{H}{2} regions in the tail is estimated to about $10^7 M_\odot$. ESO~137-001 is expected to host a significant amount of \ion{H}{1} and H$_2$ initially. To a weak limit of $5\times 10^8 M_\odot$ no \ion{H}{1} was detected with ATCA \citep[Australia Telescope Compact Array,][]{vollmer2001}\footnote{The upper limit is lower than in \citet{vollmer2001} since a lower luminosity distance of 69.6~Mpc is adopted for the A3627 cluster. It is possible that some (extended) \ion{H}{1} emission was filtered out by the ATCA interferometric observation. No single-dish data are available.}. {\it Spitzer} IRS observations however revealed more than $10^7 M_\odot$ of warm H$_2$ ($\sim 160$~K) in the galaxy and inner 20~kpc of the tail \citep{sivanandam2010}. As this warm gas is likely a small fraction of the total molecular hydrogen, deep \ion{H}{1} and CO observations are expected to reveal the cold component in the galaxy. ESO~137-001 is an excellent candidate for an ongoing transformation from a blue, gas-rich to a red, gas-poor galaxy due to violent removal of its ISM by ram pressure stripping. It has the most dramatic tail of a late-type galaxy observed up today, making it an ideal laboratory for detailed studies of the complex processes that take place during ram pressure stripping. A3627 is a rich cluster where ram pressure can be 1-2 orders of magnitude stronger than in Virgo. The high pressure (including thermal pressure) environment might therefore be strong enough to affect even denser (molecular) gas. HST observations revealed a complex structure with disrupted dust content, filaments of young stars, and bright extraplanar star clusters in the inner tail of ESO~137-001 (see Fig.~\ref{FigPoints}, right panel). Detailed study of these observations will be published elsewhere. {\it Herschel} PACS and SPIRE imaging shows a dust trail emanating from the galaxy that is coaligned with the warm H$_2$, H$\alpha$ and the more prominent of the two X-ray tails (Sivanandam et al., in prep.). In this paper we want to answer basic questions about the presence, amount, spatial distribution, and origin of molecular gas in the star-forming stripped tail of ESO~137-001. With APEX, we searched for $^{12}$CO(2-1) emission in regions covering the main body of the galaxy, as well as in the H$\alpha$ emission peaks in the tail. The paper is structured in the following way: observations performed are introduced in Section~2, the results are presented in Section~3, the efficiency of star formation in the system is studied in Section~4, the structure of the stripped gas is analyzed in Section~5, the ram pressure operating on the galaxy is semi-analytically estimated in Section~6. Discussion follows in Section~7, and the conclusions in Section~8. We adopt a cluster redshift of 0.0163 for A3627 \citep{woudt2008}. Assuming $H_0= 71$~km\,s$^{-1}$\,Mpc$^{-1}$, $\Omega_M= 0.27$, and $\Omega_\Lambda= 0.73$, the luminosity distance is 69.6~Mpc, and $1''= 0.327$~kpc. | We present new APEX $^{12}$CO(2-1) observations of ESO~137-001, a Norma cluster spiral galaxy that is currently being violently transformed from a late to an early-type by strong ram pressure stripping. A prominent 80~kpc X-ray double-structure tail extends from the galaxy, together with a 40~kpc H$\alpha$ tail. It also contains warm H$_2$ emission in the inner tail. ESO~137-001 is an excellent example of extreme ram pressure stripping and may become completely gas-free in the near future. Our APEX observations reveal large amounts of cold molecular gas traced by $^{12}$CO(2-1) emission in the disk of ESO~137-001 as well as in its gas-stripped tail. It is the first time that a large amount of cold H$_2$ is found in a ram pressure stripped tail. The main results of our analysis are: \begin{enumerate} \item More than $10^9~M_\odot$ of molecular gas was detected in the three APEX 230~GHz apertures along the tail of ESO~137-001, including a $\sim 40$~kpc distant intra-cluster region in its outer part where both X-ray and H$\alpha$ emission peak. Although the X-factor is uncertain in the special environment of a gas-stripped tail, we assume the Galactic value because the metallicity measured in the tail is close to solar ($\sim 0.6~Z_\odot$). As suggested by the high warm to cold (mid-IR to CO) molecular gas mass ratio measured in the inner part of the tail, the CO emission may trace not only cold but also warmer molecular gas. Consequently, the standard value of the X-factor could overestimate the H$_2$ content in the tail. Nevertheless, currently there may be more molecular gas in the tail of the galaxy than in its main body. \item In the most distant ($\sim 40$~kpc) tail region, more than $10^8~M_\odot$ of H$_2$ was revealed. Since the estimated tidal truncation radius of the galaxy is 15~kpc, the detected molecular gas may already be released from the gravitational well of the galaxy. The detected amount is similar to typical molecular masses of tidal dwarf galaxies. We speculate that a ram pressure dwarf galaxy (RPDG) could be forming in this location. More detailed observations measuring the self-gravitation of the object are needed, though. \item About $1\times 10^9~M_\odot$ of molecular gas was detected in the APEX aperture centered on the main body of ESO~137-001. This is a factor of at least $\sim 2$ less than the original molecular gas content of the galaxy, as estimated from typical amounts expected in unperturbed spiral galaxies of the same stellar mass. \item Our observations show that H$_2$, H$\alpha$, and X-ray emission can be at observable levels in a single ram pressure stripped tail. The amounts of cold and hot gas in the tail are large and similar ($\sim 10^9~M_\odot$) and together nearly account for the missing original gas in the disk. Following our measurements, the amount of molecular gas decreases along the tail, while masses of other gas phases (X-ray, ionized) are roughly constant. This could correspond to a decreasing mean gas density along the tail, to long timescales of heating, or to increasing ram pressure that has been able to recently push denser gas to the inner tail regions. \item The star formation efficiency was found to be very low in the tail environment ($\tau_{\rm dep, H_2}> 10^{10}$~yr), while it is consistent with other spiral galaxies in the main body of ESO~137-001. This indicates that most of the stripped gas does not form stars but remains gaseous and ultimately joins the ICM. Similarly low SFEs are found for example in the outer disks of spiral galaxies where however \ion{H}{1} is likely to represent most of the ISM and CO is mostly undetected. This is in contrast to the CO bright tail of ESO~137-001 where \ion{H}{1} was measured only to upper limits. Star clusters formed in the tail from the gas accelerated by ram pressure to high velocities exceeding the escape speed from the galaxy, will contribute to the intra-cluster light population. \item The ICM thermal (+ ram) pressure at the location of ESO~137-001 in the Norma cluster is similar to midplane gas pressures that occur in the (inner) disks of galaxies. Moreover, the lower limits on the molecular-to-atomic gas ratio in the tail of ESO~137-001 (corresponding to our APEX detections and the ATCA \ion{H}{1} upper limits) are consistent with values measured in galactic disks. Nevertheless, the star formation efficiency in the tail is much lower than in the galaxies. We suggest that this is due to a low average gas density in the tail, or turbulence driven from interaction with the surrounding ICM, preventing the stripped cold gas from star formation. The elevated ratio of warm-to-cold molecular gas $>0.1$ in the inner tail of ESO~137-001 is close to ratios measured in cool cores of cluster and group central galaxies or in environments where molecular gas is heated by shocks or cosmic rays rather than UV-heated. \item Our semi-analytic modeling of possible orbits of ESO~137-001 in the Norma cluster indicate that the galaxy may be at a high velocity of $\sim 3000$~km\,s$^{-1}$ in order to be consistent with a first infall scenario. Consequently, the ram pressure experienced by ESO~137-001 possibly has been strong enough to shift or strip from the disk some gas clumps with column densities exceeding values found in Milky Way typical molecular clouds. Such dense gas in the tail can transform more readily into molecular gas than stripped diffuse gas. Moreover, some fraction of the stripped gas can survive in the molecular phase and contribute to the unprecedented CO brightness of the gas stripped tail of the galaxy, especially in its inner parts. The molecular gas detected in the outer tail is more likely to originate from in situ transformation of stripped diffuse atomic gas. \end{enumerate} Future ALMA observations with high spatial resolution will enable us to study ESO~137-001 in a great detail and to better understand the process of cold gas stripping and mixing with the surrounding ICM, as well as the star formation in the special environment of a ram pressure stripped tail. | 14 | 3 | 1403.2328 |
1403 | 1403.6601_arXiv.txt | Novalike cataclysmic variables have persistently high mass transfer rates and prominent steady state accretion disks. We present an analysis of infrared observations of twelve novalikes obtained from the Two Micron All Sky Survey, the {\it Spitzer Space Telescope}, and the {\it Wide-field Infrared Survey Explorer} All Sky Survey. The presence of an infrared excess at $\lambda\gtrsim3$--$5$~$\mu$m over the expectation of a theoretical steady state accretion disk is ubiquitous in our sample. The strength of the infrared excess is not correlated with orbital period, but shows a statistically significant correlation (but shallow trend) with system inclination that might be partially (but not completely) linked to the increasing view of the cooler outer accretion disk and disk rim at higher inclinations. We discuss the possible origin of the infrared excess in terms of emission from bremsstrahlung or circumbinary dust, with either mechanism facilitated by the mass outflows (e.g., disk wind/corona, accretion stream overflow, and so on) present in novalikes. Our comparison of the relative advantages and disadvantages of either mechanism for explaining the observations suggests that the situation is rather ambiguous, largely circumstantial, and in need of stricter observational constraints. | Cataclysmic variables (CVs) are interacting binary stars containing an accreting white dwarf (WD) primary and a mass-losing, late-type secondary star that fills its Roche lobe. CVs are a common pathway for binary star evolution that includes classical novae and possibly leads to the standard candles -- Type Ia supernovae -- that play a crucial role in modern cosmology (e.g., see \citealt{btn13}). In most CVs, accretion of matter from the secondary star onto the (non-magnetic) WD is mediated by a disk that extends close to the surface of the WD. CVs arguably represent the most observationally accessible disk-accreting astrophysical systems. They also include the closest examples of an accretion flow around a compact object and, hence, provide a basic laboratory for accretion disk physics that is relevant in fields ranging from star and planet formation to the central engines of quasars and active galactic nuclei. See \citet{warner03} for a thorough review of CV types and observational characteristics. All CVs vary in mean brightness on a number of characteristic timescales and amplitudes, but the overall nature of the variability probably reflects the time-averaged mass transfer rate from the secondary star. Systems with mass transfer rates below a critical value ($\lesssim10^{-9}$~M$_{\odot}$~yr$^{-1}$ for orbital periods $\lesssim8$~hr; e.g., \citealt{patterson84}) show quasiperiodic outbursts of 3--5 mag (in visible light) that last days to weeks and recur on timescales of weeks to months to (in extreme cases) years. These CVs are known as dwarf novae (DNe). The outbursts of DNe are due to a thermal instability that converts the geometrically thin disk from a low temperature, mostly unionized state to a high temperature, ionized, optically thick state \citep{cannizzo88,osaki96,lasota01}. During a DN outburst, the mass transfer rate in the inner disk rises to $\gtrsim10^{-9}$~M$_{\odot}$~yr$^{-1}$ \citep{hameury98}. In contrast, CVs with persistently high mass transfer rates ($\gtrsim10^{-9}$~M$_{\odot}$~yr$^{-1}$; \citealt{patterson84,ballouz09}) remain in the high temperature state most of the time and have prominent, optically thick accretion disks that do not display outbursts. These systems are known as novalikes (NLs). Because they are almost always in the high temperature state, NLs provide a valuable opportunity to study a prototypical steady state accretion disk. Disk-dominated CVs have been studied extensively in X-rays, the ultraviolet (UV), and visible wavelengths, where they exhibit different behavior depending on the sub-type and brightness state of the system. A variety of components contribute to the spectral energy distributions (SEDs) of CVs, including the WD onto which matter is being accreted, the accretion disk itself, the boundary layer between the WD and the disk (mainly in the UV and shorter wavelengths), the interaction region where matter from the secondary star is entrained into the disk, and the secondary star itself. When the accretion rate is high, emission from the far-UV to the infrared (IR) is dominated by the accretion disk (e.g., see \citealt{hoard09} and Section~\ref{s:models}). \citet{hoard09} used multi-wavelength archival and {\it Spitzer Space Telescope} Cycle-2 IR observations of the low-inclination (near face-on) NL V592~Cassiopeiae to construct an SED and system model from the UV to the IR. They showed that there is an excess of flux density in the IR that is not reproduced by the usual complement of CV components (WD, accretion disk, secondary star). They modeled this IR excess with a circumbinary dust disk. Through the gravitational torques that would be exerted on the central binary, circumbinary dust disks were proposed as an additional route for angular momentum loss driving the secular evolution of CVs \citep{spruit01,taam01,dubus02,taam03,belle04,willems05,willems07}. However, \citet{hoard09} found that the implied mass of dust in V592~Cas ($\sim10^{21}$~g) was many orders of magnitude too small to be effective in that regard\footnote{Recent discoveries of cyclic eclipse timing variations interpreted as evidence of circumbinary planets around several CVs and pre-CVs (e.g., RR~Caeli -- \citealt{qian12a}; UZ~Fornacis -- \citealt{potter11}; DP~Leonis -- \citealt{qian10a,beuermann11}; NN~Serpentis -- \citealt{bmd06,pmb14,mpb14}; HW~Virginis -- \citealt{lee09}; NY~Virginis -- \citealt{qian12b}; QS~Virginis -- \citealt{parsons10,qian10b}) have possibly resurrected this scenario, since the added mass of a planet could increase the gravitational torques on the inner binary to levels sufficient to affect secular evolution. However, the veracity of the planet detections is still being debated in the literature (e.g., HU~Aquarii; see \citealt{schwarz09,qian11,horner11,godz12,hinse12,wittenmyer12}). Certainly the existence of circumbinary planets as a general class of object has now been firmly established by discoveries from {\it Kepler} (e.g., Kepler-34 and Kepler-35, \citealt{welsh12}; Kepler-16, \citealt{doyle11}; Kepler-38, \citealt{orosz12a}; Kepler-47, \citealt{orosz12b}), so the possibility that a CV could host a circumbinary planet should not be casually discarded.}. The importance of the contribution of a circumbinary dust disk to the SEDs of CVs (or even the presence of dust in CVs at all) is not yet firmly established nor universally accepted. Alternative explanations for an IR excess in CVs have been proposed (e.g., bremsstrahlung; see \citealt{harrison13} and the discussion herein). We report here on our {\it Spitzer} observations of a sample of eleven additional NLs. These observations were obtained in order to study the general properties of CVs in the mid-IR; NLs were selected as targets to ensure the presence of bright accretion disks and avoid the complications imposed by DN outbursts or strong magnetic fields in other types of CV. At the same time, these NLs offer an opportunity to explore the potential observational consequences of the mass outflows from the inner binary expected in high mass transfer rate systems (e.g., disk corona/wind, stream overflow, and so on). Because these mechanisms for relocating matter out of the WD Roche lobe and into circumbinary space operate strongly in NLs, these CVs are prime candidates for probing for the presence of dust. | \label{s:conc} The presence of an IR excess over the standard model accretion disk at wavelengths longer than $\approx3$--$5$~$\mu$m is ubiquitous in our sample of 12 high mass transfer rate NLs. V592~Cas remains the NL with the most significant known IR excess out to wavelengths longer than 20~$\mu$m. Both V442~Oph and WX~Ari have IR excesses brighter than even that of V592~Cas out to 7.9~$\mu$m (IRAC-4), but we currently lack longer wavelength data to further constrain and characterize the source of the excess in these two systems. The SED of the excess component is similar in shape in all cases, and can be modelled with a circumbinary dust disk. We note that, in the context of modelling the IR SEDs of CVs, using a blackbody to represent the secondary star can lead to false-negatives for detection of IR excess, since this practice overestimates the brightness of a late-type star at long wavelengths. Despite the fact that it introduces complexity to the modeling process, it is advisable to use models that are as accurate and realistic as possible to represent all of the SED components. In our sample, there is no significant correlation between the level of IR excess and the orbital period. Thus, while the presence of an IR excess is likely linked to the overall high mass transfer rate shared by all of our targets ($\gtrsim10^{-9}$~M$_{\odot}$~yr$^{-1}$), its relative strength from system to system does not appear to be strongly dependent on the specific value of mass transfer rate over the ranges of orbital period (0.11--0.45~d; see Table~\ref{t:targets}) and mass transfer rate ($\sim1$--$100\times10^{-9}$~M$_{\odot}$~yr$^{-1}$; see Tables~\ref{t:models1} and \ref{t:models2}) spanned by our sample of NLs. Coupled with the fact that the modelled total dust masses needed to reproduce the observed IR excesses are significantly smaller than the predicted threshold necessary to influence the secular evolution of CVs (also see discussion below), this implies that the presence of dust is not a dominant factor in driving that evolution. This conclusion is only valid if the mass transfer rate at a given orbital period is primarily determined by secular evolution (and, of course, if the mass transfer rates returned by the various accretion disk models are truly representative of the situation in these CVs). On the other hand, the IR excess and system inclination show a statistically significant correlation. The increase in excess at 7.9~$\mu$m with increasing inclination amounts to an $\approx20$\% change from an inclination of $30^{\circ}$ (near face-on) to $90^{\circ}$ (edge-on). It is tempting to ascribe this relatively shallow trend to the changing view of the accretion disk at different inclinations (i.e., the hot, inner disk is increasingly self-occulted as inclination increases, leaving the accretion disk contribution to the SED to be dominated by the cooler outer disk and disk rim). However, comparison of model accretion disk SEDs computed at different inclinations suggests that this effect is likely not the sole factor in producing the observed level of change in IR excess. There is an observational test that might be able to discriminate the location of the component producing the IR excess. The IR emission from circumbinary dust should not be affected by the primary eclipse in high inclination CVs, whereas IR emission originating from the inner binary (e.g., via bremsstrahlung or extremely cool material associated with the outer accretion disk) would likely be eclipsed to some extent, barring an extreme configuration in which the IR emission originates at large vertical distances above the accretion disk. While the latter scenario could be envisioned for free-free emission in an outflowing disk wind, the analysis presented here (see Section~\ref{s:brems}) implies that if the IR excess originates in a wind, then it most likely comes from the dense, accelerating base of the wind. Time-resolved mid-IR ($\lambda\gtrsim5$~$\mu$m) observations of the eclipsing NLs in our sample (RW~Tri, V347~Pup) or other high inclination NLs confirmed to have an IR excess would be helpful in this regard. Overall, however, the presence of a strong IR excess appears to go hand-in-hand with a high mass transfer rate, possibly via the formation of circumbinary dust in material that escapes the inner binary, as discussed in \citet{hoard09}. This is not to say that CVs with lower mass transfer rates would be necessarily devoid of dust, but if present, then it is likely in a smaller amount, producing a weaker IR excess that is difficult to detect. None of the CVs we observed show evidence in their SEDs for the presence of the 10~$\mu$m emission feature that is the hallmark of the silicate dust found around numerous isolated WDs. There are a number of possible reasons why this feature could be absent even when dust is present in a CV (see Section~\ref{s:missing}), including predominantly large grain size and differences in chemical composition of the dust. The dust grain size has a strong effect on the total mass of dust required to produce an IR excess of a given amplitude. Thus, the lack of silicate emission at 10~$\mu$m has potential implications for the amount of dust that could be present around these NLs (which, in turn, has implications for the potential effect of dust on the secular evolution of CVs). The total mass of silicate dust in our models that is required to reproduce the observed IR excesses in V592~Cas, IX~Vel, UX~UMa, and RW~Sex is $\approx$1--2$\times10^{21}$~g assuming a characteristic dust grain radius of $r_{\rm grain}=1$~$\mu$m (see Table~\ref{t:models1}). For the case of large grains ($r_{\rm grain}\gtrsim5$~$\mu$m) corresponding to the absence of the 10~$\mu$m silicate emission feature, the total dust masses would be larger by a factor of $\gtrsim5$. At the low end ($r_{\rm grain}\approx5$~$\mu$m), the total mass is still insignificant compared to the prediction of $\gtrsim10^{28}$~g required to influence CV secular evolution \citep{taam03,willems07}. Even at a {\it reductio ad absurdum} limit of centimeter-scale dust ``pebbles'' ($r_{\rm grain}\approx10^{4}$~$\mu$m), the total dust mass is still 3 orders of magnitude too small to be important in this regard. While the absence of the 10~$\mu$m silicate emission feature does not necessarily imply the absence of dust, it nonetheless remains true -- and should be considered an observational priority -- that detection of this feature in any quiescent system would be compelling evidence for the presence of dust in CVs. | 14 | 3 | 1403.6601 |
1403 | 1403.6437_arXiv.txt | We present an analysis of the colour-magnitude relation for a sample of 56 X-ray underluminous Abell clusters, aiming to unveil properties that may elucidate the evolutionary stages of the galaxy populations that compose such systems. To do so, we compared the parameters of their colour-magnitude relations with the ones found for another sample of 50 ``normal'' X-ray emitting Abell clusters, both selected in an objective way. The $g$ and $r$ magnitudes from the SDSS-DR7 were used for constructing the colour-magnitude relations. We found that both samples show the same trend: the red sequence slopes change with redshift, but the slopes for X-ray underluminous clusters are always flatter than those for the normal clusters, by a difference of about 69\% along the surveyed redshift range of 0.05 $\le z <$ 0.20. Also, the intrinsic scatter of the colour-magnitude relation was found to grow with redshift for both samples but, for the X-ray underluminous clusters, this is systematically larger by about 28\%. By applying the Cram\'er test to the result of this comparison between X-ray normal and underluminous cluster samples, we get probabilities of 92\% and 99\% that the red sequence slope and intrinsic scatter distributions, respectively, differ, in the sense that X-ray underluminous clusters red sequences show flatter slopes and higher scatters in their relations. No significant differences in the distributions of red-sequence median colours are found between the two cluster samples. This points to X-ray underluminous clusters being younger systems than normal clusters, possibly in the process of accreting groups of galaxies, individual galaxies and gas. | Since \cite{baum} noticed that, within a sample of elliptical galaxies, the brightest are generally the reddest ones, several studies have demostrated that the red galaxy population traces a straight line in colour-magnitude diagrams, with a well-defined slope and small scatter \citep[$\le$ 0.1 mag; e.g.][]{Vis77,Bower3,vandokkum98, andreon,lopez,mcintosh}. This makes the colour-magnitude relation (CMR) a useful tool for getting information about the formation and evolution of galaxy cluster members. The CMR can be used for estimating the redshift of a cluster when photometry in at least two bands is available \citep[e.g.][]{Vis77, Bower3, andreon, lopez}, while a blind search for CMRs may be used for finding galaxy overdensities associated to galaxy clusters \citep[e.g.][]{Gladders00}. The slope of the CMR has been interpreted as a consequence of the mass-metallicity relation: more massive (or luminous) galaxies have redder colours \citep[e.g.][]{Faber, arimoto, kodama97}. The mass-metallicity relation, on the other hand, is thought to be originated from the tendency of galaxies to lose their metals due to galactic winds, the loss being more pronounced for galaxies with shallower potential wells or lower masses \citep[e.g.][]{arimoto,Kodama,vandokkum01,Tremonti,Gallazzi}. An alternative model \citep{kauffmann98} considers the effect of the formation of elliptical galaxies by the merging of disk systems: the mass-metallicity relation would be already established for the progenitors, and the more massive ellipticals are formed from more massive disks. Other works have shown that the CMR depends neither on cluster/group richness \citep{andreon} nor on the environment \citep{Hogg}, but luminous galaxies are more abundant in higher over-density regions and blue galaxies reside towards the outskirts of the clusters \citep{mcintosh,Hogg}, a reminiscence of the morphology-density relation \citep[e.g.][]{dressler80}. The physical interpretation of these relations and properties is not fully understood. The CMR tight scatter has been interpreted as evidence that galaxies residing in this sequence are coeval, with a small spread in their formation age, which mostly occurred at $z\,\ge\,$2.0 and evolved passively since then \citep[e.g.][]{Bower3,Bower,Bower4,Lubin3,ellis,Gladders,Kodama,vandokkum98, andreon,mcintosh}. Other works have suggested that the age of the galaxies could drive the CMR \citep[e.g.][]{Ferreras,Terlevich,trager00}. Some studies, like \citet{Skelton} and \citet{jimenez11}, have considered the effect of gas-poor mergers on the CMR with a toy model, concluding that the relation changes its slope at the bright end and becomes bluer and with lower scatter. It is worth mentioning that, besides ellipticals, lenticulars and passive spirals also populate the CMR \citep[e.g.][]{bamford09,masters10,sodre13}. On the other hand, the majority of galaxy clusters have most of their baryons in the form of a hot, diffuse plasma, that may interact with the colder interstellar gas (interstellar medium) due mainly to the motion of galaxies inside clusters. The ram-pressure effect \citep{gunn72,larson80}, i.e. the hydrodynamical interaction between the intracluster medium (ICM) and the interstellar medium, may strip the gas of the galaxies, quenching star formation or even enhancing it while the gas is being compressed, affecting galaxy evolution and hence the colours of cluster galaxies \citep{fujita99,weinberg13}. The ICM properties, such as luminosity and temperature, are observed to scale with the mass of the cluster, but possibly not in a self-similar manner, as described by the scaling relations between X-ray luminosity or temperature and virial mass \citep[$L_\mathrm{X}$-$M_\mathrm{v}$ and $T_\mathrm{X}$-$M_\mathrm{v}$, e.g.][]{Reiprich,Rykoff}, and X-ray temperature with galaxy velocity dispersion \citep[$T_\mathrm{X}$-$\sigma$, e.g.][]{Lubin,Xue}. In recent years, several studies have found galaxy systems with most properties of galaxy clusters but underluminous in X-rays \citep{Bower,Lubin2,Dietrich}, with respect to the scaling relations mentioned above. Dynamical analyses of these systems suggest that they are young systems still undergoing a phase of gas accretion and/or merging of smaller groups and galaxies; that is, they may not have yet reached the virial equilibrium. Other works, however, debate the very existence of these objects \citep[e.g.,][]{andreon2}. Our objective with the present work is to investigate the properties of the CMR of X-ray Underluminous Abell clusters (AXUs, following \citealp{p1} naming) in comparison with ``Normal'' X-ray emitting Abell clusters (AXNs) to verify whether the ICM is indeed important in shaping up the red sequence. The paper is organized as follows: the optical and X-ray data are described in \S\ref{data}. The identification of the red sequence, its analysis and comparisons between samples are presented in \S\ref{analysis}. Our main results are summarized in \S\ref{results} and final comments and conclusions in \S\ref{discussion} and \S\ref{conclusion}, respectively. We will assume a $\Lambda$CDM cosmology with $\Omega_m=$ 0.30, $\Omega_\Lambda=$ 0.70 and $H_0=$ 70 km s$^{-1}$ Mpc$^{-1}$ throughout the paper. | \label{conclusion} We compared the properties of the colour-magnitude relation, $(g-r) \times r$, of red galaxies in two samples: one with 56 X-ray underluminous clusters \citep[from][]{p1}, and the other with 50 ``normal'' X-ray emitting clusters \citep[from][]{p2}, in 5 bins of redshift. We have found that: \begin{itemize} \item[-] Our results confirm previous findings that the slope of the CMR decreases with increasing redshift. Both samples show the same trend, but the slopes of AXUs are always flatter than the slopes of AXNs, by a difference of about 69\% (0.014) along the surveyed redshift range. \item[-] The intrinsic scatter of the CMR was found to grow with redshift, for both samples. Again, there is a zero point difference between the relations (intrinsic scatter $\times$ redshift) found for the AXUs and the AXNs, in the sense that the intrinsic scatter of the AXUs is systematically larger by more than 28\% (0.043). \end{itemize} Our data allow an interpretation such as that galaxies evolve in a distinct way in different environments concerning the properties of the ICM, which may be a consequence of the different dynamical status of the systems, being subject to different levels of star formation stimulation and, consequently, having different levels of metallicities, specially the more massive galaxies. In an initial phase of structure formation, a denser ICM would be expected to enhance star formation in more massive galaxies, by exerting more hydrodynamical pressure. This scenario would lead the brightest galaxies in the AXN clusters to be more metallic than their counterparts of the AXU clusters and, consequently, generating distinct slopes in their CMRs. If the X-ray underluminous clusters are, as previously proposed, less dense galaxy systems, this scenario is in accordance with the one proposed by \citet{Tan05}, in which the CMR build-up for less dense clusters is delayed. The larger intrinsic scatter for AXUs is also in agreement with this scenario: a longer time for producing the CMR implies also a larger dispersion in formation ages. A higher rate of dry mergers in X-ray underluminous clusters would also possibly produce the different slopes, but it is difficult to explain such an excess of interaction. | 14 | 3 | 1403.6437 |
1403 | 1403.4268_arXiv.txt | Chameleon fields may modify gravity on cluster scales while recovering general relativity locally. This article reviews signatures of chameleon modifications in the nonlinear cosmological structure, comparing different techniques to model them, summarising the current state of observational constraints, and concluding with an outlook on prospective constraints from future observations and applications of the analytic tools developed in the process to more general scalar-tensor theories. Particular focus is given to the Hu-Sawicki and designer models of $f(R)$ gravity. | \label{sec:intro} Attempts to unify general relativity with the standard model interactions typically introduce an effective scalar field in the low-energy limit in addition to the gravitational tensor field. This fifth element may couple minimally or nonminimally to the matter fields and can act as an alternative to the cosmological constant as explanation for the observed late-time acceleration of our Universe. A fifth force originating from the nonminimal coupling consequently modifies the gravitational interactions between the matter fields. Local observations place tight constraints on the existence of a fifth force~\cite{will:05}. However, these constraints are alleviated for scalar field potentials that yield a scalar field inversely dependent on curvature such as is realised in chameleon models~\cite{khoury:03a, khoury:03b, brax:04, cembranos:05, mota:06}. In this case, the extra force is suppressed in high-density regions like the Solar System but at the cost of returning cosmic acceleration to be driven by the contribution of a dark energy component or a cosmological constant rather than originating from a fundamental modified gravity effect of the model~\cite{wang:12}. Meanwhile, gravitational forces remain enhanced at low curvature and below the Compton wavelength of the scalar field, causing an increase in the growth of structure and rendering nonlinear cosmological structures a vital regime for testing gravity. This article reviews the signatures of chameleon fields in the cosmological small-scale structure, summarising different techniques to model the formation of these structures and current constraints on the chameleon field amplitude and coupling strength from observations. Thereby, scalar-tensor models are considered that have a constant Brans-Dicke parameter $\omega$, match the $\Lambda$CDM background expansion history, and exhibit a chameleon suppression mechanism of the enhanced gravitational force in high-density regions. A special emphasis is given to the Hu-Sawicki~\cite{hu:07a} and designer~\cite{song:06} $f(R)$ models~\cite{buchdahl:70, starobinsky:79, starobinsky:80, capozziello:03, carroll:03, nojiri:03}, to which the scalar-tensor model can be reduced in the case of $\omega=0$. These models have been particularly well studied with constraints from current and expected from future observations reported, for instance, in Refs.~\cite{chiba:03, zhang:05, amendola:06a, amendola:06b, song:06, amendola:06c, li:07, zhang:07, song:07, hu:07a, jain:07, brax:08, zhao:08, hui:09, smith:09t, schmidt:09a, giannantonio:09, reyes:10, lombriser:10, yamamoto:10, jain:10, motohashi:10, gao:10, wang:10, ferraro:10, thomas:11, davis:11, jain:11, hojjati:11, zhao:11b, gilmarin:11, wojtak:11, lombriser:11b, lam:12a, terukina:12, divalentino:12, jain:12, samushia:12, he:12, hu:12, okada:12, hall:12, simpson:12, albareti:12, lombriser:13a, brax:13a, marchini:13a, vikram:13, abebe:13, lam:13, hellwing:13, upadhye:13, marchini:13b, he:13, hu:13, mirzatuny:13, sakstein:13, zu:13, cai:13, baldi:13, arnold:13, lombriser:13c, brax:13c, terukina:13, hellwing:14, dossett:14, davis:14, munshi:14}. The currently strongest bounds on the chameleon modifications are inferred from comparing nearby distance measurements in a sample of unscreened dwarf galaxies~\cite{jain:12} as well as from the transition of the scalar field required in the galactic halo to interpolate between the high curvature regime of the Solar System, where the chameleon mechanism suppresses force modifications, and the low curvature of the large-scale structure, where gravity is modified~\cite{hu:07a, lombriser:13c}. Cosmological observables such as cluster profiles~\cite{lombriser:11b} and abundance~\cite{schmidt:09a, lombriser:10, ferraro:10}, galaxy power spectra~\cite{dossett:14}, redshift-space distortions~\cite{yamamoto:10, okada:12}, or the combination of gas and weak lensing measurements of a cluster~\cite{terukina:13} can be used to place independent and strong bounds on the gravitational modifications. Local and astrophysical probes yield constraints that are 2-3 orders of magnitude stronger than what is inferred from cosmological observations. It is worth emphasising, however, that they test the coupling of the scalar field to baryons, whereas cosmological probes typically rely on a coupling of the scalar field to dark matter only, except for the constraints inferred using the cluster gas in Ref.~\cite{terukina:13}. The separation of coupling strengths between the different matter components can be made explicit in the Einstein frame, in which case cosmological constraints can be regarded as independent of the local and astrophysical bounds. Furthermore, dark chameleon fields that only couple to dark matter may alleviate problems arising through quantum particle production~\cite{erickcek:13a, erickcek:13b} due to high-energy fluctuations in the early universe or large quantum corrections to the scalar field potential in laboratory environments~\cite{upadhye:12a}. Hence, cosmological scales remain an interesting regime for constraining potential scalar field contributions. The chameleon mechanism is a nonlinear effect, however, that complicates the description of the cosmological small-scale structure. $N$-body simulations of chameleon models provide an essential tool for studying the nonlinear regime of structure formation and the suppression of gravitational modifications~\cite{oyaizu:08a, oyaizu:08b, li:09, li:10, zhao:10b, li:11, puchwein:13, llinares:13b}. These simulations are, however, computationally considerably more expensive than in the Newtonian scenario. Hence, for the comparison of theory to observations, allowing a full exploration of the cosmological parameter space involved, the development of more efficient modelling techniques for the cosmological small-scale structure is a necessity. Different approaches have been proposed based on phenomenological frameworks and fitting functions to simulations~\cite{hu:07b, zhao:10, li:11b, zhao:13}, analytical and numerical approximations~\cite{schmidt:10, pourhasan:11, lombriser:12, terukina:12, terukina:13}, the spherical collapse model~\cite{schmidt:08, borisov:11, li:11a, lombriser:13b, lombriser:13c}, excursion set theory~\cite{li:11a, li:12b, lam:12b, lombriser:13b, kopp:13}, the halo model~\cite{schmidt:08, lombriser:11b, lombriser:13c}, and perturbation theory~\cite{koyama:09, brax:13b}. These different methods shall be summarised and compared here. \tsec{sec:chameleonmodels} reviews chameleon gravity in the context of more general scalar-tensor theories and discusses the Hu-Sawicki and designer $f(R)$ models. \tsec{sec:chameleoncosmology} is devoted to the formation of large-scale structure in chameleon models and its description using linear cosmological perturbation theory in the quasistatic limit, dark matter $N$-body simulations, and the spherical collapse model. It furthermore discusses different modelling techniques for the matter power spectrum and the properties of chameleon clusters such as the halo mass function and linear halo bias as well as the cluster profiles of the matter density, scalar field, and dynamical mass. In \tsec{sec:observationalconstraints}, current constraints on chameleon models, in specific on $f(R)$ gravity and from cosmological observations, are summarised. Finally, \tsec{sec:outlook} provides an outlook and discussion of prospective constraints from future observations and applications of the modelling techniques developed for the chameleon modifications to more general scalar-tensor theories, before \tsec{sec:conclusion} concludes the review. | \label{sec:conclusion} The presence of a chameleon field in our Universe may modify the gravitational interactions on cluster scales while recovering general relativity locally. Whereas $N$-body simulations provide an essential tool for studying the effects of the scalar-tensor modification of gravity, especially in regions where the modification is getting suppressed due to the chameleon mechanism, semi-analytic modelling techniques become a necessity for the comparison of the theoretical signatures to observational data. These tests require an efficient interpolation and extrapolation of the simulated results between different choices of cosmological parameters and model specifications of the gravitational theories of interest. Emulator approaches will not be feasible for this task as the parameter space grows with the extra degrees of freedom introduced by the different modified gravity models and the computational methods need to be generalised accordingly. This article summarises a range of observable signatures in the nonlinear cosmological structure that are characteristic for the chameleon modification. It reviews and compares different techniques to model these observables based on $N$-body simulations, different phenomenological formalisms, fitting functions to simulations, analytical and numerical approximations, the spherical collapse model, excursion set theory, the halo model, and perturbation theory. Hereby, a particular focus is given to the well studied Hu-Sawicki and designer models of $f(R)$ gravity, for which a summary of the current state of observational constraints is provided and supplemented with an outlook on prospective constraints and novel methods for testing the chameleon modifications. The semi-analytic methods discussed here are still at an early stage of construction and need to be developed further. Their success in reproducing the important features of the nonlinear cosmological structure observed in $N$-body simulations of chameleon $f(R)$ gravity, along with similar achievements for describing the cosmological structure in Galileon and symmetron models, anticipates that a generalisation of these modelling techniques and an application thereof to the full Horndeski theory of scalar-tensor gravity may be feasible. Hence, at the nearing of the 100th anniversary since the formulation of the foundations of general relativity~\cite{einstein:16}, the study of the cosmological structure formed in the simplest extension of the Theory of Gravity, i.e., for scalar-tensor models, and the observational constraints that can be inferred on these extensions promise to remain a very interesting and active field of research. \paragraph{Acknowledgements} The author thanks Philippe Brax, Baojiu Li, Patrik Valageas, and Gong-Bo Zhao for sharing numerical results which have been used to produce Figs.~\ref{fig:hmf}, \ref{fig:matterpower1}, and \ref{fig:matterpower2}. This work has been supported by the STFC Consolidated Grant for Astronomy and Astrophysics of the University of Edinburgh. Numerical computations have been performed with Wolfram $Mathematica~9$. Please contact the author for access to research materials. | 14 | 3 | 1403.4268 |
1403 | 1403.4097_arXiv.txt | % {The evolutionary state of blue supergiants is still unknown. Stellar wind mass loss is one of the dominant processes determining the evolution of massive stars, and it may provide clues on the evolutionary properties of blue supergiants. As the H$\alpha$ line is the most oft-used mass-loss tracer in the OB-star regime, we investigate H$\alpha$ line formation as a function of $T_{\rm eff}$.} {We provide a detailed analysis of the H$\alpha$ line for OB supergiant models over an $T_{\rm eff}$ range between 30\,000 and 12\,500\,K, with the aim of understanding the mass-loss properties of blue supergiants.} {We model the H$\alpha$ line using the non-LTE code {\sc cmfgen}, in the context of the bi-stability jump at $T_{\rm eff}$ $\sim$ 22\,500\,K.} {We find a maximum in the H$\alpha$ equivalent width at 22\,500\,K - \textit{exactly} at the location of the bi-stability jump. The H$\alpha$ line-profile behaviour is characterised by two branches of effective temperature: (i) a \textit{hot branch} between 30\,000 and 22\,500\,K, where H$\alpha$ emission becomes stronger with decreasing $T_{\rm eff}$, and (ii) a \textit{cool branch} between 22\,500 and 12\,500\,K, where the H$\alpha$ line becomes \textit{weaker}. Our models show that this non-monotonic H$\alpha$ behaviour is related to the optical depth of Ly$\alpha$, finding that at the ``cool'' branch the population of the 2$^{\rm nd}$ level of hydrogen is enhanced in comparison to the 3$^{\rm rd}$level. This is expected to increase line absorption, leading to weaker H$\alpha$ flux when $T_{\rm eff}$ drops from 22\,500\,K downwards. We also show that for late B supergiants (at $T_{\rm eff}$ below $\sim$15\,000\,K), the differences in the H$\alpha$ line between homogeneous and clumpy winds becomes insignificant. Moreover, we show that at the bi-stability jump H$\alpha$ changes its character completely, from an optically thin to an optically thick line, implying that \textit{macro-clumping} should play an important role at temperatures below the bi-stability jump. This would not only have consequences for the character of observed H$\alpha$ line profiles, but also for the reported discrepancies between theoretical and empirical mass-loss rates.}{} | Blue supergiants (BSG) are key creators of heavy elements, thereby contributing to the composition of the interstellar medium; they are visible out to large distances, and dominate the spectra of star-formation galaxies. Moreover, they heat the interstellar gas and dust and produce the far-infrared luminosities of galaxies. B supergiants (Bsgs) in particular are indissoluble troublemakers in today's Astrophysics, as a proper understanding of their evolution is still in its infancy \citep{langer12}. Even their fundamental properties are not yet known, and the basic issue as to whether they are core hydrogen (H) burning main-sequence (MS) or core helium (He) burning post-MS stars is still under debate \citep{vink10,georgy13}. \cite{lam95} reported the existence of a drop in terminal wind velocities of Bsgs by a factor of two, which is referred to as the ``bi-stability jump'' \citep{pauldrach90}. According to model predictions of \citet{vink99} it is expected that the faster winds of hotter stars switch to slower winds with a $\sim$ 5 times higher $\dot{M}$ below $T_{\rm eff}$ $\sim 22\,000$\,K. Whereas the drop in terminal velocities has been confirmed by observations \citep{markova08}, the predicted increase in $\dot{M}$ is still controversial. Whilst \cite{ben07} and \cite{markova08} uncovered a local maximum in both radio and H$\alpha$ mass-loss rates at the location of the bi-stability jump, several works have highlighted significant discrepancies between theoretical and empirical mass-loss rates for B1 and later B-type supergiants \citep{vink00,trundle04,trundle05,cro06,ben07,markova08}. For the late Bsgs \cite{vink00} noted that their predictions agreed reasonably well with empirical rates from both radio and H$\alpha$ emission, but they found huge (order of magnitude) discrepancies when the H$\alpha$ line was P\,Cyg shaped or in absorption. \cite{searle08} emphasised that empirical models for Bsgs likely have an incorrect ionisation structure as they found it challenging to reproduce the optical H$\alpha$ line simultaneously with key ultraviolet (UV) diagnostics. To make the picture even more complex, one should be aware of discrepancies between mass-loss rates estimated from H$\alpha$, UV, and radio observations for OB stars in general \citep{massa03,bouret05,puls06,full06}, which may be due to distance-dependent wind clumping and/or porosity effects \citep{Oskinova07,Sundq10,sundqvist11,Muijres11,Surlan12}. In any case, the general trend seems to indicate $\dot{M}_{vink} > \dot{M}_{\rm{H}_{\alpha}}$ for B1 and later supergiants, whilst the reverse holds for earlier O supergiants. The key question is whether this discrepancy is the result of incorrect predictions or alternatively that we may not understand the mass-loss indicator H$\alpha$ well enough. What would one expect to happen when Fe\begin{small}IV\end{small} recombines, and Fe\begin{small}III\end{small} starts to control the wind driving \citep{vink99}? Over the last decade we have made a dedicated effort to improve the physics in the Monte Carlo line driving calculations. We now solve the wind dynamics more locally consistently \citep{muller08,muijres12}, we added Fe to the statistical equilibrium calculations in the {\sc isa-wind} model atmosphere \citep{dekoter93}(rather than treating this important line-driving element in a modified nebular approximation), and finally, we have studied the effects of wind clumping and porosity on the line driving \citep{Muijres11}. After all these improvements in the Monte Carlo line-driving physics, we have to admit that the basic problem of $\dot{M}_{vink} > \dot{M}_{\rm{H}_{\alpha}}$ for B1 and later supergiants, is still present, and it is time that we also consider the possibility that it is not the predictions that are at fault, but that we do not understand H$\alpha$ line formation in Bsgs sufficiently well to allow accurate mass-loss determinations from H$\alpha$. In order to obtain a more complete picture of H$\alpha$ as a mass-loss diagnostic, we need to know not only the clumping properties of BSGs, but also how sensitive H$\alpha$ is to the clumping on both sides of the bi-stability jump. Currently, $T_{\rm eff}$ dependence of the mass-loss rates from H$\alpha$ of BSGs is still uncertain, and a better knowledge is required, especially as it impacts the question of the evolutionary nature of BSGs. \begin{figure*} \centering \resizebox{\factor\hsize}{!}{\includegraphics{HaLP}\hspace{\spfactor} \includegraphics{ew__}} \caption{\textit{Left:} H${\alpha}$ line profiles for {\sc cmfgen} models with parameters as listed in Table~\ref{table:tab1}. {\bvp Black triangles} represent the line profile with the same $Q$-parameter (Eq.\,\ref{eq_Q}) as model C ($T_{\rm eff}$=12\,500\,K) but with different $\dot{M}$ and $R_{\star}$ values. \textit{Right:} H$\alpha$ line EW vs $T_{\rm eff}$ for models with only H (crosses), H+He (circles) and more sophisticated (triangles) models. {\bvp Red asterisks} represent the changes in the H$\alpha$ line when the He mass fraction in the pure H+He models is increased to 60\%. Blue squares indicate how the H$\alpha$ EW behaves as a function of a constant $Q$ value.} \label{fig:HaLP} \end{figure*} Despite the fact that the spectral modelling of Bsgs is an active area of research \citep{zorec09,fraser10,castro12,clark12,firn12}, due to a lack of observational data, the nature of Bsgs is a long-standing issue in stellar evolution. \cite{hunter08} argued on the basis of high-resolution VLT-FLAMES data that the slowly rotating Bsgs in the Large and Small Magellanic Clouds (LMC; SMC) are post-MS objects (although their large numbers would remain unexpected). \cite{vink08} and \cite{vink10} established a general lack of fast rotating Bsgs ($v$sin$i>50$ km\ s$^{-1}$) and suggested that these objects could naturally be explained as MS stars, if they lose their angular momentum via an increased mass-loss rate due to the bi-stability jump (the so-called bi-stability braking). They also pointed out that this mechanism would be efficient if the stars spend significant amounts of time on the MS. While the first hypothesis received some support by the apparently brightest supernova (SN) in the telescopic era: SN\,1987A, bi-stability braking for stars with initial masses above 40\,$M_\odot$ was confirmed by \cite{markova14}. Hot stars with high mass-loss rates are expected to have strong emission lines, predominantly formed by recombination. The H$\alpha$ line is an excellent tracer for hot-star mass loss, as its detection is possible for large numbers of stars. Moreover, the strong velocity dependence of H$\alpha$ combined with high-resolution spectroscopy could provide valuable information about velocity fields and density structures in Luminous Blue Variables (LBVs) and SN progenitors \citep{groh11}. That is why understanding the behaviour of the H$\alpha$ line is crucial to our understanding of mass loss. After this introduction, in Sect.\,2, we describe shortly the used input parameters for our supergiant models. In Sect.\,3, we show that the computed line profiles exhibit non-monotonic temperature behaviour, and provide the most likely explanation for it. Section 4 explores the impact of clumping on H$\alpha$ line equivalent width (EW) and optical depth. In Sect.\,5 we discuss the importance of our findings and finally in Sect.\,6 we summarise our results and discuss possible implications for future work. \vspace{\vfac} | \label{Conclusion} The behaviour of the H$\alpha$ line over $T_{\rm eff}$ range between 30\,000 and 12\,500\,K might be characterised by the management between two processes. Whilst the ''rise`` is the result of simple recombination ($n_{3}{^{\uparrow}}$), the ''fall`` is due to the intricate behaviour of the second level ($n_{2}{^{\uparrow}}$). As $T_{\rm eff}$ drops below 22\,500\,K, the existence of a cool branch may be summarised as follows: \begin{itemize} \item the high Lyman continuum optical depth makes ionisation from the first level unlikely. \item Ly$\alpha$ becomes optical thick. \item The drain from the second level is suppressed. \item At the coolest model level 2 diverges from higher levels, and it operates like a ground state. \item H$\alpha$ changes its character and behaves like a scattering line with a P-Cygni profile. \end{itemize} \noindent During the transition from a recombination to a scattering line, the EW decreases, because recombination lines have a larger (and basically unlimited EW, if the mass-loss rate is increased), whilst a scattering line is confined in its EW as it is dominated by the velocity field. Thus, the EW has to decrease when the line starts to change its character, i.e over the cool branch. The qualitatively similar H$\alpha$ behaviour including just H, and H+He only models, and metal-blanketed models suggests that the H$\alpha$ behaviour is not related to He or metal properties. Intriguingly, we also found that the effect of clumping on H$\alpha$ is largest at $T_{\rm eff}$ around the bi-stability jump and this is not related to the iron ionisation. Furthermore, if the mass-loss rates are increased at the bi-stability jump (as predicted), then the effect (together with clumping) on H$\alpha$ optical depth would be even stronger. Therefore it is expected that H$\alpha$ changes its character from an optically thin to an optically thick line and the micro-clumping approximation may no longer be justified. Although all codes include the physics explained in this work (except for macro-clumping), it is interesting that independent of model complexity, the H$\alpha$ EW peaks at the location of the bi-stability jump for all our models. This might have consequences for both the physics of the bi-stability mechanism, as well as the derived mass-loss rates from H$\alpha$ line profiles, as objects located below the H$\alpha$ EW peak are predicted to be weaker for a similar mass-loss rate, i.e. higher empirical mass-loss rates are required to reproduce a given H$\alpha$ EW if the star is located at a $T_{\rm eff}$ below the peak. Whether this deeper understanding of H$\alpha$ EW over the bi-stability regime would indeed lead to a resolution of the BSG problem remains to be shown with detailed comparisons of our models and observed H$\alpha$ profiles. This may also be relevant for magnetic field confinement by magnetic spots that could be induced by the sub-surface convection zone in Bsgs \citep{cantiello09}, as \cite{shultz13} noted that a pair of spots could have remained undetected by current field searches if the higher theoretical mass-loss rates are employed, but that even the largest spots are ruled out if the lower H$\alpha$ rates are correct. | 14 | 3 | 1403.4097 |
1403 | 1403.1484_arXiv.txt | Targeted searches of continuous waves from spinning neutron stars normally assume that the frequency of the gravitational wave signal is at a given known ratio with respect to the rotational frequency of the source, e.g. twice for an asymmetric neutron star rotating around a principal axis of inertia. In fact this assumption may well be invalid if, for instance, the gravitational wave signal is due to a solid core rotating at a slightly different rate with respect to the star crust. In this paper we present a method for {\it narrow-band} searches of continuous gravitational wave signals from known pulsars in the data of interferometric detectors. This method assumes source position is known to high accuracy, while a small frequency and spin-down range around the electromagnetic-inferred values is explored. Barycentric and spin-down corrections are done with an efficient time-domain procedure. Sensitivity and computational efficiency estimates are given and results of tests done using simulated data are also discussed. | Introduction} Continuous gravitational wave signals (CW) emitted by an asymmetric rotating neutron stars are among the sources currently searched in the data of interferometric gravitational wave detectors. Various mechanisms have been proposed that could allow for a time varying mass quadrupole in these stars, thus producing CW. Typically, CW searches are divided in {\it targeted}, when the source position and phase parameters are known with high accuracy, like in the case of known pulsars, and {\it blind} in which those parameters are unknown and a wide portion of the parameter space is explored. In fact, also intermediate cases can be considered, see e.g. \cite{ref:palMor} for a review of recent results. While {\it targeted} searches can be done using coherent methods, based on matched filtering or its variations, {\it blind} searches are usually performed with hierarchical approaches which strongly reduce the needed computing power at the cost of a relatively small sensitivity loss. Targeted searches typically rely on accurate measures of pulsar parameters, among which the rotational frequency and its time variation (spin-down), that come from electromagnetic observations, like those done by radio-telescopes. This means that a strict correlation between the gravitational wave frequency and the measured star rotational frequency is assumed. In the classical case of a non-axisymmetric neutron star rotating around one of its principal axes of inertia the gravitational frequency would be exactly twice the rotation frequency of the star. In fact, that such strict correlation holds for observation times of months to years is questionable and various mechanisms could break this assumption. In this paper we present a coherent search method that relaxes this assumption allowing for a small mismatch, a fraction of Hertz wide, between the gravitational frequency and two times the rotational frequency (and similarly for the spin-down parameters). For this reason such kind of search is called narrow-band. Until now \nbss have not received much attention, one notable exception being the Crab pulsar search done over LIGO S5 data \cite{ref:crab_nb}. The analysis method we will discuss is based on a computationally efficient way to perform barycentric (Doppler and relativistic effects) and spin-down corrections, first devised in \cite{ref:livas}, followed by a re-sampling of the data, and on matched filtering in the space of signal Fourier components. Such techniques have been already employed for targeted searches \cite{ref:vela_vsr2}, \cite{ref:aasi2013} but their extension and application to narrow-band searches is presented here for the first time. Conceptually, the same method we use for Doppler correction has been described in \cite{ref:pink} where, however, it is implemented in a different way and is used in the context of a different analysis procedure. Another similar method for barycentric corrections, but using data at full bandwidth, has been presented in \cite{ref:stefano}. The plan of the paper is the following. In Sec.\ref{sec:signal} we remind the main characteristics of CW. The next three sections of the paper are devoted to describe the main steps of the analysis pipeline used for the targeted search of CW from known neutron stars, of which the narrow-band search method is an extension. In Sec. \ref{sec:bary} an efficient procedure to make barycentric and spin-down correction is described in detail. In Sec. \ref{sec:targeted} the {\it 5-vectors} method, based on matched filtering in the space of signal Fourier components is briefly reminded. In Sec. \ref{sec:pvalue} the way of assessing detection significance is discussed. Following sections are dedicated to present the narrow-band search pipeline. In Sec.\ref{sec:motiv} we explain the motivations for narrow-band searches. In Sec.\ref{sec:anagen} we describe in detail the narrow-band search method. In Sec. \ref{sec:sensi} the narrow-band search sensitivity is computed. In Sec. \ref{sec:test} the validation tests done using simulated data are discussed. Finally, conclusions and future prospects are presented in Sec.\ref{sec:concl}. | 14 | 3 | 1403.1484 |
|
1403 | 1403.3953_arXiv.txt | Metal poor globular clusters (MPGCs) are a unique probe of the early universe, in particular the reionization era. Systems of globular clusters in galaxy clusters are particularly interesting as it is in the progenitors of galaxy clusters that the earliest reionizing sources first formed. Although the exact physical origin of globular clusters is still debated, it is generally admitted that globular clusters form in early, rare dark matter peaks \citep{Moore:2006bi,Boley:2009gf}. We provide a fully numerical analysis of the Virgo cluster globular cluster system by identifying the present day globular cluster system with exactly such early, rare dark matter peaks. A popular hypothesis is that that the observed truncation of blue metal poor globular cluster formation is due to reionization \citep{Spitler:2012fr,Boley:2009gf,Brodie:ip}; adopting this view, constraining the formation epoch of MPGCs provides a complementary constraint on the epoch of reionization. By analyzing both the line of sight velocity dispersion and the surface density distribution of the present day distribution we are able to constrain the redshift and mass of the dark matter peaks. We find and quantify a dependence on the chosen line of sight of these quantities, whose strength varies with redshift, and coupled with star formation efficiency arguments find a best fitting formation mass and redshift of $\simeq 5 \times 10^8 \rm{M}_\odot$ and $z\simeq 9$. We predict $\simeq 300$ intracluster MPGCs in the Virgo cluster. Our results confirm the techniques pioneered by \cite{Moore:2006bi} when applied to the the Virgo cluster and extend and refine the analytic results of \cite{Spitler:2012fr} numerically. | \label{sec:simulation} Using the RAMSES code \citep{Teyssier:2002fj} with initial conditions computed using the Eisenstein \& Hut transfer function \citep{1998ApJ...498..137E} computed using the Grafic++ code \citep{Potter:bWn-q5m9} we performed a suite of dark matter only zoom cosmological simulations in a $\Lambda CDM$ cosmology using with cosmological parameters set using WMAP5 results as listed in \ref{cosmologyparamstable}. \begin{table} \centering \begin{minipage}{140mm} \caption{Cosmological parameters for our simulations.} \label{cosmologyparamstable} \begin{tabular}{ c | c | c| c | c | c} \hline \textit{$H_0$ [\rm{km} $\rm{s}^{-1} \rm{Mpc}^{-1}$]} & \textit{$\sigma_8$} & \textit{$n_s$} & \textit{$\Omega_\Lambda$} & \textit{$\Omega_m$} & \textit{$\Omega_b$} \\ \hline 70.4 & 0.809 & 0.809 & 0.728 & 0.272 & - \\ \hline \end{tabular} \end{minipage} \end{table} The zoom technique selects a subregion of the computational domain to achieve the requisite resolution. To select this subregion, which we desire to form a halo of Virgo like mass by $z=0$ we first performed a low resolution simulation and identify dark matter halos and subhalos using the AdaptaHOP algorithm \citep{Aubert:2004im} in conjunction with a merger tree identification algorithm, as specified in \citep{Tweed:2009fh} as part of the GalICS pipeline as HaloMaker \citep{Tweed:2006wk} and TreeMaker respectively \citep{Tweed:2006wo}. Using the structure identify form a catalog of dark matter halos at each simulation output redshift and selected a subsample of halos with a mass of $1-3 \times 10^{14} \rm{M}_\odot$, on the order the observed Virgo cluster mass at $z=0$. To select our best Virgo candidate we examined assembly history using the merger trees and selected the halo that had a relatively quiescent merger history. We can consider our selected halo relaxed as its last major merger occurs at $z\sim 1.5$. The virial mass of our selected halo, which we define as $\rm{M}_{200 \rho_c}$ is $1.31 \times 10^{14} \rm{M}_\odot$ and the virial radius of our selected halo which we likewise define as $r_{200 \rho_c}$ is $1.06\rm{Mpc}$ This halo was then re-simulated in a zoom simulation focusing the computational resources in the region in which it forms. We performed three simulations of successively higher resolutions: low, high, and ultra-high of which the mass and spatial resolution is detailed in \textbf{Table \ref{massandspatialresolutiontable}}. Only the low and high resolution simulations were run to $z=0$ and were used to validate our matching technique. This matching technique allows us to run the ultra-high resolution simulation only until $z\sim4$. Using the match technique together with the high resolution simulation were are able to analyze robustly physical quantities such as the surface density and velocity dispersion profiles at $z=0$ despite not running the ultra-high resolution simulation to the present day. \begin{table} \centering \begin{minipage}{140mm} \caption{Mass and spatial resolution for our simulations} \label{massandspatialresolutiontable} \begin{tabular}{ l | c | c} \hline Name & $\mathit{m_{\rm{cdm}}} [10^6 \rm{M}_\odot]$ & $\mathit{\Delta x_{\rm{min}}} \rm[kpc/h]$ \\ \hline Low & 54 & 1.5 \\ High & 5.4 & 0.8 \\ Ultra high & 0.54 & 0.4 \\ \hline \end{tabular} \end{minipage} \end{table} | We build upon work by \cite{Spitler:2012fr} identifying MPGCs as forming in high sigma peaks of the density distribution at high redshift. We propose, validate, and utilize a novel split resolution simulation technique to push resolution to the requisite level to address to confirm the analytic results of \cite{Spitler:2012fr} numerically in an Virgo Cluster analogue. We quantify the dependency of a chosen line of sight for measurements of surface density and velocity dispersion of the globular cluster population in an Virgo Cluster analogue, finding that surface density measurements to be robust across all lines of sight, the velocity dispersion numerical measurements could have up to a $\sim 100$~km/s spread. We find the dependency on the chosen line of sight at $z=0$ of the globular cluster population to be consistent across density peak heights of the initial formation sites. Our results are: \begin{itemize} \item We show that our favored model $z~\simeq~9,M\simeq 5 \times 10^8 \rm{M}_\odot$ can consistently form the requisite BGCs by $z\simeq9$, a redshift consistent with reionization constraints. \item Our best fitting model relaxes \cite{Spitler:2012fr}'s restricted assumptions of an analytic model employing spherical symmetry and atomic cooling only. A redshift of $z\simeq 9$ is more consistent with observational evidence for the reionization window in the cluster environment, vs. the much lower $z\simeq 6$ picked out with the Spitler et al. technique. \item The tension in the velocity dispersion points naturally to further constraints that could come from observations past 130~kpc in M87. We predict a rising velocity dispersion profile. The mass normalization and concentration parameter difference between our simulated cluster and M87 could both shift the velocity dispersion profile upward, or even potentially influence its slope. \item We predict $\simeq 300$ intracluster MPGCs in the Virgo cluster. Better observational constraints on the number density of intracluster MPGCs, particularly at high radii, would support or falsify our formation scenario. \item Baryonic physics, realistic globular cluster evaporation modeling, modeling tidal stripping would bring the velocity dispersion simulation results further in line with observations, particularly at the center of the halo. \end{itemize} | 14 | 3 | 1403.3953 |
1403 | 1403.0999_arXiv.txt | Dark gas in the interstellar medium (ISM) is believed to not be detectable either in CO or H{\sc i} radio emission, but it is detected by other means including $\gamma$-rays, dust emission and extinction traced outside the Galactic plane at $|b|>5^\circ$. In these analyses, the 21-cm H{\sc i} emission is usually assumed to be completely optically thin. We have reanalyzed the H{\sc i} emission from the whole sky at $|b| > 15^\circ$ by considering temperature stratification in the ISM inferred from the {\it Planck}/{\it IRAS} analysis of the dust properties. The results indicate that the H{\sc i} emission is saturated with an optical depth ranging from 0.5 to 3 for 85\,\% of the local H{\sc i} gas. This optically thick H{\sc i} is characterized by spin temperature in the range 10\,K\,--\,60\,K, significantly lower than previously postulated in the literature, whereas such low temperature is consistent with emission/absorption measurements of the cool H{\sc i} toward radio continuum sources. The distribution and the column density of the H{\sc i} are consistent with those of the dark gas suggested by $\gamma$-rays, and it is possible that the dark gas in the Galaxy is dominated by optically thick cold H{\sc i} gas. This result implies that the average density of H{\sc i} is 2\,--\,2.5 times higher than that derived on the optically-thin assumption in the local ISM. | It is important to quantify the constituents of the interstellar medium (ISM), which mainly consists of neutral, molecular and ionized hydrogen H{\sc i}, H$_2$, and H{\sc ii}, in order to understand the role of the ISM in galactic evolution. The H{\sc i} gas has density mainly in a range from 0.01\,cm$^{-3}$ to 100\,cm$^{-3}$ while the CO probes the molecular hydrogen gas at density higher than 1000\,cm$^{-3}$, so the intermediate density regime 100\,cm$^{-3}$\,--\,1000\,cm$^{-3}$ may possibly remain unrecognized. It has been discussed that ``dark gas'' may exist, which is undetectable in radio emission, either in the 21-cm H{\sc i} or 2.6-mm CO transitions \citep{2005Sci...307.1292G,2011A&A...536A..19P}. Previous studies suggest that the dark gas probed by $\gamma$-rays and dust emission has a density regime between the H{\sc i} and H$_2$ as inferred from its spatial distribution intermediate between H{\sc i} and CO \citep{2005Sci...307.1292G,2011A&A...536A..19P}. The physical properties of the CO emitting molecular gas are relatively well understood due to transitions of its different rotational states and isotopic species, which allow us to derive physical and chemical parameters of the CO gas. On the other hand, the physical parameters of the H{\sc i} gas are more difficult to estimate, because the H{\sc i} line intensity is the only measurable quantity for a combination of two unknown parameters, the spin temperature $T_{\rm s}$ and optical depth $\tau_{\rm HI}$. The 21-cm transition is a transition characterized by the excitation temperature, called spin temperature, between the two spin-flip states in the electronic ground state. The H{\sc i} consists of warm neutral medium (WNM) and cold neutral medium \citep[CNM; for a review see][]{1990ARA&A..28..215D, 2009ARA&A..47...27K}. The mass of the H{\sc i} gas is measurable at reasonably high accuracy under the optically thin approximation, while the cold components having $T_{\rm s}$ of $\leq80$\,K may not be easily measurable because of optical depth effects. Only a comparison of the absorption and emission H{\sc i} profiles toward extragalactic radio continuum sources can be used to estimate $T_{\rm s}$ and $\tau_{\rm HI}$ \citep{2003ApJ...585..801D, 2003ApJ...586.1067H}, so the details of the cold H{\sc i} are still not fully understood. The existence of optically thick H{\sc i} in galaxies has been discussed based on line profiles, whereas a quantitative method to evaluate the physical properties has not yet been developed \citep{2012ApJ...749...87B}. A recent work on the high latitude molecular clouds MBM\,53, 54, 55, and HLCG\,92-35 has shown that the H{\sc i} emission is optically thick in the surroundings of the CO clouds \citep[][Paper I]{2014ApJ...796...59F}. These authors compared the {\it Planck}/{\it IRAS} dust opacity \citep{2014A&A...571A..11P} with H{\sc i} and CO, and estimated $T_{\rm s}$ to be 20\,K\,--\,40\,K (average is 30\,K) and $\tau_{\rm HI}$ 0.3\,--\,5 (average is 2) by assuming that the dust opacity is proportional to the ISM proton column density. They suggest that the H{\sc i} envelope is massive having more than 10 times the mass of the CO clouds, and that such optically thick H{\sc i} may explain the origin of the dark gas, an alternative to CO-free H$_{2}$. It is important to test if the H{\sc i} shows similar high optical depth in a much larger portion of the sky. In addition, it is notable that in three TeV $\gamma$-ray supernova remnants RX\,J1713.7-3946, RX\,J0852.0-4622, and HESS\,J1731-347, it is found that spatially extended cold H{\sc i} gas of $T_{\rm s} \sim 40$\,K which has no CO emission is responsible for the $\gamma$-rays via the hadronic process between the cosmic-ray protons and the interstellar protons \citep{2012ApJ...746...82F, 2012IAUS..284..389T,2013ASSP...34..249F,Fukuda2014}. The cold H{\sc i} probably represents the compressed H{\sc i} shell swept up by the stellar winds of the supernova progenitor. This finding raised independently a possibility that the cold H{\sc i} gas may be more ubiquitous than previously thought. It has been difficult to derive $T_{\rm s}$ and $\tau_{\rm HI}$ in general and our knowledge on the cold H{\sc i} remains ambiguous at best. In order to better understand the relationship between the dust emission and H{\sc i} over a significant portion of the sky, we have compared the H{\sc i} with the dust properties derived from the {\it Planck} and {\it IRAS} data beyond the area studied by Paper I. This comparison was made by using the H{\sc i} dataset at $33'$ resolution from the Leiden/Argentine/Bonn (LAB) archive data and the {\it Planck}/{\it IRAS} dust properties. We present the results of the detailed comparison. Section 2 presents the observations, Section 3 the results, Section 4 the discussion and Section 5 our conclusions. | We have carried out a study of the H{\sc i} gas properties in the local ISM by using dust properties derived from the {\it Planck}/{\it IRAS} all sky survey at sub-mm/far-infrared wavelengths. The H{\sc i} gas is in local regions within a few hundred pc of the Sun out of the Galactic plane, where giant molecular clouds do not exist. We find $W_{\rm HI}$ shows poor correlation with the sub-mm dust optical depth $\tau_{353}$, whereas the correlation becomes significantly better if $T_{\rm d}$, ranging from 13\,K to 23\,K, is analyzed in several small ranges of width 0.5\,K. We hypothesize that the H{\sc i} is optically thick and the saturation of the H{\sc i} intensity is significant. We have shown that the H{\sc i} emission associated with the highest $T_{\rm d}$ shows a good correlation expressed by a linear regression and hence derive a relationship, $W_{\rm HI}$\ =\ $1.15\times10^8\cdot \tau_{353}$. An analysis of $W_{\rm HI}$ and $N_{\rm HI}$ based on coupled equations of radiative transfer and the H{\sc i} optical depth yields both $T_{\rm s}$ and $\tau_{\rm HI}$. $T_{\rm s}$ is typically in the range from 15\,K to 35\,K and $\tau_{\rm HI}$ from 0.5 to 3.0. The cold H{\sc i} gas typically has density of 30\,cm$^{-3}$\,--\,190\,cm$^{-3}$, $N_{\rm HI}$ = $5\times10^{20}$\,cm$^{-2}$\,--\,$3\times10^{21}$\,cm$^{-2}$, and $\Delta V_{\rm HI}\cong15$\,km\,s$^{-1}$. We argue that the ``dark gas'' is explained by cold H{\sc i} gas, which is 2\,--\,2.5 times more massive than the H{\sc i} gas derived under the optically thin approximation. We consider two alternative interpretations: one is that H$_2$ is dominant instead of H{\sc i}, and the other that variation of the dust opacity relative to the gas column density is significant. The fraction of H$_2$ $f_{\rm H_2}$ measured in the UV observations is consistent with that most of the hydrogen is atomic for $N_{\rm H}$ less than $1\times10^{21}$\,cm$^{-2}$, while for $N_{\rm H}$ larger than $1\times10^{21}$\,cm$^{-2}$ UV observations are only a few, insufficient to constrain $f_{\rm H_2}$. Minimum values of $N_{\rm HI}$ estimated by the optically thin limit constrain $f_{\rm H_2}$ to be less than $\sim$0.5, supporting that H{\sc i} is at least comparable to H$_2$. Theoretical studies of H{\sc i}-cloud evolution indicate that $f_{\rm H_2}$ is less than 0.1 for $\sim$1\,--\,Myr timescale by numerical simulations, lending support for that H{\sc i} dominates H$_2$ at density 10\,cm$^{-3}$\,--\,10$^3$\,cm$^{-3}$ in the local interstellar medium. The second one the dust opacity variation is not reconciled with the general dust properties, either (equation 7). $T_{\rm s}$ and $\tau_{\rm HI}$ cannot be disentangled by H{\sc i} intensity alone. This has been an obstacle in 21-cm H{\sc i} astronomy. The {\it Planck} dust optical depth offers a potential tool to disentangle this issue for an ISM column density range $10^{20}$\,cm$^{-2}$\,--\,$10^{22}$\,cm$^{-2}$. The opacity gives a measure of $N_{\rm HI}$ for given $T_{\rm d}$, if CO is not detectable and the background H{\sc i} gas is negligible. The present study suggests that the cold H{\sc i} is dominant in the local ISM and such cold H{\sc i} has important implications on related subjects, i.e., dust properties (in particular grain size evolution), the structure of molecular and atomic clouds, the interaction of H{\sc i} with cosmic rays, and the derivation of the $X_{\rm CO}$ factor. These issues will be subjects to be pursued in follow-up studies. | 14 | 3 | 1403.0999 |
1403 | 1403.0161_arXiv.txt | This paper reports the results from three targeted searches of Milagro TeV sky maps: two extragalactic point source lists and one pulsar source list. The first extragalactic candidate list consists of 709 candidates selected from the \textit{Fermi-LAT} 2FGL catalog. The second extragalactic candidate list contains 31 candidates selected from the TeVCat source catalog that have been detected by imaging atmospheric Cherenkov telescopes (IACTs). In both extragalactic candidate lists Mkn 421 was the only source detected by Milagro. This paper presents the Milagro TeV flux for Mkn 421 and flux limits for the brighter \textit{Fermi-LAT} extragalactic sources and for all TeVCat candidates. The pulsar list extends a previously published Milagro targeted search for Galactic sources. With the 32 new gamma-ray pulsars identified in 2FGL, the number of pulsars that are studied by both \textit{Fermi-LAT} and Milagro is increased to 52. In this sample, we find that the probability of Milagro detecting a TeV emission coincident with a pulsar increases with the GeV flux observed by the \textit{Fermi-LAT} in the energy range from 0.1 GeV to 100 GeV. | 14 | 3 | 1403.0161 |
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1403 | 1403.0357_arXiv.txt | The Exoplanet Characterisation Observatory (\echo) has been studied as a space mission concept by the European Space Agency in the context of the M3 selection process. Through direct measurement of the atmospheric chemical composition of hundreds of exoplanets, EChO would address fundamental questions such as: What are exoplanets made of? How do planets form and evolve? What is the origin of exoplanet diversity? More specifically, EChO is a dedicated survey mission for transit and eclipse spectroscopy capable of observing a large, diverse and well-defined planetary sample within its four to six year mission lifetime. In this paper we use the end-to-end instrument simulator \echosim{ }to model the currently discovered targets, to gauge which targets are observable and assess the \echo{ }performances obtainable for each observing tier and time. We show that EChO would be capable of observing over 170 relativity diverse planets if it were launched today, and the wealth of optimal targets for EChO expected to be discovered in the next 10 years by space and ground-based facilities is simply overwhelming. In addition, we build on previous molecular detectability studies to show what molecules and abundances will be detectable by \echo{ }for a selection of real targets with various molecular compositions and abundances. \echo's unique contribution to exoplanetary science will be in identifying the main constituents of hundreds of exoplanets in various mass/temperature regimes, meaning that we will be looking no longer at individual cases but at populations. Such a universal view is critical if we truly want to understand the processes of planet formation and evolution in various environments. In this paper we present a selection of key results. The full results are available online ({http://www.ucl.ac.uk/exoplanets/echotargetlist/}). | Within the last two decades, the field of exoplanetary science has made breathtaking advances, both in the number of systems known and in the wealth of information. Recently we marked the 1000th extrasolar planet discovered, of which over 400 are transiting \citep{Schneider2011, Rein2012}. Such numbers are impressive in themselves but dwarfed by the 3000+ transiting exoplanet candidates \citep{tenenbaum12, fressin13, batalha13} obtained by the Kepler mission \citep{borucki96, jenkins10}, as well as the predicted tens of thousands of planets to be discovered by the GAIA mission \citep{sozzetti11}. The large number of detections suggests that planet formation is the norm in our own galaxy \citep{howard13, fressin13, batalha13, cassan12, dressing13,wright12}. Through the measurement of the planets' masses and radii we can estimate their bulk properties and get a first insight into their compositions and potential formation histories \citep{valencia13,adams08, Grasset2009,buchhave12}. To take this characterisation work to the next level, we must gain an understanding of the planet's chemical composition. The best way to probe their chemical composition is through the study of their atmospheres. For transiting planets this is feasible when the planet transits its host star in our line of sight. This allows some of the stellar light to shine through the terminator region of the planet (transmission spectroscopy). Similarly, when the star eclipses the planet (i.e. it passes behind its host star in our line of sight) we can measure the flux difference resulting from the planet's dayside emissions (emission spectroscopy). In the last decade, a large body of work has accumulated on the atmospheric spectroscopy of transiting extrasolar planets \citep[e.g.][]{beaulieu10,beaulieu11, charbonneau08, brogi12, bean11, swain08,swain08b, swain09a, crouzet12, deming13, grillmair08,thatte10, tinetti07, pont08, swain12, knutson11, sing11, tinetti10, mooij12,bean11b, stevenson10} also see \citet{tinetti13} for a comprehensive review. Given these large and ever increasing numbers of detections, it is important to understand which of these systems lend themselves to be characterised further by the use of transmission and emission spectroscopy. In the light of the mission concept The Exoplanet Characterisation Observatory, which has been studied by the European Space Agency as one of the M3 mission candidates, this question becomes critical. In this paper, we aim to quantify the number, as well as the time required to characterise spectroscopically the transiting extrasolar planets known to date. An overview of our results with examples for specific cases is given here with the full results available online ({http://www.ucl.ac.uk/exoplanets/echotargetlist/}). \subsection{\echo} In the frame of ESA's Cosmic Vision programme, \echo{ }has been studied as a medium-sized M3 mission candidate for launch in the 2022 - 2024 timeframe\footnote{http://sci.esa.int/echo/} \citep{tinetti12, Tinetti2014}. During the `Phase-A study' \echo{ }has been designed as a 1 metre class telescope, passively cooled to $\sim$50 K and orbiting around the second Lagrangian Point (L2). The baseline for the payload consists of four integrated spectrographs providing continuous spectral coverage from 0.5 to 11$\mu$m (goal 0.4 to 16$\mu$m) at a resolving power ranging from R $\sim$ 300 ($\lambda < 5\mu m$) to 30 ($\lambda > 5\mu m$). For a detailed description of the telescope and payload design, we refer the reader to the literature \citep{puig12b,puig12,tinetti12, Tinetti2014, swinyard12, eccleston12, reess12, adriani12, zapata12, pascale12, focardi12, tessenyi12payload,waldmann13}. The \echo{ }science case can be best achieved by splitting the mission lifetime into three surveys, where the instrument capabilties are optimally suited to address different classes of question. The studied targets range from super-Earth to gas giant, temperate to very hot and stellar classes M to F. The aims of these three tiers described in the \echo{ }Assessment Study Report\footnote{\label{fn:YB}http://sci.esa.int/echo/53446-echo-yellow-book/} are as follows; \begin{itemize} \item \textbf{Chemical Census}: Statistically complete sample to explore the key atmospheric features: albedo, bulk thermal properties, most abundant atomic and molecular species, clouds. \item \textbf{Origin}: Addresses the question of the origin of exoplanet diversity by enabling the retrieval of the vertical thermal profiles and molecular abundances, including key and trace gases. \item \textbf{Rosetta Stone}: Benchmark cases to get insight into the key classes of planets. This tier will provide high signal-to-noise observations yielding very refined molecular abundances, chemical gradients and atmospheric structure. Spatial and temporal resolution will enable the study of weather and climate. \end{itemize} The spectral resolving power (R) and signal-to-noise (SNR) target for each mission is shown in table \ref{tab:survey-res}. \begin{table}[h] \begin{tabular}{l|llll} Survey Name & SNR Target & R ($\lambda$ $<$ 5 $\mu$m) & R($\lambda$ $>$ 5 $\mu$m) & Target No. Planets\\ \hline Chemical Census & 5 & 50 & 30 & $>150$ \\ Origin & 10 & 100 & 30 & 50 -100 \\ Rosetta Stone & 20 & 300 & 30 & 10 - 20 \\ \end{tabular} \caption{The spectral resolving power ($R=\lambda/\Delta \lambda$) and SNR requirements of each survey mode. The SNR target is the average in a chosen spectral element (see \S \ref{sec:snr-calc}). Target number of planets refers to the number of planets expected to be observed in each mode by the mission} \label{tab:survey-res} \end{table} | EChO has been designed as a 1 metre dedicated survey mission for transit and eclipse spectroscopy capable of observing a large, diverse and well-defined planet sample within its four year mission lifetime, our results show that the majority of this diversity can be achieved with today's target sample. 173 of today's targets can be observed in \echo's broadest survey tier (Chemical Census, R = 50 at $\lambda < 5 \mu m$, SNR = 5) in transit and/or eclipse, 162 are observable in both. This sample covers a wide range of planetary and stellar sizes, temperatures, metallicities and semi-major axes. This excludes the recent discovery of over 700 planets \citep{2014Lissauer, 2014Rowe} that will be added in a future version. Out of these 173, the majority (165) can be observed in transit or eclipse (148 in both) at the higher spectral resolving power and SNR of the Origin tier (R = 100 at $\lambda < 5 \mu m$, SNR = 10). Dedicated studies show that an accurate retrieval can be performed out of origin targets, so that the physical causes of said diversity can be identified (\citet[][in prep]{Tessenyi2014}, \citet{Barstow2014}). For a subset of these, we can push the spectral resolving power to R = 300 at $\lambda < 5 \mu m$ at SNR = 20 so that a very detailed knowledge of the planets can be achieved (Rosetta Stone). Said knowledge will include spatial and temporal resolution enabling studies of weather and climate, as well as very refined chemical composition of these atmospheres to penetrate the intricacies of equilibrium and non-equilibrium chemistry and formation. While today there are 132 targets capable of being observed in this tier in transit or eclipse (of which 78 can be done in both), as the Rosetta Stone tier is very demanding of the \echo{ }schedule, this is the large sample from which the target 10-20 planets can be chosen from. \echo's unique contribution to exoplanetary science is in identifying the main constituents of hundreds of exoplanets in various mass/temperature regimes, meaning that we will be looking no longer at individual cases but at populations of planets. Such a universal view is critical if we truly want to understand the processes of planet formation and evolution and how they behave in various environments. | 14 | 3 | 1403.0357 |
1403 | 1403.7607_arXiv.txt | We analytically calculate the marginally stable surface density profile for the rotational instability of protoplanetary disks. The derived profile can be utilized for considering the region in a rotating disk where radial pressure gradient force is comparable to the gravitational force, such as an inner edge, steep gaps or bumps, and an outer region of the disk. In this paper, we particularly focus on the rotational instability in the outer region of disks. We find that a protoplanetary disk with a surface density profile of similarity solution becomes rotationally unstable at a certain radius, depending on its temperature profile and a mass of the central star. If the temperature is relatively low and the mass of the central star is high, disks have rotationally stable similarity profiles. Otherwise, deviation from the similarity profiles of surface density could be observable, using facilities with high sensitivity, such as ALMA. | Protoplanetary disks evolve via turbulent viscosity, and their evolution has been well represented by the model of \citeauthor*{Lyn74}(1974, henceforth LBP74). In the LBP74 model, the rotation profile is assumed to be time-independent or simply Keplerian. This assumption is justified if the radial pressure gradient is much smaller than the central star gravity. The temperature in the disks is generally low enough that the radial pressure gradient can be neglected in most parts of the disk. However, even in disks with low temperature, the radial pressure gradient may not be neglected in which the surface density dramatically varies in the radial direction. Such regions appear, for example, at the gap edge formed by the gravity of planets, and at the boundary between the active and inactive regions for magneto-rotational instability. For such regions, we need to modify the LBP74 model to take into account the change in the rotation profile. Interestingly, the similarity solution of the LBP74 model has an exponential cut off at the outermost region (LBP74; \citealp{Har98}). In the outer edge of the disk, the density decreases exponentially with a radial scale length, R0. Because the disk scale height, H, generally increases with the radius, the scale height becomes larger than the radial scale length at a certain point, resulting in a violation of the assumption of negligible pressure gradient. Hence, even if there is no external force modifying the disk structure, such as photoevaporation or planets, the self-similar solution of the LBP74 model violates self-consistency at the outer edge of the disk. The recent development of high-sensitivity (sub)millimeter interferometers makes it possible to observe surface density profiles of the outer regions of protoplanetary disks. The observations have suggested that the profiles are well fitted by a similarity solution of the disks (e.g., \citealp{Hug08}; \citealp{And09}, \citeyear{And10}; \citealp{Aki13}), which has a sharp density profile at the outer edge. Observations using facilities with high sensitivity, such as ALMA, however, are expected to reveal the lower density area in the outer region in which the radial pressure gradient force is non-negligible. Because of this, it is important that we investigate the outer region of the disks without the assumption of Keplerian disks. When the gas pressure gradient force becomes non-negligible compared with the gravitational force in the equation of motion in the radial direction, an assumption of Keplerian rotation becomes inadequate. When we inappropriately adopt the assumption to a disk with a steep surface density profile and a large radial pressure gradient force, we often see rotational instability. Rotational instability is one of the hydrodynamical instabilities in axisymmetric differentially rotating disks \citep{Cha61}. The Rayleigh's criterion is the discriminant for rotational stability; for an inviscid disk to be rotationally stable, the specific angular momentum ($j$) must monotonically increase with cylindrical distance from the axis of rotation ($R$) in a flow: \begin{equation} \frac{\partial j^2}{\partial R}> 0. \label{1} \end{equation} Otherwise, the disk becomes rotationally unstable and the gas radially migrates with conserving specific angular momentum. In a viscid disk, viscosity limits the onset of rotational instability. Also, in the Rayleigh's criterion, the radial entropy gradient is not taken into account. We need to use the Solberg-Hoiland criterion \citep{End78} for a disk with a radial entropy gradient, with which the rotational instability is easier to set in standard disks \citep{Sha73}. In this paper, however, we simply adopt the Rayleigh's criterion as the discriminant for rotational stability because we treat disks with low viscosity and the Rayleigh's criterion is a more severe discriminant for rotational instability than the Solberg-Hoiland criterion. Since the sharp edge could lead to rotational instability, in this paper, we investigate the condition under which the disk becomes rotationally unstable. We also analytically calculate the marginally stable surface density profile for rotational instability, which indicates that the profile becomes shallower than that of the similarity profile. The rotation velocity will be less than the Keplerian velocity in the region where the disk is rotationally unstable. If the deviation from the Keplerian velocity is observable, it will be evidence that the radial pressure gradient force is sufficiently strong in the region. We analytically examine the marginally stable disks for rotational instability in Section 2. In Section 3, we apply the result of Section 2 for protoplanetary disks. We discuss the possibility of observations of non-similarity profiles and the validity of approximations used in this work in Section 4, and we summarize our conclusions in Section 5. Although many discussions here are applicable to the outer region of accretion disks in general, we focus on protoplanetary disks in this paper. | \subsection{Possibility of Observational Detection of Non-similarity Profiles} In this section, we discuss the possibility of the observational detection of non-similarity profiles in protoplanetary disks, which depends on the value of $H_0/R_0$. In typical T Tauri disks, the scale height is roughly estimated as \begin{equation} \frac{H}{R}\approx 0.1\biggl(\frac{T}{28\mathrm{K}}\biggr)^{1/2}\biggl(\frac{M_*}{M_{\odot}}\biggr)^{-1/2}\biggl(\frac{R}{100\mathrm{AU}}\biggr)^{1/4}, \label{35} \end{equation} where we assume $T=280$K at $R=1$AU and adopt $\beta=1/2$, considering that the temperature profile is controlled by the central star. In the outer regions where the temperature is as low as that of the surrounding molecular clouds ($\sim 10-30$K, depending on low- or high-mass star forming regions), the temperature profile approaches isothermal ($\beta=0$; see below). Observationally, $R_0$ ranges from $\sim$15AU to 200AU (\citealp{And09}, \citeyear{And10}), and then $H_0/R_0\sim 0.1-0.18$ from Equation (\ref{35}) if we adopt $M_*=0.5M_{\odot}$. In this case, $r_m=R_m/R_0$ is roughly 3-10 (see Figure \ref{fig1}). For disks with a relatively less massive central star and relatively high temperature, $H_0/R_0$ would be close to 0.2. For such disks, the deviation of surface density from the similarity profile is so large near $R_m$ that the deviation will be detected by future observations. If $H_0/R_0$ is as low as 0.1, it will be difficult to observe the deviation (see Figure \ref{fig2}). We note that \citet{And07} reported some deviation from the similarity profiles in their observations of surface density profiles of protoplanetary disks. In typical Herbig Ae disks, the temperature is higher ($T\approx 100$K at $R=10$AU; e.g., \citealp{Dul04}) but the stellar mass is larger ($M_*\approx 2M_{\odot}$). Therefore, $H_0/R_0$ becomes smaller and the deviation seems more difficult to observe. For disks irradiated by nearby massive stars in young clusters, the external irradiation makes $\beta \simeq 0$ in the outer regions as in the case of protoplanetary disks in the Trapezium Cluster in the Orion Nebula (e.g., \citealp{Rob02}; \citealp{Wal13}). In this case, the scale height is roughly estimated as \begin{equation} \frac{H}{R}\approx 0.2 \biggl(\frac{T}{60\mathrm{K}}\biggr)^{1/2}\biggl(\frac{M_*}{0.5M_{\odot}}\biggr)^{-1/2}\biggl(\frac{R}{100\mathrm{AU}}\biggr)^{1/2}, \label{36} \end{equation} where we assume $T=60$K in the outer region and adopt $\beta=0$. $H_0/R_0$ approaches about 0.3 if the mass of the central star is as low as $\sim 0.2M_{\odot}$ (e.g., \citealp{Hil98}). In this case, $r_m=R_m/R_0$ is roughly 1 (see Figure \ref{fig1}), and the deviation from the similarity profile is possibly observable (see Figure \ref{fig3}). In disks near a massive star, however, the gas in the outer region escapes due to photoevaporation, which should be taken into account, (e.g., \citealp{Joh98}; \citealp{Ric00}). On the other hand, our result also suggests that the radial pressure gradient force may affect the evolution process due to photoevaporation by surrounding high-mass stars (see Section 4.3). To summarize, it is expected that deep observations in the near future can detect deviation from the similarity profile of surface density in the outer regions of the disks whose central stars are less massive and temperature is relatively high. In the disks heated by irradiation from a nearby massive star in young star clusters, the deviation will be more easily observable, but we should take into account the effect of photoevaporation on the surface density profile in the outer disks. Observations by facilities with high sensitivity, such as ALMA, will reveal the surface density profiles of the outer regions of protoplanetary disks, which tell us the physical properties of disks with sharp surface density profiles. \subsection{Break of Geometrically Thin Approximation in The Outer Region} In this paper, we assume that disks are geometrically thin. The assumption, however, breaks in the outer region of the disks. From Equations (\ref{3}) and (\ref{5}), the scale height is given by \begin{equation} \frac{H}{R}=\frac{H_0}{R_0} r^{(1-\beta)/2}. \label{37} \end{equation} Figure 4 shows the scale height, $H_m$, at $R_m\equiv R_0 r_m$ as a function of $H_0/R_0$, obtained by Equations (\ref{3}), (\ref{5}), and (\ref{21}) for $\beta =0$ (red solid line), $\beta=1/2$ (green dashed line) and $\beta=3/4$ (blue dotted line). Because $H_m/R_m \sim 0.4$ at most, the figure indicates that geometrically thin approximation is appropriate around $R_m$. Beyond $r_m$, $H/R$ exceeds unity around the minimum point of the marginally stable surface density profile in Figures \ref{fig2} and \ref{fig3} (for $\beta=1/2$, $r\sim 10^4$, 625, and 100, and for $\beta=0$, $r\sim 100$, 25, and 10 for $H_0/R_0=0.1$, 0.2, and 0.3, respectively) and the geometrically thin approximation is invalid beyond the radius. If the gas of the surrounding envelope continues to infall to the disk, the density profile in the outer edge may be more shallower than the self-similar profile. In order to consider this situation, let the density profile be a simple power-law in the whole disk. In this case, $R_m$ would be larger compared to the disk of similarity profiles, resulting in a breakdown of the geometrically thin approximation around $R_m$ (see Equations (\ref{8}) and (\ref{37})). The steep drop of the density at the exponential tail is essential to cause rotational instability. \begin{figure} \epsscale{.90} \plotone{fig4.eps} \caption{Relation between $H_m/R_m$ and $H_0/R_0$ obtained by Equations (\ref{3}), (\ref{5}) and (\ref{21}) for $\beta =0$ (red solid line), $\beta=1/2$ (green dashed line) and, $\beta=3/4$ (blue dotted line). } \label{fig4} \end{figure} \subsection{Evolution of Surface Density Profile in the Outer Region} In the previous sections, we simply assume that the surface density profiles connect smoothly from the similarity profile to the marginally stable profile at $r_m$. In reality, the surface density profile evolves so that it avoids being rotationally unstable. In this subsection, we discuss the time evolution of the surface density profile. Here, we use only three approximations that disks are axisymmetric and geometrically thin and that the self-gravitation of disks is negligible. Now, the equation of continuity is \begin{equation} R\frac{\partial \Sigma}{\partial t}+ \frac{\partial }{\partial R}\left( R\Sigma v_R \right)=0, \label{38} \end{equation} the equation of motion in the radial direction is \begin{equation} \frac{\partial v_R}{\partial t} +v_R \frac{\partial v_R}{\partial R} -\frac{j^2}{R^3}= -\frac{1}{\rho}\frac{\partial P}{\partial R}-\frac{GM}{R^2}, \label{39} \end{equation} and the equation of angular momentum transfer is \begin{equation} 2\pi R \Sigma \frac{\partial j}{\partial t} -\dot{M} \frac{\partial j}{\partial R}= \frac{\partial W}{\partial R}, \label{40} \end{equation} where $v_R$ is the velocity of the gas in the radial direction, $\dot{M}$ is the inward mass flux, and $W$ is the viscous torque caused by turbulent motion. $\dot{M}$ is defined as \begin{equation} \dot{M} \equiv -2\pi R \Sigma v_R. \label{41} \end{equation} $W$ is defined as \begin{equation} W \equiv 2\pi R^2 T_{R \varphi} =2\pi R^3 \Sigma \nu \frac{\partial \Omega}{\partial R}, \label{42} \end{equation} where $\varphi$ is the azimuthal component in the cylindrical coordinate system and $T_{R\varphi}$ is the $R \varphi$ component of the viscous stress tensor. We assume that the other components of the viscous stress tensor are negligible. Using Equations (\ref{41}) and (\ref{42}), Equations (\ref{38})-(\ref{40}) are \begin{eqnarray} \frac{\partial \Sigma}{\partial t} &=&\frac{1}{2\pi R} \frac{\partial \dot{M}}{\partial R}, \label{43} \\ \frac{\partial \dot{M}}{\partial t} &=& -2\pi R \Sigma \left(\frac{j^2}{R^3} -\frac{GM}{R^2} -\frac{1}{\rho} \frac{\partial P}{\partial R} \right) \nonumber \\ &&-\frac{\dot{M}^2}{2\pi R^2 \Sigma}\left(1+ \frac{\partial \mathrm{ln}~\Sigma}{\partial \mathrm{ln}~R} -2\frac{\partial \mathrm{ln}~\dot{M}}{\partial \mathrm{ln}~R} \right), \label{44} \\ \frac{\partial j}{\partial t} &=& \frac{1}{2\pi R\Sigma} \left(\dot{M} \frac{\partial j}{\partial R} +\frac{\partial W}{\partial R} \right). \label{45} \end{eqnarray} Equation (\ref{43})-(\ref{45}) are differential equations of $\Sigma(R, t)$, $\dot{M}(R, t)$, and $j(R, t)$. In the previous sections, we ignore the terms that contain second-order of $\dot{M}$ and the terms of $(\partial \dot{M}/ \partial t)$ and $(\partial j / \partial t)$. In general, we cannot ignore these terms when $\partial j/\partial R$ approaches 0. Here, in order to qualitatively comprehend how the surface density profile evolves when $\partial j/\partial R$ approaches 0, we retain only the term which contains second-order of $\dot{M}$, ignoring the terms $(\partial \dot{M}/ \partial t)$ and $(\partial j / \partial t)$. Then Equations (\ref{43})-(\ref{45}) are rewritten as \begin{eqnarray} \frac{\partial \Sigma}{\partial t} &=&\frac{1}{R}\frac{\partial}{\partial R}\left[ \frac{1}{\left( \frac{\partial j}{\partial R} \right)} \frac{\partial }{\partial R}\left\{\nu j \Sigma \left(2- \frac{\partial \mathrm{ln}~ j}{\partial \mathrm{ln}~ R} \right) \right\} \right], \label{46} \\ j^2&=&GMR +\frac{R^3}{\rho}\frac{\partial P}{\partial R} \nonumber \\ &&-\frac{1}{\Sigma^2 \left(\frac{\partial j}{\partial R} \right)^2}\left[\frac{\partial}{\partial R} \left\{\nu j \Sigma \left(2- \frac{\partial \mathrm{ln}~ j}{\partial \mathrm{ln}~ R} \right) \right\} \right]^2 \nonumber \\ &&\left(1+ \frac{\partial \mathrm{ln}~\Sigma}{\partial \mathrm{ln}~R} -2\frac{\partial \mathrm{ln}~\dot{M}}{\partial \mathrm{ln}~R} \right), \label{47} \\ \dot{M} &=& \frac{2\pi}{\left(\frac{\partial j}{\partial R} \right)}\frac{\partial}{\partial R} \left\{ \nu j \Sigma \left(2- \frac{\partial \mathrm{ln}~ j}{\partial \mathrm{ln}~ R} \right) \right\}. \label{48} \end{eqnarray} Equation (\ref{46}) is the evolution of the surface density of a geometrically thin viscous disk (similar to Equation (\ref{12}), but without an assumption of the Keplerian rotation) and Equation (\ref{47}) is the equation for radial force balance (similar to Equation (\ref{2})). Equations (\ref{46}) and (\ref{48}) indicate that when $(\partial j/ \partial R)$ approaches 0 around $R\sim R_m$, the surface density diffuses fast and $\dot{M}$ becomes large, and then the third term on right side of Equation (\ref{47}) becomes non-negligible. However, since the diffusion velocity should be subsonic, the accretion rate is limited to $|\dot{M}|=2\pi R\Sigma c_s$. In this case, $(\partial j/\partial R)$ is roughly estimated from Equation (\ref{48}) as \begin{eqnarray} \frac{\partial j}{\partial R}&=&\frac{2\pi}{\dot{M}}\frac{\partial}{\partial R} \left\{ \nu j \Sigma \left(2- \frac{\partial \mathrm{ln}~ j}{\partial \mathrm{ln}~ R} \right) \right\} \nonumber \\ &\sim& \frac{2\pi}{2\pi R\Sigma c_s}\frac{1}{R}(2\alpha c_s H j\Sigma) \nonumber \\ &\sim& \alpha c_s\Omega/\Omega_K, \label{49} \end{eqnarray} where we adopt $\nu=\alpha c_s H$, $H=c_s/\Omega_K$ and $j=\Omega R^2$. Thus, around $R\sim R_m$, $(\partial j/\partial R)$ is much smaller than that of the disk rotating with the Keplerian velocity, $\partial j/\partial R\sim v_K$, since $c_s<v_K$ and $\Omega<\Omega_K$. Therefore, the surface density profile around $R\sim R_m$ will be close to the marginally stable profile, $\sigma_{\mathrm{ms}}$, obtained in Section 3.1. However, it is not exactly the same as $\sigma_{\mathrm{ms}}$ since $\partial j/\partial R\neq 0$. In order to obtain the actual surface density profile, we need to solve Equations (\ref{43})-(\ref{45}) in future work. | 14 | 3 | 1403.7607 |
1403 | 1403.2028_arXiv.txt | X-ray observations of highly ionized metal absorption lines at $z=0$ provide critical information of the hot gas distribution in and around the Milky Way. We present a study of more than ten-year {\sl Chandra} and {\sl XMM}-Newton observations of 3C~273, one of the brightest extragalactic X-ray sources. Compared with previous work, We obtain much tighter constraints of the physical properties of the X-ray absorber. We also find a large, non-thermal velocity at $\sim 100 - 150 \rm\ km\ s^{-1}$ is the main reason for the higher line equivalent width when compared with other sightlines. Using joint analysis with X-ray emission and ultraviolet observations, we derive a size of 5 -- 15 kpc and a temperature of (1.5--1.8)$\times10^6$ K for the X-ray absorber. The 3C~273 sightline passes through a number of Galactic structures, including the radio Loop I, IV, the North Polar Spur, and the neighborhood of the newly discovered ``{\sl Fermi} bubbles". We argue that the X-ray absorber is unlikely associated with the nearby radio Loop I and IV; however, the non-thermal velocity can be naturally explained as the result of the expansion of the ``{\sl Fermi} bubbles". Our data implies an shock-expansion velocity of $200 - 300 \rm\ km\ s^{-1}$. Our study indicates a likely complex environment for the production of the Galactic X-ray absorbers along different sightlines, and highlights the significance of probing galactic feedback with high resolution X-ray spectroscopy. | Since the launch of the {\sl Chandra} and {\sl XMM}-Newton X-ray telescopes, the on-board high resolution X-ay spectrometers open a new window of studying the interstellar medium (ISM) in our Galaxy. Numerous absorption features, produced by metal species with ionization stages ranging form neutral to hydrogen-like, were detected in the X-ray spectra of bright background sources such as the active galactic nuclei (AGNs) and Galactic X-ray binaries (XRB) (see, e.g., \citealp{nicastro2002, fang2003, rasmussen2003, yao2005, williams2005, bregman2007, pinto2010, hagihara2010, pinto2012, gorczyca2013, liao2013}). Due to the distance constraint, most XRBs can only probe the ISM within the Galactic disk, while AGNs can help study the ISM that may distribute beyond the disk and extend into the Galactic halo. AGN study of the Milky Way ISM, however, is constrained by the brightness of background sources. The most prominent absorption line produced by highly ionized metals at $z=0$ is the \ion{O}{7} K$\alpha$ transition at 21.6 \AA.\ So far, only a handful of targets are bright enough to detect other absorption line features, especially the crucial \ion{O}{7} K$\beta$ transition at 18.63 \AA,\ and enable the diagnose of the X-ray absorbing gas using high resolution X-ray spectroscopy. Mkn~421, PKS~2155 and 3C~273 are the three brightest extragalactic X-ray sources that have been repeatedly observed with {\sl Chandra} and {\sl XMM}-Newton. Despite sampling very different directions of Mkn~421 and PKS~2155-304, the two sightlines display a very similar distribution of hot gas (see \citealp{williams2005,williams2007,gupta2012}). The X-ray observation of the 3C~273 sightline, on the other hand, showed a quite different picture. Previous studies indicated that the detected \ion{O}{7} K$\alpha$ line EW along the 3C~273 sightlinee is about twice higher (see, e.g., \citealp{fang2003, rasmussen2003}). By comparing with the Mkn~421 sightline, \citet{yao2007a} concluded that the X-ray emission/absorption along the 3C~273 sightline line is enhanced by a Galactic Central Soft X-ray Enhancement (GCSXE) component. \begin{figure*}[t] \center \includegraphics[height=0.45\textheight,width=1\textwidth]{f1} \vskip-2cm \caption{{\sl ROSAT} All-sky survey map (3/4 keV). Loop I and IV are the big and small dashed loops, respectively. North Polar Spur is the bright structure that starts at around $l=30^{\circ}$ near the Galactic plane and extends (nearly) perpendicular to above $b=60^{\circ}$. We label the direction of 3C~273, as well as two other AGNs, Mkn~421 and PKS~2155-304 with cross. The two red dots near the 3C~273 sightline are the {\sl XMM}-Newton pointings that we used for X-ray emission line analysis. The cyan circles are features identified in the {\sl Fermi}-LAT 1 -- 5 GeV data. These features include a giant bubble in the center, the northern arc (the two lines made up of cyan circles right next to the bubble) that extends up to $b\sim50^{\circ}$ and coincides with NPS, and a giant loop-shape structure that aligns with the radio Loop I and IV.} \vskip0.4cm \label{f1} \end{figure*} The sightline toward 3C~273 passes through part of the sky that is enriched with supernova (SN) activities (see the next section for details). Furthermore, since the early work of \citet{yao2007a}, two giant gamma-ray bubbles (``Fermi bubbles", see \citealp{su2010}) were discovered in the Galactic center, and the 3C~273 sightline passes through the edge of the northern bubble. Also, new data from both X-ray emission and absorption observations along this sightline were collected. Our goal of this paper is therefore to investigate the role of the Galactic structures along the 3C~273 sightline by making use of the latest data. Our paper is organized as follows. In section \S2 we give a detailed description of the Galactic structures along the 3C~273 sightline. We perform the {\sl Chandra} data reduction and analysis in section \S3. In section \S4 we discuss the implication of our results by combining the results from the X-ray absorption observations with those from UV and X-ray emission observations. Last section is summary and discussion. | In this paper, we have analyzed the {\sl Chandra} and {\sl XMM}-Newton grating observations of 3C~273, one of the brightest extragalactic X-ray sources, with a focus on the X-ray absorption lines produced by highly ionized metal species at $z=0$. We summarize our finding below. Using high resolution X-ray spectroscopy we measured the physical properties of the X-ray absorber along the 3C~273 sightline. Our measured line properties are largely consistent with previous work of \citet{yao2007a} based on a subset of the data used in this paper, while better photon statistics allows us to put much tighter constraints. The column density ratios between \ion{O}{7}, \ion{O}{8}, and \ion{Ne}{9} suggested a temperature of $(1.5 - 1.8) \times10^6$ K of the X-ray absorbing gas. This gas is either in collisional ionization equilibrium, or cooling at constant density or constant pressure. A joint analysis with the X-ray emission data suggests that the X-ray absorber likely has a density of $(1.2 - 1.8) \times 10^{-3}\rm\ cm^{-3}$, with a linear size of $\sim$ 5 to 15 kpc. We compare the 3C 273 sightline with the sightlines of Mkn~421 and PKS~2155-304, which have similar or even better quality X-ray spectra. We find the line $EW$s of the 3C~273 are significantly higher than the other two sightlines. In particular, we find the large $EW$s are the result of higher Doppler-$b$ parameter, rather than large column density. While the Doppler-$b$ parameters of the X-ray absorbers detected in the Mkn~421 and PKS~2155-304 sightlines can be naturally explained by thermal broadening, a significant non-thermal component of $b_{nt} \sim 100 - 150\rm\ km\ s^{-1}$ is presented in the 3C~273 X-ray absorber. Such non-thermal velocity has been suggested before as an evidence of an outflow, possibly produced by stellar wind and supernova activities in the Galactic center and the bulge region \citep{yao2007a}. Large scale, bi-polar outflow was also proposed based on {\sl ROSAT} and other observations (see, \citealp{sofue2000, bland-hawthorn2003}). We suggest here an alternative that the non-thermal velocity we detected in the 3C~273 sightline can be naturally explained as the expansion of the newly discovered ``Fermi bubble", with a shock velocity of $\sim 200 - 300\rm\ km\ s^{-1}$. The derived expansion velocity is much less than predictions from recent theoretical modeling (see, \citealp{guo2012, yang2013}), as suggested by \citet{kataoka2013}. | 14 | 3 | 1403.2028 |
1403 | 1403.2502_arXiv.txt | The effect of the vector interaction on three flavor magnetized matter is studied within the SU(3) Nambu--Jona-Lasiono quark model. We have considered cold matter under a static external magnetic field within two different models for the vector interaction in order to investigate how the form of the vector interaction and the intensity of the magnetic field affect the equation of state as well as the strangeness content. It was shown that the flavor independent vector interaction predicts a smaller strangeness content and, therefore, harder equations of state. On the other hand, the flavor dependent vector interaction favors larger strangeness content the larger the vector coupling. We have confirmed that at low densities the magnetic field and the vector interaction have opposite competing effects: the first one softens the equation of state while the second hardens it. Quark stars and hybrid stars subject to an external magnetic field were also studied. Larger star masses are obtained for the flavor independent vector interaction. Hybrid stars may bare a core containing deconfined quarks if neither the vector interaction nor the magnetic field are too strong. Also, the presence of strong magnetic fields seems to disfavor the existence of a quark core in hybrid stars. | Early investigations performed with the Walecka model for nuclear matter \cite{walecka} show that the inclusion of a vector-isoscalar channel is an essential ingredient for an accurate description of nuclear matter. Later, such a channel has been considered to extend the standard Nambu--Jona-Lasinio model (NJL), which originally included only a scalar and a pseudoscalar type of channels, in order to obtain a saturating chiral theory for nuclear matter described only by fermions \cite {volker}. As discussed in Ref. \cite{ruggieri2009} the introduction of the vector interaction, and thus of the vector excitations, is also important in determining the properties of strongly interacting matter at intermediate densities where vector mesons mediate the interactions and their exchange might be responsible for kaon condensation at high density. Recently, the presence of a vector interaction in the NJL model was crucial to reproduce the measured relative elliptic flow differences between nucleons and anti-nucleons as well as between kaons and antikaons at energies carried out in the Beam-Energy Scan program of the Relativistic Heavy Ion Collider \cite {ko}. Regarding the QCD phase diagram at finite quark density it has been established that the net effect of a repulsive vector contribution is to weaken the first order transition \cite {fuku08}. Indeed, it has been observed that the first order transition region shrinks, forcing the critical end point (CEP) to appear at smaller temperatures, while the first order transition occurs at higher chemical potential values when the vector interaction increases. Since the finite density region of the QCD phase diagram is not yet accessible to lattice simulations one usually employs model approximations to study the associated phase transitions as well as to evaluate the equation of state (EOS) to be used in stellar modeling. One of the most popular models adopted in these investigations is the NJL which, as already referred, can be easily extend to accommodate a vector channel while keeping the original symmetries. At present, despite its importance, the vector term coupling $G_V$ cannot be determined from experiments and lattice QCD simulations, although there have been some attempts to determine its value. For instance, in Ref. \cite{klimt} a vector coupling constant of the order of magnitude of the scalar--pseudoscalar coupling was obtained by fitting the nucleon axial charge or masses of vector mesons and in \cite{hanauske}, the pion mass and the pion decay constant were recalculated as a function of the vector interaction and shown to vary by about 10\% when for $0 < x < 1$, where $x=G_V/G_S$, $G_S$ being the scalar coupling. Eventually, the combination of neutron star observations and the energy scan of the phase-transition signals at FAIR/NICA may provide us some hints on the precise numerical value. Meanwhile, $G_V$ has been taken as a free parameter in most works. Finally, note that this channel interaction can be generated by higher order (exchange type of contributions) which are present in approximations which go beyond the large-$N_c$ limit like the the nonperturbative Optimized Perturbation Theory (OPT) \cite {prcopt}. The fact that a strong enough vector term may turn the first order phase transition, which is expected at the low temperature part of the QCD phase diagram, into a smooth cross over (for the realistic case of quarks with finite current masses) may also have astrophysical implications affecting the structure of the compact stellar objects. In Ref. \cite{hanauske} a variable vector coupling was used in the discussion of the possible properties of quark stars and the authors have shown that depending on the value of the vector coupling the star could either be self-bound and present a finite density at the surface or bear a very small density at the surface, behaving as a standard (hadronic) neutron star. The maximum stellar mass obtained, $M=1.6\, M_\odot$, corresponds to the largest vector coupling considered, $x=1$, i.e., $G_V=G_S$. After these seminal works, a repulsive vector term was also used in many other investigations involving hybrid stars and possible phase transitions to a quark phase \cite{pagliara}. Recently, the importance of the vector interaction in describing massive stars has also been extensively discussed \cite{bonanno,lenzi2012,logoteta,shao2013,sasaki2013,masuda2013}. Another timely important problem concerns the investigation of the effects produced by a magnetic field $B$ on the QCD phase diagram and also on the EOS used to model neutron stars. The motivation stems from the fact that strong magnetic fields may be produced in non central heavy ion collisions \cite {kharzeev09,tuchin}, as well as being present in magnetars \cite {magnetars}. Regarding stellar matter the low temperature part of the QCD phase diagram, where a first order (chiral) phase transition is expected to occur \cite {scavenius, prcopt}, constitutes the relevant region to be investigated. The question of how this region is affected by magnetic fields has been addressed in Refs. \cite {prd} and \cite{pedro2013} in the framework of the three flavor NJL and PNJL models respectively. One of the main results of Ref. \cite {prd} shows that in this regime the symmetry broken phase tends to shrink with increasing values of $B$. At these low temperatures, the chemical potential value associated with the first order transition decreases with increasing magnetic fields, effect known as the inverse magnetic catalysis phenomenon (IMC). This result has been previously observed with the two flavor NJL, in the chiral limit \cite {inagaki}, as well as with a holographic one-flavor model \cite {andreas} and more recently with the planar Gross-Neveu model \cite {novo}. A model-independent physical explanation for IMC is given in Ref. \cite {andreas} while a recent review with new analytical results for the NJL can be found in Ref. \cite {imc}. Another interesting result obtained in Ref. \cite {prd} concerns the size of the first order segment of the transition line which expands with increasing $B$ in such a way that the critical point becomes located at higher temperature and smaller chemical potential values. Note that, depending on the adopted parametrization, this region can display a rather complex pattern with multiple weak first order transitions taking place \cite {norberto}. Concerning the low temperature portion of the phase diagram one notices that so far most applications have considered effective models with scalar and pseudoscalar channels only. However, as already pointed out, the presence of a vector interaction can be an important ingredient to reproduce some experimental results or compact star observations, and so, should also be taken into account in the computation of the EOS for magnetized quark matter. A step towards this type of investigation has been recently taken in Ref. \cite {robson} where two flavor magnetized quark matter in the presence of a repulsive vector coupling, described by the NJL model, has been considered. The results show that the vector interaction counterbalances the effects produced by a strong magnetic field. For instance, in the absence of the vector interaction, high magnetic fields ($eB \ge 0.2 \, {\rm GeV}^2$) increase the first order transition region. On the other hand a decrease of this region is observed for a strong vector interaction and vanishing magnetic fields. Also, at low temperatures and $G_V=0$, the coexistence chemical potential decreases with an increase of the magnetic field (IMC) \cite{prd}, however, the inclusion of a the vector interaction results in the opposite effect. The presence of a magnetic field together with a repulsive vector interaction gives rise to a peculiar transition pattern since $B$ favors the appearance of multiple solutions to the gap equation whereas the vector interaction turns some metastable solutions into stable ones allowing for a cascade of transitions to occur \cite {robson}. The most important effects take place at intermediate and low temperatures affecting the location of the critical end point as well as the region of first order chiral transitions. More realistic physical applications require that one considers more sophisticated versions of the simple two flavor model considered in Ref. \cite {robson}. Strangeness is a necessary ingredient when describing the structure of compact stellar objects or the QCD phase diagram. Therefore, the purpose of the present work is to study magnetized strange quark matter in the presence of a repulsive vector interaction. We are also interested in understanding the properties of strongly interacting matter described by two different vector interactions \cite{klimt,hanauske} and \cite{fuku08} and two commonly used parametrizations of the NJL model \cite{hatsuda,reh}. In the following we refer to the extended version of the NJL model that incorporates a vector interaction as NJLv model. We first evaluate the similarities and differences at zero temperature of pure quark matter obtained with the two models by investigating the behavior of the constituent quark masses and the related EOS for two different physical situations, namely matter with the same quark chemical potentials and the same quark densities. Once the underlying physics is understood, we move to stellar matter conditions. Having in mind two recently $2M_\odot$ pulsars measured PSR J1614-2230 \cite{Demorest10}, $1.97\pm 0.04\, M_\odot$, and PSR J0348+0432 \cite{j0348}, $2.01\pm 0.04\, M_\odot$, we discuss which form of the vector interaction results in higher compact star masses. We devote special attention to the zero temperature part of the phase diagram which is currently not accessible to lattice simulations and which constitutes the important region as far as the physics of compact stars is concerned. We do not consider the color superconducting phase in the interior of hybrid stars, which would make the equation of state softer. Our conclusions on the maximum star masses should, therefore, be regarded as upper limits. | We next analyze two different physical situations: pure quark matter, of interest in the studies of the QCD phase diagram, and stellar matter applied to investigate possible quark and hybrid stars. \subsection{Pure quark matter} In the present section we discuss two distinct physical situations: quark matter defined by equal chemical potentials for three flavors $u,\, d, \, s$ and for equal quark densities. We discuss the effect of the vector interaction on the EOS and strangeness fraction. In particular, we take $G_V=x G_S$, where $x$ is a free parameter which we vary such that $0 < x < 1$, as proposed in \cite{hanauske}. We present results for both possible forms of the vector interaction discussed in the previous section, which are designated by P1 and P2, respectively, the flavor dependent/independent form. We also compare two popular parametrizations of the SU(3) NJL model designated by HK \cite{hatsuda} and RKH \cite{reh}. \begin{figure}[ht] \begin{tabular}{cc} \includegraphics[width=1\linewidth,angle=0]{1a.eps}\\ \includegraphics[width=1\linewidth,angle=0]{1b.eps} \end{tabular} \caption{The pressure versus baryonic density for model 1 (P1) and 2 (P2) for different values of $x$ and parametrization RKH, under the conditions a) $\mu_u=\mu_d=\mu_s$, b) $\rho_u=\rho_d=\rho_s$ (thick lines) and $\mu_u=\mu_d=\mu_s$ (thin lines).} \label{fig1} \end{figure} The effect on the EOS of the different forms for the vector interaction is seen in Fig. \ref{fig1}a), where the parametrization RKH is used with different strengths of the vector interaction, for both P1 and P2 under the equal chemical potentials constraint. Several conclusions are in order: a) the models coincide until $\sim 3-4\rho_0$, where $\rho_0=0.17$ fm$^{-3}$ is the nuclear matter saturation density, depending on the magnitude of $x$. The larger $x$ the earlier the two models differ. This is due to the onset of the strangeness that occurs at smaller densities with form P1 as is shown latter; b) once the strangeness sets on the EOS becomes softer, therefore, for large enough densities P1 is softer than P2; c) the pressure is negative for some values of $G_V$, including $G_V=0$, a feature observed and discussed in \cite{hanauske}, with consequences on possible coexisting phases and associated phase transition; d) for a large enough $G_V$ the first order phase transition observed for densities below 2$\rho_0$ disappears, and the pressure increases monotonically with the baryonic density. For the parametrization RKH this occurs for $x=0.71$ and is represented by the pink curves in the figure. In Fig. \ref{fig1}b), we compare two different scenarios, $\mu_u=\mu_d=\mu_s$ and $\rho_u=\rho_d=\rho_s$ represented, respectively, by the thin and thick lines. The equal flavor densities, corresponding to matter generally designated by strange quark matter, is softer, gives rise to a larger density discontinuity at the first order phase transition. In this scenario the EOS for models P1 and P2 differ for all baryonic densities because the vector interaction form given in Eq. (\ref{p2}) results in different contributions in each case. This scenario may be approximately realized at the center of a quark star. \begin{figure*}[ht] \begin{tabular}{cc} \includegraphics[width=0.75\linewidth,angle=0]{2.eps}\\ \end{tabular} \caption{Pressure versus baryonic density for equal chemical potentials and models P1 and P2 for different values of x, and several intensities of the magnetic field: $eB=0$, $eB=0.1$ GeV$^2$, $eB=0.3$ GeV$^2$ and $eB=0.6$ GeV$^2$.} \label{fig2} \end{figure*} The effect of the magnetic field on the EOS is seen comparing the four graphs of Fig. \ref{fig2}. We first discuss the scenario $\mu_u=\mu_d=\mu_s$. We have chosen three values of $eB$, 0.1, 0.3 and 0.6 GeV$^2$ corresponding to $5m_\pi^2$, $15m_\pi^2$ and $30 m_\pi^2$. The van-Alphen oscillations due to the filling of the Landau levels are already seen for $eB=0.1$ GeV$^2$. The EOS becomes harder at large densities, and the larger $eB$ the harder the EOS, although locally, when the filling of a new Landau level begins, the EOS becomes softer. This increased softness is immediately overtaken by an extra hardness. The larger $B$ the larger the amplitude of the fluctuations and the smaller the number of them, because less Landau levels are involved. The softening occurring when a new Landau level starts being occupied has a strong effect at the smaller densities giving rise to a pressure that is negative within a larger range of densities. For $eB=0.3$ GeV$^2$, a magnetic field that could occur at LHC experiments, negative pressures occur beyond $\rho_B=0.5$ fm$^{-3}$ and this range increases until $\sim 1-1.5$fm$^{-3}$ for $eB=0.6$ GeV$^2$. The vector interaction P2 gives always the hardest EOS due to the smaller strangeness content. \begin{figure}[th] \begin{tabular}{cc} \includegraphics[width=0.8\linewidth,angle=0]{3.eps} \end{tabular} \caption{Pressure versus baryonic density for model 2 (P2) for different values of $x$. Two parametrizations of the NJL are compared HK and RKH with magnetic field intensities: a) $eB=0$; b) $eB=0.3$ GeV$^2$.} \label{fig3} \end{figure} In Fig. \ref{fig3} the EOS obtained with interaction P2 and the two different parametrizations of the NJL model are compared for $eB$=0 and 0.3 GeV$^2$. For $G_V=0$ the EOS obtained with the HK parametrization does not cross the RKH EOS. This is no longer valid for a finite $G_V$. The RKH EOS becomes stiffer and the two EOS cross within the range of densities shown in the figure. This feature is still present for a finite magnetic field (see Fig. \ref{fig3}b). \begin{figure}[ht] \begin{tabular}{cc} \includegraphics[width=0.8\linewidth,angle=0]{4.eps} \end{tabular} \caption{Pressure versus baryonic density for models P1 and P2 for equal quark densities, different values of $x$ for: a) $eB=0$; b) $eB=0.6$ GeV$^2$.} \label{fig4} \end{figure} Now we move to the scenario of equal flavor densities. The EOS are plotted in Fig. \ref{fig4} for $eB=0$ and $0.6$ GeV$^2$. As already referred before, this scenario is softer than the equal chemical potentials one for the range of densities shown. However, at sufficiently large densities both scenarios converge. In fact, above chiral symmetry restoration it is expected that equal chemical potentials correspond to equal densities. The effect of a strong magnetic field is very different in both scenarios: while the equal chemical potentials EOS presents very strong oscillations, these are not seen for the scenario of equal densities. In the equal chemical potentials the $s$-quark density remains zero until a quite high baryonic density, and, therefore, for a given density below the strangeness onset the $u$ and $d$-quark densities are much larger than in the equal quark densities. Larger $u$ and $d$ quark densities give rise to the restoration of chiral symmetry at lower baryonic densities. Since the effect of the magnetic field is stronger the smaller the masses, this explains the differences in the bottom graphs of Fig. \ref{fig4} between the two scenarios. \begin{figure*}[ht] \begin{tabular}{cc} \includegraphics[width=0.75\linewidth,angle=0]{5.eps} \end{tabular} \caption{The quark constituent masses as a function of the baryonic density for models P1 and P2, different values of $x$ for $eB=0$ (top figures) and $eB=0.3$ GeV$^2$ (bottom figures).} \label{fig5} \end{figure*} The difference between the chiral symmetry restoration in the two scenarios presented above is clearly seen in Fig. \ref{fig5}, where the constituent masses of the $u$, $d$, and $s$ quarks are plotted for different strengths of the vector interaction and the two models P1 and P2. We first comment on the $eB=0$ results and the two vector interactions, top panels of Fig. \ref{fig5}. The chiral restoration of $u$ and $d$ quarks does not depend on the interaction. However, a difference is observed between the equal chemical potentials and equal densities scenarios. In the scenario of equal densities (gray lines), one can see that the chiral symmetry restoration of the $u$ and $d$ quarks occurs at larger densities than in the situation with equal chemical potentials (red lines) because the $u$ and $d$ quark densities are larger in the last situation. For the $s$ quark, the opposite occurs. Including the vector interaction does not affect the quark masses in model P2, but it does affect the $s$ quark mass in model P1. In this case the larger $G_V$ the faster the chiral restoration of the $s$-quark mass, due to the larger $s$-quark density. At finite $B$ similar conclusions are drawn, but also new aspects arise. First of all the constituent masses of $u$ and $d$ quarks do not coincide anymore due to the charge difference. Since the $u$ quark has a larger charge, $M_u>M_d$ in the scenario of equal densities. In the scenario of equal chemical potentials there is a competition between the effect of the charge and the effect of density. For the larger magnetic field considered discontinuities are obtained. These correspond to first order phase transitions associated to the filling of the Landau levels. The above results on the constituent quark masses confirm that the large oscillations of the EOS seen in Fig. \ref{fig4}b) for the equal chemical potentials is in fact due to the small masses of the $u$ and $d$ quarks. \begin{figure}[ht] \begin{tabular}{cc} \includegraphics[width=0.8\linewidth,angle=0]{6.eps} \end{tabular} \caption{The strangeness fraction as a function of the baryonic density for models P1 and P2 and different values of $G_V$, and a) $B=0$; b) $eB=0.3$ GeV$^2$. } \label{fig6} \end{figure} It is interesting to compare the strangeness content of matter under the conditions discussed until this point. We next analyze once more the situation of equal chemical potentials. In Fig. \ref{fig6} the strange quark fraction for P1 and P2 models, three values of $G_V$, and $eB=0$ and 0.3 GeV$^2$ are displayed. We also report results for the parametrizations RKH (thick) and HK (thin). One aspect that is immediately observed is that the P2 model presents the least amount of strange quarks, and its content does not depend on $G_V$, both for zero and a finite magnetic field. However, the P1 model does affect the strange quark content and the larger $G_V$ the earlier is the onset of the $s$-quark, and the larger its content. One should notice that the definition of the effective chemical potentials in equations (\ref{mup1}) and (\ref{mup2}) is directly reflected on the strangeness content. The magnetic field does not erase this feature. Nevertheless, the filling of new Landau levels decreases the rate of the increase of the $s$-quark content as observed in Fig. \ref{fig6}b). Parametrizations RKH and HK behave in a similar way with RKH predicting an onset of $s$-quarks at smaller densities, and a larger amount of strangeness for a given baryonic density. \subsection{Stellar matter: quark stars} We next move to the study of stellar matter, i.e., matter where $\beta$-equilibrium and charge neutrality are enforced. In this case, leptons are introduced in the system, so that equations \begin{equation} \mu_s=\mu_d=\mu_u+\mu_e, \qquad \mu_e=\mu_\mu. \label{qch} \end{equation} and \begin{equation} \rho_e+\rho_\mu=\frac{1}{3}(2\rho_u-\rho_d-\rho_s). \label{chneutrality} \end{equation} are satisfied. \begin{figure}[t] \includegraphics[width=0.8\linewidth,angle=0]{7.eps} \caption{The pressure versus energy density (EOS) for model P1 (thin lines) and P2 (thick lines) for different values of $G_V$ and a) $B=0$; b) $B=10^{18}$ and $10^{19}$ G. Both figures were obtained for the parametrization RKH.} \label{figs1} \end{figure} Since, to date, there is no information available on the star interior magnetic field, we assume that the magnetic field is baryon density-dependent as suggested in \cite{chakra97}. In the following we consider a magnetic field that increases with density according to \begin{equation} B=B_{surf} +B_0(1-\exp[-\beta {(\rho/\rho_0)}^\gamma]), \quad \beta=0.02,\, \gamma=3, \label{mag} \end{equation} $B_{surf}=10^{15}$ G is the magnetic field at the surface of the star. As our aim in this section is to compare results with astrophysical observations, the use of magnetic fields in Gauss units is more adequate. We have considered that $eB=1$ GeV$^2$ corresponds to $B=1.685 \times 10^{20}$ G. In the following we start by investigating the effects of the vector interaction in stellar matter applied do quark stars and subsequently we choose the best possible model and parameter set to build hybrid stars and look at their macroscopic properties. \begin{figure}[ht] \begin{tabular}{cc} \includegraphics[width=0.8\linewidth,angle=0]{8.eps} \end{tabular} \caption{EOS for model 2 (P2) for different values of $G_V$, and a) $B=3.1 \times B=10^{18}$ G obtained with parametrizations HK and RKH and b) two intensities of the magnetic field: $B=10^{17}$ G and $B=3.1 \times 10^{18}$ G for parameter set HK.} \label{figs3} \end{figure} Once again, we start from the non-magnetized case and check the differences arising from both models with the RKH parameter set and different values of $G_V$ in Fig. \ref{figs1}. The same conclusions reached from the pure quark matter case can be drawn here, mainly that P2 gives rise to a harder EOS and that at very low energy densities, the pressure becomes slightly negative. This difference can be easily understood if one looks at Eqs. (\ref{pressp1}) and (\ref{pressp2}), from where it is seen that the contribution from the vector term to the pressure is larger in model P2 because in this case it is flavor blind. The effect of the magnetic field on the quark matter is stronger for the large densities when the magnetic field is more intense due to the density dependence we have considered, see Eq. (\ref{mag}), and much larger when we consider $B_0=10^{19}$ G. The fluctuations arising due to the filling of new Landau levels seem larger and more frequent for the smaller vector coupling on an energy density versus pressure curve. This arises because for a stronger vector term a larger energy density is obtained for the same density, and therefore, the fluctuations are spread over a larger energy density range. We then reobtain the EOS for the cases where $B=10^{17}$ and $3.1 \times 10^{18}$ G. These values were chosen as the limiting ones because below $B=10^{17}$ G, all EOS coincide with the non-magnetized case and $3.1 \times 10^{18}$ G is the maximum value that allows us to avoid anisotropic pressures \cite{veronica}. This is also the maximum intensity supported by a star bound by the gravitational interaction before the star becomes unstable \cite{lai91}. However, as we are using a density dependent magnetic field, this value may be never reached in the star core. In Fig.\ref{figs3}a), we compare both parametrizations for a fixed magnetic field equal to $3.1 \times 10^{18}$ G and different values of $G_V$. We can observe that HK yields harder EOS than RKH. The van Alphen oscillations are noticeable for this field intensity. The feature of HK and RKH EOS crossing with the increase of the vector interaction, observed when pure quark matter is analyzed, occurs at energy densities larger than the ones shown in the figure. In Fig. \ref{figs3}b), we fix the HK parametrization and plot the EOS for the two intensities of the magnetic field mentioned above. It is interesting to observe that at large densities an EOS obtained with a smaller magnetic field becomes harder for certain values of $G_V$ than an EOS obtained with a much stronger magnetic field and a smaller value of $G_V$. \begin{figure}[ht] \begin{tabular}{cc} \includegraphics[width=0.8\linewidth,angle=0]{9.eps} \end{tabular} \caption{Strangeness fraction as a function of the baryonic density for $B=0$, parameter sets HK and RKH a) for models 1 (P1) and 2 (P2) and different values of $x$ and b) model 2 (P2) for different values of $x$ with $B=3.1 \times 10^{18}$ G.} \label{figs2} \end{figure} \begin{table*} \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{3}{ |c| }{} &\multicolumn{3}{ |c| }{HK}&\multicolumn{3}{ |c| }{RKH} \\ \hline \multicolumn{3}{ |c| }{} & $x=0.1$ & $x=0.3$ & $x=0.6$ & $x=0.1$ & $x=0.3$ & $x=0.6$ \\ \hline $B=0$~G & P1 & $M_{max}$ ($M_{0}$) & 1.49 & 1.58 & 1.69 & 1.27 & 1.35 & 1.46 \\ \cline{3-9} & & R (km) & 9.13 & 10.89 & 11.98 & 8.01 & 8.17 & 9.41 \\ \cline{3-9} & & $\varepsilon_{c}$ ($\mathrm{fm}^{-4}$) & 7.23 & 6.96 & 6.52 & 9.42 & 9.61 & 9.84 \\ \cline{3-9} \cline{2-9} & P2 & $M_{max}$ ($M_{0}$) & 1.56 & 1.72 & 1.91 & 1.35 & 1.54 & 1.74 \\ \cline{3-9} & & R (km) & 9.15 & 10.61 & 11.47 & 8.22 & 8.60 & 9.91 \\ \cline{3-9} & & $\varepsilon_{c}$ ($\mathrm{fm}^{-4}$) & 7.35 & 7.37 & 6.92 & 8.71 & 8.58 & 8.09 \\ \cline{3-9} \hline \hline \multicolumn{2}{ |c| }{$B=10^{17}$~G} & $M_{max}$ ($M_{0}$) & 1.56 & 1.72 & 1.91 & 1.35 & 1.54 & 1.74 \\ \cline{3-9} \multicolumn{2}{ |c| }{P2} & R (km) & 9.16 & 10.16 & 10.95 & 8.21 & 8.58 & 9.60 \\ \cline{3-9} \multicolumn{2}{ |c| }{} & $\varepsilon_{c}$ ($\mathrm{fm}^{-4}$) & 7.41 & 7.36 & 6.98 & 8.80 & 8.94 & 8.11 \\ \cline{3-9} \hline \hline \multicolumn{2}{ |c| }{$B=3.1\times10^{18}$~G} & $M_{max}$ ($M_{0}$) & 1.96 & 2.03 & 2.12 & 1.81 & 1.88 & 1.98 \\ \cline{3-9} \multicolumn{2}{ |c| }{P2} & R (km) & 9.98 & 10.43 & 11.05 & 9.03 & 9.21 & 9.90 \\ \cline{3-9} \multicolumn{2}{ |c| }{} & $\varepsilon_{c}$ ($\mathrm{fm}^{-4}$) & 7.41 & 7.22 & 6.78 & 8.74 & 8.21 & 7.80 \\ \cline{3-9} \hline \end{tabular} \caption{Stellar macroscopic properties obtained from EOS of non-magnetized matter for models P1 and P2 and for magnetized matter with model P2 and two values of magnetic field intensities. $M_{max}$ is the maximum mass, R is the star radius and $\varepsilon$ the star central energy density.} \label{table1} \end{table*} We proceed to the analysis of the strangeness content for non-magnetized matter, whose curves are depicted in Fig. \ref{figs2}a). As in the case of pure quark matter, the amount of strange quarks remains unchanged with any variation of $G_V$ with model P2 while it increases with the increase of $G_V$ if model P1 is used. RKH presents higher strangeness content than HK with consequences in the maximum stellar masses, as we show next. For the sake of completeness, we show the strangeness fraction for $B=3.1 \times 10^{18}$ G and the two parameter sets discussed in the present work in Fig. \ref{figs2}b) for the strangeness blind vector interaction P2. As already expected from the softness of the EOS, we see that HK introduces a smaller strangeness content in the system and if we compare the values obtained with different values of the magnetic field ranging from $B=10^{17}$ G to $B=3.1 \times 10^{18}$ G, we can see that the amount of strange quarks remains practically unaltered for both parameter sets. \begin{figure}[ht] \begin{tabular}{cc} \includegraphics[width=0.8\linewidth,angle=0]{10.eps} \end{tabular} \caption{Mass radius curves obtained with model 2 (P2) for different values of $G_V$, two intensities of the magnetic field ($B=10^{17}$ G and $B=3.1 \times 10^{18}$ G) and parametrizations a) HK and b) RKH.} \label{figs4} \end{figure} Finally, we use the EOS discussed above as input to the Tolman-Oppenheimer-Volkoff equations \cite{tov} and show our results in Fig. \ref{figs4} and Table \ref{table1}. A general trend is that HK, being harder with less strange quarks, produces higher maximum masses. A not so common feature is that for some combination of $G_V$ values and magnetic field intensities, the quark stars behave as hadronic stars in the sense that the densities attained at low pressure are indeed very small. This is seen in Fig.~\ref{figs4} in all cases where the low mass stars have very large radii. This feature has already been observed in Ref.\cite{hanauske} for non-magnetized stars and it is related to the existence/non existence of negative pressures at very low densities for small/large values of the vector interaction coupling. We see that the maximum masses obtained with zero and low magnetic field intensities ($B=10^{17}$ G) are always coincident, but the radii are slightly different due to the small differences in the central energy densities. Within RKH the most massive neutron stars have less $\sim 0.2\, M_\odot$ than if the HK parametrization is used. HK can reach quite high maximum mass values, of the order of 2 $M_\odot$, for either large values of the vector interaction even with low or zero magnetic fields or for high magnetic fields and any value of the vector interaction. Concerning the radii, some comments are in order: in \cite{Hebeler}, the radii of the canonical $1.4\,M_\odot$ neutron star was estimated to lie in the range 9.7-13.9 Km. More recently, there was a prediction that they should lie in the range $R=9.1^{+1,3}_{-1.5}$ Km \cite{guillot} and another one stating that the range should be $10-13.1$ Km~\cite{Lattimer2013}. From Fig. \ref{figs4}, one can see that there is a window of values for $G_V$ and $B$ which result in radii accepted by any of the above mentioned analyzes. \begin{figure}[ht] \begin{tabular}{cc} \includegraphics[width=1\linewidth]{11a.eps}\\ \includegraphics[width=1\linewidth]{11b.eps}\\ \end{tabular} \caption{Hybrid star - a) EOS and b) Mass radius curves obtained with model 2 (P2) for different values of $G_V$, two intensities of the magnetic field ( $B=10^{17}$ G and $B=3.1 \times 10^{18}$ G) and parametrization HK.} \label{figs5} \end{figure} \subsection{Stellar matter: hybrid stars} To make our analysis of the vector interaction as broad as possible, we dedicate this subsection to revisit the case of hybrid stars under the influence of strong magnetic fields. We study the structure of hybrid stars based on the Maxwell condition (without a mixed phase), where the hadron phase is described by the GM1 \cite{GM1} parametrization of the non-linear Walecka model \cite{Serot} and the quark phase by the NJL model with the inclusion of the vector interaction as discussed in the previous subsection. As stated in the Introduction, hybrid stars have already been extensively discussed for the non-magnetized case \cite{pagliara,bonanno,lenzi2012,logoteta,shao2013, sasaki2013,masuda2013}. For the possible existence of magnetars that can be described by hybrid stars, the reader can refer to \cite{panda} and \cite{hybrid} and we refrain from writing the mathematical expressions here. \begin{table*}[ht] \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{2}{ |c| }{HK} & $M_{max}$ & $M_{b}$ & R & $\varepsilon_{c}$ & $\varepsilon$ (onset) & $\rho_{c}$ & $\rho$ (onset) & $\mu_{B}(\varepsilon_{c})$ & $\mu_{B}$ (onset) \\ \multicolumn{2}{ |c| }{} & ($M_{0}$) & ($M_{0}$) & (km) & ($\mathrm{fm}^{-4}$) & ($\mathrm{fm}^{-4}$) & & & (MeV) & (MeV) \\ \hline $B=10^{17}$~G & $x=0$ & 1.91 & 2.18 & 12.78 & 4.57 & 3.47 & 0.78 & 0.62 & 1360 & 1330 \\ \cline{2-11} P2 & $x=0.10$ & 1.99 & 2.30 & 12.14 & 6.27 & 5.05 & - & 0.84 & - & 1503 \\ \cline{2-11} & $x=0.22$ & 2.00 & 2.31 & 11.82 & 5.93 & 7.79 & 0.95 & 1.18 & 1580 & 1726 \\ \hline $B=3.1\times10^{18}$~G & $x=0$ & 2.27 & 2.60 & 12.82 & 4.69 & 3.30 & 0.70 & 0.54 & 1324 & 1261 \\ \cline{2-11} P2 & $x=0.10$ & 2.35 & 2.70 & 12.34 & 5.29 & 5.59 & 0.74 & 0.78 & 1427 & 1453 \\ \cline{2-11} & $x=0.22$ & 2.35 & 2.70 & 12.35 & 5.27 & 9.03 & 0.74 & 1.18 & 1426 & 1730 \\ \hline \hline \multicolumn{2}{ |c| }{RKH} & $M_{max}$ & $M_{b}$ & R & $\varepsilon_{c}$ & $\varepsilon$ (onset) & $\rho_{c}$ & $\rho$ (onset) & $\mu_{B}(\varepsilon_{c})$ & $\mu_{B}$ (onset) \\ \multicolumn{2}{ |c| }{} & ($M_{0}$) & ($M_{0}$) & (km) & ($\mathrm{fm}^{-4}$) & ($\mathrm{fm}^{-4}$) & & & (MeV) & (MeV) \\ \hline $B=10^{17}$~G & $x=0$ & 1.97 & 2.26 & 12.48 & 4.29 & 4.28 & - & 0.74 & - & 1422 \\ \cline{2-11} P2 & $x=0.10$ & 2.00 & 2.31 & 11.91 & 7.51 & 5.67 & - & 0.92 & - & 1557 \\ \cline{2-11} & $x=0.19$ & 2.00 & 2.31 & 11.83 & 5.91 & 7.83 & 0.95 & 1.18 & 1579 & 1728 \\ \hline $B=3.1\times10^{18}$~G & $x=0$ & 2.33 & 2.69 & 12.79 & 4.69 & 4.19 & - & 0.63 & - & 1335 \\ \cline{2-11} P2 & $x=0.10$ & 2.35 & 2.70 & 12.34 & 5.30 & 6.52 & 0.74 & 0.88 & 1428 & 1531 \\ \cline{2-11} & $x=0.19$ & 2.35 & 2.70 & 12.34 & 5.30 & 9.05 & 0.74 & 1.18 & 1428 & 1731 \\ \hline \end{tabular} \caption{Stellar macroscopic properties obtained from EOS of magnetized hybrid stars built with GM1 and SU(3) NJL with HK and RKH parametrizations. $M_{max}$ is the maximum gravitational mass, $M_{b}$ is the maximum baryonic mass, $R$ is the star radius, $\varepsilon_{c}$ is the star central energy density, $\mu_{B}(\varepsilon_{c})$ is the chemical potential for neutron at $\varepsilon_{c}$ and $\mu_{B}$(onset) is the baryonic chemical potential at the onset of the quark phase. }\label{tableh} \end{table*} In face of the results we have obtained for quark stars, we next choose to construct hybrid stars with the P2 model and both HK and RKH parameter sets because this vector interaction term yields the hardest quark matter EOS. For the hadronic phase, we use the GM1 parametrization \cite{GM1} and hyperon meson coupling constants equal to fractions of those of the nucleons, so that $g_{iH}=X_{iH} g_{iN}$, where the values of $X_{iH}$ are chosen as $X_{\sigma H}=0.700$ and $X_{\omega H}=X_{\rho H}=0.783$ \cite{glen}. This is the same choice as in \cite{hybrid} for the case of hybrid stars with the quark phase described by the NJL model (without the vector interaction). The EOS obtained with a Maxwell construction for magnetic fields equal to $B=10^{17}$ G and $B=3.1 \times 10^{18}$ G are shown in Fig.\ref{figs5}a) for two values of $x$, being $x=0.22$ the maximum possible value for which a hybrid star can be built with parameter set HK. For values larger than 0.22, the quark matter EOS becomes too hard and in a pressure versus baryonic chemical potential, the hadronic and quark EOS no longer cross each other. For an EOS built with GM1 and RKH, the curves are very similar, but the maximum possible value of $x$ for the crossing of the hadronic and the quark EOS is 0.19. Taking into account that NJL does not describe the confinement feature of QCD, we cannot, in fact, fix the low-density normalization of the pressure. In order to account for this uncertainty the authors of \cite{pagliara,lenzi2012,bonanno,logoteta} have included an extra bag pressure that allows the density at which the transition to deconfinement occurs vary. Including this term in such a way that the deconfinement transition occurs at lower densities than the ones obtained in the present study would have allowed us to choose a larger $G_V$ and therefore, a larger maximum mass would be possible. In the present study we renormalize the pressure in such a way that it is zero for zero baryonic density and do not discuss the effect of including an extra bag pressure. In Fig. \ref{figs5}b) the mass radius curves obtained for the HK parametrization from the solution of the TOV equations are displayed. These macroscopic results are also shown in Table \ref{tableh}. In this table we present results for both the HK and RKH parametrizations, three values of the vector couplings, $x= 0,\, 0.1,$ and the maximum possible value of $x$ for each parameter set, and two values of the magnetic field intensity $B=10^{17}$ and $3.1\times 10^{18}$ G. Some of the entrances for the central baryonic density are not indicated because they lie on an intermediate value between the density of the hadronic phase at the quark phase onset and the corresponding density of the quark phase. The only maximum mass configuration that really has a quark core is obtained for $B=10^{17}$ G and $G_V=0$ within the HK parametrization, giving rise to a 1.91 $M_\odot$ star. It is worth pointing out that the largest maximum masses are now obtained, in general, with the parameter set RKH and not HK, the case of quark stars. This is due to the fact that the quark phase sets in at smaller densities for the HK parametrization making the EOS softer. This result had already been obtained in \cite{hybrid,paoli}. One can see that the maximum stellar masses depend very little on the vector interaction strength. For the larger magnetic field considered, the onset of quark matter occurs at a larger density than the central density of the maximum mass hadronic star configuration, for both parametrizations. The same occurs for $B=10^{17}$ G and $G_V=0.22$ ($G_V=0.19$) for the HK (RKH) parameter set. In these cases the properties of the quark phase do not affect the star properties. On the order hand, from Fig. \ref{figs5}b) for $B=10^{17}$ G and $G_V=0.1$, it seems that as soon as the quark phase sets in the star becomes unstable. Nevertheless, if we compare the baryonic density at the centre of the star with the baryonic density at the onset of quarks, we conclude that this maximum mass star could, in principle, contain a quark core. Had we performed a Gibbs construction, the star core would be in a mixed phase. All other stars are ordinary hadronic stars. As an overall conclusion, it may be stated that a star that is subject to a strong magnetic field attains a smaller baryonic density in its centre, and, therefore, the quark phase is not favored. This same conclusion was obtained in \cite{panda} where the quark phase was described within the MIT bag model. Moreover, since the inclusion of a vector interaction makes the quark EOS harder, it is also natural to expect that a quark EOS with a large $G_V$ difficults the occurrence of a quark core. The weak point of the standard NJL model is the fact that it does not include confinement, and, therefore, the normalization considered for the pressure is not well defined. Stars with very high masses are predicted and maximum masses of observed compact stars may set an upper limit for the largest possible magnetic field at the centre of the star, ∼$2 \times 10^{18}$ G for 2$M_\odot$ stars. Of course, had we chosen the P1 model to build the hybrid star, the $x$ value that would allow for a Maxwell construction would certainly be larger than 0.19 or 0.22, depending on the choice of parameters, but the stellar maximum mass would probably be smaller than 2 $M_\odot$. It is worth remembering that all results presented here depend also on the choice of the coupling constants and meson-hyperon parameters for the hadron phase. | 14 | 3 | 1403.2502 |
1403 | 1403.5114_arXiv.txt | { The direct dark matter search experiment CRESST uses scintillating CaWO$_4$ single crystals as targets for possible WIMP scatterings. An intrinsic radioactive contamination of the crystals as low as possible is crucial for the sensitivity of the detectors. In the past CaWO$_4$ crystals operated in CRESST were produced by institutes in Russia and the Ukraine. Since 2011 CaWO$_4$ crystals have also been grown at the crystal laboratory of the Technische Universität München (TUM) to better meet the requirements of CRESST and of the future tonne-scale multi-material experiment EURECA. The radiopurity of the raw materials and of first TUM-grown crystals was measured by ultra-low background $\gamma$-spectrometry. Two TUM-grown crystals were also operated as low-temperature detectors at a test setup in the Gran Sasso underground laboratory. These measurements were used to determine the crystals' intrinsic $\alpha$-activities which were compared to those of crystals produced at other institutes. The total $\alpha$-activities of TUM-grown crystals as low as $1.23\,\pm\,0.06\,\text{mBq/kg}$ were found to be significantly smaller than the activities of crystals grown at other institutes typically ranging between $\sim\,15\,\text{mBq/kg}$ and $\sim \, 35 \, \text{mBq/kg}$.} | \label{sec:introduction} The CRESST (Cryogenic Rare Event Search with Superconducting Thermometers) experiment aims at the direct detection of WIMP\footnote{Weakly Interacting Massive Particle} dark matter using scintillating CaWO$_4$ crystals operated as low-temperature detectors \cite{angloher12}. The EURECA (European Rare Event Calorimeter Array) project \cite{kraus09} is a future tonne-scale multi-material experiment which combines efforts of cryogenic dark matter searches in Europe (CRESST, EDELWEISS\footnote{Exp\'{e}rience pour DEtecter Les WIMPs En Site Souterrain}, ROSEBUD\footnote{Rare Objects SEarch with Bolometers UndergrounD}) and possibly also of SuperCDMS\footnote{Super Cryogenic Dark Matter Search} in the US. \\ Because of the expected low event rate in experiments searching for dark matter it is crucial to achieve an efficient reduction of backgrounds originating from cosmic radiation and natural radioactivity in and around the detectors. Therefore, these experiments have to be located in underground laboratories and require several layers of additional shielding as well as a method of active background discrimination. In CRESST such a background discrimination on an event-by-event basis is achieved by the simultaneous detection of phonons and scintillation light produced in the CaWO$_4$ target crystals by a particle interaction \cite{angloher12, meunier99}. Compared to electron recoils (e$^-$/$\gamma$-events) $\alpha$-events produce only $\sim$~22\,\% of light \cite{angloher12}, nuclear recoils (n, WIMPs) even less (between $\sim 2$\,\% for W and $\sim 11$\,\% for O \cite{strauss14}) which leads to different bands of event classes in the light energy - phonon energy plane (see, e.g., \cite{TungstenAlpha}). WIMP scatterings are expected in the nuclear recoil bands below 40\,keV \cite{angloher12}. \\ In the past the CaWO$_4$ crystals used in CRESST were provided by different institutes in Russia and the Ukraine (commercial crystals). Since recently, CaWO$_4$ crystals are also produced within the collaboration using a dedicated Czochralski furnace at the crystal laboratory of the Technische Universit\"{a}t M\"{u}nchen (TUM) \cite{erb13}. The aim of this effort was to have direct influence on the selection of the raw materials, the crystal growth and the after-growth treatment in order to improve radiopurity and scintillation properties as, e.g., the light output of the crystals. Both - a lower radioactive contamination as well as a higher light output - increase the sensitivity of the detectors for WIMP detection. \\ In this work we have investigated the radioactive contamination of the raw materials used for crystal growth at the TUM (CaCO$_3$ and WO$_3$ powders as well as CaWO$_4$ powder produced from them) and of first crystals grown from these powders using ultra-low background $\gamma$-spectrometry. Furthermore, two CaWO$_4$ crystals grown at the TUM were operated as low-temperature detectors. With these measurements the radiopurity of the crystals could be investigated by using intrinsic $\alpha$-decays, of which each single decay is observed, for an absolute $\alpha$-activity determination. As these events are located in the MeV range of the $\alpha$-band they are clearly separated from all other event types, especially from the region of interest for dark matter search \cite{angloher12}. However, several $\alpha$-decays are correlated to the important background of low-energy $\beta$-decays and $\gamma$-emissions (in the keV range) in the same decay chains. An example is the isotope $^{227}$Ac with Q$_{\beta}$=44.8\,keV and excited states of 24.5\,keV and 9.3\,keV. Its activity can be calculated from the $\alpha$-emitters $^{227}$Th and $^{223}$Ra that are in equilibrium with $^{227}$Ac. The results of $\alpha$-activities of the two TUM-grown crystals are compared to those of commercial crystals using data from the previous CRESST run concluded in 2011 \cite{angloher12}. | \label{sec:conclusion} We have investigated the radiopurity of several CaWO$_4$ crystals grown by the TUM as well as by other institutes and of the raw materials used for the production of TUM crystals. Measurements with HPGe detectors have shown that in two samples of the CaCO$_3$ powders used for crystal growth a contamination with $^{226}$Ra of $\sim25\,\text{mBq/kg}$ and $\sim60\,\text{mBq/kg}$ depending on the supplier of the raw material is present. It was further shown that Ra is rejected during crystal growth and accumulated in the melt with an estimated segregation coefficient of $s_{\text{Ra}}<0.12$ (90\%~CL). Such a behavior was also observed for Th. This offers the possibility to improve the radiopurity of the crystals in a reproducible way by using only a fresh melt for crystal growth as well as by multiple crystallization steps \cite{danevich11}. \\ The total $\alpha$-activities of TUM-grown crystals as low as $1.23\,\pm\,0.06\,\text{mBq/kg}$ were found to be significantly smaller than the activities of crystals from other institutes ranging between $3.05\,\pm\,0.02\,\text{mBq/kg}$ and $107.13\,\pm\,0.14\,\text{mBq/kg}$. Generally, $\alpha$-decays can easily be identified and due to their high energies are not a background for dark matter search. However, several of them are correlated to low-energy $\beta$-decays and $\gamma$-emissions (in the same decay chains). Such intrinsic contaminations of the crystal including, e.g., the isotope $^{227}$Ac belong to the dominating backgrounds for dark matter search. The reduction of such backgrounds has direct impact on the sensitivity of CRESST for dark matter search and is, thus, of crucial importance. A quantitative study is currently under investigation. \\ A cross-check of activities determined by $\gamma$-spectrometry and by analysis of $\alpha$-decays in low-temperature detectors is planned for the future. Several of the crystals produced at the TUM are now installed in CRESST which has started a new dark matter run in summer 2013. This will also allow a more precise determination of the crystals' intrinsic $\alpha$-activities. In addition, the investigation of the contamination with $\beta$-decaying isotopes will help to further improve the radiopurity of the crystals. | 14 | 3 | 1403.5114 |
1403 | 1403.2391_arXiv.txt | An understanding of cosmic magnetism requires converting the polarization properties of extragalactic radio sources into the rest-frame in which the corresponding polarized emission or Faraday rotation is produced. Motivated by this requirement, we present a catalog of multiwavelength linear polarization and total intensity radio data for polarized sources from the NRAO VLA Sky Survey (NVSS). We cross-match these sources with a number of complementary measurements -- combining data from major radio polarization and total intensity surveys such as AT20G, B3-VLA, GB6, NORTH6CM, Texas, and WENSS, together with other polarization data published over the last 50 years. For 951 sources, we present spectral energy distributions (SEDs) in both fractional polarization and total intensity, each containing between 3 and 56 independent measurements from 400~MHz to 100~GHz. We physically model these SEDs, and where available provide the redshift of the optical counterpart. For a superset of 25,649 sources we provide the total intensity spectral index, $\alpha$. Objects with steep versus flat $\alpha$ generally have different polarization SEDs: steep-spectrum sources exhibit depolarization, while flat-spectrum sources maintain constant polarized fractions over large ranges in wavelength. This suggests the run of polarized fraction with wavelength is predominantly affected by the local source environment, rather than by unrelated foreground magnetoionic material. In addition, a significant fraction (21\%) of sources exhibit `repolarization', which further suggests that polarized SEDs are affected by different emitting regions within the source, rather than by a particular depolarization law. This has implications for the physical interpretation of future broadband polarimetric surveys. | The combination of cosmic magnetic fields and charged particles, both of which are ubiquitous in the universe, results in the emission of synchrotron radiation from radio sources \citep[e.g.][]{2011hea..book.....L}. This radiation is fundamentally linearly polarized, and both the fractional polarization and electric vector polarization angle (EVPA) of this emission show significant frequency-dependence \citep[e.g.][]{1966MNRAS.133...67B}. This frequency-dependence is due to Faraday rotation and depolarization which, for extragalactic sources, are typically considered to be caused by magnetoionic material that either intervenes between us and the observed emitting region, or is intermixed with the emitting region itself \citep[e.g.][]{1966MNRAS.133...67B,1991MNRAS.250..726T,1998MNRAS.299..189S,2009A&A...502...61M}. Understanding of Faraday rotation and astrophysical depolarization requires broadband radio measurements, and a large number of facilities are currently available or planned that will have the necessary bandwidth to study cosmic magnetic fields. For example, the Australian Square Kilometre Array Pathfinder (ASKAP) will observe at frequencies between 700~MHz and 1.8~GHz, \citep{2008ExA....22..151J}, the Australia Telescope Compact Array (ATCA) at $\ge1.1$~GHz \citep[e.g.][]{2011MNRAS.416..832W}, the Giant Metrewave Radio Telescope (GMRT) at frequencies $<$1.4~GHz \citep[e.g.][]{FARNESETAL}, the GALFA Continuum Transit Survey (GALFACTS) with Arecibo between 1.2 and 1.5~GHz \citep{2010ASPC..438..402T}, the Karl~G.~Jansky Very Large Array (JVLA) at $>$1.2~GHz \citep[e.g.][]{2009IEEEP..97.1448P}, the Low-Frequency Array (LOFAR) at $<$230~MHz \citep{2013A&A...556A...2V}, and the Murchison Widefield Array (MWA) between 80 and 300~MHz \citep{2013PASA...30....7T}. Many of these facilities are pathfinders towards the Square Kilometre Array (SKA) Cosmic Magnetism Project \citep{2004NewAR..48.1003G,2011arXiv1111.5802B}. The SKA will detect up to $\approx10^{7}$ polarized extragalactic sources on the sky at a mean spacing of $\sim90$~arcsec \citep{2004NewAR..48.1003G}, and provide broadband measurements of both the polarized fraction and Faraday rotation. The polarimetric measurements that result will be used to construct a densely-sampled `Rotation Measure grid' \citep{2004NewAR..48.1289B,2005AAS...20713703G} that allow for analysis and reconstruction of the Galactic magnetic field \citep[e.g.][]{2009ApJ...702.1230T,2012ApJ...757...14J,2012A&A...542A..93O}, for investigation of the evolution of magnetic fields over cosmic time \citep[e.g.][]{2008ApJ...676...70K,2012arXiv1209.1438H,2013MNRAS.435.3575B}, and can reveal physical properties of the central engines in radio sources \citep[e.g.][]{2012MNRAS.421.3300O}. Making sense of such data will require two capabilities: fast cross-matching algorithms for identification of counterpart sources with known redshifts at complementary wavelengths, and more importantly `$k$-corrections' that will allow for the polarization properties to be determined in the emitting frame of a source. These $k$-corrections will be necessary for the polarized fractions, the rotation measures, and possibly also for Faraday rotators that have a non-linear relationship between the EVPA and $\lambda^2$. In order to $k$-correct the polarized fraction to the emitting frame, we will require well-defined polarized spectral energy distributions (SEDs). Such SEDs can also be used to investigate the predominant causes of depolarization, and to classify individual sources. As continuous broadband polarization data for a large number of sources will not be available until the next generation of radio telescopes, we can instead attempt to construct SEDs from existing data, to enable $k$-corrections of polarized sources. Polarized SEDs can be reconstructed using the considerable amount of archival polarimetric radio data, but require careful consideration of numerous systematics including resolution effects, beam depolarization, multiple source components, time-variability, Rician bias, differing uncertainties, outliers, and the use of either an interferometer or a single dish for data collection. The polarized fractions and rotation measures of 37,543 sources have been determined previously at 1.4~GHz using the NRAO VLA Sky Survey (NVSS) \citep{1998AJ....115.1693C,2009ApJ...702.1230T}. Polarized fractions and EVPAs have also been presented in a large number of other radio catalogs \citep[e.g.][]{1980A&AS...40..319S,1980A&AS...39..379T,1981A&AS...43...19S,1982A&AS...48..137S,1999A&AS..135..571Z,2003A&A...406..579K,2003PASJ...55..351T,2010MNRAS.402.2403M}. In addition, surveys that provide total intensity data allow for measurement of the spectral index and any spectral curvature \citep[e.g.][]{1991ApJS...75....1B,1996AJ....111.1945D,1996ApJS..103..427G,1997A&AS..124..259R}. Furthermore, the NVSS Rotation Measures (RMs) have recently been matched against optical catalogs, providing spectroscopic redshifts for more than 4,000 polarized radio sources \citep{2012arXiv1209.1438H}. This conglomeration of data not only provides the EVPAs, polarized fractions, and redshifts needed to construct and then $k$-correct a polarized SED, but also accumulates a large number of complementary parameters that are relevant to efforts for understanding cosmic magnetism. In this paper, we cross-correlate the aforementioned data using a K-Dimensional Tree \citep[as described by][]{bentley1975}. Such a technique is able to rapidly eliminate large numbers of sources from a list of possible cross-matches. Consequently, the algorithm allows for a computationally inexpensive nearest-neighbor search -- reducing the problem from $\mathcal{O}(N^2)$ to $\mathcal{O}(N \log N)$. By accumulating data obtained at different frequencies, the algorithm allows us to construct a polarized radio SED with measurements between 0.4~GHz to 100~GHz. We then present a catalog of model fits to the polarized SEDs. The catalog also contains narrow and broadband RMs, total intensity spectral indices, estimates of the depolarization, and spectroscopic redshifts. We carefully detail the systematics and limitations of the catalog, including resolution effects, and the effect of multiple source components. This catalog constitutes the most comprehensive database of linear radio polarization currently publicly available, and increases the number of well-defined polarized SEDs by over an order of magnitude \citep[e.g.][]{2003A&A...406..579K,2004A&A...427..465F,2008A&A...487..865R,2009A&A...502...61M}. In this paper, we present the catalog of measurements of compact polarized radio sources, and define the possible uses and limits of our sample. Thorough scientific exploitation of this catalog is beyond the scope of this paper and will be the subject of future studies. Throughout this paper, we characterize Faraday rotation as a rotation of the observed EVPA as a function of wavelength, so that \begin{equation} \Theta_{\textrm{EVPA}} = \Theta_{\textrm{0}} + \text{RM}\lambda^2 \,, \label{rotationmeasureequation} \end{equation} where $\lambda$ is the observing wavelength, $\Theta_{\textrm{EVPA}}$ and $\Theta_{\textrm{0}}$ are the measured and intrinsic EVPA respectively, and the factor of proportionality RM, the rotation measure, is the gradient of the EVPA with $\lambda^2$. A more generalised quantity to parameterize Faraday rotation is the fundamental physical quantity, the Faraday depth. As a special case, the Faraday depth at which all polarized emission is produced is equal to the RM if there is only one emitting source along the line of sight, which has no internal Faraday rotation, and is not affected by beam depolarization, and there are only Faraday screens along the sight line \citep[for further detail, please see][]{2005A&A...441.1217B}. In such a case \begin{equation} \label{RM2} \text{RM} = \frac{e^3}{2 \pi m_{\rm e}^2 c^4} \int_{d}^0 n_{\rm e} {\bf B} \cdot \text{d}{\bf s} \,, \end{equation} where \(n_{\rm e}\) is generally the electron number density of the plasma and \(\bf B\) is the magnetic field strength. The constants \(e\), \(m_{\rm e}\), and \(c\) are the electronic charge, the mass of the electron, and the speed of electromagnetic radiation in a vacuum respectively. The integral is performed along the line of sight from the source (at distance \(d\)) to the observer. The paper is structured as follows: Section~\ref{accumulating} details the collection and preparation of the data used from various radio facilities. The cross-matching and fitting of each SED are explained in Sections~\ref{crossmatching} and \ref{sourcefitting} respectively. The catalog itself is presented in Section~\ref{catalog}, and possible systematic effects on the catalog are considered in Section~\ref{systematics}. The results are presented in Section~\ref{results}. Possible future applications and a general discussion are presented in Section~\ref{discussion}. The total intensity spectral index, $\alpha$, is defined such that $S_{\nu}\propto\nu^{+\alpha}$, where $S_{\nu}$ is the radio flux density and $\nu$ is the observing frequency. The polarized SEDs are fit using a number of applicable models, which include a polarization spectral index; $\beta$ is defined such that $\Pi \propto \lambda^{\beta}$, where $\Pi$ is the polarized fraction and $\lambda$ is the observing wavelength. Note that $\beta$ is defined in the opposite sense to the total intensity spectral index, $\alpha$, in that it is the exponent of observing frequency rather than wavelength. We refer to `polarization' on multiple occasions, in all cases we are referring to linear radio polarization -- circular polarization is beyond the scope of this work. | \label{discussion} We have presented a multiwavelength catalog of radio polarization that increases the number of well-defined polarized SEDs by over an order of magnitude. The resulting polarized SEDs have a frequency range of 0.4~GHz to 100~GHz, and our best sources are constrained by up to 56 independent polarization measurements. We have used a K-Dimensional tree for the cross-matching, reducing the computational expense by a factor of $(\log n)/n$, and have used an automated classification algorithm based on the Bayesian Information Criterion to distinguish between different models for the Faraday depolarization. The catalog also contains constraints on the total intensity spectral index and curvature, the broadband RM, spectroscopic redshift, angular size, and estimated non-thermal rest-frame luminosity at 1.4~GHz. The catalog will allow a number of parameters to be explored in the effort to understand cosmic magnetic fields. In this paper, we have found that our sample is consistent with two populations of core- and jet-dominated sources based on the clustering in the plane of the polarized fraction versus total intensity spectral indices. This is consistent with the optically-thin jet/lobe-dominated sources undergoing significantly more depolarization relative to the optically-thick core-dominated sources. Such a connection implies that radio source depolarization predominantly occurs within the local source environment, rather than being due to intervening Faraday screens. Importantly, the catalog will be of particular use in $k$-correcting polarized SEDs into the source rest-frame. These $k$-corrections can be performed by using the statistical tests provided in the catalog to select good quality SEDs, and to use the depolarization model selected by the BIC. The $k$-corrected polarized fraction, i.e.\ in the source rest-frame, for equivalent emission to that at 1.4~GHz and $z=0$ is then the corresponding polarized fraction at $\lambda= 21.414/(1+z)$~cm. The $k$-corrected Faraday depth can be obtained using a multiplicative factor of $(1+z)^2$ to correct for the effects of cosmological expansion, however this assumes that all of the Faraday rotation is occurring at the source. Such a correction will break down if there is any Galactic or intervening contribution. The $(1+z)^2$ correction to the Faraday depth also assumes a linear relationship between the EVPA and $\lambda^2$ -- if the relationship is non-linear and the Faraday depth measured using a narrowband, then it will be necessary to $k$-correct the polarization angle SED in a similar way to $k$-correcting the polarized fraction, i.e.\ by sliding the SED and then reestimating the Faraday depth. This catalog is an enabling step for such $k$-corrected studies, as an increased sample of polarized SEDs will not be available until the advent of the SKA and other next generation facilities such as ASKAP -- which will yield the necessary broadband polarization data in combination with a redshift. The results of the $k$-corrections themselves constitute an extensive additional study, as such studies of magnetic field evolution are hindered by the ability to classify different source types (e.g.\ normal versus active galaxies, by viewing angle, core- versus lobe- dominated), by luminosity effects/Malmquist bias, and possibly by other evolutionary effects such as changes in the bulk Lorentz factor of radio jets. Furthermore, as $k$-correction of the RM into the rest-frame by a factor of $(1+z)^2$ assumes that the Faraday rotating medium is all local to the source -- reliable removal of Galactic contributions, together with measures of the magnetoionic content along typical lines of sight, are essential to probe the evolution of cosmic magnetism. Other parameters such as the total intensity spectral indices will assist in the process of source classification and correcting for luminosity effects, although higher resolution data are necessary to reveal how reliably this separates core- and lobe-dominated sources. In addition to $k$-corrections, there are also many subsidiary applications, including studies of where Faraday rotation occurs along the line of sight, the spectral index versus redshift \citep[e.g.][]{2006MNRAS.371..852K}, measurements of the Galactic magnetic field \citep[e.g.][]{2008ApJ...676...70K}, and investigations of intervening Mg~II absorption systems and their effects on SED type and depolarization \citep[e.g.][]{2008Natur.454..302B,2012ApJ...761..144B}. Previous similar catalogs have not focused on polarization measurements \citep[e.g.][]{2008AJ....136..684K}. This therefore is the most comprehensive catalog of polarization measurements available to date. Our catalog is reliable, with more than 95\% of polarization measurements being correctly associated, and more than 93\% of total intensity measurements. The reliability is further improved by the source fitting procedures. Nevertheless, while we have selected our catalog as a 1.4~GHz flux-limited polarized sample, selection effects are still likely considerable and are hard to constrain. The sky coverage of the accumulated data is patchy, and typically taken via shallow observations on the brightest known sources. As the brightest sources have typically been observed repeatedly, we obtain many more measurements for the brightest sources, and consequently the SEDs of the fainter sources are less well-constrained. Despite these inevitable effects, the listed polarized SEDs can reveal the physical form of depolarization, and allow for physical models of the intervening magnetic field structure to be ascertained. The predominant depolarizing mechanism is important for modelling polarized source counts at low radio frequencies, which will have a substantial impact on the number of polarized sources detectable by facilities such as LOFAR, MWA, and the SKA \citep{2004NewAR..48.1289B,2007mru..confE..69S,2011AAS...21714232H,halesmnras13}. Alongside the multiple possible analyses of the catalog we have presented, additional future work will allow for expansion of these data. Numerous other polarization measurements are available in the literature. Furthermore, our catalog currently uses the NVSS RM catalog of \citet{2009ApJ...702.1230T} as the reference data; if a source is not listed as polarized in the \citet{2009ApJ...702.1230T} catalog at 1.4~GHz, then polarization measurements at other frequencies are not accumulated into our catalog. Furthermore, polarization measurements in the Southern sky (at declinations $<-40^{\circ}$) are currently not included in our catalog. Future work could therefore use a larger reference catalog. For example, the Sydney University Molonglo Sky Survey (SUMSS) \citep{1999AJ....117.1578B} explores a similar parameter space to the NVSS in the Southern sky (albeit without polarization information). A combination of the full total intensity NVSS measurements \citep{1998AJ....115.1693C}, together with the total intensity measurements from SUMSS, would therefore greatly expand our reference catalog. Using an NVSS+SUMSS reference catalog for cross-matching with additional polarization measurements accumulated from across the literature \citep[e.g.][]{2000A&A...363..141R,2010MNRAS.401.1388J,2011ApJ...732...45S,2013arXiv1309.2527M}, would lead to a much larger sample of polarized SEDs -- including those sources that undergo the most extreme depolarization. More recent polarization surveys, such as the S-band Polarization All Sky Survey (S-PASS) at 2.3~GHz, will provide $\approx5,000$ polarized sources in the Southern sky \citep{2011JApA...32..457C,2013Natur.493...66C} -- corresponding to a significant increase in sample size. In addition, possible upcoming polarization surveys will also be able to make substantial contributions to such an effort -- detecting up to 2.2$\times$10$^5$ sources in polarized intensity at 2 to 4~GHz \citep[e.g.][]{2014arXiv1401.1875M}. Such cross-matched catalogs, particularly when combined with large samples of redshifts, will continue to constitute useful resources for probing magnetic fields and other astrophysical phenomena. | 14 | 3 | 1403.2391 |
1403 | 1403.5264_arXiv.txt | Variability in the time series brightness of a star on a timescale of 8\,hours, known as ``flicker'', has been previously demonstrated to serve as a proxy for the surface gravity of a star by \citet{bastien:2013}. Although surface gravity is crucial for stellar classification, it is the mean stellar density which is most useful when studying transiting exoplanets, due to its direct impact on the transit light curve shape. Indeed, an accurate and independent measure of the stellar density can be leveraged to infer subtle properties of a transiting system, such as the companion's orbital eccentricity via asterodensity profiling. We here calibrate flicker to the mean stellar density of 439 \emph{Kepler} targets with asteroseismology, allowing us to derive a new empirical relation given by $\log_{10}(\rho_{\star}\,[\mathrm{kg}\,\mathrm{m}^{-3}]) = 5.413 - 1.850 \log_{10}(F_8\,[\mathrm{ppm}])$. The calibration is valid for stars with $4500<T_{\mathrm{eff}}<6500$\,K, $K_P<14$ and flicker estimates corresponding to stars with $3.25<\log g_{\star}<4.43$. Our relation has a model error in the stellar density of 31.7\% and so has $\sim8$ times lower precision than that from asteroseismology but is applicable to a sample $\sim40$ times greater. Flicker therefore provides an empirical method to enable asterodensity profiling on hundreds of planetary candidates from present and future missions. | \label{sec:intro} In recent years, there has been an increased interest in exploiting time series brightness variations of stars to infer fundamental stellar properties. This upsurge has been largely motivated by the transiting exoplanet survey missions, such as CoRoT \citep{baglin:2006} and \emph{Kepler} \citep{borucki:2009}, which have provided an avalanche of high signal-to-noise and high cadence photometry. In addition, such missions require accurate stellar characterization to infer the correct parameters for the associated transiting planet candidates. The strongest constraints on a star's fundamental parameters using time series photometry come from asteroseismology \citep{chaplin:2013}, the study of stellar oscillations. Giants, sub-giants and bright dwarfs provide data on solar-like oscillations, and in these cases fundamental parameters may be determined to the percent level. Another technique, known as gyrochronology, exploits a star's gradual angular momentum loss to date stars to $\sim15$\% accuracy using empirical calibrations from open clusters \citep{skumanich:1972,barnes:2007, epstein:2014}. Here, the primary input is a stellar rotation period, which is revealed via rotational modulations in a photometric time series \citep{walkowicz:2013}. Recently, a new characterization technique has been proposed by \citet{bastien:2013} (B13), which uses the variability over an 8-hour timescale, ``flicker'', as a proxy for the surface gravity of a star, $g_{\star}$. Flicker is able to reproduce $\log g_{\star}$ to within $\sim0.10$\,dex for FGK dwarfs and giants down to apparent magnitudes of 14 and is thought to be physically caused by stellar granulation on the star's surface \citep{mathur:2011,cranmer:2014}. Whilst asteroseismology undoubtedly provides tighter constraints on a star's basic parameters, the ability of flicker to infer $\log g_{\star}$ for a much larger number of stars in a magnitude-limited survey, such as \emph{Kepler}, makes it highly appealing. In conjunction with these recent developments in stellar characterization, several authors have recently explored how an accurate determination of the mean stellar density, $\rho_{\star}$, plus a high quality transit light curve may be used to infer various properties of an exoplanet \citep{MAP:2012, dawson:2012,AP:2014}. Asterodensity profiling (AP) compares the stellar density derived from the transit light curve shape \citep{seager:2003}, $\rho_{\star,\obs}$, to some independent measure, $\rho_{\star,\tru}$. Relative differences can be caused by numerous phenomena, including orbital eccentricity and blend scenarios \citep{AP:2014}. Whilst asteroseismology directly yields the mean stellar density for those targets with detected oscillations \citep{ulrich:1986}, flicker is currently only calibrated to surface gravity. In this letter, we show that flicker is also able to determine the bulk density of a star to within $\sim30$\% across a wide range of spectral types and apparent magnitudes. This new empirical relation opens the door to conducting AP on many hundreds of transiting planet candidates detected by both \emph{Kepler} and future missions. We describe our methodology for deriving this relation in \S\ref{sec:method}, followed by an exploration of the results in \S\ref{sec:results}. We close in \S\ref{sec:discussion} by discussing the potential of this relation for AP with both previous and future missions. | \label{sec:discussion} \subsection{Flicker as an Input for Asterodensity Profiling} \label{sub:AP} Asterodensity profiling (AP) has recently emerged as a valuable tool for characterizing exoplanets using time series photometry \citep{MAP:2012,sliski:2014,AP:2014}. AP exploits the fact that for a planet on a Keplerian circular orbit transiting an unblended star with a symmetric intensity profile, the shape of the light curve reveals $\rho_{\star,\obs}$ \citep{seager:2003}. If any of the idealized assumptions are invalid, then $\rho_{\star,\obs}$ will differ from the true value, $\rho_{\star,\tru}$, and the direction and magnitude of the discrepancy reveals information about the transiting system \citep{AP:2014}. Using independent $\rho_{\star}$ estimates from asteroseismology, \citet{sliski:2014} provide an example of the utility of AP by showing that the false positive rate of transiting planet candidates associated with giant stars is much higher than that of dwarf stars. In this work, we have shown that flicker may also be used as an input for the independent measure of $\rho_{\star,\tru}$ required for AP. Despite uncertainties in $\rho_{\star}$ increasing to $\sim30$\% from a flicker-based determination versus $\sim4$\% using asteroseismology, flicker can be used on many more targets in a magnitude-limited photometric survey like \emph{Kepler}, since it works reliably down to $K_P=14$ (see later discussion in \S\ref{sub:implications}). We do not claim that the derived relation is the optimal choice of regressors or parametric form, merely that it provides a simple, empirical recipe for estimating $\rho_{\star}$. For example, including effective temperature may improve the relation, since cooler stars seem to be found at higher flicker values (see Fig.~\ref{fig:relation}). However, including such terms would make our relation no longer purely photometric, which we would argue is the principal benefit of the flicker technique. Whilst we direct those interested to \citet{AP:2014} for details on the theory and range of effects which can cause AP discrepancies, we here provide an example calculation of the sensitivity of AP using flicker to detect eccentric exoplanets via the so-called ``photo-eccentric'' effect \citep{dawson:2012}. For a planet on an eccentric orbit, the derived light curve stellar density will differ from the true value by \citep{investigations:2010}: \begin{align} \Big( \frac{\rho_{\star,\obs}}{\rho_{\star,\tru}} \Big) &= \frac{(1+e\sin\omega)^{3}}{(1-e^2)^{3/2}}, \label{eqn:psi} \end{align} where $e$ is the orbital eccentricity and $\omega$ is argument of periastron. \citet{dawson:2012} show how to first order, constraints on $e$ scale with $\rho_{\star,\tru}^{1/3}$ and thus even a weak prior on the density can lead to useful constraints on $e$. With one observable and two unknowns, a unique solution to Equation~\ref{eqn:psi} is not possible. However, one can derive the minimum eccentricity, $e_{\mathrm{min}}$, of the planet and the associated uncertainty, $\sigma_{e_{\mathrm{min}}}$, using Equations~39\&40 of \citet{AP:2014} respectively. Let us assume that the uncertainty in $(\rho_{\star,\obs}/\rho_{\star,\tru})$ is dominated by the denominator's error, which in turn was found using our flicker relation and equals 31.7\%. We may now plot the term $(e_{\mathrm{min}}/\sigma_{e_{\mathrm{min}}})$ as a function of $e_{\mathrm{min}}$ in Fig.~\ref{fig:eminplot}, to illustrate the ability of flicker to detect eccentric planets. Using the classic \citet{lucy:1971} test, we mark several key confidence levels with grid lines, demonstrating that flicker can detect eccentricities of $e_{\mathrm{min}}=0.25$ to $\geq2$\,$\sigma$ confidence and $e_{\mathrm{min}}=0.32$ to $\geq3$\,$\sigma$. With the power of large number statistics, we anticipate that flicker will be particularly powerful for inferring the ensemble distribution of orbital eccentricities. \begin{figure} \begin{center} \includegraphics[width=8.4 cm]{eminplot.eps} \caption{\emph{Sensitivity of flicker to detecting eccentric exoplanets via the photo-eccentric effect. We here assume a fractional error in $\rho_{\star,\tru}$ from a flicker-based measurement of 31.7\%. Several key confidence levels are marked with dashed grid lines for reference. }} \label{fig:eminplot} \end{center} \end{figure} \subsection{Implications} \label{sub:implications} Between the two catalogs of \citet{huber:2013} and \citet{chaplin:2014}, there are 588 unique targets with asteroseismology detections yielding $\rho_{\star}$ measurements with a median uncertainty of 4.1\%. In contrast, there are $28,577$ \emph{Kepler} targets with $K_P<14$, $4500<T_{\mathrm{eff}}< 6500$\,K and $3.25<\log g<4.43$ (NASA Exoplanet Archive). Making the simple assumption that the same fraction of these targets will satisfy the range criterion defined earlier in \S\ref{sub:fullresults}, then we expect $\sim25,000$ targets to be amenable for a flicker-based estimate of $\rho_{\star}$ with a model accuracy of 31.7\%. This translates to an increase in the number of AP targets by a factor of $\sim40$ at the expense of an increase in the measurement uncertainty by a factor of $\sim8$. By any accounts, this is an acceptable compromise and opens the door to conducting AP on hundreds of \emph{Kepler} planetary candidates (we estimate $\sim630$). An alternative method to determine $\rho_{\star,\tru}$ for targets without detectable oscillations would be via spectroscopy (e.g. \citealt{dawson:2012}). Here, one observes a spectrum of the target, compares it to a catalog of library spectra with various $T_{\mathrm{eff}}$, $[\mathrm{M}/\mathrm{H}]$ and $\log g_{\star}$ and then finally one finds the best matching stellar evolution isochrones to these basic parameters. This procedure has several drawbacks compared to a flicker-based determination though. Firstly, this method requires that one obtain high SNR spectra, whereas F8 can be measured from the data obtained directly from a photometric mission like \emph{Kepler}. Secondly, the final determination of $\rho_{\star}$ is strongly model dependent using both stellar evolution models and spectra template matching laden with challenging degeneracies. Finally, it is worth noting that the formal uncertainty on a spectroscopic determination of $\rho_{\star,\tru}$ is typically no better than the flicker-based empirical relation for Sun-like stars. For example, \citet{dawson:2012} report $\rho_{\star,\tru}=1.02_{-0.29}^{+0.45}$\,$\rho_{\odot}$ for the $K_P=13.6$ Sun-like target KOI-686 and our flicker technique yields $(0.97\pm0.44)$\,$\rho_{\odot}$. In general then, we argue that for determinations of $\rho_{\star}$, the empirical and largely model independent flicker technique is preferable to spectroscopy, provided the target satisifies our sample criteria. For the future TESS mission \citep{ricker:2010}, the smaller lens aperture of 12\,cm will lead to higher photon noise than \emph{Kepler}, for the same target. We therefore expect the 14$^{\mathrm{th}}$ magnitude cut-off of our flicker calibration to drop to $\sim11.5$. The same effect will lead to only very bright stars having asteroseismology detections though, with preliminary estimates suggesting $\sim5\times10^3$ asteroseismology targets out of $\sim5\times10^5$ target stars. In contrast, we expect that $\sim10^5$ TESS targets will be amenable to a flicker-based determination of their stellar densities (with the exact number depending upon the as yet unknown target list). Similarly, we expect flicker to have majorly benefit the upcoming PLATO 2.0 mission \citep{rauer:2013} for both moderately bright targets near the edge of the field and faint targets in the center. Since AP is not only a method for characterizing exoplanets but also for vetting them \citep{sliski:2014}, then we expect flicker to be an invaluable tool in the TESS and PLATO era. | 14 | 3 | 1403.5264 |
1403 | 1403.0677_arXiv.txt | If binaries consisting of two $\sim100~M_\odot$ black holes exist they would serve as extraordinarily powerful gravitational-wave sources, detectable to redshifts of $z\sim2$ with the advanced LIGO/Virgo ground-based detectors. Large uncertainties about the evolution of massive stars preclude definitive rate predictions for mergers of these massive black holes. We show that rates as high as hundreds of detections per year, or as low as no detections whatsoever, are both possible. It was thought that the only way to produce these massive binaries was via dynamical interactions in dense stellar systems. This view has been challenged by the recent discovery of several $\gtrsim150~M_\odot$ stars in the R136 region of the Large Magellanic Cloud. Current models predict that when stars of this mass leave the main sequence, their expansion is insufficient to allow common envelope evolution to efficiently reduce the orbital separation. The resulting black-hole--black-hole binary remains too wide to be able to coalesce within a Hubble time. If this assessment is correct, isolated very massive binaries do not evolve to be gravitational-wave sources. However, other formation channels exist. For example, the high multiplicity of massive stars, and their common formation in relatively dense stellar associations, opens up dynamical channels for massive black hole mergers (e.g., via Kozai cycles or repeated binary-single interactions). We identify key physical factors that shape the population of very massive black-hole--black-hole binaries. Advanced gravitational-wave detectors will provide important constraints on the formation and evolution of very massive stars. | In the early universe massive ($M\gtrsim100\,M_\odot$) black holes (BHs) are believed to form from the collapse of massive stars \citep{Fryer01}, and these BHs may be the seeds of the supermassive BHs at the nuclei of galaxies \citep{Madau01,Whalen12}. These massive BHs have also been invoked to explain ultraluminous X-ray sources (so termed because they emit at 10--100 times the Eddington rate for a $10\,M_\odot$ BH) in the nearby universe \citep{colbert99,colbert04}. Until recently, both observations of stellar clusters, e.g., \citet{Figer05} (although see also \cite{Massey03}), and some theoretical arguments \citep{Mckee07} have suggested that stars above $150\,M_\odot$ do not form at non-zero metallicities. Including the effects of mass loss from winds, even at 1/10th solar metallicity, this assumption produces masses of BH systems in the nearby universe in the tens of solar masses \citep{2010ApJ...714.1217B}. However, the discovery of several stars with current masses greater than $150\,M_\odot$ and initial masses up to $\sim 300\msun$ in the R136 region of the Large Magellanic Cloud \citep{2010MNRAS.408..731C} requires a rethinking of this argument. There are at least some environments in which stellar masses can apparently extend well beyond $150\,M_\odot$, and if these stars do not have extremely large wind loss rates, then after their cores collapse they may leave behind BHs with masses in excess of $100\,M_\odot$. It has been suggested that stars with initial masses between roughly $150~M_\odot$ and $300~M_\odot$ at low to moderate metallicities explode due to an instability produced when the core gets so hot that it produces electron/positron pairs, resulting in a loss of energy which reduces the pressure and causes the core to contract. As this happens the nuclear burning accelerates and can disrupt the star entirely if the star is unable to stabilize itself. If some fraction of superluminous supernovae are in fact pair-instability supernovae \citep{woosley07,galyam09,cooke09,ofek14} \citep[see, however,][]{Nicholl13}, then at least at metallicities around $\sim 0.1Z_\odot$ (where $Z_\odot=0.014$) massive stars above $150~M_\odot$ exist. Gravitational waves (GWs) can potentially provide additional evidence for the formation and evolution of these massive stars. Massive stars are usually found in binaries or multiple systems \citep[e.g.,][]{Kobulnicky07,Kobulnicky12,2012Sci...337..444S,2013A&A...550A.107S} with mass ratios that are flat \citep{2013MNRAS.432L..26S}. Indeed, the most massive known binary has an estimated total mass of $200$--$300\,M_\odot$ and a possible initial mass of $\sim 400\,M_\odot$ \citep{2013MNRAS.432L..26S}. Thus massive BHs formed from the evolution of these massive stars are likely to be partnered with comparably massive BHs. If very massive stars (VMS) with initial masses above $150\,M_\odot$ also follow these trends, these stars may produce massive BH binaries, some of which may merge. Keeping the binary's mass ratio fixed, the total energy emitted in GWs is proportional to the binary's total mass, so coalescing massive BH binaries can be detected much farther than stellar-mass BH binaries. Thus, they could be very significant sources for advanced GW detectors. In this paper, we explore in detail the evolution of binaries with initial (zero-age main sequence) component masses above $150 M_\odot$ and the formation of very massive BH-BH binaries; the fate of binaries with initial component masses up to $150 M_\odot$ was explored elsewhere \citep{2012ApJ...759...52D}. The formation of merging, massive BH binaries depends sensitively on a range of issues in stellar evolution --- for example the evolution of the core, the expansion in the giant phase, and the details of the pair-instability supernovae. We discuss how these uncertainties lead to a wide range of predictions for the merger rates for these systems. Even an approximate measurement of the merger rates will place insightful constraints on these stellar processes. We discuss these uncertainties in detail, calculating the full range of rate predictions for advanced LIGO/Virgo. In Section~2 we discuss the physical processes and uncertainties involved in the evolution of very massive binaries. In Section~3 we provide a range of predictions for the rates of formation and merger of massive binary stellar-mass BHs, based on different assumptions with different codes. In Section~4 we consider dynamical effects, particularly Kozai cycles and three-body interactions, and find that even if most or all massive BH binaries are too widely separated to merge on their own within a Hubble time, many will be induced to merge by interactions with other objects. In Section~5 we map these coalescence rate predictions for massive binaries to predictions for detection rates in future GW observatories. We emphasize the importance of the merger and ringdown phases of the gravitational waveform and cosmological effects, due to the high masses of the BHs and the significant redshift out to which they can be observed. Our discussion and conclusions are in Section~6. | Since GWs from massive BH binaries can be detected to cosmological distances, we have explored the event rates for the mergers of these systems. We find that only low-metallicity environments ($Z\ltorder 0.1$--$0.4\,Z_\odot$) may be favorable for the formation of very massive stellar-origin BHs with mass exceeding $100\msun$. The formation of such BHs is possible if {\it (i)} the initial mass function (IMF) extends above $500\msun$, {\it (ii)} pair-instability SNe do not disrupt all stars above $500\msun$, and {\it (iii)} stellar winds for such massive stars are not greatly underestimated. The formation of close massive BH-BH binaries requires that after the main sequence {\it (iv)} very massive stars above $500\msun$ expand significantly (by more than a factor of $2$), {\it (v)} their H-rich envelopes have a mass larger than $10$--$100\msun$, {\it (vi)} the evolution of such a binary involves a common envelope phase, and {\it (vii)} the binary can survive the common envelope phase while the donor star is a very massive Hertzsprung gap star. If conditions {\it (iv)} through {\it (vii)} are not met, then isolated binary evolution (i.e., field stellar populations) may produce only wide massive BH-BH binaries. We point out that even if these requirements are not met, there are several dynamical processes that could lead to efficient lowering of the coalescence time of wide massive BH-BH binaries both in dense stellar environments (cluster binary-single interactions) and in low-density field populations (Kozai mechanism in triple systems). The resulting BH-BH merger rates depend sensitively on the amount of star forming mass with low metallicity at redshifts $z<2$ (the maximum distance at which a $100$--$100\msun$ BH-BH binary will be detectable with the advanced LIGO/Virgo network). The amount of low metallicity star formation in the last Gyr may have been as high as $\sim 50\%$ of total star formation \citep{2008MNRAS.391.1117P}, and may have been even higher at the redshifts $z>1$ that dominate our overall rates. Population synthesis models predict that $75\%$ of the close massive BH-BH systems merge within 1 Gyr of formation. Based on simple estimates we find that realistic advanced LIGO/Virgo detection rates for these massive BH-BH systems are on the order of a few per year. However, the large uncertainties that burden our predictions allow for rates as high as hundreds of detections per year to as low as no detections at all. BH-BH systems originating from isolated binaries of very massive stars would likely have rather large mass ratios ($q \gtorder 0.8$) and aligned spins. For a core collapse of a massive star that was spin-aligned with the orbit via tidal interactions with its companion, and that ejects no mass and has no linear momentum kick resulting from the collapse, our strong expectation is that the compact remnant would have a spin aligned with the orbit. Given our still-rudimentary understanding of core collapses there are of course situations in which this might not be accurate (e.g., oppositely-directed neutrino jets on opposite sides of the proto-neutron star could impart spin angular momentum without imparting linear momentum), but at present such scenarios seem contrived. Regular ($M_{\rm zams} < 150 \msun$) stars could not produce binaries with total mass in the $M_{\rm tot} \gtrsim 100$--$200 \msun$ range. Therefore, detections of coalescences between massive, aligned, rapidly spinning BHs would uniquely identify systems originating from isolated binaries of very massive stars. Such detections would indicate that the stellar IMF extends well beyond previously considered limits, and probably as high as $M_{\rm zams} > 500 \msun$, and that massive progenitor binaries survive common envelope events even if the donors initiating these events are still in early evolutionary stages (i.e., on Hertzsprung gap). This would also argue against models of very massive stars that predict minimal expansion during post main-sequence evolution. If observations show evidence for significant misalignment of BH spins, then either these systems received kicks via asymmetric neutrino emission or dynamical processes must have been involved in the formation of the merging BH-BH system. Moreover, \citet{Kalogera:2000} argued that significant spin--orbit misalignment is unlikely even with supernova kicks, unless dynamical effects are involved. This latter scenario would support the first set of published models of very massive stars that show no (or very small) radial expansion \citep{2013MNRAS.433.1114Y}. Alternatively, mergers of intermediate-mass BHs could be a consequence of dynamical processes in globular clusters or involving globular cluster mergers \citep{Fregeau:2006,AmaroSeoaneSantamaria:2009,2011GReGr..43..485G}. Regardless, the detection of such systems would yield valuable information about dynamical encounters and/or the multiplicity of very massive stars. If instead we do not detect any massive BH-BH binaries with advanced LIGO/Virgo, any or all of the effects {\it (i)--(vii)} discussed above may have contributed. When mass is transferred from the secondary to the primary after the primary has evolved to become a BH, the binary may be visible as an ultra-luminous X-ray source (ULX), as the mass loss rate from the massive secondary can be very high. This stage is likely to be quite short, given that both companions are assumed to be massive and will have quite similar lifetimes. If 10\% of all such binaries have a ULX stage lasting 1 million years---or, equivalently, all binaries have a ULX stage lasting 100,000 years---the space density of observable ULXs created through this channel will be equal to the merger rate times $10^5$ years. Since this is only one of several channels for creating ULXs, an observed ULX space density of a few $\times 10^{-2}$ Mpc$^{-3}$ \citep{Swartz:2011} yields an upper limit on the massive binary merger rate of a few $\times 10^{-7}$ Mpc$^{-3}$ yr$^{-1}$. This is a factor of several hundred higher than our very rough estimate of $10^{-9}$ Mpc$^{-3}$ yr$^{-1}$, so it would be easy to hide the population of interest among the observed ULXs. One possible constraint on the population of massive stars comes from rates of pair-instability supernovae. If an IMF slope of $\sim -2.5$ is extended to arbitrarily high masses, then $\sim1\%$ of all stars having a ZAMS mass above $8 M_\odot$ will have a ZAMS mass above $200 M_\odot$. Hence, if a significant fraction of very massive stars end their life in pair-instability supernovae, one might expect as many as 1\% of all core-collapse supernovae to be pair-instability supernovae. Meanwhile, recent work by \cite{Nicholl13} finds that this fraction is no more than $10^{-4}$, and may be $< 10^{-5}$, if the so-called ``superluminous'' supernovae are inconsistent with expectations of pair instability supernovae \citep{Nicholl13}. If pair-instability supernovae only produce superluminous supernovae, these observations constrain either the number of massive stars exceeding $\sim 150\,M_\odot$ or the mass range of stars that produce pair-instability supernovae. In such a scenario, if advanced LIGO/Virgo observes a large fraction of massive binary BH mergers, it would place constraints on the pair-instability mechanism and the mass range for which it occurs. Unfortunately, pair-instability supernovae seem to be able to produce a wide range of light curves \citep{Kasen11,Whalen14} and until these light-curves can be better understood, it will be difficult to make any firm conclusions using superluminous supernova observations. In conclusion, advanced LIGO/Virgo detectors are sensitive to the merger of massive BH binaries out to extraordinary distances ($z\sim2$). We argue that the rate density of these mergers is such that event rates of a few per year, and perhaps as many as hundreds per year, are possible given current uncertainties in stellar evolutionary physics. The upper limits or detections expected from the coming generation of advanced ground-based GW instruments will provide unique insights into the evolution of very massive stars. | 14 | 3 | 1403.0677 |
1403 | 1403.0488_arXiv.txt | We present an analysis of the role of feedback in shaping the neutral hydrogen (HI) content of simulated disc galaxies. For our analysis, we have used two realisations of two separate Milky Way-like ($\sim$L$\star$) discs - one employing a conservative feedback scheme (MUGS), the other significantly more energetic (MaGICC). To quantify the impact of these schemes, we generate zeroth moment (surface density) maps of the inferred HI distribution; construct power spectra associated with the underlying structure of the simulated cold ISM, in addition to their radial surface density and velocity dispersion profiles. Our results are compared with a parallel, self-consistent, analysis of empirical data from THINGS (The HI Nearby Galaxy Survey). Single power-law fits ($P$$\propto$$k^\gamma$) to the power spectra of the stronger-feedback (MaGICC) runs (over spatial scales corresponding to $\sim$0.5~kpc to $\sim$20~kpc) result in slopes consistent with those seen in the THINGS sample ($\gamma$$\sim$$-$2.5). The weaker-feedback (MUGS) runs exhibit shallower power law slopes ($\gamma$$\sim$$-$1.2). The power spectra of the MaGICC simulations are more consistent though with a two-component fit, with a flatter distribution of power on larger scales (i.e., $\gamma$$\sim$$-$1.4 for scales in excess of $\sim$2~kpc) and a steeper slope on scales below $\sim$1~kpc ($\gamma$$\sim$$-$5), qualitatively consistent with empirical claims, as well as our earlier work on dwarf discs. The radial HI surface density profiles of the MaGICC discs show a clear exponential behaviour, while those of the MUGS suite are essentially flat; both behaviours are encountered in nature, although the THINGS sample is more consistent with our stronger (MaGICC) feedback runs. | \label{sec:Introduction} The feedback of energy into the interstellar medium (ISM) is a fundamental factor in shaping the morphology, kinematics, and chemistry of galaxies, both in nature and in their simulated analogues \citep[e.g.][and references therein]{Thacker2000,Gov10,Schaye2010,Hambleton2011,Brook12, Scannapieco2012,Durier2012,Hopkins2013}. Perhaps the single-most frustrating impediment to realising accurate realisations of simulated galaxies is the spatial `mismatch' between the sub-pc scale on which star formation and feedback operates, and the 10s to 100s of pc scale accessible to modellers within a cosmological framework. Attempts to better constrain `sub-grid' physics, on a macroscopic scale, have driven the field for more than a decade, and will likely continue to do so into the foreseeable future. The efficiency and mechanism by which energy from massive stars (both explosive energy deposition from supernovae and pre-explosion radiation energy), cosmic rays, and magnetic fields couple to the ISM can be constrained indirectly via an array of empirical probes, including (but not limited to) stellar halo \citep{Brook2004} and disc \citep{Pilkington2012b} metallicity distribution functions, statistical measures of galaxy light compactness, asymmetry, and clumpiness \citep{Hambleton2011}, stellar disc age-velocity dispersion relations \citep{House2011}, rotation curves and density profiles of dwarf galaxies \citep{Maccio2012}, low- and high-redshift `global' scaling relations \citep{Brook12}, background QSO probes of the ionised circum-galactic medium \citep{Stinson2012}, and the spatial distribution of metals (e.g., abundance gradients and age-metallicity relations) throughout the stellar disc \citep{Pilkington2012a,Gibson2013}. In \citet{Pilkington11}, we explored an alternate means by which to assess the efficacy of energy feedback schemes within a cosmological context: specifically, the predicted distribution of structural `power' encoded within the underlying cold gas of late-type \it dwarf \rm galaxies. Empirically, star forming dwarfs present steep spatial power-law spectra ($P$$\propto$$k$$^\gamma$) for their cold gas, with $\gamma$$<$$-3$ on spatial scales $\simlt$1~kpc \citep{Stan99,Combes2012}, consistent with the slope expected when HI density fluctuations dominate the ISM structure, rather than turbulent velocity fluctuations (which dominate when isolating `thin' velocity slices). Our simulated (dwarf) disc galaxies showed similarly steep ISM power-law spectra, albeit deviating somewhat from the simple, single, power-law seen by Stanimirovic et~al. In comparison, the cold gas of late-type \it giant \rm galaxies appears to possess a more complex distribution of structural power. \citet{Dutta13} demonstrate that while such massive discs also present comparably steep (if not steeper) power spectra on smaller scales ($\gamma$$\sim$$-$3, for $\simlt$1kpc), there is a strong tendency for the power to `flatten' to significantly shallower slopes on larger scales ($\gamma$$\sim$$-$1.5, for $\simgt$2~kpc). Dutta et~al. propose a scenario in which the steeper power law component is driven by three-dimensional turbulence in the ISM on scales smaller than a given galaxy's scaleheight, while the flatter component is driven by two-dimensional turbulence in the plane of the galaxy's disc. In what follows, we build upon our earlier work on dwarf galaxies \citep{Pilkington11}, utilising the Fourier domain approach outlined by \citet{Stan99}, but now applied to a set of four simulated massive ($\sim$L$\star$) disc systems. The simulations have each been realised with both conventional (i.e., moderate) and enhanced (i.e., strong/efficient) energy feedback. The impact of the feedback prescriptions upon the distribution of power in the ISM of their respective neutral hydrogen (HI) discs will be used, in an attempt to constrain the uncertain implementation of sub-grid physics. HI moment maps will be generated for each simulation \it and \rm (for consistency) massive disc from The HI Nearby Galaxy Survey (THINGS: \citealt{wal08}), to make a fairer comparison with the observational data. In \S\ref{sec:method}, the basic properties of the simulations are reviewed, including the means by which the HI moment maps, and associated Fourier domain power spectra, were analysed. The resulting radial surface density profiles, velocity dispersion profiles, and distributions of power in the corresponding cold interstellar media are described in \S\ref{sec:analysis}. Our conclusions are presented in \S\ref{sec:conclusions}. | \label{sec:conclusions} We have presented an analysis of the cold gas and HI content of simulated discs with both 'standard' (MUGS) and `enhanced' (MaGICC) energy feedback schemes, as well as re-scaled dwarf variants of the massive (MaGICC) simulations. Radial density profiles were generated for the MUGS and MaGICC $\sim$L$\star$ variants of \tt g1536 \rm and \tt g15784 \rm (Fig~2). These were generated using their respective zeroth HI moment maps; the weaker feedback associated with MUGS resulted in very flat radial HI distributions, with sharp cut-offs at galactocentric radii of $\sim$12$-$15~kpc, while the stronger feedback associated with MaGICC resulted in HI discs with exponential surface density profiles (with scalelengths of $\sim$6$-$8~kpc) which were $\sim$2$-$3$\times$ more extended (at an HI column density limit of $\sim$10$^{19}$~cm$^{-2}$). The exponential profiles exhibited by the enhanced feedback runs are consistent with the typical profile observed in nature \citep{bigiel2008,Obr10}. The majority of the THINGS radial density profiles show evidence of exponential components, indicating that the MaGICC simulations distribute the column density in a way that better matches observational evidence. The power spectra generated for the massive ($\sim$L$\star$) discs with enhanced (MaGICC) feedback are steeper than their weaker (MUGS) feedback counterparts. In other words, the stronger feedback shifts the power in ISM from smaller scales to larger scales. Forcing a single component power-law to the MaGICC spectra yields slopes consistent with similarly forced single component fits to the empirical THINGS spectra. also well-described by a single component power law; having said that, the MaGICC spectra are more consistent with a two-component structure, with a steeper slope on sub-kpc spatial scales, flattening to shallower slopes on larger scales. The massive discs realised with the MUGS feedback scheme are both shallower than MaGICC, but also well-fit with a single power-law across all spatial scales. The dwarf galaxies realised in our work with enhanced feedback possess steeper slopes than their more massive counterparts, with values that are in agreement with \citet{Stan99} and \citet{Pilkington11}. It is arguable that several of the THINGS power spectra warrant multiple-component fits (namely NGC 2403, 3031, 3184, 3198 and 7793) and the multi-component fits performed on NGC 2403 and the two large disc MaGICC galaxy power spectra indicate that the large-scale slopes agree well, whereas the small scale slopes differ largely. This indicates that the MaGICC feedback scheme distributes HI structures on a scale that is comparable to those of observational results, but there is a lack of small-scale structure. It is apparent that there is no 1:1 match to the THINGS data from either the MUGS or MaGICC feedback schemes, but MaGICC appears to fare better than the MUGS feedback scheme from a single-component fit in an average sense. The lack of a 1:1 relation may be largely due to the challenges in converting from 'cold gas' to 'HI' as well as a lack of exactly face-on systems observed in nature and in the THINGS survey. | 14 | 3 | 1403.0488 |
1403 | 1403.2996_arXiv.txt | {Column-density maps of molecular clouds are one of the most important observables in the context of molecular cloud- and star-formation (SF) studies. With the {\sl Herschel} satellite it is now possible to precisely determine the column density from dust emission, which is the best tracer of the bulk of material in molecular clouds. However, line-of-sight (LOS) contamination from fore- or background clouds can lead to overestimating the dust emission of molecular clouds, in particular for distant clouds. This implies values that are too high for column density and mass, which can potentially lead to an incorrect physical interpretation of the column density probability distribution function (PDF). In this paper, we use observations and simulations to demonstrate how LOS contamination affects the PDF. We apply a first-order approximation (removing a constant level) to the molecular clouds of Auriga and Maddalena (low-mass star-forming), and Carina and NGC3603 (both high-mass SF regions). In perfect agreement with the simulations, we find that the PDFs become broader, the peak shifts to lower column densities, and the power-law tail of the PDF for higher column densities flattens after correction. All corrected PDFs have a lognormal part for low column densities with a peak at \av\, $\sim$2 mag, a deviation point (DP) from the lognormal at \av(DP)$\sim$4--5 mag, and a power-law tail for higher column densities. Assuming an equivalent spherical density distribution $\rho \propto r^{-\alpha}$, the slopes of the power-law tails correspond to $\alpha_{PDF}$ = 1.8, 1.75, and 2.5 for Auriga, Carina, and NGC3603. These numbers agree within the uncertainties with the values of $\alpha \approx$ 1.5, 1.8, and 2.5 determined from the slope $\gamma$ (with $\alpha = 1 - \gamma$) obtained from the radial column density profiles ($N \propto r^\gamma$). While \mbox{$\alpha \sim 1.5$--$2$} is consistent with a structure dominated by collapse (local free-fall collapse of individual cores and clumps and global collapse), the higher value of $\alpha >$ 2 for NGC3603 requires a physical process that leads to additional compression (e.g., expanding ionization fronts). From the small sample of our study, we find that clouds forming only low-mass stars and those also forming high-mass stars have slightly different values for their average column density (1.8 10$^{21}$cm$^{-2}$ vs. 3.0 10$^{21}$cm$^{-2}$), and they display differences in the overall column density structure. Massive clouds assemble more gas in smaller cloud volumes than low-mass SF ones. However, for both cloud types, the transition of the PDF from lognormal shape into power-law tail is found at the same column density (at \av$\sim$4--5 mag). Low-mass and high-mass SF clouds then have the same low column density distribution, most likely dominated by supersonic turbulence. At higher column densities, collapse and external pressure can form the power-law tail. The relative importance of the two processes can vary between clouds and thus lead to the observed differences in PDF and column density structure.} | \label{intro} Recent years have seen significant progress in understanding the link between the column density and spatial structure of molecular clouds and star formation. Molecular line surveys enabled us to study the velocity structure of clouds and yielded substantial results. Just to name a few, the very complex velocity structure of filamentary clouds was shown in a large Taurus survey (Goldsmith et al. \cite{goldsmith2008}, Hacar et al. \cite{hacar2013}), the influence of large-scale convergent flows as a possible formation mechanism for molecular clouds was demonstrated by Motte et al. (2014), and the importance of global collapse of filaments for the formation of OB clusters was shown in Schneider et al. (2010). However, molecular tracers are restrained by their critical densities and optical depths effects, thus limiting their functionality to study only certain gas phases (for example, low-J CO lines for low-density gas or N$_2$H$^+$ for cold, high-density gas). On the other hand, widefield extinction maps obtained by near-IR color-excess techniques cover a wider range of column densities, typically from N(H+H$_2$) $\sim$0.1--40 10$^{21}$ cm$^{-2}$ (Lada et al. \cite{lada1994}; Lombardi \& Alves \cite{lombardi2001}; Lombardi \cite{lombardi2009}; Cambr\'esy et al. 2011, 2013; Rowles \& Froebrich \cite{rowles2009}; Schneider et al. \cite{schneider2011}). Some major results obtained from these studies are, for example, that there is a relation between the rate of star formation and the amount of dense gas in molecular clouds (Lada et al. \cite{lada2010}), that a universal threshold in visual extinction of \av\ $\approx$6 mag for the formation of stars could exist (Froebrich \& Rowles \cite{froebrich2010}), and that there are characteristic size scales in molecular clouds, indicating the dissipation and injection scales of turbulence (Schneider et al. \cite{schneider2011}). The large-scale far-infrared dust emission photometric observations of {\sl Herschel}\footnote{Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.} (Pilbratt et al. \cite{pilbratt2010}) allow us now to make column density maps with a very wide dynamic range N(H$_2$)$\sim$10$^{20}$ cm$^{-2}$ to a few hundred 10$^{23}$ cm$^{-2}$ at an angular resolution of $\sim$25$''$ to $\sim$36$''$ that provide an exceptional database to better understand the composition and structure of the interstellar medium. One result of {\sl Herschel} is the importance of filaments for the star-formation process. Though the filamentary structure of molecular clouds has always been recognized, only the detailed investigation of the column density structure of filaments (Molinari et al. \cite{molinari2010}, Arzoumanian et al. \cite{doris2011}, Palmeirim et al. \cite{pedro2013}), their link to core formation (e.g., Andr\'e et al. \cite{andre2010}, \cite{andre2014}, Polychroni et al. \cite{poly2013}, K\"onyves et al., in prep.), and their high mass input to form OB clusters (Schneider et al. \cite{schneider2012}, Hennemann et al. \cite{hennemann2012}) emphasized their role for the formation of stars. Despite this progress, there are still a number of important questions that are open. 1. What is the {\sl \emph{relative importance of turbulence, gravity, magnetic fields, and radiative feedback}} for regulating the overall column density structure of molecular clouds? 2. Are there differences in the column density structure of clouds forming \emph{\emph{{\sl \emph{low-mass stars or high-mass stars}}}}? 3. Is there a {\sl \emph{universal (column) density threshold}} for the formation of self-gravitating prestellar cores? 4. Does the\emph{ {\sl \emph{star formation efficiency}}} (SFE) and \emph{{\sl \emph{star-formation rate}}} (SFR) depend on the column density structure of molecular clouds? In a series of papers using column density maps obtained with {\sl Herschel} data and with near-IR extinction and the results of numerical simulations, we address these questions. This paper makes a start with a detailed study of the validity of column density maps and their probability distribution functions (PDFs) obtained from {\sl Herschel}. We show that line-of-sight (LOS) confusion, i.e., emission from diffuse dust mixed with low-density gas as well as denser clouds in front or behind the bulk emission of the molecular cloud, leads to a significant overestimation in the column density maps. Apart from this observational approach, we quantify how the PDF properties change by using numerical simulations in which we add noise and foreground and/or background emission to an uncontaminated PDF. Using the corrected maps, we then study their PDFs and column density profiles to address the question of whether all molecular clouds have a similar column density structure. | In this paper, we present column density maps of four molecular clouds obtained from {\sl Herschel}. These are the Auriga and Maddalena clouds, forming low-mass stars, and Carina and NGC3603 that are UV-illuminated, high-mass star-forming GMCs. We present a simple method of correcting for line-of-sight (LOS) contamination from fore- or background clouds by removing a constant layer of emission and then study the effect of this procedure on the resulting column density structure and the probability distribution functions of column density in observations and simulations. Our findings are: \noindent $\bullet$ The PDFs for all observed clouds become broader, the peak shifts to lower column densities, and the power-law tail of the PDF for higher column densities flattens after correction. \\ \noindent $\bullet$ We simulated the effect of LOS contamination by generating a PDF with typical observational parameters, consisting of a lognormal part and a power-law tail, and then `contaminated' this PDF by adding a constant level to all map values. The simulations show that LOS-contamination strongly compresses the lognormal part of the PDF, consistent with what is observed for distant clouds. The peak of the PDF and the value where the PDF turns from lognormal into a power-law tail (\av(DP)) increases, and the slope of the power-law tail becomes steeper.\\ \noindent $\bullet$ We created plots in which for various contamination levels the change in the PDF width ($\sigma_\eta$) and slope of the power-law tail ($s$) can be assessed. For a contamination of \dav=2 mag, $\sigma_\eta$ is already reduced by more than a factor two, and $s$ has steepened from $-2.0$ to $-2.4$. \\ \noindent $\bullet$ The convolution of the map with the beam has only a minor effect on the high-column density tail of the PDF and no influence on the lower density lognormal distribution. Resolution effects are thus less important when analyzing column density PDFs and cumulative mass functions. \\ \noindent $\bullet$ All observed PDFs that were corrected for LOS-contamination have a lognormal part for low column densities with a peak at \av\, $\sim$2 mag and a deviation point (DP) from the lognormal at \av(DP)$\sim$4--5 mag. For higher column densities, all PDFs have a power-law tail with an average slope of --2.6$\pm$0.5. \\ \noindent $\bullet$ Assuming an equivalent spherical density distribution $\rho \propto r^{-\alpha}$, this average slope corresponds to an exponent $\alpha_{PDF}$ = 1.9$\pm$0.3 consistent with the view that the gas in the power-law tail is dominated by self-gravity (local free-fall of individual cores and global collapse of gas on larger scales, such as filaments). \\ \noindent $\bullet$ Our PDF study suggests that there is a common column density break at \av\ $\sim$4--5 mag for all cloud types where the transition between supersonic turbulence and self-gravity takes place. Our value is lower than the one found by Froebrich \& Rowles (2010) with \av\ = 6.0$\pm$1.5 mag but consistent with cloud simulations of self-gravitating turbulent gas (Ward et al. 2014). \\ \noindent $\bullet$ The average column density for low-mass SF regions (1.8 10$^{21}$ cm$^{-2}$) is slightly lower than the one for high-mass SF clouds (3.0 10$^{21}$ cm$^{-2}$). Because of the small sample (four clouds), and the uncertainties introduced by cropping effects, it is not clear whether this difference is statistically significant. \\ \noindent $\bullet$ Radial column density profiles of three clouds in our sample show a distribution that is compatible with (global) gravitational collapse for Auriga and Carina (slopes correspond to $\alpha$ = 1.5 and 1.8), but requires an additional compression process for NGC3603 ($\alpha$ = 2.5). We suggest that compression from the expanding ionization fronts from the associated \hii\ region leads to a forced collapse. This is consistent with the higher mass fraction at higher column densities in the cumulative mass function and corresponds well with numerical simulations based on compressive driving. \\ \noindent $\bullet$ In view of the differences observed for the slopes of the power-law tail of the PDF and the variation in the run of the column density profiles, we find that the column density structure of clouds forming low-mass stars and the ones forming massive stars are not the same. \\ \noindent $\bullet$ The cumulative mass distributions for high-mass SF regions is shallower than the one for low-mass SF clouds for high column densities, indicating a higher concentration of dense gas in smaller cloud volumes. | 14 | 3 | 1403.2996 |
1403 | 1403.3168_arXiv.txt | We report a systematic multi-wavelength investigation of environments of the brightest cluster galaxies (BCGs), using the X-ray data from the Chandra archive, and optical images taken with 34' $\times$ 27' field-of-view Subaru Suprime-Cam. Our goal is to help understand the relationship between the BCGs and their host clusters, and between the BCGs and other galaxies, to eventually address a question of the formation and co-evolution of BCGs and the clusters. Our results include: 1) Morphological variety of BCGs, or the second or the third brightest galaxy (BCG2, BCG3), is comparable to that of other bright red sequence galaxies, suggesting that we have a continuous variation of morphology between BCGs, BCG2, and BCG3, rather than a sharp separation between the BCG and the rest of the bright galaxies. 2) The offset of the BCG position relative to the cluster centre is correlated to the degree of concentration of cluster X-ray morphology (Spearman $\rho$ = -0.79), consistent with an interpretation that BCGs tend to be off-centered inside dynamically unsettled clusters. 3) Morphologically disturbed clusters tend to harbour the brighter BCGs, implying that the ``early collapse'' may not be the only major mechanism to control the BCG formation and evolution. | 14 | 3 | 1403.3168 |
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1403 | 1403.4865_arXiv.txt | {The Gaia-ESO Survey is a large public spectroscopic survey that aims to derive radial velocities and fundamental parameters of about 10$^5$ Milky Way stars in the field and in clusters. Observations are carried out with the multi-object optical spectrograph FLAMES, using simultaneously the medium resolution (R$\sim$20,000) GIRAFFE spectrograph and the high resolution (R$\sim$47,000) UVES spectrograph. In this paper, we describe the methods and the software used for the data reduction, the derivation of the radial velocities, and the quality control of the FLAMES-UVES spectra. Data reduction has been performed using a workflow specifically developed for this project. This workflow runs the ESO public pipeline optimizing the data reduction for the Gaia-ESO Survey, performs automatically sky subtraction, barycentric correction and normalisation, and calculates radial velocities and a first guess of the rotational velocities. The quality control is performed using the output parameters from the ESO pipeline, by a visual inspection of the spectra and by the analysis of the signal-to-noise ratio of the spectra. Using the observations of the first 18 months, specifically targets observed multiple times at different epochs, stars observed with both GIRAFFE and UVES, and observations of radial velocity standards, we estimated the precision and the accuracy of the radial velocities. The statistical error on the radial velocities is $\sigma\sim$0.4 $\rm km~s^{-1}$ and is mainly due to uncertainties in the zero point of the wavelength calibration. However, we found a systematic bias with respect to the GIRAFFE spectra ($\sim0.9~ \rm km~s^{-1}$) and to the radial velocities of the standard stars ($\sim0.5~ \rm km~s^{-1}$) retrieved from the literature. This bias will be corrected in the future data releases, when a common zero point for all the setups and instruments used for the survey will be established. } | The Gaia-ESO Survey is a large public spectroscopic survey aimed at deriving radial velocities (RVs), stellar parameters, and abundances of about 10$^5$ Milky Way stars in the field and in clusters \citep{Gilmore:2012, Randich:2013}. The observations started at the end of 2011 and are expected to last for about 5 years. The observations are carried out with the multi-object optical spectrograph FLAMES \citep{Pasquini:2002}. This instrument is located at the Nasmyth focus of the UT2 at the Very Large Telescope (VLT) and is composed of a robotic fibre positioner equipped with two sets of 132 and 8 fibres, which feed the optical spectrographs GIRAFFE (R$\sim$20,000) and UVES (R$\sim$47,000), respectively. A good fraction of the spectra ($\sim$3500 from GIRAFFE and $\sim$300 from UVES) observed during the first six months (December 2011-June 2012) have been released and are available at the webpage http://www.eso.org/sci/observing/phase3/data\_releases.html. Twenty working groups (WGs) are in charge of the workflow, which includes all steps from the selection of the targets to be observed to the derivation of the stellar parameters. This paper describes the methods and software used for the reduction of the FLAMES-UVES spectra and for the derivation of RVs and rotational velocities projected along the line of sight ($v \sin i$). We will focus on the spectra gathered during the first 18 months of observations (from December 2011 to June 2013). Whilst all other steps of the workflow are performed in a distributed fashion, namely several nodes analyse the same data, and the results are finally made homogeneous by the WG coordinators, the work discussed in this paper has been carried out by one team based at INAF-Osservatorio Astrofisico di Arcetri. The content of the paper is summarized as follows: in Sect. 2 we briefly describe the target sample and the observations; in Sect. 3 we explain the procedures used for the data reduction of the FLAMES-UVES spectra; in Sect. 4 we describe the methods used to derive RVs and $v\sin i$; in Sect. 5 we summarize our quality control procedure; in Sect. 6 we list the final products of our WG; and in Sect. 7 a summary of the paper is provided. | 14 | 3 | 1403.4865 |
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1403 | 1403.3674_arXiv.txt | As a backend to the first station of the Long Wavelength Array (LWA1) the Prototype All Sky Imager (PASI) has been imaging the sky $>$ -26$^{\circ}$ declination during 34 Gamma Ray Bursts (GRBs) between January 2012 and May 2013. Using this data we were able to put the most stringent limits to date on prompt low frequency emission from GRBs. While our limits depend on the zenith angle of the observed GRB, we estimate a 1$\sigma$ RMS sensitivity of 68, 65 and 70 Jy for 5 second integrations at 37.9, 52.0, and 74.0 MHz at zenith. These limits are relevant for pulses $\geq$ 5 s and are limited by dispersion smearing. For pulses of length 5 s we are limited to dispersion measures ($DM$s) $\leq$ 220, 570, and 1,600 pc cm$^{-3}$ for the frequencies above. For pulses lasting longer than 5s, the $DM$ limits increase linearly with the duration of the pulse. We also report two interesting transients, which are, as of yet, of unknown origin, and are not coincident with any known GRBs. For general transients, we give rate density limits of $\leq$ $7.5\times10^{-3}$, $2.9\times10^{-2}$, and $1.4\times10^{-2}$ yr$^{-1}$ deg$^{-2}$ with pulse energy densities $>1.3\times 10^{-22}$, $1.1\times 10^{-22}$, and $1.4\times 10^{-22}$ J m$^{-2}$ Hz$^{-1}$ and pulse widths of 5 s at the frequencies given above.\\ | Since the discovery of Gamma Ray Bursts (GRBs) by Klebesadel et al. (1973) there have been several groups to propose mechanisms capable of producing prompt low frequency ($< $100 MHz) radio emission observable from Earth. Usov \& Katz (2000) suggested that low frequency radiation could be created by oscillations in the current sheath that separates a strongly magnetized jet and the surrounding ambient plasma. This emission would peak at 1 MHz and drop off following a power law at higher frequencies. The bulk of the emission lies below the ionospheric cutoff of about 10 MHz, but the high frequency tail of this might extend up to frequencies observable by ground based telescopes. The flux density of the high frequency tail is approximated with a power law $\propto \nu^{-1.6}$. As an example they provide a best case estimate of $\sim$10$^{2}$ Jy at 30 MHz. Sagiv \& Waxman (2002) also predict low frequency emission to occur in the early stages of the afterglow (10s after the GRB). In this scenario a strong synchrotron maser condition is created at frequencies below 200 MHz, due to an excess of low energy electrons. The excess is created by a build up of injected electrons that cool to low energies through synchrotron radiation. The effect is amplified when the jet propagates into a medium denser than the ISM. Such a dense environment would exist around high mass Wolf-Rayet stars, which are thought to be the progenitors of long duration GRBs. While no prompt low frequency emission has yet been detected, a future detection would yield a number of constraints on the parameters of GRBs. The dispersion measure (DM) of prompt radio emission would allow estimates of the physical conditions of the region immediately surrounding nearby ($z$ $\lesssim$ 0.5)\footnote{A redshift of 0.5 is chosen because above this point the DM contribution from the intergalactic medium would be roughly equal to the maximum contribution from a galaxy similar to our own (Ioka, 2003). However if the DM of the host galaxy is larger than that of our own, ``nearby'' would include larger redshifts.} GRBs, telling us about the environment in which GRB progenitors are formed. For more distant GRBs the DM would be dominated by the InterGalactic Medium (IGM), thus giving a measurement of the number of baryons in the universe (Ginzburg 1973). For extremely distant ($z$ $>$ 6) GRBs a dispersion measure could act as a probe of the reionization history (Ioka 2003). Over the past three decades there have been many searches for prompt, low frequency GRB emission (Baird et al. 1975, Dessenne et al. 1996, Koranyi et al. 1995, Benz \& Paesold, 1998, Balsano 1999, Morales et al. 2005, Bannister et al. 2012). Of these studies, 2 have been below 100 MHz. Benz \& Paesold (1998) covered the range from 40 - 1000 MHz, had a RMS sensitivity of $\sim 10^{5}$ Jy, and observed during 7 GRBs between February of 1992 and March of 1994. Balsano (1999) covered 72.8 - 74.7 MHz, observed 32 GRBs between September of 1997 and March of 1998, and had a wide range in root mean square (RMS) sensitivities for each GRB. The best limit reported in Balsano (1999) was $\sim$200 Jy for 50 ms integrations. Both of these studies used BATSE triggers, which had a position uncertainty typically around a few degrees. Morales et al. (2005) reported on a planned study centered at 30 MHz. In this paper we present a search for prompt low frequency emission from 34 GRBs using the all-sky imaging capabilities of the Prototype All Sky Imager (PASI), a backend to the first station of the Long Wavelength Array (LWA1). While our objective was to find or place limits on prompt emission from GRBs, we also conducted a search for generic transients occurring during our observations but located elsewhere in the sky. In \S2 we describe the LWA1 telescope and the PASI backend, in \S3 we describe the NASA GCN/TAN (Gamma- ray Coordinates Network / Transient Astronomy Network) and how we made use of it for our observations, in \S4 we discuss how dispersion would effect prompt emission from GRBs, in \S5 we discuss our data, analysis and our results, in \S6 we describe our search for generic transients and our results, in \S7 we describe rate density limits on generic transients, and \S8 is a discussion of our findings. | We have carried out a search for prompt low frequency radio emission from 34 GRBs at 37.9, 52.0, and 74.0 MHz. In this search we found no burst-like emission but have placed limits at these frequencies. Our $1\sigma$ limits for each frequency are listed in Table 1 and range from $\sim$ 200-80 Jy, for $\geq$ 5 second bursts. The range of $DM$s that we are sensitive to depends on the duration of the burst. For 5 second bursts we could see to a maximum of 220, 570, and 1,600 pc cm$^{-3}$ for 37.9, 52.0 and 74.0 MHz. While these limits do not disprove any of the possible emission mechanisms discussed in the introduction of this paper these are the most stringent to this date. In the future we plan to improve our sensitivity by applying deconvolution and phase calibration to our images. We also report two transient events, 121024 and 121118, at 37.9 and 29.9 MHz respectively, that lasted for 75 and 100 seconds. We limit their $DM$s to be approximately $\leq$ 450 and $\leq$ 250 pc cm$^{-3}$. We also have placed rate density limits on general transients with pulse energy densities $>1.3\times 10^{-22}$, $>1.1\times 10^{-22}$, and $1.4\times 10^{-22}$ J m$^{-2}$ Hz$^{-1}$ and pulse widths of 5 s at 37.9, 52.0, and 74.0 MHz. Using the entire sky higher than $30^{\circ}$ above the horizon we find a maximum rate limits of $\leq$ $7.5\times10^{-3}$, $2.9\times10^{-2}$, and $1.4\times10^{-2}$ yr$^{-1}$ deg$^{-2}$ for the frequencies above. If it is true that we should see one FRED transient for every $\leq$ 115 hours of observation at 37.9 MHz then a full analysis on the 1000s of hours of data PASI has collected at this frequency should yield several more. A forthcoming paper will address the results of such a large scale search. | 14 | 3 | 1403.3674 |
1403 | 1403.6117_arXiv.txt | Aberration kernels describe how harmonic-space multipole coefficients of cosmic microwave background (CMB) observables transform under Lorentz boosts of the reference frame. For spin-weighted CMB observables, transforming like the CMB temperature (i.e. Doppler weight $d=1$), we show that the aberration kernels are the matrix elements of a unitary boost operator in harmonic space. Algebraic properties of the rotation and boost generators then give simple, exact recursion relations that allow us to raise or lower the multipole quantum numbers $\ell$ and $m$, and the spin weight $s$. Further recursion relations express kernels of other Doppler weights $d\neq 1$ in terms of the $d=1$ kernels. From those we show that on the full sky, to all orders in $\beta=\varv/c$, $E$- and $B$-mode polarization observables do not mix under aberration if and only if $d=1$. The new relations, fully non-linear in the boost velocity $\beta$, form the basis of a practical recursive algorithm to accurately compute any aberration kernel. In addition, we develop a second, fast algorithm in which aberration kernels are obtained using a set of ordinary differential equations. This system can also be approximately solved at small scales, providing simple asymptotic formulae for the aberration kernels. The results of this work will be useful for further studying the effect of aberration on future CMB temperature and polarization analysis, and might provide a basis for relativistic radiative transfer schemes. | \label{sec:intro} The temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation provide a great deal of information about the origin and evolution of our Universe~\cite{Smoot1992, Mather1994, Hinshaw:2012aka,Ade:2013zuv}. Inflation predicts that the primordial CMB fluctuations have isotropic and gaussian statistics around an average temperature of $\bar T=2.7260 \pm 0.0013~\mathrm{K}$~\cite{Fixsen:1996nj, Fixsen2009} in the CMB rest frame. The anomalously large temperature dipole ($\ell=1$) $\Delta T=3.355 \pm 0.008~\mathrm{mK}$~\cite{dipole} towards Galactic coordinates $(l,b)=(263.99\degree\pm0.14\degree,48.26\degree\pm0.03\degree)$~\cite{Hinshaw:2008kr}, however, indicates that the solar system is moving with respect to the CMB rest frame with a speed $\beta=\varv/c=0.00123$. Therefore, due to the Lorentz boost from the CMB rest frame into our frame, the observed radiation deviates from what would be seen in the CMB rest frame. In addition to the change of the photon energy caused by the Doppler effect (leading to the temperature dipole), due to light aberration the photon's apparent propagation direction is also modified under a Lorentz boost (and so are the polarization direction and plane). This induces coherent, (nearly) dipolar departures from statistical isotropy in both the temperature and the polarization field. Although the Doppler and aberration effects occur independently, by {\it aberration} we henceforth refer to both of them simultaneously, unless stated otherwise. Aberration-induced off-diagonal elements in the CMB covariance matrix can serve as an independent handle to determine the observer's motion~\cite{Challinor:2002zh, Burles:2006xf,Kosowsky:2010jm,Amendola:2010ty,Aghanim:2013suk}. The motion-induced distortion of the CMB statistics should be corrected for before accurate cosmological information can be extracted from the observed temperature/polarization power spectra. Although Ref.~\cite{Challinor:2002zh} first found that the correction is $\mathcal{O}(\beta^2)\sim 10^{-6}$ for the idealistic full-sky situation, it was later on realized that in practice the bias can be $\mathcal{O}(\beta)\sim 10^{-3}$ due to asymmetric sky masks~\cite{Pereira:2010dn,Catena:2012hq,Jeong:2013sxy,Jeong:future}. Moreover, current or incoming experiments with high resolution, e.g. Planck~\cite{Ade:2013kta}, SPT~\cite{Story:2012wx}, ACT~\cite{Fowler:2010cy}, ACTpol~\cite{Niemack:2010wz} and SPTpol~\cite{Austermann:2012ga}, push the investigation of the aberration effects to even larger multipole $\ell$ (i.e., smaller scales). This will be particularly important for polarization data, which encode primordial information to larger $\ell$~\cite{Austermann:2012ga,Niemack:2010wz}. All those aspects call for modelling the aberration effects, for both temperature and polarization anisotropies, on very small angular scales and with great precision. One could in principle undo the aberration effects by ``de-boosting'' the sky in real space~\cite{Menzies2005, Notari:2011sb,Yoho:2012am}. In reality, however, real-space methods suffer from inaccuracies due to the resolution of the pixelization scheme and imperfect knowledge of the window function, because aberration does not preserve the shape and the area of each pixel. This also causes changes to the effective beam of the instrument that have to be considered carefully. To avoid these problems, Ref.~\cite{Jeong:2013sxy} proposed a harmonic-space strategy in which one first boosts the full sky in harmonic space and then transforms into real space to apply the sky mask. The precision of the harmonic-space approach is then guaranteed by accurate determination of the {\it aberration kernels} --- the linear transformation from multipole coefficients in the rest frame to those in the observer's frame. The aberration kernels depend not only on the spherical harmonic multipole numbers $\ell,m$, but also on the spin weight $s$ ($s=0$ and $s=\pm2$, for temperature and polarization, respectively). Furthermore, they differ for different Doppler weight $d$ (which is the power of Doppler factor present in the transformation rules), depending on whether the thermodynamic temperature ($d=1$), the specific intensity ($d=3$) or the frequency-integrated intensity ($d=4$) are being boosted \cite{Challinor:2002zh, Amendola:2010ty}. Below the typical angular scale of aberration, corresponding to $\ell \gtrsim 1/\beta \simeq 800$ or $\delta \theta \simeq 4'$, analytical results up to $\mathcal{O}(\beta^2)$~\cite{Challinor:2002zh} for the kernels break down~\cite{Chluba:2011zh}, and algorithms non-perturbative in $\beta$ are needed. General integral expressions for the kernels have been known, but their highly oscillatory nature makes direct numerical integration unfeasible. The first efficient algorithm for computation of the kernel elements based on recursions was developed in Ref.~\cite{Chluba:2011zh} to push into the non-perturbative regime. Fitting formula for the kernel integrals, approximately valid at small angular scales and tested up to intermediate $\ell\lesssim 700$, were given in Ref.~\cite{Notari:2011sb} to go beyond a power expansion in $\beta$. In this work, we take a more systematic route than previous studies. We show that the $d=1$ kernels are the matrix elements of a unitary boost operator, analogous of the Wigner $D$-functions being the matrix elements of a rotation operator in harmonic space. The unitary operator lives in the Hilbert space of all spin-weighted functions on the sky. It is the exponentiation of the boost generator (valid for infinitesimal boost), parameterized by the rapidity parameter $\eta=\tanh^{-1}\beta$ that is additive under successive boosts. Using rapidity instead of $\beta$ to describe the boost is one of the new insights into the problem that allowed us to generalize previous discussions. The Lorentz algebra, formed by the generators of rotation and boost in harmonic space, then leads to simple linear recursions that relate kernels of different $\ell$, different $m$ and general spin weight $s$. In particular, these expressions are more compact than those given in Ref.~\cite{Chluba:2011zh} and do not require an order-by-order treatment. Moreover, the $d \neq 1$ kernels can be obtained from those of $d=1$ through another set of straightforward recursions. This is particularly interesting since the $d=1$ kernels follow special symmetries that ease their computation. Based on our novel representation of aberration kernels, we obtain two efficient and accurate algorithms to cross check against each other: (i) an elegant recursive algorithm that improves upon Ref.~\cite{Chluba:2011zh} and accounts for kernels of arbitrary $s$ and $d$ (see \refsec{recur}); (ii) a scheme in which kernels are computed using ordinary differential equations (ODEs) as flows in the rapidity $\eta$ (\refsec{ode-rep}). We explain how to implement both algorithms as powerful solutions to boosting the sky in harmonic space. The ODE approach furthermore allows us to derive simple analytic approximations valid at small-scales. The expressions are very similar to those obtained by Ref.~\cite{Notari:2011sb}, however, here we derive them from analytic considerations also improving the range of applicability and testing them to very small scales (\refsec{asymp_exp}). Our code will be available at \url{www.Chluba.de/Aberration}. This paper is organized as follows. \refsec{aber-kernel} reviews the definitions of harmonic-space aberration kernels (for general $s$ and $d$), their integral representations, and their basic properties. In \refsec{matrix-element-rep}, we introduce operators that generate a Lorentz boost in harmonic space, and derive the matrix-element representations for the $d=1$ kernels. In \refsec{EB-mixing}, we show that aberration does not generate mixing between $E$ and $B$ modes for polarization observables with Doppler weight $d=1$. Then in \refsec{recur}, based on the matrix-element representation, we make use of operator algebra and derive recursion relations that relate $d=1$ kernels with adjacent values of $\ell$, $m$, and the spin weight $s$. Immediately following those recursion relations, a practical recursive algorithm to compute the aberration kernels needed is then presented in detail. An alternative method based on solving ODEs, also derived from the operator approach, is developed in \refsec{ode-rep}. We offer some concluding remarks in \refsec{concl}. In \refapp{integral-form}, we include a covariant derivation of the integral forms for both temperature and polarization kernels (we illustrate by the $d=1$ case, but the derivation can be easily generalized to $d \neq 1$). Some symmetry properties of the kernels are proved in \refapp{proofs}. \refapp{Yz-action} is a brief derivation of how the boost generator acts on spherical harmonic base functions. \refapp{sign-spinweight} details a key steps used to prove the conclusion of \refsec{EB-mixing}. \refapp{sP_lm} elaborates on a few numerical techniques that provide initial conditions for our recursive algorithm and quadrature. | \label{sec:concl} In this paper, we found a novel matrix representation for the harmonic-space aberration kernels. Several useful and exact relations are then derived by utilizing the commutation relations for the rotation and boost operators. CMB observables with Doppler weight $d=1$ (e.g., the polarization-averaged temperature and the temperature-weighted Stokes parameters), have the simplest transformation properties. We showed that the $d=1$ kernels are the matrix elements of a boost operator, parameterized by the additive rapidity parameter, between two spherical harmonic base states. The unitarity of the boost operator leads to power conservation laws under aberration, which are valid for $d=1$. The Lorentz algebra, satisfied by generators of rotations (both space-fixed and body-fixed) and boosts, lead to recursion relations that raise or lower the spherical harmonic quantum numbers $\ell$ and $m$, or the spin weight $s$ by one unit. These provide useful identities in analytical calculations. Applying these recursions repeatedly, starting from known kernels of the lowest $\ell$, $|m|$ and $|s|$ as suitable boundary conditions, yields kernels with arbitrary $\ell$, $m$ and $s$. Based on this, the new recursion scheme developed here greatly simplifies previous recursive algorithms at both conceptual and technical levels. It also provides exact values for the aberration kernels to benchmark the accuracy of existing fitting formula. We proved that aberration does not mix up $E$ and $B$ modes for $d=1$ polarization observables to all orders in $\beta$. We argued that for perfect blackbody spectra, $d=1$ kernels are the relevant ones for the study of CMB aberration, independent of experimental details. In the presence of spectrum distortions and foreground emissions, the correct way to account for the aberration effect deserves further consideration. For general purposes, we provided recipes to compute aberration kernels of Doppler weight $d \neq 1$, relevant for boosting, e.g., the specific intensity or the frequency-integrated intensity. Those have been shown to be related to the $d=1$ kernels via $d$-raising/lowering recursions. Another major result derived from the matrix-element representation is the flow of the $d=1$ aberration kernels with the rapidity parameter $\eta$. This leads to coupled ODEs for a set of aberration kernels that in practice can be effectively truncated. The ODE approach is very advantageous because the initial conditions needed, i.e. the kernels for $\eta=0$, are in all cases trivial, and therefore extremely straightforward to set up. Utilizing standard recipes, the ODE approach can improve upon the recursive approach by a factor $\sim 25$ in terms of computational speed, for moderate values of $\beta \sim 10^{-3}$. Parallelization is straightforward in the ODE approach, pushing the computation of the aberration kernel to a few seconds. In the limit of large $\ell$, we find simple asymptotic approximations for the kernel elements from the differential equation system (Sec.~\ref{sec:asymp_exp}). While similar to the expressions given earlier by \cite{Notari:2011sb}, we obtain our approximations with purely analytic arguments. Our approximation generally work very well ($\simeq 0.1\%-5\%$ for $\beta =10^{-3}$ and $\ell \leq 4000$), however, when comparing with our ODE approach we find several cases for which the approximation is very far off. For $\Delta \ell/\ell \ll 1$, our expressions also capture the main dependence of the kernel even for $\beta\simeq 0.1$; however, since the kernel becomes very wide once $\ell\gg 1/\beta$, the approximation still has limited applicability. We thus do not recommend using the expression for real computations, also because the ODE approach already is very fast and reliable. Finally, we emphasize that most of the analytical results obtained in this paper apply to all angular scales $\ell$, arbitrary spin weight $s$ and Doppler weight $d$, being fully non-linear in $\beta$. Therefore, our formalism might find applications in other studies, where anisotropic radiation seen in a (relativistically) boosted reference frame is involved. One example is the scattering of diffuse photon backgrounds by fast-moving charged particles within the jets of active galactic nuclei~\cite{Leismann2005, Mimica2007, Mimica2009}. | 14 | 3 | 1403.6117 |
1403 | 1403.3732_arXiv.txt | The strength and structure of the large-scale magnetic field in protoplanetary discs are still unknown, although they could have important consequences for the dynamics and evolution of the disc. Using a mean-field approach in which we model the effects of turbulence through enhanced diffusion coefficients, we study the time-evolution of the large-scale poloidal magnetic field in a global model of a thin accretion disc, with particular attention to protoplanetary discs. With the transport coefficients usually assumed, the magnetic field strength does not significantly increase radially inwards, leading to a relatively weak magnetic field in the inner part of the disc. We show that with more realistic transport coefficients that take into account the vertical structure of the disc and the back-reaction of the magnetic field on the flow as obtained by Guilet \& Ogilvie (2012), the magnetic field can significantly increase radially inwards. The magnetic-field profile adjusts to reach an equilibrium value of the plasma $\beta$ parameter (the ratio of midplane thermal pressure to magnetic pressure) in the inner part of the disc. This value of $\beta$ depends strongly on the aspect ratio of the disc and on the turbulent magnetic Prandtl number, and lies in the range $10^4-10^7$ for protoplanetary discs. Such a magnetic field is expected to affect significantly the dynamics of protoplanetary discs by increasing the strength of MHD turbulence and launching an outflow. We discuss the implications of our results for the evolution of protoplanetary discs and for the formation of powerful jets as observed in T-Tauri star systems. | The conditions prevailing in protoplanetary discs and their evolution with time are crucial ingredients in the theory of the formation of planetary systems. Magnetic fields have an important impact on the dynamics of protoplanetary discs: they are thought to cause MHD turbulence through the magnetorotational instability \citep{balbus91}, and can launch an outflow through the magnetocentrifugal mechanism \citep{blandford82,ferreira06}. Both of these processes transport angular momentum and therefore largely determine the mass accretion rate and the time-evolution of the disc until its dispersal. The presence of a magnetic field could furthermore directly influence the structure of planetary systems by changing the rate and/or direction of migration of planets embedded in the disc \citep[e.g.][]{terquem03,baruteau11,guilet13a} The presence of a {\it large-scale} poloidal magnetic field is of particular importance for this dynamics. A strong large-scale poloidal magnetic field is indeed necessary for the launching of a magnetocentrifugal outflow from the inner parts of the disc that could explain the powerful collimated jets observed in T-Tauri star systems \citep{ferreira06}. A weaker poloidal field could also enable the launching of a wind at larger radii that could significantly contribute to driving accretion \citep{suzuki09,fromang13,bai13a,bai13b,suzuki13}. The strength of the large-scale poloidal field is furthermore a key ingredient determining the intensity of MRI-driven turbulence, which is generally more vigorous in the presence of a significant poloidal field \citep{hawley95,bai13a}. Numerical simulations of MRI turbulence in the presence of ambipolar diffusion have even suggested that a net vertical magnetic field in the outer parts of protoplanetary discs is necessary to explain observed mass accretion rates \citep{simon13b}. Despite its crucial consequences, the strength of the magnetic field remains very uncertain, both from an observational point of view (since direct measurements of its strength are still lacking) and from a theoretical perspective. The evolution of a large-scale magnetic field in an accretion disc has indeed been a long-standing theoretical problem since \citet{lubow94a} and \citet{heyvaerts96} found that the (outward) diffusion of this field was much more efficient than its (inward) advection in a geometrically thin disc. Their analysis was based on a kinematic mean-field approach in which turbulence is modelled by effective diffusion coefficients: a viscosity $\nu$ and a resistivity $\eta$. The radial diffusion of magnetic flux is driven mostly by the vertical diffusion of radial magnetic field across the vertical scaleheight $H$ of the disc, at a typical speed $\eta/H$. On the other hand, advection is driven by viscous transport of angular momentum at a typical speed $\nu/r$ (where $r$ is the radius) if the magnetic flux is assumed to be transported at the same velocity as mass. The ratio of advection to diffusion velocities is therefore $\frac{\nu}{\eta}\frac{H}{r} = \Pm h$ where $\Pm \equiv \nu/\eta$ is the turbulent magnetic Prandtl number and $h=H/r$ is the aspect ratio of the disc. For a realistic magnetic Prandtl number of order unity as expected from MHD turbulence \citep{pouquet76,lesur09,fromang09,guan09}, this ratio is very small if the disc is geometrically thin. As a consequence of this inefficient advection, the magnetic field strength is almost uniform, leading to a negligibly weak magnetic field in the inner parts of the disc, which is problematic for magnetically driven jet models. Since then, several ideas have been put forward that could increase the advection speed or decrease the diffusion rate of the magnetic field \citep{spruit05,bisnovatyi-kogan07,guilet12}. It was realized, in particular, that the vertical averaging of the induction equation should not be density-weighted as is usually done for hydrodynamical variables, but rather conductivity-weighted, where the conductivity is the inverse of the effective resistivity \citep{ogilvie01,guilet12,guilet13b}. The vertical structure of the disc (in particular of the resistivity and radial velocity) could therefore significantly change the transport rates compared to the crude estimates of \citet{lubow94a}. \citet{bisnovatyi-kogan07} and \citet{rothstein08} have for example proposed that a non-turbulent surface layer could reduce the diffusion rate of the magnetic field. \citet{guilet12,guilet13b} have performed a radially local calculation of the transport rates taking into account the vertical structure of the disc and the back-reaction of the mean magnetic field on the flow. They have found that a non-turbulent surface layer is ineffective at reducing the diffusion, unless it extends into MRI-unstable regions of the disc which are in fact expected to be turbulent. They also found that for strong magnetic fields such that the magnetic pressure is comparable to the midplane thermal pressure, the estimates of \citet{lubow94a} were a good approximation. On the other hand, for weaker fields they showed that the vertical structure of the disc leads to a faster advection by up to a factor 10 compared to the advection of mass, and a slower diffusion of the magnetic field by a factor up to 4 compared to the estimate of \citet{lubow94a}. Indeed, the diffusion rate decreases with decreasing magnetic field strength because the magnetic field lines can bend over a larger height, while the advection velocity increases because of the faster radial velocity in the low-density region away from the midplane. This encouraging result suggests that the magnetic field could be efficiently advected and therefore increase radially inwards, which could therefore potentially solve this long-standing problem. Determining the radial structure and intensity of the magnetic field requires however the study of a global model of an accretion disc, which is the subject of this paper. The theory of star formation suggests that protoplanetary discs may actually form in a highly magnetized state. In fact, if magnetic flux is conserved during the collapse, the magnetic field is too strong and too efficient at removing angular momentum for a rotationally supported disc to form. In the star-formation community the main interest is therefore in how to expel the magnetic flux in order to enable disc formation \citep[e.g.][]{li14}, in contrast to the accretion-disc community which tries to find a way for advection to be more efficient. While part of the magnetic flux may already diffuse out during the collapse itself (for example due to a turbulent resistivity \citep{santos-lima12,joos13}), it is likely that some significant flux remains in the disc when it forms. We will therefore also study the evolution of a protoplanetary disc from a highly magnetized initial condition, and determine on what timescale any initial strong magnetic flux can be diffused out. To better understand the global structure and time-evolution of the large-scale magnetic field in protoplanetary discs, we study a global one-dimensional model of a thin accretion disc. We use a mean-field approach with the effects of turbulence being modelled by diffusion coefficients and we neglect any additional dynamo effect caused by MRI-driven turbulence. The time-evolution of the magnetic field is determined by transport rates (with contributions from both advection and diffusion) for which we consider different prescriptions. We start by considering simple transport rates following \citet{lubow94a}, which are kinematic and therefore independent of the magnetic field strength. These transport rates do not allow much magnetic field advection if a realistic magnetic Prandtl number is used; however, increasing this parameter to larger values enables us in a simple way to study general properties of the magnetic-field structure in a thin accretion disc when advection is efficient. This part of our study is similar to that of \citet{takeuchi13} and \citet{okuzumi13}, who considered the limit of very efficient advection, except that we also study the regime in which advection and diffusion velocities are comparable. We then use the more realistic transport rates computed by \citet{guilet12}, which take into account the vertical structure of the disc and the back-reaction of the mean magnetic field on the flow. In contrast to the transport rates used previously, these depend on the strength of the magnetic field and we will show that they allow a significant advection weaker magnetic fields for a realistic turbulent magnetic Prandtl number. The plan of this paper is as follows. The physical and numerical setup used in this paper is described in Section~\ref{sec:setup}. In Section~\ref{sec:lubow}, we study the time-evolution of the magnetic field when the simple transport coefficients of \cite{lubow94a} are used. We then use the more \textbf{realistic} transport coefficients of \cite{guilet12} in Section~\ref{sec:vertical_structure}. Finally, in Section~\ref{sec:conclusion}, we summarize our results and discuss their consequences for protoplanetary disc evolution and the launching of an outflow. | \label{sec:conclusion} \subsection{Summary of the results} We studied the global structure of the poloidal magnetic field in an accretion disc, with a particular attention to protoplanetary discs. We first used the simple transport rates of the magnetic flux usually assumed in the literature \citep{lubow94a}, which come from a crude kinematic vertical averaging and which are therefore independent of magnetic field strength. If a realistic turbulent magnetic Prandtl number of order unity is used these transport rates do not allow a significant advection of the magnetic field. Varying the magnetic Prandtl number to larger values nevertheless allows us to study in a simple way general properties of the magnetic-field structure and evolution when advection is efficient. We find that the magnetic-field profile evolves towards a stationary state that is independent of the initial magnetic-field profile in the disc (but depends on the assumed uniform ambient magnetic field, i.e.\ the strength of the interstellar magnetic field). It is also independent of the radial profile of effective viscosity (or $\alpha$ parameter) and depends only on the ratio of advection to diffusion velocities (which is here given by ${\textstyle\frac{3}{2}}\Pm h$, with $\Pm$ being the magnetic Prandtl number and $h$ the aspect ratio of the disc). In our simple disc model with uniform aspect ratio and magnetic Prandtl number, this stationary profile is well described by a self-similar solution with a power-law dependence of the magnetic field strength. The ratio of advection to diffusion velocities sets the power-law index of the magnetic-field profile varying between $b=0$ for an inefficient advection when $\Pm h \ll 1$ to $b=-2$ for a very efficient advection when $\Pm h \gg 1$. In this limit of very efficient advection our results are therefore consistent with those of \citet{okuzumi13} with a maximum magnetic field scaling like $r^{-2}$. The normalization of this profile is set by the uniform ambient magnetic field. The magnetic field strength at the outer edge of the disc is always lower or comparable to the strength of the ambient magnetic field, while the total magnetic flux threading the disc is a factor of $1$--$2$ larger than that coming from the ambient magnetic field. The fact that the advection of magnetic field by the disc cannot increase the magnetic field at the outer edge of the disc can be understood by noting that a current ring in the disc tends to increase the magnetic field at smaller radii but to {\rm decrease} it at larger radii. At the outer edge of the disc, the currents in the disc (located at smaller radii) therefore tend to decrease the magnetic field with respect to its interstellar value. We also studied the time-evolution of the magnetic-field profile towards the steady state. Starting from an initial profile shallower than the equilibrium profile, the steady state is reached in an advective timescale (i.e.\ viscous timescale in this simple model), while an initially steeper magnetic-field profile is diffused in a resistive timescale, which is shorter than the viscous timescale by a factor $\Pm h$. We then used the more realistic transport velocities of the magnetic flux that were computed by \citet{guilet12}. These transport velocities take into account the vertical structure of the disc as well as the back-reaction of the magnetic field on the flow. Because they are not kinematic, they depend on the strength of the magnetic field in contrast to the simple model studied before. When the magnetic pressure is comparable to the midplane thermal pressure these transport velocities agree with those of \citet{lubow94a}. For lower magnetic field strength, however, the advection velocity increases reaching up to 10 times higher than the advection velocity of mass, while the diffusion rate decreases by a factor of up to 4. This difference comes from the fact that the advection velocity of the magnetic flux is a conductivity-weighted average (rather than a density-weighted average for the advection of mass) and is therefore strongly affected by large radial velocities occurring at a height where the density is low. The dependence on the magnetic field strength is due to the fact that this average should be taken up to the height where the magnetic pressure equals the thermal pressure, which increases when the magnetic field strength is decreased. Using these transport rates, we showed for the first time that the magnetic field can be efficiently advected in a protoplanetary disc with a realistic turbulent magnetic Prandtl number of order unity. Owing to this advection, the magnetic field at the inner edge of the protoplanetary disc is found to be up to five orders of magnitudes larger than its interstellar value, when the ratio of outer to inner disc radii is $10^3$. This is only slightly less than the six orders of magnitudes expected for a very efficient advection as studied by \citet{okuzumi13}. Note that this amplification factor would be even larger if the disc were more extended. Because the transport rates depend on the magnetic field strength, the radial profile of magnetic field in a stationary state can be more complicated than the self-similar power law found in the calculation with simple transport rates. We nevertheless find a tendency of the magnetic-field profile to tend towards a self-similar configuration where the ratio of midplane thermal pressure to magnetic pressure $\beta_0$ is independent of radius. This is possible for an equilibrium value of $\beta_0$, which depends steeply on the aspect ratio of the disc and the turbulent magnetic Prandtl number. For a turbulent magnetic Prandtl number of order unity, the equilibrium value of $\beta_0$ is found to be in the range $\beta_0 \sim 10^4-10^7$ for aspect ratios typical of protoplanetary discs in the range $h = 0.03-0.1$. If the interstellar magnetic field strength (which roughly sets the magnetic field strength at the outer edge of the disc) corresponds to a value of $\beta$ at the disc outer edge larger than its equilibrium value, then the magnetic-field profile is steeper than the self-similar profile such that the equilibrium value of $\beta$ is reached at smaller radii. Conversely, if the interstellar magnetic field is larger than the equilibrium value at the outer edge of the disc, the magnetic profile is shallower, and $\beta$ increases with radius until it reaches its equilibrium value. This behaviour is due to the fact that the ratio of advection to diffusion velocities increases with decreasing magnetic field strength, such that weak fields lead to steeper magnetic-field profiles than stronger fields. The relevance to protoplanetary discs of this steady-state magnetic-field configuration depends on the time it takes for the initial magnetic-field configuration to evolve towards its final steady state. Protoplanetary discs are likely to form in a rather strongly magnetized state, although some magnetic flux may already be lost to enable disc formation \citep{joos13}. We therefore studied the time-evolution of the magnetic field from a strongly magnetized initial condition (while the disc is kept fixed in a steady state). We find that a significant fraction of the excess magnetic flux is expelled from the disc in a resistive timescale which is significantly shorter than the viscous timescale driving the evolution of the protoplanetary disc. \subsection{Consequences for protoplanetary discs} Our results show that the strength of the large-scale poloidal magnetic field at the outer edge of a protoplanetary disc is roughly equal to (or slightly smaller than) the interstellar ambient magnetic field. Owing to the inward advection of magnetic flux counterbalancing its outward diffusion, the magnetic field increases radially inwards from this value. The slope of the profile is such that at smaller radii it reaches an equilibrium value of the ratio of midplane thermal pressure to magnetic pressure in the range $\beta_0 \sim 10^4-10^7$ (depending on the aspect ratio of the disc, with thicker discs leading to stronger magnetic fields). Such a magnetic field strength is rather weak in the sense that the magnetic pressure remains significantly smaller than the thermal pressure at the disc midplane. It can however have profound consequences on the dynamics of protoplanetary discs. At radii of 1 to a few AU, it could for example quench MRI turbulence and enable the launching of an outflow powerful enough to drive accretion at a rate compatible with observations, when the effects of ambipolar diffusion are taken into account \citep{bai13b,bai13c}. At larger radii of a few tens of AU where ambipolar diffusion is significant, it could by contrast foster the development of MRI turbulence \citep{simon13b}. It is remarkable that the range of equilibrium $\beta_0$ found in our analysis coincides with the values needed in these studies in order to explain the observed mass accretion rates. One major motivation to study the large-scale magnetic field in protoplanetary discs is to explain the powerful collimated jets observed in T-Tauri star systems. The collimation is most likely caused by a large-scale magnetic field \citep[e.g.][]{cabrit07b}, and \citet{ferreira06} argued that a self-collimated extended disc wind launched by a magnetocentrifugal mechanism is needed to explain the observations. Our finding that the magnetic field strength increases radially inwards is very encouraging in this respect. But is it enough? Self-similar models of outflows magnetocentrifugally launched from a disc \citep[e.g.][]{ferreira97,casse00} require a strong magnetization of the disc with $\beta_0 \sim 1-10$. This is significantly lower than the values found in this paper, which might indicate at first sight that the magnetic field amplification we find is not sufficient for these models. However, note that because the outflow is very efficient at removing angular momentum from the disc, the surface density of such a jet-emitting disc can be several orders of magnitudes lower than that of a standard $\alpha$ disc with the same mass accretion rate \citep{combet08}. As a consequence the same magnetic field strength could correspond to a large value of $\beta_0$ in a standard accretion disc and to a low value of $\beta_0$ in a jet-emitting disc. In a jet-emitting disc where the jet is responsible for the angular momentum extraction from the disc, the vertical magnetic field strength depends on the mass accretion rate through: \begin{equation} B_{\rm jet} = 0.2\, \left(\frac{M}{M_\odot} \right)^{1/4}\left( \frac{\dot{M}}{10^{-7}M_\odot/{\rm year}}\right)^{1/2}\left(\frac{r}{1\,{\rm AU}}\right)^{-5/4} \frac{1}{q^{1/2}}\, {\rm G}, \label{eq:B_jet} \end{equation} where $q$ is the ratio of azimuthal to vertical magnetic field strength at the surface of the disc. In an $\alpha$-disc model, where angular momentum is transported by a turbulent viscosity, the magnetic field strength is related to the mass accretion rate and the $\beta_0$ parameter by: \begin{eqnarray} B_{\alpha - \rm disc } &=& 0.15\, \left(\frac{M}{M_\odot} \right)^{1/4}\left( \frac{\dot{M}}{10^{-7}M_\odot/{\rm year}}\right)^{1/2}\left(\frac{r}{1\,{\rm AU}}\right)^{-5/4} \nonumber \\ && \left(\frac{10^{-2}}{\alpha}\right)^{1/2} \left(\frac{0.05}{h}\right)^{1/2} \left(\frac{10^4}{\beta_0}\right)^{1/2} \, {\rm G}. \label{eq:B_alphadisc} \end{eqnarray} This opens the possibility that a standard accretion disc with a value of $\beta_0$ comparable to the low end of equilibrium $\beta_0$ found in this study could have a transition in its inner parts to a jet-emitting disc (with a value of $\beta_0$ of order unity). Combining the two above equations, the ratio of the magnetic field strength in a jet-emitting disc to that in the outer $\alpha$-disc with the same accretion rate is: \begin{equation} \frac{B_{\rm jet}}{B_{\alpha-{\rm disc}}} = \frac{3\alpha h \beta_0}{8 q}, \label{eq:B_ratio_jet_alpha-disc} \end{equation} This ratio can equal 1 (as required at the transition) for $\beta_0=10^4$ in the outer disc, and plausible parameter values of $\alpha=10^{-2}$, $h=0.05$ and $q=2$. Note that, for $h=0.05$ as typical of the inner parts of protoplanetary discs, we have found in Section~\ref{sec:vertical_structure_stationary} an equilibrium value of $\beta_0\simeq 2.10^5$, corresponding to a magnetic field strength $4-5$ times weaker than required for this transition to a jet emitting disc. However, the right equilibrium field strength would be obtained by assuming a turbulent magnetic Prandtl number of $\Pm=2$ (instead of 1), since $\beta_0=10^4$ is obtained for $\Pm h=0.1$ (Figure~\ref{fig:betaeq_h}). Such a value of $\Pm$ is plausible, as numerical simulations suggest that the turbulent magnetic Prandtl number is of order unity within a factor of a few \citep{lesur09,fromang09,guan09}. The magnetic field strength required for a transition to a jet-emitting disc in the inner parts of the protoplanetary disc can therefore be obtained within the uncertainties of our model. This scenario should be studied further in a model that includes the outflow and its feedback on accretion. An alternative scenario is that an outflow could be launched from a rather weakly magnetised disc as suggested by local disc models \citep{suzuki09,fromang13,bai13a,bai13b}. Whether such outflows can explain the observations remains, however, to be established. Observational constraints on the magnetic field in protoplanetary discs can come from the polarisation (or lack of it) of submillimeter emission. Above a critical magnetic field strength, dust grains are indeed expected to align with magnetic field lines and therefore to emit polarised radiation \citep{lazarian07,cho07}. Despite early claims of such detection \citep{tamura99}, recent observations have so far been unable to detect any polarisation and have put stringent constraints on the polarisation level coming from protoplanetary T-Tauri and Herbig Ae/Be discs \citep{hughes09,hughes13,krejny09}. This lack of detection could be explained either by an inefficient grain alignment, a disordered magnetic field structure or a weak magnetic field strength \citep{hughes09}. We note that the rather low magnetic field strength we predict in the outer parts of protoplanetary discs (due to the efficient diffusion of a potentially strong initial field) is well below the critical strength for grain alignment of $10-100\, {\rm mG}$ estimated by \citet{hughes09}. This may be part of the explanation for the lack of polarisation detection in T-Tauri and Herbig Ae/Be discs. The recent detection of polarisation from a young embedded disc (in the class 0 protostellar system IRAS 16293-2422) may be an indication that the magnetic field strength does indeed decrease with time \citep{rao14}. Note, however, that our analysis only predicts the mean poloidal magnetic field strength, and that a stronger potentially disordered magnetic field may well be present in the disc. Sensitive, higher resolution observations with ALMA could shed more light on this issue by resolving the disc scale height and/or probing inner regions of the disc. The lifetime of a protoplanetary disc is set by the viscous timescale at the outer edge of the disc, or the timescale at which an outflow can drive accretion if such an outflow can be launched at these large radii. Both of these processes should depend on the strength of the large-scale poloidal magnetic field at the outer edge of the disc. Indeed, the viscous timescale depends on the strength of MRI driven turbulence, which is enhanced by the presence of such a field \citep{simon13b}, and the presence of an outflow removing angular momentum requires a large-scale magnetic field. Our results show that advection of magnetic field cannot increase the magnetic field strength at the outer edge of the disc, which remains weaker or comparable to the interstellar ambient magnetic field. We also found that an excess magnetic flux initially present in the disc would be diffused away in a timescale shorter than the lifetime of the disc. This suggests that the lifetime of a protoplanetary disc should be anticorrelated with the strength of the ambient interstellar magnetic field surrounding it (independently of the initial magnetic field in the disc), with stronger magnetic field leading to shorter lifetime. \citet{armitage13} have proposed a model to explain the observed two-timescale dispersal of protoplanetary discs, which relies on the evolution of a disc in the presence of a large-scale poloidal magnetic field. In this scenario, the disc first spreads viscously due the action of MHD turbulence. In a second step, a magnetically driven outflow disperses the disc in a much shorter timescale, once the surface density has decreased enough for the outflow to have a significant impact. A crucial ingredient of this scenario is the time-evolution and radial profile of the large-scale poloidal magnetic field. \citet{armitage13} did not compute it consistently, but deduced it from two simplifying assumptions: the total magnetic flux enclosed inside the disc is conserved during evolution, and the radial profile of magnetic field strength is such that the ratio of the midplane thermal pressure to magnetic pressure is uniform (though the effect of relaxing this second assumption was also studied). Our results provide some support for the second assumption, albeit mostly if the ambient interstellar magnetic field corresponds to the equilibrium value of $\beta$ at the outer edge of the disc. On the other hand, our analysis contradicts the first assumption. According to our results, an excess magnetic flux initially present in the disc should diffuse away in a timescale that is shorter than the viscous timescale. Once the magnetic field has reached a steady state (for a given disc profile at a given time), the total magnetic flux enclosed within the disc should then be between 1 and 2 times the flux of the uniform ambient interstellar field at the outer edge of the disc (which evolves with time). While this raises questions about the quantitative results of \citet{armitage13}, it does not disqualify the scenario they envisage. According to our results, once the magnetic-field configuration has reached a quasi-steady state, the magnetic field at the outer edge of the disc should be approximately independent of time, and as the surface density decreases with time due to viscous spreading the value of $\beta$ should decrease, and ultimately a magnetically driven outflow might indeed be able to drive a fast dispersal. It would be interesting to study this scenario more quantitatively by considering a time-evolving protoplanetary disc model with the magnetic-field evolution computed like in this paper. Last but not least, we stress that our analysis is restricted by a number of simplifying assumptions, the validity of which should be quantitatively checked in the future. Firstly, our mean-field analysis relies on a very simple description of turbulence by isotropic effective diffusion coefficients (viscosity and resistivity). The effects of turbulence may be much more complex than this, with for example anisotropic diffusion as well a dynamo $\alpha$ effect that could impact our results and may enable a large-scale dynamo in addition to the advection-diffusion picture studied here. Secondly, we assumed that no outflow was launched from the disc. The presence of an outflow could change our results in several ways. It could play an important role in driving accretion \citep{bai13b,bai13c}, which may help reaching even larger magnetic fields. The presence of currents in the outflow could also change the magnetic-field structure, for example changing the inclination of the magnetic field lines at the surface of the disc for a given flux distribution. Thirdly, we considered a very simple steady-state underlying disc in order to focus on the magnetic-field evolution. A real disc should be viscously spreading with time, which can affect the magnetic-field structure \citep{okuzumi13}. Finally, we have not taken into account ambipolar diffusion and the Hall effect, which are expected to have an important impact on the outer parts of protoplanetary discs \citep{simon13b,kunz13}. Future work should take these processes into account in order to obtain a more precise description of the magnetic-field evolution. | 14 | 3 | 1403.3732 |
1403 | 1403.5672_arXiv.txt | Determining the equation of state of matter at nuclear density and hence the structure of neutron stars has been a riddle for decades. We show how the imminent detection of gravitational waves from merging neutron star binaries can be used to solve this riddle. Using a large number of accurate numerical-relativity simulations of binaries with nuclear equations of state, we find that the postmerger emission is characterized by two distinct and robust spectral features. While the high-frequency peak has already been associated with the oscillations of the hypermassive neutron star produced by the merger and depends on the equation of state, a new correlation emerges between the low-frequency peak, related to the merger process, and the total compactness of the stars in the binary. More importantly, such a correlation is essentially universal, thus providing a powerful tool to set tight constraints on the equation of state. If the mass of the binary is known from the inspiral signal, the combined use of the two frequency peaks sets four simultaneous constraints to be satisfied. Ideally, even a single detection would be sufficient to select one equation of state over the others. We test our approach with simulated data and verify it works well for all the equations of state considered. | 14 | 3 | 1403.5672 |
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1403 | 1403.2787_arXiv.txt | Research teams are the fundamental social unit of science, and yet there is currently no model that describes their basic property: size. In most fields teams have grown significantly in recent decades. We show that this is partly due to the change in the character of team-size distribution. We explain these changes with a comprehensive yet straightforward model of how teams of different sizes emerge and grow. This model accurately reproduces the evolution of empirical team-size distribution over the period of 50 years. The modeling reveals that there are two modes of knowledge production. The first and more fundamental mode employs relatively small, {\it core} teams. Core teams form by a Poisson process and produce a Poisson distribution of team sizes in which larger teams are exceedingly rare. The second mode employs {\it extended} teams, which started as core teams, but subsequently accumulated new members proportional to the past productivity of their members. Given time, this mode gives rise to a power-law tail of large teams (10-1000 members), which features in many fields today. Based on this model we construct an analytical functional form that allows the contribution of different modes of authorship to be determined directly from the data and is applicable to any field. The model also offers a solid foundation for studying other social aspects of science, such as productivity and collaboration. | The significant change in the character of team-size distribution is the key insight underlying the proposed model. Previous studies have shown a marked increase in the {\it mean} team size in recent decades, not only in astronomy [e.g, 2, 22], but in all scientific fields [5]. Specifically, the average team size in astronomy grew from 1.5 in 1961-1965 to 6.7 in 2006-2010 (marked by arrows in Fig.\ 1, which shows, on a log-log scale, team-size distributions in the field of astronomy in two time periods). However, Figure 1 reveals even more: a recent distribution (2006-2010) is not just a scaled-up version of the 1961-1965 distribution shifted towards larger values; it has a profoundly different shape. Most notably, while in 1961-1965 the number of articles with more than five authors was falling precipitously, and no article featured more than eight authors, now there exists an extensive tail of large teams, extending to team sizes of several hundred authors. The tail closely follows the {\it power-law} distribution (red line in Fig.\ 1). The power-law tail is seen in recent team-size distributions of other fields as well [23]. In contrast, the ``original'' 1961-1965 distribution did not feature a power-law tail. Instead, most team sizes were in the vicinity of the mean value. The shape of this original distribution can instead be described with a simple Poisson distribution (blue curve in Fig.\ 1), an observation made in some previous works [10, 20]. Note that the time when the distribution stopped being Poisson would differ from field to field. \begin{figure} \centering \includegraphics[width=0.5\textwidth]{Figure1.pdf}\caption{Distribution of article team sizes in astronomy in two time periods separated by 45 years. The distribution from 1961-1965 is well described by a Poisson distribution (blue curve). This is in contrast to 2006-2010 distribution, which features an extensive power-law tail (red line). Arrows mark the mean values of each distribution. For $k >10$ ($k>5$for 1961-65) the data are binned in intervals of 0.1 decades, thus revealing the behavior far in the tail, where the frequency of articles of a given size is up to million times lower than in the peak. All distributions in this and subsequent figures are normalized to the 2006-2010 distribution in astronomy. Error bars in this and subsequent figures correspond to one standard deviation. The full dataset consists of 154,221 articles published between 1961 and 2010 in four core astronomy journals (listed in SI), which publish the majority of research in this field [24]. Details on data collection are given elsewhere [25].} \label{fig:emp} \end{figure} We interpret the fact that the distribution of team sizes in astronomy in the 1960s is well described as a stochastic variable drawn from a Poisson distribution to mean that {\it initially} the production of a scientific paper used to be governed by a {\em Poisson process} [26, 27]. This is an intuitively sound explanation because many real-world phenomena involving low rates arise from a Poisson process. Examples include pathogen counts [28], highway traffic statistics [29], and even sports scores [30]. Team assembly can be viewed as a low-rate event, because its realization involves few authors out of a very large possible pool of researchers. Poisson rate ($\lambda$) can be interpreted as a characteristic number of authors that are necessary to carry out a study. The actual realization of the process will produce a range of team sizes, distributed according to a Poisson distribution with the mean being this characteristic number. In contrast, the dynamics behind the power-law distribution that features in team sizes in recent times is fundamentally different from a simple Poisson process, and instead suggests the operation of a process of {\em cumulative advantage}. Cumulative advantage, also known as the Yule process, and as preferential attachment in the context of network science [31, 32], has been proposed as an explanation for the tails of collaborator and citation distributions [23, 32-38]. Unlike the Poisson process, cumulative advantage is a dynamic process in which the properties of a system depend on its previous state. How did a distribution characterized by a Poisson function evolve into one that follows a power law? Does this evolution imply a change in the mode of the team assembly? Does a Poisson process still operate today? Figure 1 shows that for smaller team sizes ($k < 10$) the power law breaks down, forming instead a ``hook.'' This small-$k$ behavior must not be neglected because the great majority of articles (90\%) are still published in teams with fewer than ten authors. The hook, peaking at teams with two or three authors, may represent a vestige of what was solely the Poisson distribution in the past. This simple assumption is challenged by the fact that no single Poisson distribution can adequately fit the small-$k$ portion of the 2006-10 team-size distribution. Namely, the high ratio of two-author papers to single-author papers in the 2006-10 distribution would require a Poisson distribution with $\lambda = 2 P_{k=2}/ P_{k=1} = 5.5$. Such distribution produces a peak at $k = 5$, which is significantly offset compared to its actual position. Evidently, the full picture involves some additional elements. In the following section we present a model that combines the aforementioned processes and provides answers to the questions raised in this section, demonstrating that knowledge production occurs in two principal modes. | The model proposed in this paper successfully explains the evolution of the sizes of scientific teams as manifested in author lists of research articles. It demonstrates that team formation is a multi-modal process. Primary mode leads to relatively small core teams the size of which may represent the typical number of researchers required to produce a research paper. The secondary mode results in teams that expand in size, and which are presumably employed to carry out research that requires expertise or resources from outside of the core team. These two modes are responsible for producing the hook and the power law-tail in team size distribution, respectively. This two-mode character may not be exclusive to team sizes. Interestingly, a similarly shaped distribution consisting of a hook and a power-law tail is characteristic of another bibliometric distribution, that of the number of citations that an article receives. Recently a model was proposed that successfully explained this distribution [33] by proposing the existence of two modes of citation, direct and indirect, where the latter is subject to cumulative advantage. Understanding the distribution of the number of coauthors in a publication is of fundamental importance, as it is one of the most basic distributions that underpin our notions of scientific collaboration and the concept of ``team science''. The principles of team formation and evolution laid out in this work have the potential to illuminate many questions in the study of scientific collaboration and communication, and may have broader implications for research evaluation. | 14 | 3 | 1403.2787 |
1403 | 1403.7155.txt | {\emph{Kepler} ultra-high precision photometry of long and continuous observations provides a unique dataset in which surface rotation and variability can be studied for thousands of stars. Because many of these old field stars also have independently measured asteroseismic ages, measurements of rotation and activity are particularly interesting in the context of age-rotation-activity relations. In particular, age-rotation relations generally lack good calibrators at old ages, a problem that this \emph{Kepler} sample of old-field stars is uniquely suited to address. We study the surface rotation and photometric magnetic activity of a subset of 540 solar-like stars on the main-sequence and the subgiant branch for which stellar pulsations have been measured. The rotation period was determined by comparing the results from two different analysis methods: i) {the projection onto the frequency domain of the time-period analysis}, and ii) the autocorrelation function (ACF) of the light curves. Reliable surface rotation rates were then extracted by comparing the results from two different sets of calibrated data and from the two complementary analyses. General photometric levels of magnetic activity in this sample of stars were also extracted by using a photometric activity index, which takes into account the rotation period of the stars. We report rotation periods for 310 out of 540 targets (excluding known binaries and candidate planet-host stars); our measurements span a range of 1 to 100 days\footnote{Tables 3 and 4 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/}. The photometric magnetic activity levels of these stars were computed, and for 61.5\% of the dwarfs, this level is similar to the range, from minimum to maximum, of the solar magnetic activity. We demonstrate that hot dwarfs, cool dwarfs, and subgiants have very different rotation-age relationships, highlighting the importance of separating out distinct populations when interpreting stellar rotation periods. Our sample of cool dwarf stars with age and metallicity data of the highest quality is consistent with gyrochronology relations reported in the literature. } | Stellar rotation fundamentally modifies stellar interiors \citep[e.g.][]{1992A&A...265..115Z, 1997ARA&A..35..557P, 2004A&A...425..229M,2009A&A...495..271D, 2010A&A...519A.116E, 2013A&A...555A..54C, 2013A&A...549A..74M}. When this is considered in the stellar evolution models, the inferred age of the star is modified, which has severe consequences in planetary systems, for example \citep[e.g.][]{2009Natur.462..168P}. Surface rotation can also be used as an observable to determine the age of the star. Gyrochronology --the empirical relationship between rotation period, color, and age -- provides means by which surface rotation can be used to infer ages of cool stars. These relationships, however, must be calibrated for different stellar populations, and rely on systems in which both rotation periods and stellar ages can be independently measured. The relationship between rotation period and age was first noted by \citet{1972ApJ...171..565S}, followed by many studies relating rotating periods to magnetic activity \citep[e.g.][]{1984ApJ...287..769N,1984ApJ...279..763N,1987A&A...177..155R,1995A&A...294..515H,2008ssma.book.....S}. In 1999, \citeauthor{lachaume1999} used surface rotation rates for the first time as an age diagnostic. Gyrochronology relations have since been developed and refined by works such as \citet{pace2004}, \citet{2007ApJ...669.1167B}, \citet{cardini2007}, \citet{mamajek2008}, \citet{2009ApJ...695..679M}, \citet{2011ApJ...733..115M}, \citet{barnes2010}, and \citet{2012ApJ...746..102C} and have been used to unveil solar twins and analogs in the \emph{Kepler} sample of stars \citep{2014ApJ...790L..23D}. In general, these authors found relationships with a similar time dependence, but expanded upon the color and mass dependencies that become evident with larger datasets. Corresponding theoretical work seeks to provide angular momentum loss laws that reproduce the observed spin-down \citep{1988ApJ...333..236K,reiners2012} and produce the gyrochronology relationship. Both these theoretical endeavours and a refinement of gyrochronology as a tool require independent period and age calibrators to make further progress. This existing body of work focuses exclusively on main-sequence stars, but subgiants and evolved stars are also expected to show an interesting period evolution \citep[e.g.][]{schrijver1993} with a different relationship between period and age \citep{2013ApJ...776...67V}. During the past decades, the detailed knowledge of stellar evolution has been improved thanks to the observational constraints provided by helio- and asteroseismology \citep[e.g.][]{2010AN....331..866C}. Solar-type stars show global physical characteristics similar to the Sun. In particular, they have stochastically excited modes as a result of an outer convective envelope \citep[e.g.][]{1977ApJ...212..243G,1994ApJ...424..466G,2008A&A...478..163B}. %These oscillations continue to be excited when the star becomes a red giant \citep[e.g.][]{2009Natur.459..398D,2010ApJ...713L.176B,2010A&A...517A..22M} and even in massive B-type stars as shown by \citet{2009Sci...324.1540B}. Solar-type stars are generally slow rotators (in most cases $v \sin \rm{i} < 20$ kms$^{-1}$), and the influence of rotation on the oscillation frequencies is well known. However, distortion due to the centrifugal force can have a strong impact on the oscillation frequencies even for slow rotators \citep[e.g.][and references therein]{2009LNP...765...45G,2010AN....331.1038R}. This effect is stronger for acoustic (p) modes with small inertia, which are more sensitive to the outer layers of the star. Therefore, their frequencies are more sensitive to the physical properties of the surface, where the centrifugal force becomes more efficient \citep[e.g.][]{2010ApJ...721..537S,2012A&A...542A..99O}. The induced perturbations are of the same order of magnitude --or even stronger-- as the effects of turbulence or diffusion, which are currently considered the origin of the so-called surface effects. It is thus important to study the surface rotation of other stars that are similar to the Sun and have higher rotational velocities. This could allow us to better understand the role of rotation in comparison to other surface effects and, hence, to properly interpret the oscillation spectra of solar-like stars, at least in the high-frequency domain. With the advent of the detection of mixed modes in subgiant and giant stars \citep[e.g.][]{2011Sci...332..205B,2011Natur.471..608B,2011A&A...532A..86M,2013ApJ...765L..41S,2013ApJ...767..158B,2014ApJ...781L..29B} --including some belonging to a few clusters \citep{2011ApJ...739...13S,2011ApJ...729L..10B}-- it is now possible to infer the core rotation rate of these stars \citep{2012Natur.481...55B,2012A&A...548A..10M,2013EPJWC..4303012D,2013A&A...549A..75G}, which is still difficult to determine for solar-like stars and even for the Sun \citep[e.g.][]{GarCor2004,2007Sci...316.1591G,2008AN....329..476G}. In a few cases it is not only possible to obtain an averaged internal rotation rate \citep[e.g.][]{2013PNAS..11013267G,2013A&A...549A..12M,2013ApJ...766..101C}, but indications of the rotation profile from the external outer convection zone to the inner radiative core using inversion techniques \citep[][]{2012ApJ...756...19D,2014A&A...564A..27D,2014A&A...564A..36B}, as is also commonly done for the Sun \citep[e.g.][]{ThoJCD2003,2008SoPh..251..119G,2008A&A...484..517M,2013SoPh..287...43E}. Unfortunately, in the stellar case --because only low-degree modes are observable-- the inversion is increasingly uncertain close to the surface and measurements of the surface rotation rate are required. A better knowledge of the rotation profiles would be fundamental to answering long-standing questions about stellar interiors, transport of angular momentum, and rotational mixing. Hence the seismic analysis and the complementary study of the surface rotation are crucial. High-quality photometric time series obtained by the \emph{Kepler} mission \citep{2010Sci...327..977B,2010ApJ...713L..79K} can be used to study the surface rotation and magnetic activity of solar-like stars in which eigenmodes are measured. Indeed, when a star is active \citep[e.g.][]{2010Sci...329.1032G,2010IAUS..264..120L}, starspots periodically cross the visible stellar disk. This produces a modulation in the brightness of the star that can be measured \citep[e.g.][]{2009A&A...506..245M,2012ASPC..462..133G,2012A&A...548L...1D}. The time evolution of these fluctuations provides a measurement of the surface velocity at the latitudes of the spots \citep[e.g.][]{2009A&A...506...41G,2011A&A...530A..97B,2013MNRAS.432.1203M,2013A&A...557L..10N}, which can also lead to a determination of the surface differential rotation \citep[e.g.][]{2009A&A...506...51B,2009arXiv0908.2244M,2010A&A...518A..53M,2012A&A...543A.146F,2013A&A...557A..11R,2014arXiv1402.6691L}. The photometric variability of stars observed by \emph{Kepler} \citep[e.g.][]{2010ApJ...713L.155B,2013ApJ...769...37B} can be related to the surface magnetism at the time scales associated with the rotation periods. Therefore, the amplitude of the photometric modulation in the light curve can be used as an indicator of the surface magnetic variability, as recently demonstrated for the Sun \citep[e.g.][]{2013JPhCS.440a2020G,2014JSWSC...4A..15M}, on long and short timescales. Using a variability metric directly obtained from the light curve, \citet{2014ApJ...783..123C} confirmed that amplitudes of solar-like oscillations are suppressed in stars with increased levels of surface magnetic activity. %The set of stars used in this paper corresponds to the one analysed by \citet{2014ApJS..210....1C}. It contains solar-like stars exhibiting p-mode pulsations. Knowledge of their magnetic variability, associated with their rotation rate, will add extra constraints to the seismic ones. %{\it Indeed, \citet{2013JPhCS.440a2020G} showed that the variance of \textbf{the more than 16 years-long VIRGO/SPM} \citep{1995SoPh..162..101F} time series is \textbf{highly} correlated with the radio flux at 10.7 cm, which is one of the common magnetic proxies used to characterize the solar magnetic cycle.} In the present work, we study the surface rotation rate and the photometric magnetic variability in the subset of 540 \emph{Kepler} solar-like stars studied by \citet{2014ApJS..210....1C}, for which accurate fundamental global parameters such as radius, masses, and ages have been inferred from the combination of asteroseismic and photometric observations. This seismic stellar sample has a potential impact on the field of gyrochronology, in which stellar rotation periods are used as a proxy for age. The period-age relations are empirically calibrated with stellar systems for which independent ages and rotation periods are measured. Several calibrations are reported in the literature \citep{pace2004,2007ApJ...669.1167B, mamajek2008, 2009ApJ...695..679M, 2011ApJ...733L...9M}, but they consistently struggle to find a calibration set at old ages and long rotation periods. \emph{Kepler} light curves provide means to measure both the stellar age through asteroseismology, and the rotation periods through spot modulation for an old field star population, and as such represent an important contribution to the gyrochronological calibrators. We describe the preparation of the \emph{Kepler} light curves in Sect.~\ref{Sec:obs}, extract precise rotation periods in Sect.~\ref{Sec:rot}, and study the projected photospheric magnetic-activity levels in Sect.~\ref{Sec:sph}. Finally, in Sect. 5, we explore the correlation between asteroseismic age, rotation, evolutionary state, and mass. We also discuss surface magnetic activity diagnostics as inferred from \emph{Kepler} light curves. %Help from Mark, Jen, etc | \label{Conclu} We have analysed a homogeneous set of 540 main-sequence and subgiant pulsating stars presented in \citet{2014ApJS..210....1C} and extracted reliable surface rotation periods and photometric activity indexes for 310 stars. To do so, we combined two detection methods (GWPS and ACF) with two ways of preparing the light curves (PDC-MAP and KADACS). Special care was taken to properly identify all the binaries in the sample in the bibliography. These stars were divided into three different categories, hot stars ($T_{\rm{eff}} >$ 6250 K), cool main-sequence dwarfs ($T_{\rm{eff}} \leq$ 6250 K, $\log g >$ 4.0), and subgiants (green, $T_{\rm{eff}} \leq$ 6250K, $\log g \leq$ 4.0). As expected, the hotter stars spin faster than the cool main-sequence dwarfs because their thin convective envelopes and presumably weak dynamos result in very weak magnetic braking. Subgiants can have periods of $\sim$10-100 days, depending on the main-sequence temperature and degree of expansion that the star has undergone on the subgiant branch. A total of 15 KOIs were in our sample. We failed to find any close-in planet around fast-rotating stars, confirming the results obtained by \citet{2013ApJ...775L..11M}. We found important differences in the rotation-age relationship between hot dwarfs, cool dwarfs, and subgiants. These differences highlight the importance of population effects for interpreting gyrochronology relationships. A subset of the data in which we have very precise age estimates from the detailed analysis of individual frequencies and spectroscopic constraints has a slope different from that of the entire sample and consistent with expectations from the literature. As soon as more precise asteroseismic ages (based on individual oscillation frequencies and spectroscopic observations) are determined for other stars in this sample, it will be possible to expand the gyrochonology seismic analysis to more \emph{Kepler} field stars. We found that the photometric magnetic activity $\langle S_{ph,k=5} \rangle$ for most of the solar-like pulsating stars in our sample is similar to that of the Sun during its magnetic activity cycle. Indeed, 61.5\% of the dwarfs have values similar to those of the Sun. However, the high dispersion found in our results might reflect that we did not cover the full magnetic activity cycle of many of the stars in our sample. Other factors, such as the unknown stellar inclination axis, will also contribute to this dispersion. Therefore, we for stars similar to the Sun, $\langle S_{ph,k=5} \rangle$ is probably a good indicator of the magnetic activity of the star during the observed time. However, because \emph{Kepler} has ``only'' observed during four years so far, the variability of the star might not be representative of the average stellar magnetic activity during its full stellar magnetic cycle, and hence, we were unable to extract any reliable activity-rotation or age-activity relations. Further studies will be necessary to extract a subset of stars for which at least a full magnetic cycle has been observed and then be able to properly establish these relations. %\appendix % | 14 | 3 | 1403.7155 |
1403 | 1403.1926_arXiv.txt | {The previously identified source SSTB213 J041757 is a proto brown dwarf candidate in Taurus, which has two possible components A and B. It was found that component B is probably a class 0/I proto brown dwarf associated with an extended envelope.} {Studying molecular outflows from young brown dwarfs provides important insight into brown dwarf formation mechanisms, particularly brown dwarfs at the earliest stages such as class 0, I. We therefore conducted a search for molecular outflows from SSTB213 J041757.} {We observed SSTB213 J041757 with the Submillimeter Array to search for CO molecular outflow emission from the source.} {Our CO maps do not show any outflow emission from the proto brown dwarf candidate.} {The non-detection implies that the molecular outflows from the source are weak; deeper observations are therefore needed to probe the outflows from the source.} | Since molecular outflows are a basic component of the star formation process, studying the molecular outflow properties will help us understand the star formation mechanism. For brown dwarfs (BD), some observations have been carried out in the past few years to characterize jets and molecular outflows in class II BDs, very low-mass (VLM) stars (Whelan et al. \cite{whelan05}, Phan-Bao et al. \cite{pb08,pb11}), and proto BD candidates (Bourke et al. \cite{bourke}, Kauffmann et al. \cite{kau}). These observations have suggested that the outflow process occurs in BDs as a scaled-down version of that in low-mass stars, providing additional evidence that BDs form like stars. However, it is still unclear how this physical process occurs at earlier stages, such as at classes 0, I of the BD formation process, because we lack identification and studies of BDs at these classes. Therefore, observations of molecular outflows from BDs at these earliest stages are clearly important to complete our understanding of BD formation mechanism. These observations will also provide strong constraints on BD formation theory (e.g., Machida et al. \cite{machida}). Taurus is a nearby star-forming region ($\sim$145 pc) where many class II BDs have been identified and studied. The region is therefore a good target to study the BD formation process. For class II BDs and VLM stars, Phan-Bao et al. (\cite{pb11}) have reported the first detection of a bipolar molecular outflow from MHO~5, a VLM star of 90~$M_{\rm J}$. The molecular outflow from MHO~5 shows similar properties as seen in ISO-Oph~102 (a young BD in $\rho$ Ophiuchi, Phan-Bao et al. \cite{pb08}) such as low-velocity ($<$5~km~s$^{-1}$), compact structure (500$-$1000~AU), small outflow mass ($10^{-6}-10^{-3}M_{\odot}$), and low mass-loss rate ($10^{-10}-10^{-6}M_{\odot}yr^{-1}$). For BDs at ealier classes, Barrado et al. (\cite{barrado}) have reported the detection of a proto BD candidate SSTB213 J041757 (hereafter J041757) with two possible components, SSTB213 J041757 A and SSTB213 J041757 B (hereafter J041757-A and J041757-B). Luhman et al. (\cite{luhman10}) spectroscopically classified J041757-A as an M2 background dwarf star and suggested that the proper motion of J041757-B is inconsistent with membership in Taurus. Palau et al. (\cite{palau}) recently reported a detection of centimeter continuum emission at the position of J041757-B, which is attributed to thermal free-free emission due to shocks in the jet of J041757-B driven by a central object. The detection has implied that J041757-B might be a proto BD. J041757-B is therefore a good target for our ongoing program of characterizing molecular outflows in the substellar domain. We thus conducted a search for molecular outflows from the proto BD candidate with the Submillimeter Array (SMA). This paper presents our millimeter observations of J041757 and discusses the nature of the source. \begin{table*} \caption{SMA observing log for SSTB213 J041757} \label{log} $$ \begin{tabular}{llccc} \hline \hline \noalign{\smallskip} Target & ~~~~~~~~~~~~~~~~Position & Configuration & Beam size & 1.3~mm continuum emission \\ & $\alpha$(J2000)~~~~~~~~~~~$\delta$(J2000) & & ($\arcsec \times \arcsec$) & (mJy) \\ J041757 & 04$^{\rm h}$ 17$^{\rm m}$ 57.75$^{\rm s}$ +27$^{\rm o}$ 41$\arcmin$ 05.5$\arcsec$ & Compact & $3.34 \times 2.79$ & $<$1 \\ \hline \end{tabular} $$ \end{table*} | We presented our SMA observations of the proto BD candidate J041757-B and discussed two possible scenarios on the nature of the source: a proto BD in Taurus and a background giant. Based on our observations and currently available data, we conclude that the molecular outflows from the proto BD candidate are weak, therefore, more sensitive radio observations are required to explore the outflows and the dense envelope/core associated with J041757-B to confirm its nature. | 14 | 3 | 1403.1926 |
1403 | 1403.1103_arXiv.txt | We consider the dynamics of a cosmological substratum of pressureless matter and holographic dark energy with a cutoff length proportional to the Ricci scale. Stability requirements for the matter perturbations are shown to single out a model with a fixed relation between the present matter fraction $\Omega_{m0}$ and the present value $\omega_{0}$ of the equation-of-state parameter of the dark energy. This model has the same number of free parameters as the $\Lambda$CDM model but it has no $\Lambda$CDM limit. We discuss the consistency between background observations and the mentioned stability-guaranteeing parameter combination. | Introduction} Among the alternative approaches to describe the dark cosmological sector, consisting of dark matter (DM) and dark energy (DE), so called holographic DE models have received considerable attention \cite{cohen,li}. The underlying holographic principle states that the number of degrees of freedom in a bounded system should be finite and related to the area of its boundary \cite{tH}. On this basis, a field theoretical relation between a short distance (ultraviolet) cutoff and a long distance (infrared) cutoff was established \cite{cohen}. Such relation ensures that the energy in a box of size $L$ does not exceed the energy of a black hole of the same size. If applied to the dynamics of the Universe, $L$ has to be a cosmological length scale. Different choices of this cutoff scale result in different DE models. For the most obvious choice, the Hubble scale, only models in which DM and DE are interacting with each other also nongravitationally, give rise to a suitable dynamics \cite{DW,HDE}. Following Ref.~\onlinecite{li}, there has been a considerable number of investigations based on the future event horizon as cutoff scale. All models with a cutoff at the future event horizon, however, suffer from the serious drawback that they cannot describe a transition from decelerated to accelerated expansion. A future event horizon does not exist during the period of decelerated expansion. We are focussing here on a further option that has received attention more recently, a model based on a cutoff length proportional to the Ricci scale. A distance proportional to the Ricci scale has been identified as a causal connection scale for perturbations \cite{brustein}. As a cutoff length in DE models it was first used in Ref.~\onlinecite{gao}. Subsequent investigations include Ref.~\onlinecite{cai} and, for the perturbation dynamics, Refs.~\onlinecite{fengli,karwan,yuting}.\\ Here, we reconsider the dynamics of a two-component system of pressureless DM and Ricci-type DE both in the homogeneous and isotropic background and on the perturbative level\cite{SRJW,SRJW2}. Whereas most dynamic DE scenarios start with an assumption for the equation-of-state (EoS) parameter for the DE, the starting point of holographic models is an expression for the DE energy density from which the EoS is then derived. As was pointed out in Ref.~\onlinecite{SRJW}, the mere definition of the holographic DE density, independently of the choice of the specific cutoff length, implies an interaction with the DM component. Requiring this interaction to vanish is equivalent to impose an additional condition on the dynamics. In the case of Ricci-type DE this condition establishes a simple relation between the matter fraction and the necessarily time-dependent EoS parameter. Of course, a time-varying EoS parameter is not compatible with a cosmological constant. Our main aim here is to perform a gauge-invariant perturbation analysis for this model. It will turn out that the general perturbation dynamics suffers from instabilities. There exists just one single configuration without instabilities at finite values of the scale factor $a$ \cite{karwan,SRJW2}. We also update previous tests of the homogeneous and isotropic background dynamics using recent results for the differential age of old objects based on the $H(z)$ dependence, data from SNIa and from BAO. | Summary} Noninteracting Ricci-type DE is characterized by a necessarily time-dependent EoS parameter. This makes it an observationally testable alternative to the $\Lambda$CDM model. There exists a a relationship between this EoS parameter and the matter content of the Universe. The ratio of the energy densities of DM and DE varies considerably less than for the $\Lambda$CDM model. Since the time of radiation decoupling it has changed by about one order of magnitude compared with roughly nine orders of magnitude for the $\Lambda$CDM model. This amounts to a remarkable alleviation of the coincidence problem. Ricci-type DE behaves almost as dust at high redshift. Our statistical analysis, based on recent observational data from SNIa, BAO and $H(z)$, results in a preferred value of $c^{2}\approx 0.46$ for the Ricci-DE parameter which confirms earlier studies in the literature \cite{gao}. Within a gauge-invariant analysis we calculated the matter perturbations as a combination of the total energy perturbations of the cosmic medium and the relative perturbations of the components. The perturbation dynamics suffers from instabilities that exclude a present phantom-type EoS. It is only for a specific relation between the values $\Omega_{m0}$ of the present matter density and the present EoS parameter $\omega_{0}$ that the dynamics remains stable for any finite scale-factor value. This relation corresponds to a Ricci-DE parameter $c^{2}= 0.5$ \cite{karwan}. Holographic Ricci-type DE represents a theoretically appealing scenario which does not need additional parameters except $H_{0}$ and $\Omega_{m0}$. Despite of its attractive features, the stable configuration is only marginally consistent with the observationally preferred background values of $\Omega_{m0}$ and $\omega_{0}$. | 14 | 3 | 1403.1103 |
1403 | 1403.8022_arXiv.txt | {} {An improved method for estimating distances to open clusters is presented and applied to Hipparcos data for the Pleiades and the Hyades. The method is applied in the context of the historic Pleiades distance problem, with a discussion of previous criticisms of Hipparcos parallaxes. This is followed by an outlook for Gaia, where the improved method could be especially useful.} {Based on maximum likelihood estimation, the method combines parallax, position, apparent magnitude, colour, proper motion, and radial velocity information to estimate the parameters describing an open cluster precisely and without bias. } {We find the distance to the Pleiades to be $120.3 \pm 1.5$ pc, in accordance with previously published work using the same dataset. We find that error correlations cannot be responsible for the still present discrepancy between Hipparcos and photometric methods. Additionally, the three-dimensional space velocity and physical structure of Pleiades is parametrised, where we find strong evidence of mass segregation. The distance to the Hyades is found to be $46.35\pm 0.35$ pc, also in accordance with previous results. Through the use of simulations, we confirm that the method is unbiased, so will be useful for accurate open cluster parameter estimation with Gaia at distances up to several thousand parsec.} {} | Open clusters have long been used as a testing ground for a large number of astronomical theories. Determining the distances to nearby open clusters is critical, since they have historically formed the first step in the calibration of the distance scale. Because all stars within an open cluster are expected to have the same age and metallicity, accurate distance estimates are highly useful in calibrating the main sequence and checking stellar evolutionary theory through comparison with theoretical isochrones. Until recently, accurate distances to even the most nearby clusters have not been possible. The Hipparcos astrometric mission of 1989 \citep{Hipparcos} for the first time gave accurate parallax measurements for over one hundred thousand stars and has been used extensively to give direct distance measurements to more than 30 open clusters. Still, many questions remain. While revolutionary in its time, the milliarcsecond astrometry and limiting magnitude ($H_p$\textless$12.5$) of Hipparcos allow calculating distances to only the nearest open clusters, and even then do so with a precision no better than a few percentage points. Owing to the relatively small size of most open clusters compared with their distances and the precision of measurements, the Hipparcos data has been unable to give definitive answers about the internal structure and physical size of such clusters. Additionally, the release of the Hipparcos catalogue in 1997 has led to some controversy. The most famous is the case of the Pleiades, where methods based on Hipparcos data (\cite{FVL1997}, \cite{robichon}, \cite{mermilliod}) gave a distance estimate that was some 10\% shorter than works based on photometric methods (\cite{MSfitting1}, \cite{MSfitting2}, \cite{photometricDistance}) (see Sect. \ref{sec:correlations}). With the launch of Gaia, the European Space Agency's second major astrometric satellite, the situation is set to change. Building on the success of Hipparcos, Gaia will provide micro-arcsecond astrometric precision and a limiting magnitude of 20, which will revolutionise many aspects of astronomy. With the above in mind, it is apparent that a new method is required that is capable of squeezing the maximum precision from the currently available data and is capable of utilising information from the full range of observed quantities (astrometric, photometric, and kinematic information). This will be particularly true after the launch of Gaia, which will produce a rich dataset that will include not only accurate parallax measurements, but also photometry at millimag precision and a full set of kinematics obtained from proper motions combined with radial velocity measurements from the on-board radial velocity spectrometer (for stars with $G_{RVS}$\textless$17$). The use of trigonometric parallaxes can be problematic, and care must be taken to account for effects such as the \cite{lutzkelker} or \cite{malmquist} biases, sample selection effects and non-linear transformations, such as those highlighted by \cite{Arenou2} and \cite{Arenou1}. In Sect. \ref{sec:methods} the rationale behind the method is described, followed by the exact mathematical formulation in Sect. \ref{sec:math}. A description of the observational data used is given in Sect. \ref{sec:data}, and the results of application of the method to the Pleiades and Hyades given in Sects. \ref{sec:pleiades} and \ref{sec:hyades}. The possible effects of correlated errors in the Hipparcos catalogue are discussed in Sect. \ref{sec:correlations}. The use of the method with Gaia data is tested using simulations in Sect. \ref{sec:OutlookForGaia}. | \label{sec:discussion} An improved method for estimating the properties of open clusters has been presented, and tested using real data on two nearby and well studied open clusters. In addition to distance estimation, internal kinematics and spatial structure were probed, with mass segregation detected in the case of the Pleiades. These results confirm that the method performs as expected and highlight the potential future uses of such a method when high quality parallax information is available from the Gaia mission. After revisiting the `Pleiades problem', we find that an explanation cannot be found in error correlation problems in Hipparcos. Through the use of simulations we find that Gaia will measure the distance to Pleiades stars with precision of a fraction of a percent, enabling a conclusion to this long running discrepancy. The ML method can be extended further to give more detailed information, such as including a model for cluster ellipticity and orientation. It is possible to include and compare different spatial and kinematic distributions, allowing one to test predictions on spatial structure, mass segregation, and peculiar motions, and to test for other properties such as cluster rotation. In the case of the absolute magnitude distribution, it would be possible to give age and metallicity estimates by fitting and comparing sequences of different theoretical isochrones. Unresolved binaries, which complicate studies of open clusters, can be detected using the posterior distances calculated using the ML method and the resulting colour-magnitude diagram. It is possible to extend the method to use a distribution in absolute magnitude that is asymmetrical around the main sequence, in order to consider undetected unresolved binaries within the method. As mentioned in Sect. \ref{sec:pleiades}, a lack of quality radial velocity data for Hipparcos Pleiades stars limits the application of the method in fitting the full three-dimensional kinematics of the open cluster. This is expected to change when Gaia comes to fruition, because all stars with $G_{RVS}<17$ will have radial velocity information from the on-board radial velocity spectrometer. Additionally, very high quality radial velocities for stars in more than 100 open clusters will become available through the Gaia ESO Survey \citep{GES}, expanding the scope of the method's application to clusters at much greater distances. | 14 | 3 | 1403.8022 |
1403 | 1403.5839.txt | Despite years of high accuracy observations, none of the available theoretical techniques has yet allowed the confirmation of a moon beyond the solar system. Methods are currently limited to masses about an order of magnitude higher than the mass of any moon in the solar system. I here present a new method sensitive to exomoons similar to the known moons. Due to the projection of transiting exomoon orbits onto the celestial plane, satellites appear more often at larger separations from their planet. After about a dozen randomly sampled observations, a photometric orbital sampling effect (OSE) starts to appear in the phase-folded transit light curve, indicative of the moons' radii and planetary distances. Two additional outcomes of the OSE emerge in the planet's transit timing variations (TTV-OSE) and transit duration variations (TDV-OSE), both of which permit measurements of a moon's mass. The OSE is the first effect that permits characterization of multi-satellite systems. I derive and apply analytical OSE descriptions to simulated transit observations of the \textit{Kepler} space telescope assuming white noise only. Moons as small as Ganymede may be detectable in the available data, with M stars being their most promising hosts. Exomoons with the 10-fold mass of Ganymede and a similar composition (about 0.86 Earth radii in radius) can most likely be found in the available \textit{Kepler} data of K stars, including moons in the stellar habitable zone. A future survey with \textit{Kepler}-class photometry, such as \textit{Plato 2.0}, and a permanent monitoring of a single field of view over 5 years or more will very likely discover extrasolar moons via their OSEs. | \label{sec:context} Although more than 1000 extrasolar planets have been found, no extrasolar moon has been confirmed. Various methods have been proposed to search for exomoons, such as analyses of the host planet's transit timing variation \citep[TTV;][]{1999A&AS..134..553S,2007A&A...470..727S}, its transit duration variation \citep[TDV;][]{2009MNRAS.392..181K,2009MNRAS.396.1797K}, direct photometric observations of exomoon transits \citep{2011ApJ...743...97T}, scatter analyses of averaged light curves \citep{2012MNRAS.419..164S}, a wobble of the planet-moon photocenter \citep{2007A&A...464.1133C}, mutual eclipses of the planet and its moon or moons \citep{2007A&A...464.1133C,2009PASJ...61L..29S,2012MNRAS.420.1630P}, excess emission of transiting giant exoplanets in the spectral region between 1 and 4\,$\mu$m \citep{2004AsBio...4..400W}, infrared emission by airless moons around terrestrial planets \citep{2009AsBio...9..269M,2011ApJ...741...51R}, the Rossiter-McLaughlin effect \citep{2010MNRAS.406.2038S,2012ApJ...758..111Z}, microlensing \citep{2002ApJ...580..490H}, pulsar timing variations \citep{2008ApJ...685L.153L}, direct imaging of extremely tidally heated exomoons \citep{2013ApJ...769...98P}, modulations of radio emission from giant planets \citep{2013arXiv1308.4184N}, and the generation of plasma tori around giant planets by volcanically active moons \citep{2014ApJ...785L..30B}. Recently, \citet{2012ApJ...750..115K} started the \textit{Hunt for Exomoons with Kepler} (HEK),\footnote{\href{http://www.cfa.harvard.edu/HEK}{www.cfa.harvard.edu/HEK}} the first survey targeting moons around extrasolar planets. Their analysis combines TTV and TDV measurements of transiting planets with searches for direct photometric transit signatures of exomoons. Exomoon discoveries are supposed to grant fundamentally new insights into exoplanet formation. The satellite systems around Jupiter and Saturn, for example, show different architectures with Jupiter hosting four massive moons and Saturn hosting only one. Intriguingly, the total mass of these major satellites is about $10^{-4}$ times their planet's mass, which can be explained by their common formation in the circumplanetary gas and debris disk \citep{2006Natur.441..834C}, and by Jupiter opening up a gap in the heliocentric disk during its own formation \citep{2010ApJ...714.1052S}. The formation of Earth is inextricably linked with the formation of the Moon \citep{1976LPI.....7..120C}, and Uranus' natural satellites indicate a successive ``collisional tilting scenario'', thereby explaining the planet's unusual spin-orbit misalignment \citep{2012Icar..219..737M}. Further interest in the detection of extrasolar moons is triggered by their possibility to have environments benign for the formation and evolution of extrasolar life \citep{1987AdSpR...7..125R,1997Natur.385..234W,2013AsBio..13...18H}. After all, astronomers have found a great number of super-Jovian planets in the habitable zones (HZs) of Sun-like stars \citep{IJA:9150120}. In this paper, I present a new theoretical method that allows the detection of extrasolar moons. It can be applied to discover and characterize multi-satellite systems and to measure the satellites' radii and orbital semi-major axes around their host planet, assuming roughly circular orbits. This assumption is justified because eccentric moon orbits typically circularize on a million year time scale due to tidal effects \citep{2011ApJ...736L..14P,2013AsBio..13...18H}. The method does not depend on a satellite's direction of orbital motion (retrograde or prograde), and it relies on high-accuracy averaged photometric transit light curves. I refer to the physical phenomenon that generates the observable effect as the Orbital Sampling Effect (OSE). It causes three different effects in the phase-folded light curve, namely, (1) the photometric OSE, (2) TTV-OSE, and (3) TDV-OSE. Similarly to the photometric OSE, the scatter peak method developed by \citet{2012MNRAS.419..164S}Ê\ makes use of orbit-averaged light curves. But I will not analyze the scatter. While the scatter peak method was described to be more promising for moons in wide orbits, the OSE works best for close-in moons. Also, with an orbital semi-major axis spanning $82\,\%$ of the planet's Hill sphere, the example satellite system studied by \citet{2012MNRAS.419..164S} would only be stable if it had a retrograde orbital motion \citep{2006MNRAS.373.1227D}. | \label{subsec:conclusions} This paper describes a new method for the detection of extrasolar moons, which I refer to as the Orbital Sampling Effect (OSE). It is the first technique that allows for reproducible detections of extrasolar multiple satellite systems akin to those seen in the solar system. The OSE appears in three flavors: (1) the photometric OSE (Section~\ref{sub:photoOSE}), (2) the TDV-OSE (Section~\ref{subsec:TDV-OSE}), and (3) the TTV-OSE (Section~\ref{subsec:TTV-OSE}). The photometric OSE can reveal the satellite radii in units of stellar radii as well as the planet-moon orbital semi-major axes, but it cannot constrain the satellite masses. TDV-OSE and TTV-OSE can both constrain the satellite mass. PhotometricÊ\, OSE, TDV-OSE, and TTV-OSE offer important advantages over other established techniques for exomoon searches because (1) they do not require modeling of the moons' orbital movements around the planet-moon barycenter during the transit, (2) planet-moon semi-major axes, satellite radii, and satellite masses can be measured or fit with analytical expressions (Equations~(\ref{eq:OSE_multi}), (\ref{eq:ProbDens_TDV}), (\ref{eq:ProbDens_TTV})), and (3) the photometric OSE is applicable to multi-satellite systems. TDV-OSE and TTV-OSE can also reveal the masses of moons in multi-satellite systems, but this parameterization is beyond the scope of this paper. My simulations of photometric OSE detections with \textit{Kepler}-class photometry show that Ganymede-sized exomoons orbiting Sun-like stars cannot possibly be discovered in the available \textit{Kepler} data. However, they could be found around planets as far as 0.1\,AU from a $0.7$ solar mass K star or as far as 0.2\,AU from a $0.4\,M_\odot$ M dwarf. The latter case includes planet-moon binaries in the stellar HZ. Exomoons with the 10-fold mass of Ganymede and Ganymede-like composition (implying radii around $0.86\,R_\oplus$) are detectable in the \textit{Kepler} data around planets orbiting as far as 0.2\,AU from a Sun-like host star, 0.4\,AU from the K dwarf star, or about 0.2\,AU from the M dwarf. The latter two cases both comprise the respective stellar HZ. What is more, such large moons are predicted to form locally around super-Jovian host planets \citep{2006Natur.441..834C,2010ApJ...714.1052S} and are therefore promising targets to search for. To model realistic light curves or to fit real observations with a photometric OSE model, stellar limb darkening needs to be included into the simulations (Heller et al., in preparation). Effects on $N_\mathrm{obs}$ are presumably small for planet-moon systems with low impact parameters, because the stellar brightness increases to roughly $60\,\%$ when the incoming moon has traversed only the first $5\,\%$ of the stellar radius during a transit \citep{2004A&A...428.1001C}. What is more, effects of red noise have not been treated in this paper, and so the numbers presented in Figure~\ref{fig:Nobs} are restricted to systems where either (1) the host star is photometrically quiet at least on a $\approx10$ hr timescale or (2) removal of red noise can be managed thoroughly. The prescriptions of the three OSE flavors delivered in this paper can be enhanced to yield the sky-projected angle between the orbital planes of the satellites and the diameter of the star. In principle, the photometric OSE allows measuring the inclinations of each satellite orbit separately. The effect of mutual moon eclipses will be small in most cases but offers further room for improvement. Ultimately, when proceeding to real observations, a Bayesian framework will be required for the statistical assessments of moon detections. As part of frequentists statistics, the $\chi^2$ method applied in this paper is only appropriate because I do not choose between different models since the injected moon architecture is known a priori. Another application of the OSE technique, which is beyond the scope of this paper, lies in the parameterization of transiting binary systems. If not only the secondary constituent (in this paper the moon) shows an OSE but also the primary (in this paper the planet), then both orbital semi-major axes ($a_1$ and $a_2$) around the common center of mass can be determined. If the total binary mass $M_\mathrm{b}=M_1+M_2$ were known from stellar radial velocity measurements, then it is principally possible to calculate the individual masses via $a_1/a_2=M_2/M_1$ and substituting, for example, $M_1=M_\mathrm{b}-M_2$. This procedure, however, would be more complicated than in the model presented in this paper, because the center of the primary transit could not be used as a reference anymore. Instead, as both the primary and the secondary orbit their common center of mass, this barycenter would need to be determined in each individual light curve and used as a reference for phase-folding. To sum up, the photometric OSE, the TDV-OSE, and the TTV-OSE constitute the first techniques capable of detecting extrasolar multiple satellite systems akin to those around the solar system planets, in terms of masses, radii, and orbital distances from the planet, with currently available technology. Their photometric OSE signals should even be measurable in the available data, namely, that of the \textit{Kepler} telescope. After the recent failure of the \textit{Kepler} telescope, the upcoming \textit{Plato 2.0} mission is a promising survey to yield further data for exomoon detections via OSE. To increase the likelihood of such detections, it will be useful to monitor a given field of view as long as possible, that is, for several years, rather than to visit multiple fields for shorter periods. \appendix | 14 | 3 | 1403.5839 |
1403 | 1403.3089_arXiv.txt | *{} \abstract{Models of radiation transport in stellar atmospheres are the hinge of modern astrophysics. Our knowledge of stars, stellar populations, and galaxies is only as good as the theoretical models, which are used for the interpretation of their observed spectra, photometric magnitudes, and spectral energy distributions. I describe recent advances in the field of stellar atmosphere modelling for late-type stars. Various aspects of radiation transport with 1D hydrostatic, LTE, NLTE, and 3D radiative-hydrodynamical models are briefly reviewed.} | \label{sec:1} Models of stellar atmospheres and spectral line formation are a crucial part of observational astrophysics. The models are our ultimate link between observations of stars and their fundamental physical parameters. On the one side, the models allow us to go from observable quantities, i.e stellar fluxes, spectral energy distributions, and photometric magnitudes, to physical parameters of stars, such as effective temperature $\teff$, surface gravity $\logg$, metallicity $\feh$, abundances, rotation and turbulent velocities. The atmospheric models also allow us to convert theoretical bolometric luminosities from stellar evolution models to their observable quantities, theoretical colours, which are then compared with observations. E.g., model vs observed colour-magnitude diagrams are used to determine distances and ages of clusters and field stars. The shapes of stellar energy distributions (SED) serve as a diagnostics of inter-stellar and circumstellar reddening. There are mass- and age-sensitive diagnostics in stellar spectrum, such as the ultra-violet Ca H and K lines, which may help to tell a young star from an old star. Detailed chemical abundances are arguably the most important physical quantities, which can be only deciphered from a stellar spectrum. They link stellar properties to nucleosynthesis of elements in the Big Bang, in stars at the end of their life-times, in violent explosions, caused by stellar interactions, and by cosmic ray acceleration in the interstellar medium. This connection forms the basis of important diagnostics methods to constrain formation and evolution of stars, stellar populations, and galaxies. In short, all fundamental physical stellar quantities critically depend on the models we use for the analysis of observations. Until recently, we could only use the simplest 1D hydrostatic models in local thermodynamic equilibrium (LTE) for stellar parameter determinations, for more sophisticated models were far too computationally expensive. Calculation of a 3D radiative-hydrodynamical (3D RHD) model required months of CPU time, which was of little use for any practical application in spectroscopic analysis. Moreover, the accurate solution of radiation transport even in the time-independent scheme has been too demanding for quantitative applications. Non-local thermodynamic equilibrium (NLTE) calculations were disfavoured for several reasons. First, inversion of large matrices in the complete linearisation scheme (for solving coupled statistical equilibrium equations in non-LTE) was prohibitive for atoms with complex atomic structure. Furthermore, lack of accurate ab initio calculations or experimental atomic data lead to the need to introduce simplified treatment of several types of atomic processes in vastly more complex non-LTE calculations, which caused a wide-spread misconception that non-LTE calculations are of questionable advantage. \begin{svgraybox} It is crucial to realise that non-LTE is not an approximation, in contrast to LTE, which approximates all collision rates by the infinitely large numbers, and fully ignores the influence of radiation field in stellar atmospheres on the energy distribution of matter. One may however, solve time-dependent rate equations, or drop the time dependence, which reduces the problem to solving the equations of statistical equilibrium only (see below). \end{svgraybox} However, the theory of radiative transfer in stellar atmospheres is one of the most mature fields in astrophysics (e.g. the fundamental work by \citealt{Mihalas:1979ux}) and the numerical implementation of the theory has seen substantial improvement over the past decade. Moreover, we have enough computational power to simulate stellar convection in 3D and solve for radiative transfer explicitly taking into account the interaction of gas particles with the radiation field. In this lecture I summarise the main progress in modelling atmospheres and spectra of cool, FGKM, stars, that has been made during the past decade, and provide a timeline for the developments in the field which can be expected in the near future. I do not touch upon the problems of radiative transfer in more complex cases, such as expanding supernova shells \citep{Lucy:1999wd} or dusty AGB envelopes \citep[][ and ref. therein]{Hofner:2003vf}, or chromospheres \citep[e.g.][]{Hansteen:2007wn}. | We are now entering the new era of observational stellar astrophysics, moving away from 1D hydrostatic models with LTE - which is known as 'classical' approach - to 3D radiative hydrodynamics with non-LTE. The transition is slow, mostly because of the associated computational challenges. However, the need for more realistic models, which provide more accurate and un-biased results, i.e. fundamental stellar parameters and element abundances, is now as urgent as never before. Large-scale stellar surveys (like Gaia-ESO and APOGEE) provide observed spectra of unprecedented quality and pave the way to massive applications of the new models. From the recent developments in theory, it seems that most promising approach is to compute NLTE line formation with the averages of full 3D RHD models. \begin{acknowledgement} Figure 1 reproduced by permission of the authors; the image was observed with the Swedish 1-m Solar Telescope. The SST is operated on the island of La Palma by the Institute for Solar Physics in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. The Institute for Solar Physics is a national research infrastructure under the Swedish Research Council. It is managed as an independent institute associated with Stockholm University through its Department of Astronomy. Figure 2: Asplund et al. A\&A, 359, 729, 2000, reproduced with permission (c) ESO. Figures 3, 4 reproduced by permission of the AAS. Figure 8: Lind et al. A\&A, 554, A96, 2013, reproduced with permission (c) ESO. We thank R. Collet and R. Trampedach for the figures from the papers in preparation, and K. Lind for the useful comments to the manuscript. This work was partly supported by the European Union FP7 programme through ERC grant number 320360. \end{acknowledgement} | 14 | 3 | 1403.3089 |
1403 | 1403.1874_arXiv.txt | We use our variable Eddington tensor (VET) radiation hydrodynamics code to perform two-dimensional simulations to study the impact of radiation forces on atmospheres composed of dust and gas. Our setup closely follows that of Krumholz \& Thompson, assuming that dust and gas are well-coupled and that the radiation field is characterized by blackbodies with temperatures $\gtrsim 80$ K, as might be found in ultraluminous infrared galaxies. In agreement with previous work, we find that Rayleigh-Taylor instabilities develop in radiation supported atmospheres, leading to inhomogeneities that limit momentum exchange between radiation and dusty gas, and eventually providing a near balance of the radiation and gravitational forces. However, the evolution of the velocity and spatial distributions of the gas differs significantly from previous work, which utilized a less accurate flux-limited diffusion (FLD) method. Our VET simulations show continuous net acceleration of the gas, with no steady-state reached by the end of the simulation. In contrast, FLD results show little net acceleration of the gas and settle in to a quasi-steady, turbulent state with low velocity dispersion. The discrepancies result primarily from the inability of FLD to properly model the variation of the radiation field around structures that are less than a few optical depths across. We conclude that radiation feedback remains a viable mechanism for driving high-Mach number turbulence. We discuss implications for observed systems and global numerical simulations of feedback, but more realistic setups are needed to make robust observational predictions and assess the prospect of launching outflows with radiation. | Observations of star-formation in the Milky way and other galaxies provide consistent evidence that some feedback mechanism or mechanisms hamper the collapse of interstellar gas to form stars. For example, The Kenicutt-Schmidt law \citep{Kennicutt1998} implies that, on average, only a few percent of the available gas actually collapses to form stars per dynamical time. Observations of molecular gas in rapidly star-forming ultraluminous infrared galaxies (ULIRGs) indicate that turbulent velocities of up to $\sim 100 \; \rm km \; s^{-1}$ are present \citep[e.g.][]{DownesSolomon1998}. And most dramatically, galaxy scale outflows of cold, neutral gas are inferred in galaxies ranging from nearby dwarf starbursts to ULIRGs and rapidly star-forming galaxies at high redshift \citep[e.g.][]{Heckmanetal1990,Pettinietal2001,SchwarzMartin2004,Rupkeetal2005}. Although a number of promising mechanisms have been proposed to explain these observations, we restrict our attention to the potential role of radiation pressure on dust grains in driving turbulence, hampering gravitational collapse, and launching outflows in such environments \citep{Scoville2001,Murrayetal2005,Thompsonetal2005}. This possibility has been explored extensively in recent years, with a number of studies considering how (in)effective radiation driving may be in various environments \citep[e.g.][]{KrumholzMatzner2009,AndrewsThompson2011,Hopkinsetal2011,Hopkinsetal2012,Wiseetal2012,KrumholzThompson2012,KrumholzThompson2013,SocratesSironi2013} Here we focus specifically on the implications of the Rayleigh-Taylor instability \citep[hereafter RTI; see e.g.][]{Chandrasekhar1961}. In recent work, \citet[ hereafter KT12]{KrumholzThompson2012} and \citet{KrumholzThompson2013} have argued that the RTI may play a significant role in limiting the exchange of momentum between radiation and dusty gas, ultimately reducing the role of radiation feedback in star-forming environments. A general, analytical calculation of the linear growth of the radiative RTI does not exist \citep[see e.g.][]{MathewsBlumenthal1977,Krolik1977,JacquetKrumholz2011,Jiangetal2013}, and non-linear evolution can generally only be explored via numerical simulations \citep[KT12;][]{Jiangetal2013}. In this paper, we attempt to replicate the results of KT12, who numerically solve the equations of radiation hydrodynamics using an implementation of the flux-limited diffusion algorithm in the ORION code \citep{Krumholzetal2007}. We utilize both a variable Eddington tensor method \citep{Davisetal2012,Jiangetal2012} and our own version of the flux-limited diffusion method (Jiang et al., in preparation), each of which are implemented as part of the Athena astrophysical fluid dynamics code \citep{Stoneetal2008}. Although we reproduce some aspects of the KT12 results, we find significant discrepancies that arise from innacuracies of the flux-limited diffusion treatment. The plan of this work is as follows: We review the equations solved and summarize our numerical methods in section \ref{equations}. We describe the setup of our numerical simulations, including formulations for the opacities, boundary conditions, and initial conditions in section \ref{setup}. We summarize our key results from our numerical simulation in section \ref{results} and discuss their implications in section \ref{discussion}. We provide our conclusions in section \ref{summary}. | \label{summary} We have considered the role of the Rayleigh-Taylor instability in the interaction of infrared radiation fields, dust, and gas in rapidly star-forming environments. We have focused on the regime of radiation supported, dense gas that may be present in some systems, such as ULIRGs. Our primary results stem from the numerical simulation of such environments, which are studied in a simplified problem setup with a constant gravitational acceleration, a constant incident infrared flux on the base of the domain, and initialized with a perturbed isothermal atmosphere to match previous calculations in KT12. In the stable regime, we find that the atmosphere settles down into an equilibrium solution in agreement with the previous results. In the unstable regime, we confirm that the RTI develops and has a significant impact on subsequent evolution. However, we find that after the growth of the RTI, the evolution depends significantly on the choice of algorithm for modeling radiation transfer. Our VET simulations show a stronger coupling between radiation and dusty gas, leading to continuous net upward acceleration of the gas. No steady state is reached before the end of the calculation, when high density material had reached the top of the domain. The mean velocities and velocity dispersion are both increasing at the end of the run. In contrast, our FLD calculations broadly reproduce the FLD results of KT12, finding weaker coupling between gas and radiation. This leads to a short initial burst of acceleration, followed by a period of fallback, finally settling into quasi-steady state turbulence with zero mean velocity and low velocity dispersion. As a result, our VET calculations imply a much larger scale height and higher velocity dispersion than the FLD-based calculations. We argue that these discrepancies result from limitations in the diffusion-based FLD algorithm, which lead to inaccuracies in modeling how the radiation field responds to structure in the gas distribution that is a few optical depths or smaller in size. These errors are related to the FLD radiation field's tendency to diffuse around denser, optically-thicker structures even when the diffusion limit does not apply. Relative to our VET calculations, this leads the FLD radiation forces to be more effective at opening and reinforcing low density channels but less effective at disrupting high density filaments, ultimately reducing the coupling between radiation and dusty gas. Despite the discrepancies in the scale height and velocity distributions, it appears that both the VET and FLD simulations trend towards an approximate balance between the volume-averaged radiation and gravitational forces at late times. If this behavior is general, it confirms one of the key results of KT12 \citep[see also][]{KrumholzThompson2013}, suggesting the rate of momentum transfer between radiation and dusty gas may scale approximately as $\sim \tau_{\rm E} L/c$, where $L$ is the luminosity, $\tau_{\rm E}= \kappa_{\rm E} \Sigma$, $\Sigma$ is the mass surface density, and $\kappa_{\rm E} = c g/F_*$ is the opacity for which the radiation and gravitational accelerations balance. Since $\kappa_{\rm R}$ is generally larger nearer to the midplane, $\tau_{\rm E}$ will be lower than estimates of $\tau_{\rm IR}$ that assume volume-average or mid-plane opacities. For example, in the simulation parameters considered here ($\Sigma =1.4 \rm \; g \; cm^{-2}$), we infer a total optical depth $\tau_{\rm IR} \sim 9$ using a volume-averaged opacity, which must be reduced by an efficiency factor $\eta \simeq 0.68$ to obtain the correct rate of momentum transfer. However, if the Eddington ratio is always near unity, this efficiency factor may be lower for gas disks or clouds with larger surface densities. Although the simulation setup considered here is useful for studying the development and saturation of the RTI, it is not optimally suited for making observational predictions. Future work with more realistic assumptions, such as a vertically varying gravitational acceleration, non-grey opacity, distributed radiation sources, and physically relevant simulation volumes will be necessary to provide robust predictions and facilitate direct comparison with observations. | 14 | 3 | 1403.1874 |
1403 | 1403.5499_arXiv.txt | We present a simple empirical function for the average density profile of cosmic voids, identified via the watershed technique in $\Lambda$CDM $N$-body simulations. This function is universal across void size and redshift, accurately describing a large radial range of scales around void centers with only two free parameters. In analogy to halo density profiles, these parameters describe the scale radius and the central density of voids. While we initially start with a more general four-parameter model, we find two of its parameters to be redundant, as they follow linear trends with the scale radius in two distinct regimes of the void sample, separated by its compensation scale. Assuming linear theory, we derive an analytic formula for the velocity profile of voids and find an excellent agreement with the numerical data as well. In our companion paper [Sutter \emph{et al.}, \mnras~\textbf{442}, 462 (2014)] the presented density profile is shown to be universal even across tracer type, properly describing voids defined in halo and galaxy distributions of varying sparsity, allowing us to relate various void populations by simple rescalings. This provides a powerful framework to match theory and simulations with observational data, opening up promising perspectives to constrain competing models of cosmology and gravity. | 14 | 3 | 1403.5499 |
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1403 | 1403.0105_arXiv.txt | The dynamical generation of wormholes within an extension of General Relativity (GR) containing (Planck's scale-suppressed) Ricci-squared terms is considered. The theory is formulated assuming the metric and connection to be independent (Palatini formalism) and is probed using a charged null fluid as a matter source. This has the following effect: starting from Minkowski space, when the flux is active the metric becomes a charged Vaidya-type one, and once the flux is switched off the metric settles down into a static configuration such that far from the Planck scale the geometry is virtually indistinguishable from that of the standard Reissner-Nordstr\"om solution of GR. However, the innermost region undergoes significant changes, as the GR singularity is generically replaced by a wormhole structure. Such a structure becomes completely regular for a certain charge-to-mass ratio. Moreover, the nontrivial topology of the wormhole allows to define a charge in terms of lines of force trapped in the topology such that the density of lines flowing across the wormhole throat becomes a universal constant. To the light of our results we comment on the physical significance of curvature divergences in this theory and the topology change issue, which support the view that space-time could have a foam-like microstructure pervaded by wormholes generated by quantum gravitational effects. | The Vaidya metric \cite{Vaidya} \begin{equation} ds^2=-\left[ 1-\frac{2m(v)}{r} \right] dv^2 +2\epsilon \,dv dr +r^2 d \Omega^2, \end{equation} is a nonstatic spherically symmetric solution of the Einstein equations generated by a null stream of radiation. Depending on $\epsilon=+1(-1)$ it corresponds to an ingoing (outgoing) radial flow and $m(v)$ is a monotonically increasing (decreasing) function in the advanced (retarded) time coordinate $-\infty<v<+\infty$. Both the Vaidya solution and its extension to the charged case, the Bonnor-Vaidya solution \cite{BV}, have been widely employed in a variety of physical situations, including the spherically symmetric collapse and the formation of singularities \cite{Lake92}, the study of Hawking radiation and black hole evaporation \cite{radiation}, the gravitational collapse of charged fluids (plasma) \cite{Lasky07} or as a testing tool for various formulations of the cosmic censorship conjecture. In addition to this, several theorems on the existence of exact spherically symmetric dynamical black hole solutions have been established \cite{theor}. In the context of modified gravity, Vaidya-type solutions have been found in metric $f(R)$ gravity coupled to both Maxwell and non-abelian Yang-Mills fields \cite{Ghosh12a} and in Lovelock gravity \cite{Cai08}. The Vaidya metric has also been used to consider whether a wormhole could be generated out of null fluids. More specifically, in \cite{Hayward02} a crossflow of a two-component radiation was considered, and the resulting solution was interpreted as a wormhole (this analysis extended the results presented in \cite{Gergely02}). It was indeed shown that a black hole could be converted into a wormhole by irradiating the black-hole horizon with pure phantom radiation, which may cause a black hole with two horizons to merge and consequently form a wormhole. Conversely, switching off the radiation causes the wormhole to collapse to a Schwarzschild black hole \cite{Hayward:2001ma}. These results were further extended in \cite{Hayward04} showing that two opposite streams of radiation may support a static traversable wormhole. Furthermore, analytic solutions describing wormhole enlargement were presented, where the amount of enlargement was shown to be controlled by the beaming in and the timing of negative-energy and positive-energy impulses. It was also argued that the wormhole enlargement is not a runaway inflation, but an apparently stable process. The latter issue addressed the important point that though wormholes were possible, and even expected at the Planck scale, macroscopic wormholes were unlikely. In fact, the generation/construction of wormholes has also been extensively explored in the literature, in different contexts. The late-time cosmic accelerated expansion implies that its large-scale evolution involves a mysterious cosmological dark energy, which may possibly lie in the phantom regime, i.e., the dark energy parameter satisfies $w<-1$ \cite{Planck2}. Now, phantom energy violates the null energy condition, and as this is the fundamental ingredient to sustain traversable wormholes \cite{Morris}, this cosmic fluid presents us with a natural scenario for the existence of these exotic geometries \cite{phantomWH}. Indeed, due to the fact of the accelerating Universe, one may argue that macroscopic wormholes could naturally be grown from the submicroscopic constructions, which envisage transient wormholes at the Planck scale that originally pervaded the quantum foam \cite{Wheeler}, much in the spirit of the inflationary scenario \cite{Roman:1992xj}. It is also interesting to note that self-inflating wormholes were also discovered numerically \cite{Hayward:2004wm}. In the context of dark energy, and in a rather speculative scenario, one may also consider the existence of compact time-dependent dark energy stars/spheres \cite{Lobo:2005uf}, with an evolving dark energy parameter crossing the phantom divide \cite{DeBenedictis:2008qm}. Once in the phantom regime, the null energy condition is violated, which physically implies that the negative radial pressure exceeds the energy density. Therefore, an enormous negative pressure in the center may, in principle, imply a topology change, consequently opening up a tunnel and converting the dark energy star into a wormhole. The criteria for this topology change were also discussed, in particular, a Casimir energy approach involving quasi-local energy difference calculations that may reflect or measure the occurrence of a topology change. As the Planck scale plays a fundamental importance in quantum gravitational physics, an outstanding question is whether large metric fluctuations may induce a change in topology. Wheeler suggested that at distances below the Planck length, the metric fluctuations become highly nonlinear and strongly interacting, and thus endow space-time with a foamlike structure \cite{Wheeler}. This behaviour implies that the geometry, and the topology, may be constantly fluctuating, and thus space-time may take on all manners of nontrivial topological structures, such as wormholes. However, paging through the literature, one does encounter a certain amount of criticism to Wheeler's notion of space-time foam, for instance, in that stability considerations may place constraints on the nature or even existence of Planck-scale foamlike structures \cite{Redmount:1992mc}. Indeed, the change in topology of spacelike sections is an extremely problematic issue, and a number of interesting theorems may be found in the literature on the classical evolution of general relativistic space-times \cite{acausal}, namely, citing Visser \cite{Visser}: (i) In causally well-behaved classical space-times the topology of space does not change as a function of time; (ii) In causally ill-behaved classical space-times the topology of space can sometimes change. Nevertheless, researchers in quantum gravity have come to accept the notion of space-time foam, in that this picture leads to topology-changing quantum amplitudes and to interference effects between different space-time topologies \cite{Visser}, although these possibilities have met with some disagreement \cite{dewitt}. Despite the fact that topology-changing processes, such as the creation of wormholes and baby universes, are tightly constrained \cite{Visser:1989ef}, this still allows very interesting geometrical (rather than topological) effects, such as the shrinking of certain regions of space-time to umbilical cords of sufficiently small sizes to effectively mimic a change in topology. Recently, the possibility that quantum fluctuations induce a topology change, was also explored in the context of Gravity's Rainbow \cite{Garattini:2013pha}. A semi-classical approach was adopted, where the graviton one-loop contribution to a classical energy in a background space-time was computed through a variational approach with Gaussian trial wave functionals \cite{Garattini} (note that the latter approach is very close to the gravitational geon considered by Anderson and Brill \cite{geons4b}, where the relevant difference lies in the averaging procedure). The energy density of the graviton one-loop contribution, or equivalently the background space-time, was then let to evolve, and consequently the classical energy was determined. More specifically, the background metric was fixed to be Minkowskian in the equation governing the quantum fluctuations, which behaves essentially as a backreaction equation, and the quantum fluctuations were let to evolve; the classical energy, which depends on the evolved metric functions, is then evaluated. Analyzing this procedure, a natural ultraviolet (UV) cutoff was obtained, which forbids the presence of an interior space-time region, and may result in a multiply-connected space-time. Thus, in the context of Gravity's Rainbow, this process may be interpreted as a change in topology, and in principle results in the presence of a Planckian wormhole. In this work, we consider the dynamical generation of wormholes in a quadratic gravity theory depending on the invariants $R=g_{\mu\nu}R^{\mu\nu}$ and $Q=R_{\mu\nu}R^{\mu\nu}$, which are Planck scale-suppressed [see Eq.(\ref{eq:grav-lagrangian}) below for details]. This theory is formulated {\it a la} Palatini, which means that the metric and connection are regarded as independent entities. Though in the case of General Relativity (GR) this formulation is equivalent to the standard metric approach (where the connection is imposed \emph{a priori} to be given by the Christoffel symbols of the metric) this is not so for modified gravity. Interestingly, the Palatini formulation yields second-order field equations that in vacuum boil down to those of GR and, consequently, are ghost-free, as opposed to the usual shortcomings that plague the metric formulation. To probe the dynamics of our theory, in a series of papers \cite{or12a,lor13} we have studied spherically symmetric black holes with electric charge. As a result we have found electrovacuum solutions that macroscopically are in excellent qualitative agreement with the standard Reissner-Nordstr\"om solution of GR, but undergo important modifications in their innermost structure. Indeed, the GR singularity is generically replaced by a wormhole structure with a throat radius of order $r_c \sim l_P$. The behaviour of the curvature invariants at $r_c$ shows that for a particular charge-to-mass ratio the space-time is completely regular. The topologically non-trivial character of the wormhole allows us to define the electric charge in terms of lines of electric force trapped in the topology, such that the density of lines of force is given by a universal quantity (independent of the specific amounts of mass and charge). These facts allow to consistently interpret these solutions as geons in Wheeler's sense \cite{Wheeler} and raise the question on the true meaning of curvature divergences in our theory since their existence seems to pose no obstacle for the wormhole extension. Let us note that these wormhole solutions correspond to static solutions of the field equations. Here we shall see that such solutions can be dynamically generated by probing the Minkowski space with a charged null fluid. In this way we obtain a charged Vaidya-type metric such that when the flux is switched off, the space-time settles down into a Reissner-Nordstr\"om-like configuration containing a wormhole structure and thus a multiply-connected topology in its interior. As we shall see, these results have important consequences for the issue of the foam-like structure of space-time. This work largely extends the results and discussion of \cite{lmor14}. This paper is organized in the following manner: In Sec. \ref{secII}, we present the Palatini formalism for Ricci-squared theories that are used throughout the paper. In Sec. \ref{secIII}, we consider general electrovacuum scenarios with a charged null fluid, and in Sec. \ref{secIV} we solve the gravitational field equations. In Sec. \ref{secV}, we analyze the different contributions to the metric and discuss some particular scenarios. A discussion on the physical implications of these results follows in Sec. \ref{secVI}, where we conclude with a brief summary and some future perspectives. | \label{secVI} We have worked out a simplified scenario of gravitational collapse in which new gravitational physics at high energies is introduced by means of quadratic curvature corrections in the gravitational Lagrangian. We have made use of two elements that simplify the mathematical analysis, namely, 1) spherical symmetry, and 2) a pressureless fluid. These simplifications have been traditionally used in theoretical discussions about gravitational collapse and the study of the properties of singularities. Obviously, neither 1) nor 2) can be exactly realized in nature but, nonetheless, they are very useful for theoretical analysis of the type considered here. Note, in this sense, that already in the first models of gravitational collapse worked out by Oppenheimer and Snyder \cite{FN-S}, the internal pressures of the collapsing fluids were neglected as it was understood that, above a certain threshold, rather than helping to prevent the collapse they contribute to increase the energy density, which further accelerates the process. Similarly, in the case of electrically charged black holes (the well-known Reissner-Nordstr\"om solution), for instance, the repulsive electric force of the collapsed matter does not help to alleviate the strength of the central singularity. Rather, the squared of the Riemann tensor increases its degree of divergence, going from ${R^\alpha}_{\beta\mu\nu}{R_\alpha}^{\beta\mu\nu}\sim 1/r^4$ in the Schwarzschild case to ${R^\alpha}_{\beta\mu\nu}{R_\alpha}^{\beta\mu\nu}\sim 1/r^8$ in the charged case. The energy of the electric field, therefore, worsens the degree of divergence of the curvature scalars. In our model, we have considered a radiation fluid carrying a certain amount of energy and also electric charge. The repulsive forces or pressures that the particles making up the fluid could feel have been neglected as they are not essential for the study of the end state of the collapse. As a result, the fluid follows geodesics of the metric, which have been determined dynamically by taking into account the energy and charge conveyed by the fluid. The fluid motion, therefore, is not given a priori, but follows from the consistent resolution of the coupled system of radiation, electric field, and gravity. The key point of this work has been the study of the end state of the collapse of this idealized system. In general relativity, this configuration unavoidably leads to the formation of a point-like singularity. In our model, however, the geometry and the topology undergo important changes. When the energy density of the collapsing fluid reaches a certain scale (of order the Planck scale), gravity is no longer attractive and becomes repulsive. This has a dramatic effect on the geodesics followed by the fluid which, rather than focusing into a point-like singularity, expand into a growing sphere. The wormhole is thus somehow produced by the repulsive character of gravitation at high energy-densities and the need to conserve the electric flux. In principle, in our model wormholes of arbitrary charge and mass can be formed. However, this cannot be completely true since our results are valid as long as the approximations involved hold with sufficient accuracy. Therefore, one should note that in low-energy scenarios pressure and other dispersion effects should act so as to prevent the effective concentration of charge and energy way before it can concentrate at Planckian scales, thus suppressing wormhole production. However, for adequate concentrations of charge and energy, gravitational collapse cannot be halted and our analysis should be regarded as a good approximation. In this sense, we note that Hawking already analyzed the process of classical collapse in the early universe, finding that (primordial) black holes with a Planck mass or higher and up to 30 units of charge could be formed out of a charged plasma \cite{Hawking:1971ei}. Stellar collapse offers another robust mechanism to generate the conditions under which our approximations are valid. In fact, in order to build a completely regular configuration with a solar mass, about $\sim 10^{57}$ protons, one needs $\sim 2.91 \times 10^{21}$ electrons \cite{or12a}, which is a tiny fraction of the total available charge ($10^{-31}$) and mass. Therefore, the generation of wormholes under realistic situations is possible. The dynamical generation of wormholes outlined above, in the context of charged fluids in quadratic Palatini gravity, differs radically in nature to the construction of general relativistic traversable wormholes, with the idealization of impulsive phantom radiation considered extensively in the literature \cite{Gergely02,Hayward02, Hayward:2001ma,Hayward04,Koyama:2002nh,Koyama:2004uh,Shinkai:2002gv,Hayward:2009yw}. In the latter, it was shown that two opposing streams of phantom radiation, which form an infinitely thin null shell, may support a static traversable wormhole \cite{Hayward02}. Essentially, one begins with a Schwarzschild black hole region, and triggers off beams of impulsive phantom radiation, with constant energy density profiles, from both sides symmetrically, consequently forming Vaidya regions. Now, in principle, if the energies and the emission timing are adequately synchronized, the regions left behind the receding impulses after the collision results in a static traversable wormhole geometry. Furthermore, it is interesting to note that it was shown that with a manipulation of the impulsive beams, it is possible to enlarge the traversable wormhole (see \cite{Hayward04} for more details). These solutions differ radically from the self-inflating wormholes discovered numerically \cite{Shinkai:2002gv} and the possibility that inflation might provide a natural mechanism for the enlargement of Planck-size wormholes to macroscopic size \cite{Roman:1992xj}. The difference lies in the fact that the amount of enlargement can be controlled by the amount of energy or the timing of the impulses, so that a reduction of the wormhole size is also possible by reversing the process of positive-energy and negative-energy impulses outlined in \cite{Hayward04}. The theory presented here allows to generate static wormholes by means of a finite pulse of charged radiation, without the need to keep two energy streams active continuously or to synchronize them in any way across the wormhole. Regarding the size of the wormholes, we note that if instead of using $l_P^2$ to characterize the curvature corrections one considers a different length scale, say $l_\epsilon^2$, then their area would be given by $A_{WH}=\left(\frac{l_\epsilon}{l_P}\right)\frac{2N_q}{N_q^c}A_P$, where $A_P=4\pi l_P^2$, $N_q=|q/e|$ is the number of charges, and $N_q^c\approx 16.55$. Though this could allow to reach sizes orders of magnitude larger than the Planck scale, it does not seem very likely that macroscopic wormholes could arise from any viable theory of this form, though the role that other matter/energy sources could produce might be nontrivial. Relative to the issue of classical singularities, the meaning and implications of the latter has been a subject of intense debate in the literature for years. Their existence in GR is generally interpreted as a signal of the limits of the theory, where quantum effects should become relevant and an improved theory would be necessary. This is, in fact, the reason that motivates our heuristic study of quadratic corrections beyond GR. As pointed out above and shown in detail in \cite{or12a}, the curvature divergences for the static wormhole solutions arising in quadratic Palatini gravity with electrovacuum fields (and also in the Palatini version of the Eddington-inspired Born-Infeld theory of gravity, see \cite{orh14}) are much weaker than their counterparts in GR (from $\sim 1/r^8$ in GR to $\sim 1/(r-r_c)^3$ in our model). Additionally, the existence of a wormhole structure that prevents the function $r^2$ from dropping below the scale $r_c^2$ implies that the total energy stored in the electric field is finite (see \cite{orh14,lor13} for details), which clearly contrasts with the infinite result that GR yields. Therefore, even though curvature scalars may diverge, physical magnitudes such as total mass-energy, electric charge, and density of lines of force are insensitive to those divergences, which demands for an in-depth analysis of their meaning and implications. In this sense, we note that topology is a more primitive concept than geometry, in the sense that the former can exist without the latter. Comparison between a sphere and a cube is thus pertinent and enlightening in this context to better understand the physical significance of curvature divergences. It turns out that a cube and a sphere are topological equivalent. However, the geometry of the former is ill-defined along its edges and vertices. The divergent behavior of curvature scalars for certain values of $\delta_1$, therefore, simply indicates that for those cases the geometry is not smooth enough at the wormhole throat, but that does not have any impact on the physical existence of the wormhole. Regarding the existence of curvature divergences at $x=0$ in the Schwarzschild case ($q\to 0$), our view is that there exist reasons to believe that such divergences could be an artifact of the approximations and symmetries involved in our analysis. These suspects are supported by the fact that radiation fluids (with equation of state $P/\rho=1/3$) in cosmological scenarios governed by the dynamics of the theory under study are able to avoid the Big Bang singularity, which is replaced by a cosmic bounce \cite{Barragan2010}. For the radiation fluid, the cosmic bounce occurs in both isotropic and anisotropic homogeneous scenarios when the energy density approaches the Planck scale. One would thus expect that a process of collapse mimicking the Oppenheimer-Snyder model with a radiation fluid should avoid the development of curvature divergences. This, in fact, occurs in Eddington-inspired Born-Infeld gravity \cite{orh14}, studied recently in \cite{Panietal}. The generic existence of curvature divergences in the uncharged case involving a Vaidya-type scenario with null fluids is thus likely to be due to the impossibility of normalizing the null fluid, which is therefore insensitive to the existence of a limiting density scale. The consideration of more realistic non-null charged fluids could thus help to improve the current picture and avoid the shortcomings of the uncharged ($q\to 0$) Schwarzschild configurations. As a final comment, we note that since in our theory the field equations outside the matter sources recover those of vacuum GR, Birkhoff's theorem must hold in those regions. This means that for $v<v_i$ we have Minkowski space, whereas for $v>v_f$ we have a Reissner-Nordstr\"om-like geometry of the form (\ref{eq:ds2static1}). The departure from Reissner-Nordstr\"om is due to the Planck scale corrections of the Lagrangian, which are excited by the presence of an electric field, and only affect the microscopic structure, which is of order $\sim r_c(v)$ (see Sec. \ref{sec:static} and \cite{or12a}). Due to the spherical symmetry and the second-order character of the field equations, Birkhoff's theorem guarantees the staticity of the solutions for $v>v_f$. To conclude, in this work an exact analytical solution for the dynamical process of collapse of a null fluid carrying energy and electric charge has been found in a quadratic extension of GR formulated \`{a} la Palatini. This scenario extends the well-known Vaidya-Bonnor solution of GR \cite{BV}, thus allowing to explore in detail new physics at the Planck scale. In the context of the static configurations, we have shown that wormholes can be formed out of Minkowski space by means of a pulse of charged radiation, which contrasts with previous approaches in the literature requiring artificial configurations and synchronization of two streams of phantom energy. Our results support the view that space-time could have a foam-like microstructure with wormholes generated by quantum fluctuations. Though such geometric structures develop, in general, curvature divergences, they are characterized by well-defined and finite electric charge and total energy. The physical role that such divergences could have is thus uncertain and requires an in-depth analysis, though from a topological perspective they seem not to play a relevant role. To fully understand these issues our model should be improved to address several important aspects including, for instance, the presence of gauge field degrees of freedom, to take into account the dynamics of counter-streaming effects due to the presence of simultaneous ingoing and outgoing fluxes, or to consider other theories of gravity beyond the quadratic Lagrangian (\ref{eq:grav-lagrangian}). These and related research issues are currently underway. | 14 | 3 | 1403.0105 |
1403 | 1403.2931_arXiv.txt | \ax\ and \grs\ are two transient neutron star low-mass X-ray binaries that are located within $\simeq$10$'$ from the Galactic center. Multi-year monitoring observations with the \swift/XRT has exposed several accretion outbursts from these objects. We report on their updated X-ray light curves and renewed activity that occurred in 2010--2013. | \swift\ has monitored the inner $\simeq25'\times25'$ of the Milky Way with the onboard X-Ray Telescope since 2006, using $\simeq$1~ks exposures performed every 1--4~days. This has amounted to nearly 1000 observations and $\simeq$1.1~Ms of exposure time between 2006 and 2013. This campaign provides a perfect setup to study the long-term X-ray behavior of the supermassive black hole \sgra, as well as 15 known transient low-mass X-ray binaries \citep[e.g.,][]{degenaar09_gc,degenaar2010_gc,degenaar2013_sgra}. \ax\ and \grs\ are two neutron star low-mass X-ray binaries that are frequently active; both exhibited two main outbursts in the period 2006--2009 \citep[][see also Figure~\ref{fig:longlc}]{degenaar09_gc,degenaar2010_gc}. \begin{figure}[tb] \begin{center} \includegraphics[width=0.49\textwidth]{DegenaarND_fig1a.eps} \includegraphics[width=0.49\textwidth]{DegenaarND_fig1b.eps} \caption{{ \swift/XRT light curves of \ax\ and \grs\ (2006--2013). Both sources exhibited four main outbursts. \grs\ also displayed a very weak ($L_{\mathrm{X}}^{\mathrm{peak}} \simeq 7 \times10^{34}~\lum$) and short ($\simeq$1 week) outburst in 2006 \citep[][]{degenaar09_gc}. }} \label{fig:longlc} \end{center} \end{figure} | \label{sec:conclude} In the past seven years, \ax\ and \grs\ have each displayed four distinct outbursts captured by the \swift/XRT (Figure~\ref{fig:longlc}). The main outbursts of \grs\ (i.e., neglecting the mini-outburst observed in 2006; Figure~\ref{fig:longlc}) have varying peak intensities and lengths, yet comparable fluencies \citep[Table~\ref{tab:spec}, see also][]{degenaar2010_gc}. \ax\ displays two types of outbursts: those in 2006 and 2010 were relatively faint ($L_{\mathrm{X}}\simeq4\times10^{35}~\lum$) and short (months), whereas the 2007--2008 outburst was much brighter ($L_{\mathrm{X}}\simeq 2\times10^{36}~\lum$) and longer (1.5 yr). The peak luminosity detected in 2013 was similar to that of the 2007--2008 outburst. If the duration is also similar, the source might still be active when the Galactic center becomes observable again in 2014 February. However, it was argued by \citet{degenaar2010_gc} that long and bright outbursts can only recur on a time scale of a decade. | 14 | 3 | 1403.2931 |
1403 | 1403.5516_arXiv.txt | Recent observational claims of magnetic fields stronger than $10^{-16}$ G in the extragalactic medium motivate a new look for their origin in the inflationary magnetogenesis models. In this work we shall review the constraints on the simplest gauge invariant model $f^2(\phi)F_{\mu \nu}F^{\mu \nu}$ of inflationary magnetogenesis, and show that in the optimal region of parameter space the anisotropic constraints coming from the induced bispectrum, due to the generated electromagnetic fields, yield the strongest constraints. In this model, only a very fine tuned scenario at an energy scale of inflation as low as $10^{-2}$ GeV can explain the observations of void magnetic fields. These findings are consistent with the recently derived upper bound on the inflationary energy scale. However, if the detection of primordial tensor modes by BICEP2 is confirmed, the possibility of low scale inflation is excluded. Assuming the validity of the BICEP2 claim of a tensor-to-scalar ratio $r=0.2^{+0.07}_{-0.05}$, we provide the updated constraints on this model of inflationary magnetogenesis. On the Mpc scale, we find that the maximal allowed magnetic field strength from inflation is less than $10^{-30}$ G. | Large scale coherent magnetic fields are omnipresent across the entire universe. While their presence in cosmic structures e.g. stars, galaxies and clusters of galaxies has been verified by different astronomical observations, their true origin has not yet been entirely understood (see, for instance, \cite{Ryu:2011hu, Widrow:2011hs,Durrer:2013pga} for recent reviews). It is widely believed that subsequent enhancement of pre-existing seed fields due to the galactic dynamo mechanism \cite{Brandenburg:2004jv} could lead to such magnetic fields although the strength of seed fields must be larger than $10^{-20}-10^{-30}$ G \cite{Turner:1987bw, Davis:1999bt}. Recent indirect observations of femto-Gauss magnetic fields in voids with a coherence length larger than the Mpc scale have further intensified the search for their origin \cite{Neronov:1900zz,Tavecchio:2010ja,Tavecchio:2010mk,Taylor:2011bn}. The large coherence length of void magnetic fields makes them difficult to be produced in the late universe and hints towards their origin during the inflationary epoch in the early universe. Among various possibilities, inflationary magnetogenesis has been considered a plausible mechanism for the generation of such cosmic magnetic fields. One of the simplest, gauge invariant and well studied model of inflationary magnetogenesis is described by the Lagrangian \cite{Turner:1987bw,Ratra:1991bn} \beq {\cal{L}}_{\rm EM}=-\frac{1}{4}f^2(\phi)F_{\mu \nu}F^{\mu \nu}, \label{eq:Lag} \eeq where $F_{\mu \nu}$ is the electromagnetic (EM) field tensor and is defined as $F_{\mu \nu} \equiv \pa_\mu A_\nu-\pa_\nu A_\mu$. In this model the conformal invariance of the $U(1)$ gauge field $A_\mu$ is broken by a time dependent function $f$ of a dynamical scalar field $\phi$ thereby generating an effective coupling constant $e_{\rm eff}=e/f$. Although this model has been greatly studied, there exists certain issues regarding its ability to explain the observations consistently. In \cite{Demozzi:2009fu}, it was discussed that this model always suffers from one of two main problems: backreaction due to the energy density of generated EM fields on the inflationary dynamics or strongly coupled regimes at the onset of inflation where the theory loses its predictability. The problem of strong coupling can be avoided by dropping the requirement of gauge invariance at high energies, as suggested in \cite{Bonvin:2011dt}, but we are not aware of any explicit models that can achieve this and restore gauge invariance at the end of inflation as required. Instead, in \cite{Ferreira:2013sqa}, this no-go theorem was circumvented without breaking gauge invariance by lowering significantly the energy scale of inflation wherein femto-Gauss magnetic fields could be achieved for a TeV scale inflation. Apart from the aforementioned two problems, there exists yet another problem, the anisotropies from the curvature perturbations induced by these EM fields generated during inflation may become too large \cite{Fujita:2014sna,Fujita:2012rb,Fujita:2013qxa,Nurmi:2013gpa}. In \cite{Fujita:2013qxa}, the primordial magnetic field strength was strongly constrained in the model described in eq. (\ref{eq:Lag}) by requiring that the induced perturbation spectrum at CMB scales must be in agreement with the recent Planck observations \cite{Ade:2013uln, Ade:2013ydc}. It was also concluded that the backreaction constraint is generically stronger than the constraint from curvature perturbations when the duration of inflation is much longer than the minimum required to solve the horizon problem. As we will see, the role of the two constraints are interchanged when the duration of inflation is close to the minimal required to solve the horizon problem. This should be compared with the conservative upper bound obtained for the magnetic field strength today in \cite{Fujita:2014sna}\footnote{The expression for the minimum amount of inflation appearing in the Planck paper \cite{Ade:2013uln}, also used by the authors of \cite{Fujita:2014sna}, carries a misprint \cite{pp}. The equation in \cite{Ade:2013uln} gives, for instantaneous reheating and neglecting slow-roll terms, $N_{\rm min}\simeq 71.5+1/2 \log(H/M_p)$ where $M_p$ is the reduced Planck mass, defined as $M_p^2 \equiv 1/{8 \pi G}$. However, in \cite{Ferreira:2013sqa} the same quantity was computed yielding $N_{\rm min}\simeq 66.9+1/2 \log(H/M_p)$ which is in agreement with \cite{Liddle:2003as}.} \beq \rho^{1/4}_{\rm inf}\ <\ 29.3\, \txt{GeV} \lmk \frac{k}{1\, \text{Mpc}^{-1}} \rmk^{5/4} \lmk \frac{B_{0}}{10^{-15}\, \txt{G}}\rmk^{-1},\quad k>1\, \text{Mpc}^{-1}, \label{eq:bound} \eeq where $\rho_{\rm inf}$ is the energy density during inflation and $B_{0}$ is the present day magnetic field strength. This upper bound was derived under the requirement of gauge invariance and non-strongly coupled regimes and is valid in the region where the electric field energy dominates over the magnetic field. In this paper, we shall review these constraints in the specific case of the coupling $f^2(\phi)F_{\mu \nu}F^{\mu \nu}$. We discuss backreaction constraint as well as anisotropic constraints both from the induced power spectrum and non-Gaussianities. We shall show that in the case where inflation lasts an amount of e-folds close to the minimum required to solve the horizon problem, the magnetic field strength today is constrained to be $10^{-15}$ G at $10$ MeV which is approximately $3$ orders of magnitude lower than the conservative upper bound derived in \cite{Fujita:2014sna}. Finally, in view of the recent observations of primordial tensor modes through the B-mode polarization of the CMB \cite{Ade:2014xna}, we update the resulting constraints on inflationary magnetogenesis given that the referred observations, if correct, fix the energy scale of inflation to be $\rho^{1/4}_{\rm inf} \simeq 10^{16}$ GeV which has strong consequences on the results discussed in the previous sections. | In this paper we have analyzed the constraints on the $f^2(\phi)F_{\mu \nu}F^{\mu \nu}$ model of inflationary magnetogenesis. We have focussed on constraints coming from the observed CMB anisotropies and B-modes. We have found the maximal magnetic fields achievable in the $f^2(\phi)F_{\mu \nu}F^{\mu \nu}$ model, and compared with the recent constraint derived by Fujita and Yokoyama \cite{Fujita:2014sna}. We find that backreaction constraints provide stronger constraints than the constraints from anisotropies, if inflation lasts more than about $5$ e-folds than the minimal amount of e-foldings required to solve the horizon problem. However, if inflation is shorter, we find that the constraints from anisotropies become stronger. An important outcome of this analysis is the fact that, as was also pointed out in \cite{Ferreira:2013sqa}, strong magnetic fields are permissible only when the energy scale of inflation is significantly lowered. As we have shown here, in the standard scenario where the conformal coupling is broken at the beginning of inflation, the maximal magnetic field at the horizon scale increases as the energy scale of inflation decreases yielding $B \simeq 10^{-19}$ G at $\rho^{1/4}_{\rm inf} \simeq 10$ MeV and only $\simeq 10^{-35}$ G at $\rho^{1/4}_{\rm inf}\simeq10^{15}$ GeV. In the most optimal scenario, where inflation lasts close to the minimum amount of e-folds allowed and the conformal coupling is broken at the Mpc scale, the maximal magnetic fields allowed are $\sim 10^{-15}$ G at the Mpc scale for $\rho^{1/4}_{\rm inf}\simeq10$ MeV while for high scale inflation with $\rho_{\rm inf}^{1/4} \simeq 10^{15}$ GeV, the strength drops again to $\simeq10^{-32}$ G. In comparison with the upper bound derived in \cite{Fujita:2014sna}, our best case scenario is nearly 3 orders of magnitude lower. We have also studied similar constraints arising from the trispectrum on the magnetic field strength, but they are very similar to the bispectrum constraints. The results presented here together with the previous work in the literature clearly indicate that it might be extremely difficult to explain the observations of void magnetic fields with an inflationary mechanism. This pessimism is even more justified in light of the recent observations of tensor modes by the BICEP2 experiment. If that observation is confirmed by other experiments, it would mean that the energy scale of inflation is $\rho^{1/4}_{\rm inf} \simeq 10^{16}$ GeV. With such a high scale inflation the upper bound allows for a maximal magnetic field of strength $B_k=1.3\times10^{-30}\lmk k/k_{\txt{Mpc}} \rmk^{5/4}$ G, for $k>\txt{Mpc}^{-1}$, while for $f^2(\phi)F_{\mu \nu}F^{\mu \nu}$ models the maximal value allowed for the magnetic field is $B_k=8.1\times10^{-35} \lmk k/k_{\txt{Mpc}} \rmk$ G. These results basically exclude the explanation of void magnetic fields by inflationary mechanisms, unless the BICEP2 B-mode signal is not due to primordial gravitational waves \cite{Bonvin:2014xia,Liu:2014mpa,Mortonson:2014bja} or gravitational waves are produced during inflation by some non-standard mechanism \cite{Mukohyama:2014gba,Cook:2011hg} keeping the scale of inflation low. We conclude that these constraints are very stringent even for the generation of seed magnetic fields. Although an inflationary explanation for the seeds is still allowed by the upper bound, their generation in $f^2(\phi)F_{\mu \nu}F^{\mu \nu}$ models is no longer possible at scales larger than kpc. | 14 | 3 | 1403.5516 |
1403 | 1403.6840.txt | Most massive galaxies show emission lines that can be characterized as LINERs. To what extent this emission is related to AGNs or to stellar processes is still an open question. In this paper, we analysed a sample of such galaxies to study the central region in terms of nuclear and circumnuclear emission lines, as well as the stellar component properties. For this reason, we selected 10 massive ($\sigma > $200 km $s^{-1}$) nearby (d $<$ 31 Mpc) galaxies and observed them with the IFU/GMOS (integral field unit/Gemini Multi-Object Spectrograph) spectrograph on the Gemini South Telescope. The data were analysed with principal component analysis (PCA) Tomography to assess the main properties of the objects. Two spectral regions were analysed: a yellow region (5100-5800 \AA), adequate to show the properties of the stellar component, and a red region (6250-6800 \AA), adequate to analyse the gaseous component. We found that all objects previously known to present emission lines have a central AGN-type emitting source. They also show gaseous and stellar kinematics typical of discs. Such discs may be co-aligned (NGC 1380 and ESO 208 G-21), in counter-rotation (IC 1459 and NGC 7097) or misaligned (IC 5181 and NGC 4546). We also found one object with a gaseous disc but no stellar disc (NGC 2663), one with a stellar disc but no gaseous disc (NGC 1404), one with neither stellar nor gaseous disc (NGC 1399) and one with probably ionization cones (NGC 3136). PCA Tomography is an efficient method for detecting both the central AGN and gaseous and stellar discs. In the two cases (NGC 1399 and NGC 1404) in which no lines were previously reported, we found no evidence of either nuclear or circumnuclear emission, using PCA Tomography only. | \label{sec:intro} Active galactic nuclei (AGNs) are commonly associated with the capture of matter by a supermassive black hole (SMBH), located at the central region of galaxies \citep{1998AJ....115.2285M}. In the optical, they are characterized by intense and broad emission lines. Quasars are the most luminous type of AGNs, both in optical and in radio. On the other hand, Seyfert galaxies, with prominence of high ionization lines, and low ionization nuclear emission regions (LINERs), whose low ionization emission lines tend to be more intense, belong to the low luminosity regime of AGNs. Low luminosity AGNs (LLAGNs) are found in $\sim$ 1/3 of the galaxies in the local Universe \citep{2008ARA&A..46..475H}. If one considers only early-type galaxies (ETGs), this ratio raises to 2/3, whereby most AGNs are classified as LINERs \citep{2008ARA&A..46..475H}. Seyferts and transition objects (TOs) are predominantly found in late-type galaxies \citep{2008ARA&A..46..475H}. TOs were proposed by \citet{1993ApJ...417...63H} as AGNs whose light is contaminated by H II regions. \citet{2003ApJ...583..159H} showed that TO hosting galaxies have higher inclination than those containing LINERs or Seyferts, which increases the contamination of H II regions in the nuclear spectrum, apart from having higher FIR luminosities, which is related to a more intense stellar formation. LINERs were originally defined by \citet{1980A&A....87..152H} as objects with [O II]$\lambda$3727/[O III]$\lambda$5007 $>$ 1 and [O I]$\lambda$6300/[O III]$\lambda$5007 $>$ 1/3. However, because of the difficulty of observing a large spectral range and, mainly, the high extinction of the [O II]$\lambda$3727 line, \citet{1987ApJS...63..295V} proposed the line ratios [O III]$\lambda$5007/H$\beta$ $<$ 3, [O I]$\lambda$6300/H$\alpha$ $>$ 0.05, ([S II]$\lambda$6716 + [S II]$\lambda$6731)/H$\alpha$ $>$ 0.4 and [N II]$\lambda$6583/H$\alpha$ $>$ 0.5 as a better way to separate LINERs from Seyferts and H II regions. The main reason to use these line ratios is that they are reasonably insensitive to reddening effects. Bi-dimensional plots that compare [O I]$\lambda$6300/H$\alpha$, ([S II]$\lambda$6716 + [S II]$\lambda$6731)/H$\alpha$ or [N II]$\lambda$6583/H$\alpha$ with [O III]$\lambda$5007/H$\beta$ are known as diagnostic diagrams, or BPT diagrams \citep{1981PASP...93....5B}. The [O I]$\lambda$6300 line is emitted in partially ionized zones, which are produced by high-energy photons and are larger in regions photoionized by AGNs compared to those photoionized by starbursts. [S II]$\lambda\lambda$6716, 6731 lines also show considerable emission from these zones. The reasons why [N II]/H$\alpha$ are greater in galaxies with an AGN are more complex, although a fraction of the [N II]$\lambda$6548, 6583 doublet also comes from the partially ionized zone (see \citealt{1987ApJS...63..295V}; \citealt{2006agna.book.....O} for a revision of the origin of each previously discussed line ). In short, BPT diagrams are very useful in distinguishing Seyferts, LINERs and H II regions. Several mechanisms have been proposed to explain the LINER emission. \citet{1980A&A....87..152H} associated LINER spectra with shock waves. \citet{1983ApJ...264..105F} and \citet{1983ApJ...269L..37H} showed that typical LINER line ratios may be produced by AGNs with a low-ionization parameter (log U $\sim$ -3.5 - \citealt{1983ApJ...264..105F}). The detection rates of X-rays and radio cores, typical features of AGNs, in LINER and Seyfert nuclei are quite similar \citep{2008ARA&A..46..475H}. In the optical, the detection of a broad line component in LINERs \citep{1997ApJS..112..391H} also supports the existence of an AGN in these objects. Aside from AGNs and shockwaves, instantaneous starburst models, with ages between 3 and 5 Myr and a UV continuum dominated by Wolf Rayet clusters, were proposed by \citet{2000PASP..112..753B} to explain TOs nuclei. Photoionization by old stellar populations, more specifically post asymptotic giant branch (pAGBs) stars, was proposed by \citet{1994A&A...292...13B} to account for ionized gas emission in elliptical galaxies. LINERs may also be divided in types 1 and 2, like Seyfert nuclei, within the framework of a unified model for AGN activity \citep{1985ApJ...297..621A,1993ARA&A..31..473A}. An example of a LINER with a broad component in the H$\alpha$ line is NGC 7213 \citep{1979ApJ...227L.121P,1984ApJ...285..458F}. At first sight, there are no reasons to doubt that the unified model could also be applied to LINERs. In fact, \citet{1999ApJ...525..673B} detected a hidden broad line region (BLR) in the LINER of NGC 1052. \citet{1997ApJS..112..391H} have shown that $\sim$ 20\% of the LLAGNs detected in their survey are type 1, with more than half belonging to the LINER category. Sometimes, the broad H$\alpha$ component is not detected in the first attempt, like in M 104. However, \textit{Hubble Space Telescope (HST)} observations \citep{1996ApJ...473L..91K}, as well as careful analysis with high-signal-to-noise spectra \citep{2041-8205-765-2-L40}, do reveal such a feature. However, some type 2 LINERs do not seem to possess BLRs \citep{2008ARA&A..46..475H}. This may be related to the fact that some LINERs are not photoionized by an AGN. Nevertheless, in some cases where an AGN is confirmed by X-ray or radio emission, a BLR is not detected directly or with the use of spectropolarimetry \citep{2008ARA&A..46..475H}. Indeed, BLR formation models proposed in the literature are based on the condensation of clouds caused by winds originated in the accretion discs of the SMBHs \citep{2000ApJ...530L..65N,2006ApJ...648L.101E,2011A&A...525L...8C}. Depending on the model, the formation of those structures may be controlled either by the bolometric luminosity or by the Eddington ratio of the AGNs. Both parameters are lower in LINERs when compared to Seyfert nuclei \citep{2008ARA&A..46..475H}. Hence, some AGN photoionized LINERs just may not be able to produce BLR, i.e. they are genuine type 2 LINERs. Nuclear emission lines are often seen in elliptical and lenticular galaxies. \citet{1986AJ.....91.1062P}, using long-slit spectra, detected an extended LINER-type emission in $\sim$ 12\% objects from a sample of 203 ETGs. In all cases, these researchers concluded that the extended region has a disc-like rotation. In a sample of 26 ETGs observed with a long-slit spectrograph, \citet{1989ApJ...346..653K} also suggested that the extended emission of ionized gas has a disc-like geometry, with line ratios typical of LINERs. \citet{2006MNRAS.366.1151S}, in a sample of 48 ETGs observed with the SAURON integral field spectrograph, revealed that a fraction of these objects have a circular disc of gas, and that there is a second group characterized by an integral-sign pattern in the ionized gas distribution, aside from twists in the velocity maps. In the second group, the photometry and kinematics of every object is misaligned, which may indicate that the twist in gas distribution is a consequence of non-axisymmetric potentials \citep{2006MNRAS.366.1151S}. Besides gas kinematics, \citet{1989ApJ...346..653K} also revealed that the H$\alpha$ luminosity did not match X-ray emission in galaxies from which he had both kinds of information. He argued that, aside from the mechanism that produced the X-ray in his sample of ETGs (he associated this emission with cooling flow effects), another photoionization source would be necessary to explain the extended emission in those objects. In other words, if these sources follow a power-law spectra originated at the centre (AGN case), the ionizing photons would have to infiltrate in distances of an order of kpc. Recent works have revealed that photoionization caused only by an AGN is not enough to account for the extended emission of LINERs \citep{2010ApJ...711..796E,2010MNRAS.402.2187S,2010A&A...519A..40A,2012ApJ...747...61Y}. In fact, AGNs' contribution seems to be relevant only on nuclear scales \citep{2010ApJ...711..796E,2010MNRAS.402.2187S}. Several authors (e.g. \citealt{2008ARA&A..46..475H,2008MNRAS.391L..29S,2010ApJ...711..796E,2010MNRAS.402.2187S,2011MNRAS.413.1687C}) recently provided various arguments supporting the initial idea of \citet{1994A&A...292...13B} that this additional source of ionizing photons is pAGBs stars, which are abundant in the passively evolving stellar systems such as ETGs. For instance, \citet{2011MNRAS.413.1687C} showed that the number of ionizing photons is proportional to the stellar continuum in the H$\alpha$ region (constant H$\alpha$ equivalent width) and, with a sample of 700,000 galaxies from the Sloan Digital Sky Survey (SDSS), they proposed a diagram that compares the line ratio [N II]/H$\alpha$ to the equivalent width of H$\alpha$ in order to distinguish regions photoionized by an AGN from those whose emission is accounted for old stellar populations. In this diagram, denominated WHAN by \citet{2011MNRAS.413.1687C}, objects with central gas emission showing $EW(H\alpha)$ $<$ 3\AA\ are mainly photoionized by pAGBs stars and were defined as retired galaxies. Indeed, most retired galaxies from their sample have $EW(H\alpha)$ $\sim$ 1\AA. This is the first of a series of papers whose goal is the detection and characterization of the nuclear and circumnuclear (scales of $\sim$ 100 pc) gas components from a sample of 10 ETGs, observed with the integral field spectrograph located at the Gemini South Telescope. With this instrument, one is able to obtain two-dimensional spectra from the central regions of these galaxies within a field of view (FOV) of 3.5 arcsec x 5 arcsec and a spatial resolution $<\sim$ 1 arcsec. Although the SAURON project \citep{2002MNRAS.329..513D} corresponds to a representative sample of ETGs with a larger FOV, which allows information in scales of an order of kpc, their spatial resolution is $\sim$ 3 arcsec, whereas our sample was obtained with a spatial resolution good enough to study nuclear and circumnuclear regions of ETGs in great detail. Our sample, even if not statistically complete, covers a wide range of ETGs, from low ellipticity and low stellar rotation ellipticals to fast rotator lenticular galaxies. In this work, we show that nuclear and circumnuclear regions of gas may be detected through the principal component analysis (PCA) Tomography technique (\citealt{1997ApJ...475..173H,2009MNRAS.395...64S}, see a brief review in Section \ref{pca_tomography}). In the following papers, we will validate the results from this work as they relate to the nuclear (Paper II) and circumnuclear (Paper III) regions, apart from additional results associated with these regions. This will be done using gas-only spectra (i.e. with the starlight component properly subtracted from each spectrum of the data cubes using stellar population synthesis techniques) of the central regions of the galaxies. | \label{sec:conc} PCA Tomography applied to data cubes in the optical range is a recently developed technique for information extraction \citep{1997ApJ...475..173H,2009MNRAS.395...64S} and noise treatment (\citealt{2009MNRAS.395...64S}; Steiner et al. in preparation). The interpretation of the results is, frequently, subtle. Observations in other wavelengths are, often, important to reliably interpret the data. In this work, we showed that the eigenvector 2, related to data cubes of galaxies with emission lines, may be interpreted as dominated by correlations caused by an AGN. Thus, a new and powerful methodology for this kind of research is unveiled. Splitting the data cubes in two spectral regions, one dominated by the variance of absorption lines (5150-5800 \AA), of stellar origin, and the other dominated by the variance of the emission lines (6250-6850 \AA), allows us to study the stellar or gaseous kinematics. With this methodology, we are able to identify stellar and gaseous discs and to conclude that, notwithstanding a small sample, the angular moment of both structures is uncoupled. This finding is important in discussing the origin of the circumnuclear gas in ETGs. One should be caution, however, with this conclusion, as some of the disc-like features could actually be contaminated by outflows. \citet{1986AJ.....91.1062P} observed 9 of 10 galaxies from our sample and only in NGC 1399 and NGC 1404 they did not detect any sign of the [N II] and H$\alpha$ emission lines. In both objects, PCA Tomography did not reveal any sign of emission lines either. NGC 4546 was the only galaxy of the sample which was not observed by \citet{1986AJ.....91.1062P}; however, \citet{1987ApJ...318..531G} related emission lines in the central region of this object. Eigenspectra 2 presented in this work have shown line ratios typical of LINERs for seven galaxies of the sample. For ESO 208 G-21, it was not possible to detect the H$\beta$ and [O III] emission lines. However, low-ionization lines like [O I], [N II], and [S II], when compared to H$\alpha$, have typical intensities of LINERs in this object. The detection of extended kinematic features in eight galaxies of the sample suggests that the circumnuclear gas emission is quite common. Since the eigenspectra related to the gas kinematics are characterized by anti correlations between the red and blue wings of the emission lines, it is not possible to estimate their line ratios. However, the observed eigenspectra show strong correlations in the low ionization lines, typical of LINERs. Point-like sources unveiled by the tomograms related to the eigenspectra 2 support the hypothesis that the LINERs seen in nuclear regions of the eight galaxies are, indeed, photoionized by an AGN. Moreover, in IC 1459, the eigenspectrum 2 showed evidences of the featureless continuum emitted by the AGN. One could argue that if these galaxies have an AGN, broad components from the BLR should be appearing in some emission lines, particularly in H$\alpha$. However, the detection of this component should be carried out by carefully decomposing the nuclear emission lines. Since even in eigenspectra 2 there might be kinematic effects superposed on the correlation between the emission lines (see, for instance, the case of NGC 3136 and, less obviously, in IC 5181, especially in the [O III]$\lambda$5007 line of this object), it is not recommended to decompose the emission lines when manipulating eigenspectra. Radio observations have supported the presence of an AGN in NGC 2663 and NGC 7097 \citep{1994MNRAS.269..928S}. \citet{2010MNRAS.402.2187S} argued that an AGN must be responsible for the H$\beta$ emission in the nuclear region of NGC 4546. The evidences of an AGN in IC 1459 were discussed in Section \ref{case_IC1459}. With regard to the others galaxies of the sample, a careful analysis of their nuclear spectra will be performed in Paper II. In two galaxies (IC 1459 and NGC 7097), the gas and the stellar discs are counter-rotating in their central regions. This has already been discussed in the literature (IC 1459 - \citealt{1988ApJ...327L..55F,2002ApJ...578..787C}; NGC 7097 - \citealt{1986ApJ...305..136C}). In NGC 1380 and ESO 208 G-21, both structures are corotating. In two other objects (IC 5181 and NGC 4546), the rotating planes are not coincident. Curiously, in both galaxies the stellar discs seem to be asymmetric, as revealed by PCA Tomography. In NGC 4546, \citet{2006MNRAS.366.1151S} measured the difference between the P.A. of the gaseous and stellar discs and found P.A.$_{stellar}$ - P.A.$_{gas}$ = -144$^o$, which matches our calculation of -129$^o$ (see table \ref{tab_PA_pca}). Although it has been proposed that the detected gas kinematics would indicate gas discs in seven galaxies, one should not discard outright that these structures may be related to ionization cones. The co-rotation between the gas and stellar kinematics seen in NGC 1380 and ESO 208 G-21 is compatible with the idea of a gas disc, with an internal origin (e.g. stellar mass loss). In IC 1459, NGC 7097 and NGC 4546, the gas kinematics have the same P.A. as the gas discs found in regions more distant from the nuclei of these galaxies \citep{2002ApJ...578..787C,1986ApJ...305..136C,2006MNRAS.366.1151S}. In fact, for NGC 7097, \citet{2011ApJ...734L..10R} proposed that an ionization cone is observed in the perpendicular direction of the gas disc. Since tomograms represent weights that involve intensities and kinematics, a more extended emission indicates that, in NGC 3136, tomogram 2 of the red spectral region (Fig. \ref{tomogram_N3136_2}) reveals an emission with an opening angle that is wider than in other galaxies. This suggests that the emission might not be associated with a disc and possibly represents ionization cones or, perhaps, a combination of both, disc and cones. In the case of NGC 2663, no evidences of gaseous disc have been published before. In IC 5181, \citet{2013A&A...560A..14P} also found that the stellar and the gaseous components are orthogonally rotating. Ionization cones may be present in both cases. In IC 5181, the difference between the P.A. of the stellar and gaseous kinematics is $\sim$ 112.5$^o$, which means that both components do not rotate in the same direction. In this case, it is also not possible to claim that the circumnuclear region of gas is really a disc. Maybe an ionization cone in regions closer to the nucleus is important and may have an effect on the tomogram, since the most internal regions are more intense and, therefore, have greater weight in the tomograms. Thus, the gas kinematic analysis, along with other methods (e.g. radial velocity extraction or the application of PCA Tomography to synthetic discs or ionization cones), is important to confirm the nature of this component. The extended emission will be revisited in Paper III. It is worth mentioning that, with PCA Tomography, one is able to obtain information about the kinematics of an object in a few minutes, while extracting the stellar velocity map with standard fitting techniques (e.g. ppxf - \citealt{2004PASP..116..138C}) takes several hours for a typical GMOS data cube. Also the presence of AGN activity is revealed in a faster way than subtracting the stellar components of all spectra of a data cube. Moreover, tomograms and eigenspectra are quite useful to have a first qualitative look in data cubes. Besides AGN activity and kinematics, PCA Tomography may be also very helpful in detecting other and previously unsuspected physical phenomena. For example, in NGC 7097, only with PCA Tomography, \citet{2011ApJ...734L..10R} proposed that the light of the AGN is reflected in our line of sight by an ionization cone. If this scenario may be recovered for others objects, one may select, more effectively, a sample galaxies to be observed by using spectropolarimetry. Although we highlighted the importance of PCA Tomography to extract preliminary information, we actually propose to analyse data cubes using both PCA Tomography and standard techniques, since it may be complementary. In the case of this work, Papers II and III will provide the complement of this Paper I. PCA Tomography is also an efficient way of summarizing the information in a data cube. Usually, $\sim$ 5 eigenvectors/tomograms explain more than 99\% of the variance. Finally, PCA is a nonparametric method and, therefore, does not depend on previous assumptions. The interpretation, however, may frequently be quite subtle. Below, we summarize our findings. \begin{itemize} \item The PCA Tomography method is efficient to detect LINER emissions, either nuclear or circumnuclear, in massive galaxies with previously known emission lines. This methodology is also effective to detect stellar discs. \item All objects from our sample, previously selected as having emission lines, may be classified as nuclear LINERs, photoionized by an AGN and, also, as presenting circumnuclear emission. \item We found that in IC 1459, the Fe5270 stellar absorption feature is correlated with the AGN emission lines, suggesting the presence of a featureless continuum. \item We found that the nuclear region, expressed in eigenspectra 2, is usually reddened and, when so, associated with interstellar Na D absorption, indicating the presence of dust and neutral gas. \item In two galaxies (NGC 1399 and NGC 1404) whose emission lines were not previously known, PCA Tomography also did not detect any sign of ionized gas. \item Six of eight galaxies with an AGN detected by PCA Tomography also present a circumnuclear emission of gas with disc-like features. \item The elliptical galaxy NGC 3136 shows intense emission lines and may be classified as a LINER, but it has a complex structure. With PCA Tomography, we detected two point-like objects and features that seem to be co-existing disc and ionization cones. \item In seven galaxies of the sample (four S0 and three E), the stellar component has a disc-like kinematical signature. \item In two galaxies, the stellar and gaseous discs are in co-rotation, whereas in other two they are counter-rotating; the discs appear not to be aligned in two objects. This decoupling of the angular momentum of the gas and of the stars suggests that the origin of the gas is not internal and argues against the idea that the gas and stellar ionization sources are spatially close. \item NGC 2663 shows only a gas kinematics (disc or ionization cone), but does not have a stellar disc. On the other hand, NGC 1404 has only a stellar disc. \end{itemize} | 14 | 3 | 1403.6840 |
1403 | 1403.4931.txt | Recoiling supermassive black holes (SMBHs) are considered one plausible physical mechanism to explain high velocity shifts between narrow and broad emission lines sometimes observed in quasar spectra. If the sphere of influence of the recoiling SMBH is such that only the accretion disc is bound, the dusty torus would be left behind, hence the SED should then present distinctive features (i.e. a mid-infrared deficit). Here we present results from fitting the Spectral Energy Distributions (SEDs) of 32 Type-1 AGN with high velocity shifts between broad and narrow lines. The aim is to find peculiar properties in the multi-wavelength SEDs of such objects by comparing their physical parameters (torus and disc luminosity, intrinsic reddening, and size of the 12$\mu$m emitter) with those estimated from a control sample of $\sim1000$ \emph{typical} quasars selected from the Sloan Digital Sky Survey in the same redshift range. We find that all sources, with the possible exception of J1154+0134, analysed here present a significant amount of 12~$\mu$m emission. This is in contrast with a scenario of a SMBH displaced from the center of the galaxy, as expected for an undergoing recoil event. %We also find that the high velocity-shift objects (1)~cover a wide range of SED shapes, (2)~present, on average, a moderately higher level of intrinsic disc obscuration than that in the control sample, and (3)~show to some extent larger average sizes for the $12\mu$m emitter (perhaps because the inner surface of the 12$\micron$ emitter is pushed outwards by the AGN radiation). Objects showing a large velocity shift between broad lines and narrow lines appear to be intrinsically brighter than the QSOs in the control sample. Obscuration differences between the two samples cannot be simply due to inclination effects (i.e., more edge on), but are presumably the result of intrinsic differences in disc structures. | \label{Introduction} It is now widely accepted that galaxies host supermassive black holes (SMBHs) in their centre with masses of the order of $10^{6-9}M_\odot$ \citep{1964ApJ...140..796S,1969Natur.223..690L}. Locally, the SMBH mass correlates with the mass (\citealt{1998AJ....115.2285M,2003ApJ...589L..21M}), with the velocity dispersion (\citealt{2000ApJ...539L...9F,2002ApJ...574..740T}), and with the luminosity of the host galaxy bulge (\citealt{1995ARA&A..33..581K}). The existence of these correlations implies that the growth of the SMBH is tightly linked with the galaxy evolution, playing a crucial role in the star-formation history of the galaxy itself. \par From the theoretical point of view, according to the hierarchical galaxy formation model, a main channel of galaxy growth is through mergers, that enhance star formation and trigger active galactic nuclei (AGN). Given that SMBH ubiquitously populate the center of galaxies, it is expected that black hole binaries (BHB) will be formed in the course of a merger event. \par If the binary hypothesis is correct, BHB systems should leave characteristic features in the spectrum of the system such as a shift of the peak of their broad emission lines (BLs associated to the central BHs) with respect the narrow ones (NLs associated to the host galaxy; \citealt{1980Natur.287..307B,1983LIACo..24..473G}). For example, objects showing {\it double-peaked emission} lines (DPEs) in their spectra might be interpreted as possible BHB candidates. Those systems present displaced broad-line peaks (one blueshifted and one redshifted compared with the narrow line redshift) as a result of the orbital motion of the ionized gas gravitationally bound to the BH pairs. To date, long multiepoch campaigns have ruled out the BHB interpretation for most of the DPEs studied (e.g., \citealt{1994ApJS...90....1E}). However, AGN showing single peaked shifted BLs are still considered plausible BHB candidates, as they could be related to close binaries in which only one MBH is active (e.g. \citealt{2009ApJ...697..288B, 2009MNRAS.398L..73D}) and monitoring campaigns are ongoing to prove their nature (e.g. \citealt{2013MNRAS.433.1492D} hereafter Paper I, \citealt{2012ApJS..201...23E,2013arXiv1312.6694L}; \rev{\citealt{2013ApJ...777...44J}}). \par Other alternative scenarios that might explain the BLs displacement are: {\it 1)} the projection of two unrelated quasars (QSOs) viewed, by chance, along similar sight lines, {\it 2)} a recoil induced by the anisotropic emission of gravitational waves in the final merge of SMBHs pairs (\citealt{PhysRev.128.2471}). The first interpretation relies on the probability of finding two unassociated quasars aligned with the line of sight. This turns out to be unlikely in several cases (see for example \citealt{2009Natur.458...53B,2009MNRAS.397..458D}). %while in the second one the SMBHs may not reside right at the centers of their host galaxies. The latter is a prediction of general relativity, confirmed by numerical simulations, which imply that, after BHB coalescence, the resulting BH can recoil at velocities up to several thousand km s$^{-1}$ due to anisotropic gravitational wave emission (e.g. \citealt{2007ApJ...668.1140B, 2007ApJ...659L...5C, 2007PhRvL..98w1102C, 2012PhRvD..85h4015L, 2013PhRvD..87h4027L}). %(e.g. \citealt{1984MNRAS.211..933F,2005ApJ...635..508B})). Observationally, the recoiling SMBH and its surrounding gas would give rise to spectra where BLs are shifted from NLs of the host galaxy (e.g., \citealt{2008ApJ...678L..81K}; \rev{\citealt{2009ApJ...702L..82C}}; \citealt{2012AdAst2012E..14K,2012ApJ...752...49C}). \par %A key observational evidence in favour of the BHB scenario would be a periodical shift and/or an amplitude change of the BLs system with respect to the NLs over orbital periods around $1-500$ yr depending on the BHs geometrical configuration and their masses (\citealt{1997ApJ...490..216E,2009MNRAS.398L..73D,2009ApJ...703..930L}). %This requires time consuming monitoring campaigns to study line-continuum correlations and long-term evolution of the BLs, in order to exclude any possible contamination from AGN variability (e.g., \citealt{2007ApJ...668..708S}). \par From a multi-wavelength perspective we expect the spectral energy distribution (SED) of DPEs or BHB candidates to have features similar to a ``typical" QSO SED: "infrared bump" at $\sim10$ $\mu$m, and an upturn in the optical-UV, the so-called "big-blue bump" (BBB, \citealt{1989ApJ...347...29S,1994ApJS...95....1E,2006ApJS..166..470R,2011ApJS..196....2S,2012ApJ...759....6E}). The BBB is thought to be representative of the emission from the accretion disc around the SMBH, while the infrared bump is due to the presence of dust (from sub-parsec to hundreds parsec scale) which re-radiates a fraction of the optical-UV disc photons at infrared wavelengths. \par The SED of a recoiling BH significantly displaced from the center of the host galaxy might have instead different features. For example, if the sphere of influence of the recoiling BH on the gas were such that only the accretion disc is bound, all the larger scale structures (like a dusty torus) would be left behind, hence the SED should present the BBB only (\citealt{2010ApJ...724L..59H}, H10 hereafter; \citealt{2011ApJ...729..125G}). %However, \citet{2009MNRAS.394..633D} using N-body/SPH simulations show that off-nuclear QSO emission can coexist with the large-scale emission features. \par In this paper we will present the broad-band SEDs, from $\sim$1500\AA{} to $\sim$20~$\mu$m, of a sample of 32 quasars identified by \citet{2011ApJ...738...20T}. This sample has been selected from the Sloan Digital Sky Survey (SDSS; \citealt{2000AJ....120.1579Y}) spectroscopic database based on large velocity shifts ($>$1000 km s$^{-1}$) between NLs and BLs, and it spans the redshift range $0.136\leq z\leq 0.713$. In Paper I we presented their spectral properties (fluxes, line luminosities, widths, broad line profiles and their evolution). Source are subsequently divided in four classes on the basis of the shape of the line profile: {\it 1)} fairly bell-shaped, strongly shifted BLs identify good BHB candidates; {\it 2)} BLs with tentative evidence of double-horned profiles are classified as DPEs; {\it 3)} objects with lines showing a rather symmetric base, centered at the redshift of the NLs, but an asymmetric core, resulting in a shifted peak, are called ``Asymmetric"; {\it 4)} other more complex profiles, or lines with relatively small shifts, or lines with asymmetric wings but modest peak shift are labelled as ``Others" (see Fig.~2 in Paper I for examples of each class of objects). The main aim of the present analysis is to test whether the multi-wavelength information can give further hints on the BHB scenarios described above. In order to quantify the contribution of host-galaxies and AGN reddening, as well as the disc and infrared AGN luminosities ($\Ldisc$ and $\Lir$), we will make use of the SED-fitting code presented in \citet{2013ApJ...777...86L}. \par \par %All data are considered in the $\Log \nu L(\nu)-\Log \nu$ rest-frame plane. We adopted a concordance $\Lambda-$cosmology with $H_{0}=70\, \rm{km \,s^{-1}\, Mpc^{-1}}$, $\Omega_{M}=0.3$, $\Omega_{\Lambda}=1-\Omega_{M}$. | We have presented a homogeneous and comprehensive study of the broad-band properties of 32 quasars in the sample identified by \citet{2011ApJ...738...20T}. These objects have been selected to have large velocity shifts ($>$1000 km s$^{-1}$) between NLs and BLs. According to the line profiles, source are subsequently divided in four classes: {\it 1)} fairly bell-shaped, strongly shifted BLs identify good BHB candidates; {\it 2)} BLs with evidence of double-horned profiles are classified as DPEs; {\it 3)} objects with Asymmetric lines; {\it 4)} other sources with complex profiles, or having lines with relatively small shifts ($\sim$1000 km s$^{-1}$). \par One possible interpretation that might explain the BLs displacement is a recoil induced by the anisotropic emission of gravitational waves in the final merge of SMBHs pairs. This phenomenon would leave a characteristic imprint in the SED of these objects (i.e. a mid-infrared deficit). This analysis aims to investigate the multi-wavelength SEDs of such peculiar QSOs, in particular in the context of the recoiling scenario depicted above. %Additionally, we have estimated physical parameters as, for example, torus and disc luminosity, intrinsic reddening, and size of the 12$\mu$m emitter and compared those with the ones estimated from a control sample of $\sim1000$ {\it typical} quasars selected from SDSS (selected in order to have a similar redshift distribution of the one of our sample). To achieve this goal, we have employed the SED-fitting code already presented in Lusso et al. (2013), which models simultaneously three components of the AGN SED %\footnote{The original version of this code models the SED with four components. For our purposes we have neglected the additional component of cold-dust from star-forming region.} i.e. hot-dust from the torus, optical-UV emission from the evolving stellar population, and optical-UV from the accretion disc. \par Our main findings are summarized in the following: \begin{description} \item[(1)] All quasars analyzed here present a significant amount of 12~$\mu$m emission. The SED of hot-dust poor quasars should be a further indication of displaced SMBH from the center of a galaxy, maybe attributed to an undergoing recoil event. We do not find any evidence of such objects in the presented sample aside from J1154+0134, whose IR emission is a factor $\sim 10$ lower than what expected from its UV-optical emission. Further follow-ups (e.g. high resolution imaging) is required to test \rev{the nature (recoil vs DPE)} of J1154+0134. \item[(2)] We find that our sample covers a wide range in terms of SED shapes with host galaxy contamination higher with respect to the QSO control sample (modulo degeneracies between the galaxy and a highly reddened BBB). Nevertheless, SEDs of our sample show, on average, moderately higher levels of intrinsic disc obscuration than the control sample (if we match solely on redshift). %The mean disc reddening for our sample is $\langle \ebvq\rangle\simeq0.20$ with a standard dispersion of 0.24 (the median $\ebvq$ is 0.1), while the control sample has $\langle \ebvq\rangle\simeq0.08$ with $\sigma=0.14$ (median $\langle \ebvq\rangle\simeq0.03$). The two average $\ebvq$ values are statistically different at $2.7\sigma$ level. %In the context of AGN unification, this might be due to the fact that the observer has a line-of-sight close to the equatorial plane. Sources presenting a shift of the peak of the BLs with respect to NLs may have a tendency to be more edge-on. \item[(3)] Disc luminosity estimates (before applying the reddening correction but host galaxy subtracted) for our sample and for the control one are not significantly different. Given the higher disc reddening contamination in our sample, then such objects should be intrinsically brighter than the QSO control sample. \item[(4)] There is a tendency to have higher average sizes of the $12~\mu$m emitter for our sample than the one for the control sample. This is consistent with the larger intrinsic (once we have corrected for reddening) brightness in the optical of our sample with respect to the control sample. %(i.e. the inner surface of the 12$\micron$ emitter is pushed outwards by the AGN radiation pressure). \item[(5)] If we assume that the torus is optically thick to its own radiation, the infrared emission observed from a line-of-sight aligned with the torus should be smaller than one along a polar direction. Sources with high reddening values (i.e., $\ebvq\geq0.1$) are expected to have lower $\Lir$ values, and thus lower $\size$ values. However, we find that the $\size$ values for our sample are, on average, somewhat higher than the ones of the control sample. This indicates that inclination effects are not playing a major role in the optical AGN obscuration. %(otherwise we should % observe lower $\Lir$ and thus lower $\size$ values), The source of obscuration might be due to intrinsic differences in the small scale structure of the quasars in our sample. \end{description} As a note of caution we also point out that the difference in the average AGN reddening is no longer significant when we select a sub-sample in both our data-set and the control sample with similar $\Ldiscr$ and $\Lir$. Moreover objects classified BHB and DPEs in our sample have no significant difference in the intrinsic reddening even when compared to the larger control sample. | 14 | 3 | 1403.4931 |
1403 | 1403.6335_arXiv.txt | {We present 48 Herschel/PACS spectra of evolved stars in the wavelength range of 67-72 $\mu$m. This wavelength range covers the 69 $\mu$m band of crystalline olivine ($\text{Mg}_{2-2x}\text{Fe}_{(2x)}\text{SiO}_{4}$). The width and wavelength position of this band are sensitive to the temperature and composition of the crystalline olivine. Our sample covers a wide range of objects: from high mass-loss rate AGB stars (OH/IR stars, $\dot M \ge 10^{-5}$~M$_\odot$/yr), through post-AGB stars with and without circumbinary disks, to planetary nebulae and even a few massive evolved stars.} { The goal of this study is to exploit the spectral properties of the 69 $\mu$m band to determine the composition and temperature of the crystalline olivine. Since the objects cover a range of evolutionary phases, we study the physical and chemical properties in this range of physical environments.} {We fit the 69 $\mu$m band and use its width and position to probe the composition and temperature of the crystalline olivine.} {For 27 sources in the sample, we detected the 69 $\mu$m band of crystalline olivine ($\text{Mg}_{(2-2x)}\text{Fe}_{(2x)}\text{SiO}_{4}$). The 69 $\mu$m band shows that all the sources produce pure forsterite grains containing no iron in their lattice structure. The temperature of the crystalline olivine as indicated by the 69 $\mu$m band, shows that on average the temperature of the crystalline olivine is highest in the group of OH/IR stars and the post-AGB stars with confirmed Keplerian disks. The temperature is lower for the other post-AGB stars and lowest for the planetary nebulae. A couple of the detected 69 $\mu$m bands are broader than those of pure magnesium-rich crystalline olivine, which we show can be due to a temperature gradient in the circumstellar environment of these stars. The disk sources in our sample with crystalline olivine are very diverse. They show either no 69~$\mu$m band, a moderately strong band, or a very strong band, together with a temperature for the crystalline olivine in their disk that is either very warm ($\sim$600~K), moderately warm ($\sim$200~K), or cold ($\sim$120~K), respectively.} {} | Crystalline olivine ($\text{Mg}_{(2-2x)}\text{Fe}_{(2x)}\text{SiO}_{4}$) has been detected in many different circumstellar environments, like disks around pre-main-sequence stars \citep{waelkens96, meeus01, sturm13}, comets \citep{wooden02}, post-main-sequence stars \citep{waters96, mol02_3}, and active galaxies \citep{spoon06, kemper07}. In outflows around evolved stars, the features of crystalline silicates were first detected in the mid-infrared wavelength range. For crystalline olivine, the most prominent bands in this range are at 11.3, 23.6, and 33.6 $\mu$m, which come from the Si-O-Si or O-Si-O bending modes and from the translational and rotational dominated modes, respectively. Interaction between the cations and anions make these bands sensitive to the ratio Mg/Fe in the mineral \citep{koike03}. With this sensitivity it was shown that the iron content of crystalline olivine in circumstellar environments of evolved stars is lower than 10\% \citep{tielens98, mol02_3}. At longer wavelengths than 45 $\mu$m, the spectrum of crystalline olivine shows resonances around 49 and 69~$\mu$m \citep{bowey01, bowey02, koike03, koike06, suto06}. The wavelength position and width of this feature strongly depend on both the Mg/Fe ratio of the mineral, as well as on the grain temperature. The 69~$\mu$m band is isolated and sits on top of a smooth continuum, allowing for a very precise analysis of the feature. With the Herschel/PACS spectrometer \citep{pilbratt10, poglitsch10}, operating in the 50--200~$\mu$m range, it is now possible to study the 69~$\mu$m band for a broad range of targets. Such an analysis has already been done for young stellar objects, showing that the crystalline olivine in proto-planetary disks and debris disks is very magnesium-rich ($<$0-3\% iron, \cite{mulders11, devries12, sturm10, sturm13}). In this paper we describe our study of the forsterite dust observed in a sample of evolved stars of predominantly low to intermediate initial mass ($\lessapprox 8 $M$_{\odot}$). In the final stages of a stellar life, the evolution is dominated by strong mass loss. During the asymptotic giant branch (AGB) phase large amplitude pulsations bring the gas to high enough altitudes for dust particles to condense. Radiation pressure on the dust and drag between the dust and gas create a strong and dense outflow. The mass-loss rates of AGB stars can be in the range of $10^{-8}$ \nolinebreak M$_{\odot}$ \nolinebreak yr$^{-1}$ up to $10^{-4}$ M$_{\odot}$ yr$^{-1}$ \citep{HO03}. Depending on the oxygen and carbon abundance in the gas, either an oxygen- or carbon-rich chemistry is initiated in the outflow, because the less abundant element will be locked into the CO molecule. In the case of an oxygen-rich outflow (C/O$<$1), oxygen-rich dust such as olivine and pyroxene ($\text{Mg}_{1-x}\text{Fe}_{x}\text{SiO}_{3}$) is formed. In the carbon-rich case, carbon dust particles are formed. While the exact values are under debate and are certainly metal dependent, oxygen-rich stars with initial masses between 1.5 $\text{M}_{\odot}$ and 3-4 $\text{M}_{\odot}$ can transition into a carbon-rich star through dredge-up of sufficient carbon from the core to the outer layers of the star. More massive oxygen-rich stars of $\ge$3-4 $\text{M}_{\odot}$ will remain oxygen-rich because the hot bottom burning in these objects favours the production of nitrogen instead of carbon \citep{HO03}. When the AGB star is stripped of most of its outer layers, its strong pulsations cease, and the mass loss stops. In this case the star goes through a short post-AGB or proto-planetary nebula (proto-PN) phase, where the previously emitted material slowly drifts away from the star and cools, while the central stars heat up \citep{HO03}. Eventually the core becomes visible as a white dwarf, signaling the end of stellar evolution. The white dwarf briefly ionizes the emitted material, creating a PN. Studies based on thermodynamic equilibrium have shown that crystalline olivine is a mineral that is expected to form around 1400K to 1000 K if a cloud of gas with solar abundance cools \citep{sedlmayr89, tielens98}. Around these temperatures, crystalline olivine forms as its magnesium-rich end-member forsterite ($\text{Mg}_{2}\text{SiO}_{4}$). These magnesium-rich crystalline olivine grains are indeed observed to be moderately abundant in the outflow of AGB stars (2-12\% of the total dust mass \citep{devries10}). If enough SiO is present at a temperature of 1300K to1000 K, it can react with forsterite to form enstatite (MgSiO$_{3}$), the magnesium-rich end-member of the pyroxene group. Subsequent reactions with gas phase iron converts enstatite to iron containing crystalline olivine around 1100 K to 900 K. In many circumstellar environments of evolved stars, enstatite is indeed detected \citep{mol02_3}, and Fe is likely to be present (although it is not certain whether it is present in the gas phase). Based on thermodynamic equilibrium, iron containing crystalline olivine could thus be formed. However, if the densities become too low in the cooling outflows of evolved stars, thermodynamic equilibrium does not need to hold, and reactions are expected to "freeze out". Gas-phase condensation is not the only possible formation mechanism of crystalline olivine. An alternative is to form crystalline olivine by annealing amorphous olivine. When amorphous olivine is heated above the glass temperature of olivine, it can rearrange its lattice elements into a crystalline form. \cite{sogawa99} show that amorphous silicate grains accreted on precondensed corundum grains can be crystalized for high enough mass loss rates ($> 3 \times 10^{-5}$ M$_{\odot}$ yr$^{-1}$ in the case of an L$_* = 2 \times 10^4$~L$_{\odot}$ star). In their study of the Spitzer IRS spectroscopy of oxygen-rich AGB stars, \cite{jones12} find that the dust mass-loss rate has a greater influence on the crystalline fraction than the gas mass-loss rate. This would indicate that the annealing is more important than the gas phase condensation, but the uncertainties in the gas mass-loss rates precluded a firm conclusion. Heating of the dust above the glass temperature could also be caused by shocks in the circumstellar environment. It is unclear how such a process could play a role in the outflow of single stars, but shocks caused by binary interaction could create the conditions for heating up the amorphous grains sufficiently \citep{edgar08} either in the outflowing material or in a circumbinary disk. In the case of disks, it would also be possible that the grains reside in the inner part of the disk close to the central star where the temperature is high enough for annealing \citep{gail01,ruyterThesis}. Crystalline silicates are, however, also known to exist in disks that are too cold for annealing \citep{molster99}. This suggests that it should also be possible to anneal amorphous grains in-situ in colder parts of the disk by shocks or other processes \citep{desch00, abraham09, edgar08}. In this article we present Herschel/PACS spectra of 48 evolved stars in the 68-72~$\mu$m range. The sample contains stars in different post-main-sequence phases of evolution, among which are AGB (OH/IR) stars, different types of post-AGB stars, planetary nebulae, and a few massive ($>$10 $\text{M}_{\odot}$) evolved stars. The goal of this article is to (1) present the Herschel/PACS observations taken in three guaranteed and open-time programmes, together with the data reduction and (2) make a first analysis of Herschel/PACS data and determine the composition of the crystalline olivine in these sources. Subsequent publications will study the different subgroups of the sample in more detail. To study the forsterite content, including the bands at mid-infrared wavelengths, needs detailed radiative treansfer modelling because of the extreme high-density conditions in most of our sources. This would, however, be beyond the scope of this paper. A first paper by \cite{devries14} describes the results for the OH/IR stars. In Sect.~\ref{sec: data} we start with the sample selection and data reduction. In Sect.~\ref{sec: fitting} we describe how we fit and analyse the 69~$\mu$m bands in our sample. Our sample is described in more detail in Sect.~\ref{sec: resultsH4}, along with the results from fitting the 69~$\mu$m bands. We look at the laboratory studies of the 69~$\mu$m band in more detail in Sect.~\ref{sec: lab} and end this article with a discussion and conclusions in Sects.~\ref{sec: discussionH4} and \ref{sec: conclusionsH4}. The Appendices contain plots for all our reduced spectra. | \label{sec: conclusionsH4} We can summarize our conclusions as follows. \begin{itemize} \item The width and position of the 69~$\mu$m band shows that the crystalline olivine formed in outflows and disks around evolved stars is pure forsterite and contains no iron. \item The temperature indicated by the 69~$\mu$m band is ${\sim100-200~\text{K}}$. On average the crystalline olivine in the OH/IR stars has the highest temperature, with decreasing temperatures over post-AGB to PNe. \item Eight of fifteen OH/IR stars show 69~$\mu$m band detection. \cite{devries14} show that the forsterite band properties can be explained by the formation of forsterite dust in the superwind. The non-detections in our sample correspond to sources where the superwind only started recently (about a hundred years), and the coolest temperatures correspond to the longest duration of the superwind, about 1200 years. \item Most of the post-AGB stars have 69~$\mu$m bands broader than that of pure magnesium-rich olivine, which is a sign of a temperature gradient in the disk or outflow. \item The sources with confirmed disks show distinct differences. The Red Rectangle and AC Her have moderate amounts of crystalline olivine at moderate temperatures. IRAS09425's 69~$\mu$m band confirms its extreme crystallinity and shows it is relatively cold. The objects AR Pup, HD93662, and IW Car have no detectable 69~$\mu$m band, which indicates that the crystalline olivine in their disks is hot ($\sim$600 K) and situated close to the central star. \end{itemize} | 14 | 3 | 1403.6335 |
1403 | 1403.4937_arXiv.txt | We present non-linear, convective, BL~Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL~Her star, chaotic variability was claimed in several higher luminosity siblings of BL~Her stars -- RV~Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Particularly interesting are periodic windows which are intrinsic property of chaotic systems and are not necessarily caused by resonances between pulsation modes, as sometimes claimed in the literature. | Chaotic dynamics is present in many astrophysical systems and stellar variability is not an exception, although in this case, chaos was studied mostly in the context of hydrodynamic models of large amplitude pulsators. \cite{bkov87} and \cite{kovb88} found a chaotic behaviour in their radiative type-II Cepheid models (W~Vir and RV~Tau). In depth analysis of chaos in these models was conducted by \cite{skb96} and \cite{let96}. Also \cite{bm92} found chaotic behaviour in two sequences of radiative BL~Her-type models, however did not analyse the phenomenon. Recently chaotic behaviour was reported in convective hydrodynamic models of BL~Her stars \citep{sm12} and RR~Lyrae stars \citep{pkm13}. On observational side chaos was detected in type II Cepheids of RV~Tau type \citep[R~Scuti and AC~Her;][]{bks96,kbsm98} and in several semi-regular variables \citep{bkc04}, and in Mira-type variable \citep{ks03}. In this paper we report on the chaotic behaviour we have found in a sequence of non-linear convective BL~Her models. For the first time in stellar pulsation modelling we clearly demonstrate the appearance of dynamical phenomena well known and common to classical chaotic systems, both discrete (e.g. logistic or H\'enon maps) and continuous (e.g. R\"ossler or Lorenz equations). In all these systems the basic route to chaos is through a cascade of period doubling bifurcations also present in our models and in earlier studies of radiative type-II Cepheid models \citep{kovb88}. In addition, our models display a full wealth of dynamic behaviour characteristic for deterministic chaos. Within chaotic band we find several windows of non-chaotic variation (windows of order), with stable period-$n$ limit cycles. These windows are either extremely narrow or relatively large. In the latter case the periodic window is preceded by the type-I intermittent behaviour, till the periodic cycle is born through the tangent bifurcation. This periodic cycle again undergoes a series of period doubling bifurcations en route to chaos. The interior crisis bifurcations, in which separate chaotic bands merge, leading to the abrupt increase of the attractors volume are detected in our models, as well as crisis induced intermittency and type-III intermittency. Chaos was not detected in any BL~Her star so far. In our opinion however, these models are important for several reasons. ({\it i}) Chaos does occur in larger-luminosity type-II Cepheids -- RV~Tau stars, as well as in semi-regular variables. Our models may shed more light on variability of these poorly studied stars. ({\it ii}) We initiated the survey of non-linear convective pulsation models of type-II Cepheids extending to the highest luminosities (RV~Tau domain) in which chaotic variability is expected, as previous radiative models and observations indicate. In the present paper we introduce and test the methods to study chaos in such models. ({\it iii}) The striking similarity between our hydrodynamic models of pulsating stars and even the simplest chaotic systems, like logistic map, is noteworthy, indicating that many very different systems may share the same dynamical properties. ({\it iv}) Finally, although the chaotic behaviour was not detected in any BL~Her star so far, we cannot exclude such possibility in the future. We note that the period doubling effect in these stars was predicted by \cite{bm92}, based on radiative hydrodynamic models, but it took 20 years to discover the effect in the first star of this type \citep{igor11,ssm12}. In Section~\ref{sec.logistic} we summarize the properties of the logistic map, which will help us better understand phenomena occurring in our hydrodynamic models. The reader familiar with the chaos theory may safely skip this Section. In Section~\ref{sec.hydro} we briefly describe the computation and basic properties of the models. In the next Sections we present detailed analysis of the models showing both chaotic and periodic variation, including discussion of the largest Lyapunov exponents (Section~\ref{sec.lyap}). We discuss our results in Section~\ref{sec.concl} and comment on observability of the chaotic phenomena in Section~\ref{sec.obs}. Summary in Section~\ref{sec.summary} close the paper. Initial results of this study were reported in the conference proceedings of IAU Symposium No 301 ({\it Precision Asteroseismology}), \cite{sm13}. | \label{sec.concl} The non-linear stellar pulsation equations we solve, form a much more complex system than classical chaotic systems discussed in the literature. Yet the resulting dynamical scenario is qualitatively similar to that arising from the iteration of the simplest logistic map (compare the bifurcation diagrams in Figs.~\ref{fig.log_bifurcation} and \ref{fig.histo} and animations attached with the online version of this paper as supporting information). Most of conclusions about the origin of dynamical phenomena found in our models are drawn based on the analogies between our models and simpler systems for which strict analytical reasoning is possible. However, for some of the phenomena we detect, we do not find a satisfactory analogy. The appearance of period-6 window, extending between $6459.0$\thinspace K and $6468.0$\thinspace K, is one of them. The scenario that is expected and that is encountered in many other systems, and is also present in the period-3 window (between $6421.0$\thinspace K and $6438.0$\thinspace K) is the following. First, a stable period-3 cycle is born together with unstable period-3 cycle. The stable branch undergoes a series of period doubling bifurcations to form three chaotic bands, which finally collide with the unstable period-3 cycle to form one chaotic band (Section~\ref{ssec.intercrises}). To the contrary, in the window at $\approx 6468.0$\thinspace K, a stable period-6 cycle, which looks like two stable period-3 cycles born very close to each other, emerges from the chaos. We are not aware of any bifurcation that may lead to such scenario and of any other system showing such behaviour. One of the possibilities is that in fact a pair of stable and unstable period-3 cycles is born, as expected, and stable cycle immediately undergoes a period doubling bifurcation. To check this, we have computed additional models in the interesting temperature range (with $0.1$\thinspace K-step in effective temperature), but they display either chaos or a period-6 behaviour (in Section~\ref{ssec.cs2} we analysed one of these models). If the proposed scenario indeed takes place it must occur in a temperature range narrower than $0.1$\thinspace K. The situation at $\approx 6468.0$\thinspace K looks even more complex. It seems that at this temperature we deal with discontinuity -- the bifurcation diagram (Fig.~\ref{fig.histo}) divides into two parts apparently decoupled from each other. On the cool side we clearly see a gradual evolution of the chaotic bands, divided, from time to time, by periodic windows. This gradual evolution seems to continue till $6468.0$\thinspace K, but not for the band extending at higher effective temperatures. This behaviour may result from the coexistence of two attractors in the system. Note that by default we initialized all the models along a sequence in the same manner (Section~\ref{sec.hydro}). It is possible that such initialization leads to different attractors for models cooler/hotter than $6468.0$\thinspace K. To check the possible existence of other stable attractor(s) (with different basins of attraction), we have repeated the computation for many models, but with several different initializations. In all cases however, we finally arrived at the same attractor as in the case of our default initialization. At the moment the cause and nature of bifurcation we observe at $6468.0$\thinspace K remains unclear. The other phenomenon we have not discussed yet, is the appearance of chaos itself. The chaotic bands appear through a well understood period doubling route; the question is about the trigger. In the case of radiative models of \cite{bkov87} and \cite{kovb88}, analysis of the Floquet coefficients clearly shows that the first period doubling bifurcation is caused by the half-integer resonance between pulsation modes \citep[$5\!:\!2$ between fundamental and second overtone modes;][]{mb90}. The following cascade en route to chaos was not analysed. \cite{mb90} analysed a toy model of parametrically driven oscillator and showed that the first period doubling in such system results from the resonance and the following cascade is a result of increasing non-linearity. We note that the non-linearity may be the only cause of period doublings in classic chaotic systems void of internal resonances. We do not have appropriate tools (Floquet coefficients) to proof that half-integer resonance is responsible for the period doubling of single-periodic pulsation we observe at the cool and the hot sides of our computation domain. The closest resonances are (Fig.~\ref{fig.hr}) $\omega_{8}/\omega_{0}=9\!:\!2$ on the hot side of the computation domain and, $\omega_{3}/\omega_{0}=5\!:\!2$ and $\omega_{5}/\omega_{0}=7\!:\!2$ on the cool side. The loci of the $\omega_{1}/\omega_{0}=3\!:\!2$ resonance, causing the period doubled pulsation detected in a single BL~Her star \citep{ssm12} is located more than 300\thinspace K-off the hot side of the computation domain considered here and likely plays no role. We cannot exclude the possibility that non-linearity is the only cause of the observed behaviours. The appearance of periodic windows is also very interesting and important for stellar pulsation studies. As in the case of period-doubled pulsation, resonances were also invoked as a possible explanation. In a recent study \cite{pkm13} proposed that a $27\!:\!20$ resonance between the fundamental mode and the first overtone is responsible for a period-20 cycle behaviour they found in one of their RR~Lyrae models (their model H; for other model they propose a $14\!:\!19$ resonance). In this case however, a caution is needed, as inferences about the role of resonance are not based on firm theoretical grounds. The presence of first overtone cannot be deduced from the frequency spectrum. The role of resonance is most likely\footnote{\cite{pkm13} do not discuss in detail how the connection between the periodic pulsation and resonances is made.} deduced based on approximate coincidence of the model's location in the H-R diagram with the loci of the $27\!:\!20$ resonance determined with linear pulsation periods. Since pulsation periods change in the non-linear regime, and fine-tuning of such high-order resonance is difficult, claims on the possible role of resonances must be supported with other (dynamical) arguments. We are not aware of any studies showing that such high-order resonances may indeed have a noticeable effect on stellar pulsations. In a simpler explanation, period-$k$ behaviour detected in the models, is an intrinsic property of non-linear, chaotic system. The $\pm 1$\thinspace K neighbours of the discussed model of \cite{pkm13} show chaos and thus situation corresponds to periodic window within chaotic band, just as we report in this paper (Section~\ref{ssec.PW}), and as is found in many chaotic systems void of resonances. In chaotic systems the spectrum of periodic windows is dense \citep[it is one of the key properties of chaotic systems; e.g.][]{book.PJS}, but most of the windows are extremely narrow. Based on extreme similarity of our bifurcation diagram (Fig.~\ref{fig.histo}), to bifurcation diagrams for other systems, we conclude that also in the case of our computations the spectrum of periodic windows is most likely dense, but most of the windows are extremely narrow (in effective temperature). With the default $1$\thinspace K resolution of our model computation only few of the windows were detected (and most of them are narrower than $2$\thinspace K). Studying linear periods we find no tight connection between location of the periodic windows and the loci of high-order resonances between low order pulsation modes. We conclude that existence of periodic windows is an intrinsic property of non-linear system studied in this paper. There is no need to invoke resonances to explain them. \label{sec.summary} The BL~Her models discussed in this paper fall along a single stripe of constant luminosity in the H-R diagram and cover a range of only $\approx\!150$\thinspace K. Yet they display a wealth of dynamical behaviours characteristic for deterministic chaos. Many of the discussed phenomena are detected for the first time in the context of stellar pulsation models. It was possible because our model survey was dedicated to study such phenomena -- a tiny step in effective temperature, sometimes as small as $0.1$\thinspace K (and $1$\thinspace K max), allowed to follow the dynamical evolution of the system from single-periodic pulsation, through period doubling cascade to well developed chaotic regime, and back to single-periodic pulsation. The chaotic regime turned out to be a gold-mine of interesting dynamical phenomena. We found several periodic windows (with cycle-3, 5, 6, 7 and 9 behaviours). We stress that the existence of periodic windows is not related to resonances among pulsation modes, but is an intrinsic property of a chaotic system. At the edges of the largest period-3 and period-6 windows we have found intermittent behaviour and crises bifurcations. Particularly interesting is intermittency -- a sporadic switching between two qualitatively different behaviours. In type-I intermittency intervals of apparently periodic (period-$k$, in general) behaviour are interrupted with bursts of chaos. In type-III intermittency the oscillations switch between two periodic cycles. In our models we detected switching between period-9 and period-18 cycles. Detection of the discussed phenomena in the stars would be extremely interesting, however it requires a long and regularly sampled time series. The already available data from projects such as OGLE offer the best opportunity for a successful search. | 14 | 3 | 1403.4937 |
1403 | 1403.6045_arXiv.txt | { White dwarfs can be used to study the structure and evolution of the Galaxy by analysing their luminosity function and initial mass function. Among them, the very cool white dwarfs provide the information for the early ages of each population. Because white dwarfs are intrinsically faint only the nearby ($\sim 20$~pc) sample is reasonably complete. The {\Gaia} space mission will drastically increase the sample of known white dwarfs through its 5--6 years survey of the whole sky up to magnitude $V=20$--$25$. } {We provide a characterisation of {\Gaia} photometry for white dwarfs to better prepare for the analysis of the scientific output of the mission. Transformations between some of the most common photometric systems and {\Gaia} passbands are derived. We also give estimates of the number of white dwarfs of the different galactic populations that will be observed. } {Using synthetic spectral energy distributions and the most recent {\Gaia} transmission curves, we computed colours of three different types of white dwarfs (pure hydrogen, pure helium, and mixed composition with H/He$=0.1$). With these colours we derived transformations to other common photometric systems (Johnson-Cousins, Sloan Digital Sky Survey, and 2MASS). We also present numbers of white dwarfs predicted to be observed by {\Gaia}. } {We provide relationships and colour-colour diagrams among different photometric systems to allow the prediction and/or study of the {\Gaia} white dwarf colours. % We also include estimates of the number of sources expected in every galactic population and with a maximum parallax error. {\Gaia} will increase the sample of known white dwarfs tenfold to about 200\,000. {\Gaia} will be able to observe thousands of very cool white dwarfs for the first time, which will greatly improve our understanding of these stars and early phases of star formation in our Galaxy. } {} | White dwarfs (WDs) are the final remnants of low- and intermediate-mass stars. About 95\% of the main-sequence (MS) stars will end their evolutionary pathways as WDs and, hence, the study of the WD population provides details about the late stages of the life of the vast majority of stars. Their evolution can be described as a simple cooling process, which is reasonably well understood \citep{sal00,fon01}. WDs are very useful objects to understand the structure and evolution of the Galaxy because they have an imprinted memory of its history \citep{ise01,lie05}. The WD luminosity function (LF) gives the number of WDs per unit volume and per bolometric magnitude \citep{winget87,ise98}. From a comparison of observational data with theoretical LFs important information on the Galaxy \citep{winget87} can be obtained (for instance, the age of the Galaxy, or the star formation rate). Moreover, the initial mass function (IMF) can be reconstructed from the LF of the relic WD population, that is, the halo/thick disc populations. The oldest members of these populations are cool high-mass WDs, which form from high-mass progenitors that evolved very quickly to the WD stage. Because most WDs are intrinsically faint, it is difficult to detect them, and a complete sample is currently only available at very close distances. \cite{hol08} presented a (probably) complete sample of local WDs within 13~pc and demonstrated that the sample becomes incomplete beyond that distance. More recently, \citet{giammichele12} provided a nearly complete sample up to 20~pc. Completeness of WD samples beyond 20\,pc is still very unsatisfactory even though the number of known WDs has considerably increased thanks to several surveys. For instance, the Sloan Digital Sky Survey (SDSS), with a limiting magnitude of $g'=19.5$ \citep{fukugita96} and covering a quarter of the sky, has substantially increased the number of spectroscopically confirmed WDs\footnote{SDSS catalogue from \cite{eis06} added 9316 WDs to the 2249 WDs in \cite{mccook99}. A more recent publication \citep{kleinman13}, using data from DR7 release, almost doubles that amount, with of the order of $20\,000$ WDs.}. This has allowed several statistical studies \citep{eis06}, and the consequent improvement of the WD LF and WD mass distribution \citep{kleinman13,tre11,kre09,deg08,hu07,har06}. However, the number of very cool WDs and known members of the halo population is still very low. A shortfall in the number of WDs below $\log (L/L_{\odot})=-4.5$ because of the finite age of the Galactic disc, called luminosity cut-off, was first observed in the eighties \citep[e.g.][]{lie80,winget87}. The {\Gaia} mission will be extremely helpful in detecting WDs close to the luminosity cut-off and even fainter, which is expected to improve the accuracy of the age determined from the WD LF. {\Gaia} is the successor of the ESA Hipparcos astrometric mission \citep{hipparcos} and increases its capabilities drastically, both in precision and in number of observed sources, offering the opportunity to tackle many open questions about the Galaxy (its formation and evolution, as well as stellar physics). {\Gaia} will determine positions, parallaxes, and proper motions for a relevant fraction of stars ($10^9$ stars, $\sim1\%$ of the Galaxy). This census will be complete for the full sky up to $V=20-25$~mag (depending on the spectral type) with unprecedented accuracy (\citealt{perryman01}, \citealt{prusti11}). Photometry and spectrophotometry will be obtained for all the detected sources, while radial velocities will be obtained for the brightest ones (brighter than about 17$^{\mathrm{th}}$ magnitude). Each object in the sky will transit the focal plane about 70 times on average. The {\Gaia} payload consists of three instruments mounted on a single optical bench: the astrometric instrument, the spectrophotometers, and one high-resolution spectrograph. The astrometric measurements will be unfiltered to obtain the highest possible signal-to-noise ratio. The mirror coatings and CCD quantum efficiency define a broad (white-light) passband named $G$ \citep{jor10}. The basic shape of the spectral energy distribution (SED) of every source will be obtained by the spectrophotometric instrument, which will provide low-resolution spectra in the blue (330--680~nm) and red (640--1000~nm), BP and RP spectrophotometers, respectively \citep[see][for a detailed description]{jor10}. The BP and RP spectral resolutions are a function of wavelength. The dispersion is higher at short wavelengths. Radial velocities will also be obtained for more than 100 million stars through Doppler-shift measurements from high-resolution spectra ($R\sim 5000$--$11\,000$) obtained in the region of the IR Ca triplet around 860~nm by the Radial Velocity Spectrometer (RVS). Unfortunately, most WDs will show only featureless spectra in this region. The only exception are rare subtypes that display metal lines or molecular carbon bands (DZ, DQ, and similar). The precision of the astrometric and photometric measurements will depend on the brightness and spectral type of the stars. At $G=15$~mag the end-of-mission precision in parallaxes will be $\sim25$~{\uas}. At $G=20$~mag the final precision will drop to $\sim 300$~{\uas}, while for the brightest stars ($6<G<12$~mag) it will be $\sim10$~{\uas}. The end-of-mission $G$-photometric performance will be at the level of millimagnitudes. For radial velocities the precisions will be in the range 1 to 15 {\kms} depending on the brightness and spectral type of the stars \citep{katz11}. For a detailed description of performances see the {\Gaia} website\savefootnote{foot:performances}{http://www.cosmos.esa.int/web/gaia/science-performance}. An effective exploitation of this information requires a clear understanding of the potentials and limitations of {\Gaia} data. This paper aims to provide information to researchers on the WD field to obtain the maximum scientific gain from the {\Gaia} mission. \cite{jor10} presented broad {\Gaia} passbands and colour-colour relationships for MS and giant stars, allowing the prediction of {\Gaia} magnitudes and uncertainties from Johnson-Cousins \citep{bessell90} and/or SDSS \citep{fukugita96} colours. That article used the BaSeL-3.1 \citep{westera} stellar spectral library, which includes SEDs with $-1.0 < \log g < 5.5$, and thus excluded the WD regime ($7.0 < \log g < 9.0$). The aim of the present paper is to provide a similar tool for characterizing {\Gaia} observations of WDs. For that purpose, we used the most recent WD synthetic SEDs \citep[][see Sect.~\ref{sec:atmospheres}]{kil09,kil10,tre11,ber11} with different compositions to simulate {\Gaia} observations. In Sect.~\ref{sec:WDinGaia} we describe the conditions of WD observations by {\Gaia} (the obtained {\Gaia} spectrophotometry, the WD limiting distances, expected error in their parallaxes, etc.). In Sect.~\ref{sec:transformations} we provide the colour-colour transformations between {\Gaia} passbands and other commonly used photometric systems like the Johnson-Cousins \citep{bessell90}, SDSS \citep{fukugita96}, and 2MASS \citep{cohen03}. In Sect.~\ref{sec:classification} relationships among {\Gaia} photometry and atmospheric parameters are provided. Estimates of the number of WDs that {\Gaia} will potentially observe based on simulations by \cite{nap09} and {\Gaia} Universe Model Snapshot (GUMS, \citealt{rob12}) are provided in Sect.~\ref{sec:simulation}. Finally, in Sect.~\ref{sec:conclusions} we finish with a summary and conclusions. | \label{sec:conclusions} We have presented colour-colour photometric transformations between {\Gaia} and other common optical and IR photometric systems (Johnson-Cousins, SDSS and 2MASS) for the case of WDs. To compute these transformations the most recent {\Gaia} passbands and WD SED synthetic libraries \citep{tre11,ber11} were used. Two different behaviours were observed depending on the WD effective temperature. In the 'normal' regime ({\teff}~$> 5000$~K) all WDs with the same composition (pure-H or pure-He) could be fitted by a single law to transform colours into the {\Gaia} photometric system. For the very cool regime, WDs with different compositions, {\teff} and $\log g$, fall in different positions in colour-colour diagram which produces a spread in these diagrams. Colours with blue/UV information, like the $B$ Johnson passband, seem to better disctinguish the different WD characteristics, but the measurements in this regime will be rather noisy because of the low photon counts for very cool sources and in practice might be hard to use. We therefore expect that observations in near-IR passbands, combined with {\Gaia} data, might be very helpful in characterising WDs, especially in the cool regime. Estimates of the number of WDs that {\Gaia} is expected to observe during its five-year mission and the expected precision in parallax were also provided. According to the number of sources predicted by \cite{nap09} and by the {\Gaia} Universe Model Snapshot \citep{rob12}, we expect between $250\,000$ and $500\,000$ WDs detected by {\Gaia}. A few thousand of them will have {\teff}~$< 5000$~K, which will increase the statistics of these very cool WDs quite substantially, a regime in which only very few objects have been observed until now \citep{catalan12,har06}. {\Gaia} parallaxes will be extremely important for the identification and characterisation of WDs. We provided estimates of the precision in WD parallaxes that {\Gaia} will derive, obtaining that about $95\%$ of WDs will have parallaxes better than $10\%$. For cool WDs ({\teff}$<5000$~K) they will have parallaxes better than $5\%$, and about $2000$ of them will have parallaxes better than $1\%$. Additional photometry or/and spectroscopic follow-up might be necessary to achieve a better accuracy on the atmospheric parameters. A comparison of the masses obtained from the {\Gaia} parallaxes with those determined from spectroscopic fits will allow testing the mass-radius relations for WDs. A better characterisation of the coolest WDs will also be possible since it will help to resolve the discrepancy regarding the H/He atmospheric composition of these WDs that exist in the literature \citep{kowalski06,kil09,kil10}. In addition,, the orbital solutions derived for the WDs detected in binary systems will provide independent mass determinations for them, and therefore will allow for stringent tests of the atmosphere models. This will improve the stellar population ages derived by means of the WD cosmochronology and our understanding of the stellar evolution. | 14 | 3 | 1403.6045 |
1403 | 1403.4089_arXiv.txt | We study high-energy neutrino production in inner jets of radio-loud active galactic nuclei (AGN), taking into account effects of external photon fields and the blazar sequence. We show that the resulting diffuse neutrino intensity is dominated by quasar-hosted blazars, in particular, flat spectrum radio quasars, and that PeV-EeV neutrino production due to photohadronic interactions with broadline and dust radiation is unavoidable if the AGN inner jets are ultrahigh-energy cosmic-ray (UHECR) sources. Their neutrino spectrum has a cutoff feature around PeV energies since target photons are due to Ly$\alpha$ emission. Because of infrared photons provided by the dust torus, neutrino spectra above PeV energies are too hard to be consistent with the IceCube data unless the proton spectral index is steeper than 2.5, or the maximum proton energy is $\lesssim100$~PeV. Thus, the simple model has difficulty in explaining the IceCube data. For the cumulative neutrino intensity from blazars to exceed $\sim{10}^{-8}~{\rm GeV}~{\rm cm}^{-2}~{\rm s}^{-1}~{\rm sr}^{-1}$, their local cosmic-ray energy generation rate would be $\sim10\mbox{--}100$ times larger than the local UHECR emissivity, but is comparable to the averaged $\gamma$-ray blazar emissivity. Interestingly, future detectors such as the Askaryan Radio Array can detect $\sim0.1\mbox{--}1$~EeV neutrinos even in more conservative cases, allowing us to indirectly test the hypothesis that UHECRs are produced in the inner jets. We find that the diffuse neutrino intensity from radio-loud AGN is dominated by blazars with $\gamma$-ray luminosity of $\gtrsim10^{48}~{\rm erg}~{\rm s}^{-1}$, and the arrival directions of their $\sim1\mbox{--}100$~PeV neutrinos correlate with the luminous blazars detected by {\it Fermi}. | The likely discovery of astrophysical high-energy neutrinos has recently been reported from data acquired with the Gton neutrino detector, IceCube. In 2012, two PeV shower events were reported from the combined IC-79/IC-86 data period, and a recent follow-up analysis of the same data enabled the IceCube Collaboration to find 26 additional events at lower energies~\cite{PeVevents}. Interestingly, for a $E_\nu^{-2}$ spectrum, the observed diffuse neutrino intensity $E_\nu^2\Phi_{\nu_i}=(1.2\pm0.4)\times{10}^{-8}~{\rm GeV}~{\rm cm}^{-2}~{\rm s}^{-1}~{\rm sr}^{-1}$ (per flavor) is consistent with the Waxman-Bahcall bound~\cite{wb98}, which provides a benchmark intensity for neutrino astrophysics. This intensity is much higher than the nucleus-survival bound for sources of high-energy heavy nuclei~\cite{mb10}. High-energy neutrinos give an unambiguous signal of high-energy cosmic-ray (CR) acceleration, and a few PeV neutrinos probe CRs whose energy is $\sim100$~PeV per nucleon above the {\it knee} of the CR spectrum at $\sim3$~PeV. These results begin to open a new window on the high-energy astroparticle universe. Various possibilities have been proposed to explain the IceCube signal (see, e.g.,~\cite{lah+13,PeVnurev}). Galactic scenarios are being constrained by various CR experiments~\cite{anc+13,am14}. Possible isotropic Galactic emission models have also been constrained by the diffuse $\gamma$-ray background measured by {\it Fermi}, as well as sub-PeV $\gamma$-ray searches~\cite{am14,mur+13,jag+14}. Since there is no significant anisotropy toward the Galactic Center, extragalactic scenarios are the most natural (although a fraction of the neutrino events could come from Galactic sources). In any astrophysical scenario, high-energy neutrinos are produced by hadronuclear (e.g., $pp$)~\cite{mur+13} or photohadronic (e.g., $p\gamma$)~\cite{wal13} interactions. In $pp$ scenarios, as predicted before the IceCube discovery~\cite{mur+08,lw06}, an enhanced intensity of neutrino signals above the CR-induced atmospheric background intensity in the IceCube data can be explained by galaxy groups and clusters, and star-forming galaxies~\cite{mur+13}. Galaxy groups and clusters host active galactic nuclei (AGN), galaxy mergers, and have accretion and intracluster shocks, and it is plausible that they are {\it reservoirs} of $\sim100$~PeV CRs. CRs with $\sim100$~PeV energies could also be produced in starburst galaxies with strong magnetic fields~\cite{lw06,mur+13} and/or by special accelerators, such as broadline Type Ibc supernovae~\cite{mur+13,lw06,peculiarsn} and interaction-powered supernovae~\cite{mur+11}. On the other hand, $p\gamma$ scenarios, which naturally include candidate source classes of ultrahigh-energy CRs (UHECRs), include AGN~\cite{agncore,agnjet} and $\gamma$-ray bursts (GRBs)~\cite{wb97}. For AGN, IceCube already put interesting constraints on original predictions of various models. For GRBs, although their neutrino production efficiency can still be consistent with the IceCube signal, stacking analyses by IceCube have given interesting limits on this possibility~\cite{lah+13,grblim2}. Different GRB classes, such as low-luminosity GRBs~\cite{mur+06,gz07}, are possible as viable explanations of the IceCube data, and they may give contributions larger than that from classical long-duration and short-duration GRBs~\cite{mi13,ch13}. AGN are powered by supermassive black holes, and $\sim10$\% of them are accompanied by relativistic jets. They are the most prominent extragalactic sources in $\gamma$ rays. A significant fraction of the diffuse $\gamma$-ray background is attributed to blazars whose jets are pointing towards us. Imaging atmospheric Cerenkov telescopes and the recent {\it Fermi} Gamma-ray Space Telescope have discovered many BL Lac objects and flat spectrum radio quasars (FSRQs) (for a review, see~\cite{der12} and references therein). Moreover, radio galaxies that are misaligned by large angles to the jet axis and thought to be the parent population of blazars in the geometrical unification scenario~\cite{up95}, are also an important class of $\gamma$-ray sources. The blazar class has been investigated over many years as sources of UHECRs and neutrinos~\cite{agnjet,ad01,der+12,mur+12}. The spectral energy distribution (SED) of blazar jets is usually modeled by nonthermal synchrotron and inverse-Compton radiation from relativistic leptons, although hadronic emissions may also contribute to the $\gamma$-ray spectra (see, e.g.,~\cite{bot10}). It has been suggested that the SEDs of blazars evolve with luminosity, as described by the so-called blazar sequence (e.g.,~\cite{fos+98,kub+98,don+01,gt08,mar+08}). The blazar sequence has recently been exploited to systematically evaluate contributions of BL Lac objects and quasar-hosted blazars (QHBs) (including steep spectrum radio quasars as well as FSRQs) to the diffuse $\gamma$-ray background~\cite{it09,ino+10,ha12}. Besides the jet component, typical quasars---including QHBs---show broad optical and ultraviolet (UV) emission lines that originate from the broadline regions (BLRs) found near supermassive black holes. The BLR also plays a role in scattering radiation emitted by the accretion disk that feeds matter onto the black hole. In addition, the pc-scale dust torus surrounding the galactic nucleus is a source of infrared (IR) radiation that provides target photons for very high-energy CRs. In this work, we study high-energy neutrino production in the inner jets of radio-loud AGN, and examine the effects of external photon fields on neutrino production in blazars. We use the blazar sequence to derive the diffuse neutrino intensity from the inner jets. We show that the cumulative neutrino background, if from radio-loud AGN, is dominated by the most luminous QHBs. This implies a cross correlation between astrophysical neutrinos with $\sim1\mbox{--}100$~PeV energies and bright, luminous FSRQs found by {\it Fermi}. In previous works on the diffuse neutrino intensity~\cite{agncore,agnjet}, only the jet and accretion-disk components were considered as target photons, but here we show that $p\gamma$ interactions with broadline photons and IR dust emission are important when calculating the cumulative neutrino background. Our study is useful to see if radio-loud AGN can explain the IceCube signal or not. We show that the simple inner jet model has difficulty in explaining the IceCube data even when the external radiation fields are taken into account. Even so, interestingly, we find that the expected neutrino signal in the $0.1\mbox{--}1$~EeV range provides promising targets for future projects suitable for higher-energy neutrinos, such as the Askaryan Radio Array (ARA)~\cite{all+12}, the Antarctic Ross Ice-Shelf ANtenna Neutrino Array (ARIANNA)~\cite{bar07}, the Antarctic Impulsive Transient Antenna (ANITA) ultrahigh-energy neutrino detector~\cite{gor+09}, and the ExaVolt Antenna (EVA) mission~\cite{gor+11}. Throughout this work, $Q_x=Q/10^x$ in cgs units. We take Hubble constant $H_0=70~{\rm km}~{\rm s}^{-1}~{\rm Mpc}^{-1}$, and let the dimensionless density paramters for mass and cosmological constant be given by $\Omega_\Lambda=0.7$ and $\Omega_m=0.3$, respectively. | In this work, we studied high-energy neutrino production in the inner jets of radio-loud AGN, including effects of external photon fields. The diffuse neutrino intensity was obtained by characterizing the blazar SEDs assuming the validity of the blazar sequence. Our findings are summarized as follows: (1) External radiation fields can play a major role in PeV-EeV neutrino production, so they should not be neglected. In particular, broadline emission is crucial for PeV neutrino production. The typical photomeson production efficiency in the BLR is $\sim1\mbox{--}10$\%, independent of $\Gamma$ and $\delta t'$, provided that the CRs are well above threshold and accelerated inside the BLR. Photohadronic losses with IR photons from the dust torus compete with acceleration to prevent acceleration of CRs to $E'_p\gtrsim{10}^{19}$~eV energies. Therefore luminous QHBs cannot be sources of UHECR protons due to severe photohadronic cooling. Photodisintegration interactions with IR photons deplete heavy nuclei, so that production and escape of UHECR nucleons is most likely to happen in low-luminosity blazars, such as HSP BL Lac objects~\cite{mur+12}. (2) In the blazar-sequence model, the main contribution to the cumulative neutrino background comes from luminous QHBs (mainly FSRQs) rather than BL Lac objects. Interactions of $\sim100$~PeV CRs with BLR radiation is unavoidable in models that assume acceleration of high-energy CRs in the inner jets of FSRQs. We find that the cumulative neutrino background from radio-loud AGN will be dominated by dozens of blazars. The clear prediction is that, if they are the main origin of the observed diffuse neutrino intensity at $\sim1\mbox{--}100$~PeV energies, neutrino events should be correlated with luminous FSRQs. Future correlation studies can test the possibility that radio-loud AGN are the main sources of the cumulative neutrino background. (3) Implications of the inner jet model for the IceCube signal include the result that the neutrino spectra should have a cutoff feature around PeV, or they should be quite hard at sub-PeV energies. Because the inner jet model has difficulty in explaining the IceCube signal at sub-PeV energies, a different origin of sub-PeV neutrinos will be required if the inner jets of blazars explain the PeV neutrino events observed by IceCube. (4) Thanks to IR emission from the dust torus and/or internal synchrotron emission from the jet, for power-law CR spectra, the resulting neutrino spectra are too hard above PeV energies, so they are disfavored by the IceCube data because of the larger neutrino-nucleon cross section at these energies. If the CR spectra are described by a power law, which is reasonable for the explanation of UHECRs, the CR spectral index should be steeper than 2.5, or have a maximum proton energy of $\lesssim100$~PeV. (5) The diffuse neutrino intensity formed by blazars can be as high as $E_\nu^2\Phi_\nu\sim3\times{10}^{-8}~{\rm GeV}~{\rm cm}^{-2}~{\rm s}^{-1}~{\rm sr}^{-1}$ with $\xi_{\rm cr}\sim50\mbox{--}500$. Given $f_{p\gamma}\sim0.01\mbox{--}0.1$, the local CR energy injection rate that can explain the observed diffuse neutrino intensity should be larger than the observed UHECR energy generation rate. This implies that a simultaneous explanation of the neutrino and UHECR data is not easy in the simple model, although it might be possible by changing assumptions on parameters such as $f_{p\gamma}$, $\xi_{\rm cr}$ and $s$ as well as introducing another component for sub-PeV neutrinos. Low-luminosity GRBs (or transrelativistic supernovae) have also been considered as the origin of PeV neutrinos~\cite{mur+06,gz07,mi13} and/or UHECRs, and the required CR loading factor in the blazar inner jet model (e.g., $\xi_{\rm cr}\sim50$ for $s=2.0$) is comparable to or a bit larger than the values found in these GRB models. This is because, even though the $\gamma$-ray energy budget of blazars is larger than that of GRBs, their typical effective $p\gamma$ optical depth is modest, $\sim1\mbox{--}10$\%, for PeV neutrinos. (6) Whether the observed cumulative neutrino background in the PeV range is explained by the AGN inner jet model or not, we emphasize that EeV neutrino observations are crucial to test the hypothesis that radio-loud AGN are the main sources of UHECRs. Indeed, for reasonable CR loading factors (e.g., $\xi_{\rm cr}=3$ for $s=2.0$ or $\xi_{\rm cr}=100$ for $s=2.3$), the CR energy injection rate at ${10}^{19}$~eV is compatible with the UHECR energy budget at that energy, and that detections of associated EeV neutrinos are promising even in such more conservative cases. Therefore, our results suggest that future higher-energy neutrino detectors such as ARA and ARIANNA should provide an {\it indirect} clue to testing the intriguing AGN-UHECR scenario by detecting or failing to detect $\sim0.1\mbox{--}1$~EeV neutrinos from radio-loud AGN. However, the connection between UHECRs and neutrinos is likely to be nontrivial, since UHECRs mainly come from BL Lac objects while neutrinos mostly come from QHBs. As in PeV neutrinos, if the cumulative neutrino background mainly comes from radio-loud AGN, the expected diffuse neutrino intensity at $\sim0.1$~EeV energies should be correlated with bright and luminous {\it Fermi} blazars. Because of the limitations of the intensive numerical treatment, we considered only specific parameter sets for $\Gamma$ and $\delta t'$. Although the neutrino production efficiency in the blazar zone suffers from large astrophysical uncertainty as in GRBs, it is less uncertain for neutrinos due to radiation fields rom the BLR and dust torus. A parallel treatment using a less accurate but faster semianalytic model~\cite{der+14}, which makes a parameter study feasible, confirms the conclusions found here. Finally, we note that hadronic $\gamma$ rays necessarily accompany photohadronic reactions, as we already discussed. In contrast to hadronic models for blazar $\gamma$-ray emission~\cite{agnjet}, we assumed the leptonic model with only a weak or subdominant hadronic $\gamma$-ray component. This assumption can be verified by comparing neutrino luminosity with $L_\gamma$ in Figs. 2 and 9. Nevertheless, the CR-induced $\gamma$-ray emission component can produce a distinctive emission signature in the GeV-TeV spectrum of blazars, and will be reported separately. \medskip | 14 | 3 | 1403.4089 |
1403 | 1403.2385_arXiv.txt | X-ray observations of quiescent X-ray binaries have the potential to provide insight into the structure and the composition of neutron stars. \exo\ had been actively accreting for over 24 yr before its outburst ceased in late 2008. Subsequent X-ray monitoring revealed a gradual decay of the quiescent thermal emission that can be attributed to cooling of the accretion-heated neutron star crust. In this work, we report on new \chan\ and \swift\ observations that extend the quiescent monitoring to $\simeq$5~yr post-outburst. We find that the neutron star temperature remained at $\simeq$117~eV between 2009 and 2011, but had decreased to $\simeq$110~eV in 2013. This suggests that the crust has not fully cooled yet, which is supported by the lower temperature ($\simeq$95~eV) measured $\simeq$4~yr prior to the accretion phase in 1980. Comparing the data to thermal evolution simulations reveals that the apparent lack of cooling between 2009 and 2011 could possibly be a signature of convection driven by phase separation of light and heavy nuclei in the outer layers of the neutron star. | Transient neutron star low-mass X-ray binaries (LMXBs) are excellent laboratories for increasing our understanding of the structure and the composition of neutron stars, and how matter behaves under extreme physical conditions. In these binary star systems a neutron star is accompanied by a late-type star that overflows its Roche lobe and transfers matter to an accretion disk. This matter is rapidly accreted onto the neutron star during outburst episodes, whereas little or no matter reaches the compact primary during quiescent intervals. These accretion cycles have a profound effect on the interior properties of neutron stars. They cool during quiescence as they lose thermal energy via photons emitted from their surface and neutrinos escaping from their crust and core \citep[e.g.,][]{yakovlev03,page2006,steiner2009,schatz2014}. However, neutron stars can re-gain thermal energy during accretion outbursts. The accretion of matter compresses the crust of a neutron star, which causes successive electron captures, neutron emissions and pycno-nuclear fusion reactions. Together, these processes deposit an energy of $\simeq$2~MeV per accreted nucleon in the crustal layers \citep[e.g.,][]{haensel1990b,haensel1990a,gupta07,steiner2012}. This energy is thermally conducted both towards the stellar core and surface, and can effectively maintain the interior temperature of the neutron star at $\simeq10^{7}-10^{8}$~K. This temperature is set by the energy injected during its historic accretion activity and the efficiency of the neutrino cooling processes \citep[e.g.,][]{brown1998,colpi2001,yakovlev03,wijnands2012}. During quiescent episodes, thermal X-rays from the surface of the neutron star may be detected. This allows a measurement of its temperature, which can encode valuable information about its interior properties. Of particular interest are observations obtained shortly after the cessation of an outburst; heating due to accretion may lift the temperature of the crust well above that of the stellar core and the subsequent cooling may be observable once back in quiescence \citep[][]{wijnands2001,ushomirsky2001,rutledge2002}. Indeed, dedicated X-ray monitoring of six LMXBs (\ks, \mxb, \xte, \exo, \igr, and \maxisource), revealed that the temperature of the neutron star decreased for years following the cessation of accretion, consistent with the heating/cooling paradigm \citep[e.g.,][J. Homan et al., in preparation]{wijnands2002,wijnands2004,cackett2006,cackett2008,cackett2010,degenaar09_exo1,degenaar2011_terzan5_3,degenaar2010_exo2,degenaar2013_ter5,diaztrigo2011,fridriksson2010,fridriksson2011}. Comparison with thermal evolution simulations has yielded valuable insight into the thermal and transport properties of neutron star crusts \citep[][]{shternin07,brown08,degenaar2011_terzan5_3,page2013,turlione2013}. Despite these successes, interpretation of the quiescent thermal emission and crustal cooling is complicated by the question whether accretion onto the neutron star fully comes to a halt. Searching for (strong) non-thermal emission in the quiescent X-ray spectrum, irregular quiescent X-ray variability, or optical/UV signatures of the quiescent accretion stream can shed light on whether residual accretion occurs \citep[see e.g.,][for recent studies]{cackett2010_cenx4,cackett2011,cackett2013_cenx4,degenaar2012_1745,bernardini2013}. \subsection{\exo} The neutron star LMXB \exo\ was discovered almost three decades ago \citep[][]{parmar1985}. The detection of X-ray eclipses indicates that the binary is viewed at high inclination ($i\simeq75^{\circ}-83^{\circ}$), and led to a measurement of the orbital period \citep[$\simeq3.82$~hr;][]{parmar1986,wolff2008c}. The source displays thermonuclear X-ray bursts, which allows for a distance determination \citep[$\simeq7$~kpc; e.g.,][]{galloway2008}. \exo\ was first detected in outburst in 1984 with \exosat\ \citep[][]{reynolds1999}, and was serendipitously detected in quiescence with \einstein\ in 1980 \citep[][]{parmar1986,garcia1999}. The source remained in outburst for $\simeq$24~yr and during this time the flux was moderately stable with occasional excisions to higher and lower fluxes. However, its activity suddenly ceased in 2008 September \citep[][]{wolff2008,wolff2008b,hynes2008,torres2008}. Subsequent monitoring with \swift, \chan\ and \xmm\ revealed a relatively hot neutron star that gradually cooled over time \citep[][]{degenaar09_exo1,degenaar2010_exo2,diaztrigo2011}. In this work we report on new X-ray observations of \exo\ to further monitor how the accretion-heated crust cools, and to search for signs of continued low-level accretion. We also re-analyze the \einstein\ data obtained in 1980 to measure the pre-outburst temperature of the neutron star. We then compare the entire data set to crust cooling simulations. | \label{sec:discussion} \subsection{Crustal Cooling in \exo}\label{subsec:cool} Our new \chan\ and \swift\ observations of \exo\ extend the quiescent monitoring to $\simeq$4.9~yr after the cessation of its very long ($\simeq$24~yr) active period. We find that the neutron star temperature gradually decreased during this time, consistent with expectations for cooling of the accretion-heated neutron star crust. In the first year of quiescence, between 2008 and 2009, the temperature decreased from $kT^{\infty}_{\mathrm{eff}}\simeq129$ to $118$~eV. It then hovered around $117$~eV for at least $\simeq2$~yr till 2011, but our most recent observation obtained in 2013 indicates a further decrease in temperature to $kT^{\infty}_{\mathrm{eff}}\simeq110$~eV. Despite the high inclination of the binary, there are no indications that the lower temperature in 2013 is due to a changing absorption column density, such as possibly seen in \mxb\ \citep[][]{cackett2013_1659}. Whereas the apparent lack of temperature evolution after 2009 led to the suggestion that the neutron star crust restored equilibrium with the core \citep[][]{degenaar2010_exo2,diaztrigo2011}, the new data presented in this work suggests that cooling is still ongoing and that a further decrease in temperature may be expected.\footnote[14]{\citet{degenaar2010_exo2} noted that the \einstein\ flux reported by \citet{garcia1999} was consistent within the errors with that inferred from the 2010 \chan\ data. However, \citet{garcia1999} used a different physical model to fit the spectrum, which may introduce biases. Fitting the data in tandem with the post-outburst \chan\ and \xmm\ observations suggests that the pre-outburst temperature was lower than currently seen, provided the caveats mentioned in Section~\ref{subsec:einstein}.} This is supported by the lower temperature measured $\simeq4$~yr prior to the outburst in 1980; $kT^{\infty}_{\mathrm{eff}}\simeq$95~eV. \subsection{A Signature of Convection?}\label{subsec:convection} The possible ``plateau'' of stalled cooling starting $\simeq1$~yr post-outburst is reminiscent of the crust cooling curve of \xte. That source too appeared to level off within $\simeq$2 yr of entering quiescence \citep[][]{fridriksson2011}, but \citet{page2013} predicted that after a temporary plateau an accelerated temperature decay would occur, which seems to be borne out by more recent observations (J. K. Fridriksson et al., in preparation). \xte\ experienced a relatively short ($\simeq$1.6 yr) but very bright accretion phase (an average flux near the Eddington limit). As a result of this vigorous heating, the temperature in the crust likely did not reach a steady state but rather had double peaked profile, which would naturally give rise a plateau. This is in sharp contrast to \exo, which was active for 24 yr at relatively low X-ray flux ($\simeq$5\% of Eddington), implying that the crust had ample time to reach a steady state profile \citep[cf.][]{brown08}. Another mechanism that may cause a plateau in the cooling curve is a convective heat flux driven by chemical separation of light and heavy nuclei in the outer layers of the neutron star \citep[][]{horowitz2007,medin2011,medin2014}. Inclusion of the inward heat transport by compositionally-driven convection in the model calculations for \exo\ leads to an episode of slow cooling that is broadly consistent with the observations. The crust cooling curve of \exo\ may thus bear an imprint of this process, although the data can also be satisfactory modeled without convection. Perhaps another possibility is that a crustal shell of rapid neutrino cooling as recently identified by \citet{schatz2014} is connected to the period of stalled cooling. This process is highly temperature-sensitive and may be related to the fact that a plateau appears to be seen only in the two hottest crust-cooling neutron stars \exo\ and \xte. However, this could also be an observational bias, since these two sources were more intensely monitored than the others \citep[see][for a comparison]{degenaar2010_exo2}. Further theoretical investigation is required to grasp the implications of this newly identified cooling process on neutron star crust cooling curves. It is of note that the model calculations of \exo\ require rather high values for the impurity parameter ($Q_{\mathrm{imp}}=40$), and the additional heat ($Q_{\mathrm{extra}}=1.8$~MeV~nucleon$^{-1}$), to keep the crust hot as long as observed. In contrast, the crust cooling curves of \ks, \mxb, \xte, and \igr\ suggested an impurity parameter of order unity \citep[][]{brown08,degenaar2011_terzan5_3,page2013,medin2014}, consistent with expectations from molecular dynamics simulations \citep[][]{horowitz2008}. In fact, taking into account allowed ranges in mass, radius, and accretion rate, \citet{brown08} set an upper limit of $Q_{\mathrm{imp}}\lesssim 10$ for \ks\ and \mxb. The higher value that we find here could imply that the crust of \exo\ has a more impure (i.e., less organized) structure than the other neutron stars, although it is unclear why that would be the case. Moreover, the obtained value of $Q_{\mathrm{imp}}$ is sensitive to other model parameters. If we allow for a higher mass-accretion rate, e.g., $\dot{M}= 1.2\times 10^{17}~\mathrm{g~s}^{-1}$, the crust temperature rises and therefore we require a lower impurity parameter ($Q_{\mathrm{imp}}=20$), and less extra heat ($Q_{\mathrm{extra}}=0.35$~MeV~nucleon$^{-1}$). This mass-accretion rate is higher than inferred from X-ray observations \citep[$\dot{M}\simeq3\times 10^{16}~\mathrm{g~s}^{-1}$; e.g.,][]{degenaar2010_exo2,diaztrigo2011}, but not implausible. There are large uncertainties in determining the accretion rate from X-ray observations, in particular for high-inclination systems such as \exo\ when part of the central X-ray source may be blocked from our line of sight, causing $\dot{M}$ to be underestimated. Nevertheless, even for this higher accretion rate $Q_{\mathrm{imp}}$ remains considerably larger than found for the other sources. Another possible way of keeping the crust in \exo\ hot for a long time is residual accretion during quiescence. \subsection{On the Possibility of Quiescent Accretion}\label{subsec:quiescent} Our interpretation of the observations of \exo\ in the crustal heating/cooling framework relies on the assumption that accretion onto the neutron star stopped when the source transitioned to quiescence. It is not straightforward to test this hypothesis with observations. Low-level accretion may generate a thermal emission spectrum like that of a cooling neutron star \citep[][]{zampieri1995,soria2011}. However, the measured temperature would then reflect that of the stellar surface that is continuously heated by residual accretion and masks the interior temperature of the neutron star. We therefore searched for signatures of quiescent accretion in \exo. X-ray monitoring with \swift\ has revealed X-ray flares in several quiescent neutron stars, e.g., \xte, Aql X-1, Cen X-4, \kstwee, \grs, and \sax\ \citep[e.g.,][]{bernardini2013,degenaar09_gc,degenaar2013_ks1741,degenaar2012_gc,fridriksson2011,wijnands2013,cotizelati2014}. During these X-ray flares the XRT count rate increased for several days by a factor of $\simeq$2 to even $>$10 for some of these sources. A corresponding hardening of the X-ray spectrum is observed and suggests that these flares are possibly caused by a spurt of low-level accretion. \exo\ was monitored with \swift\ roughly once per month for $\simeq$10~ks between 2008 and 2011. We did not detect any irregular X-ray variability or flaring events such as seen in other sources. Regular \swift\ monitoring has therefore not revealed any indications of ongoing low-level accretion in \exo. However, accretion flares appear to be short-lived events (lasting $\simeq$~days), and could therefore easily be missed \citep[e.g.,][]{degenaar09_gc,degenaar2013_ks1741,fridriksson2011,wijnands2013,cotizelati2014}. The first \chan\ and \xmm\ observations of \exo\ (obtained in 2008, within 2 months after the outburst end) both showed the presence of non-thermal emission, albeit contributing only $\lesssim$15\% to the total unabsorbed 0.5--10 keV flux \citep[whereas this is $>$50\% in some other neutron stars such as \saxamxp, \swiftpulsar, and \exoter; e.g.,][]{heinke2009,degenaar2012_1745,degenaar2012_amxp}. Optical spectroscopic and photometric observations performed shortly after the transition to quiescence hinted the presence of an accretion disk that could allow for continued accretion onto the neutron star \citep[][]{bassa09,hynes09}. However, optical spectroscopy and Doppler tomography performed one year later did not show evidence for an accretion disk any more \citep[][]{ratti2012}. Any contribution from non-thermal X-ray emission also remained low at this time (Section~\ref{subsec:evolution}). Finally, there are no dips or other features in the quiescent X-ray light curves that might evidence the presence of a residual accretion stream or remnant disk \citep[see also][]{diaztrigo2011}. We conclude that there are no obvious signs of ongoing accretion in the quiescent state of \exo, particularly not $\gtrsim$1 yr after the outburst ended. Given the optical signatures of a quiescent accretion disk and the presence of non-thermal X-ray emission we cannot exclude, however, that matter was falling onto the neutron star shortly after the outburst appeared to have ended. | 14 | 3 | 1403.2385 |
1403 | 1403.5270_arXiv.txt | We introduce the Theoretical Astrophysical Observatory (TAO), an online virtual laboratory that houses mock observations of galaxy survey data. Such mocks have become an integral part of the modern analysis pipeline. However, building them requires an expert knowledge of galaxy modelling and simulation techniques, significant investment in software development, and access to high performance computing. These requirements make it difficult for a small research team or individual to quickly build a mock catalogue suited to their needs. To address this TAO offers access to multiple cosmological simulations and semi-analytic galaxy formation models from an intuitive and clean web interface. Results can be funnelled through science modules and sent to a dedicated supercomputer for further processing and manipulation. These modules include the ability to (1) construct custom observer light-cones from the simulation data cubes; (2) generate the stellar emission from star formation histories, apply dust extinction, and compute absolute and/or apparent magnitudes; and (3) produce mock images of the sky. All of TAO's features can be accessed without any programming requirements. The modular nature of TAO opens it up for further expansion in the future. | \setcounter{footnote}{0} Astronomy has entered an era of survey science, thanks almost solely to instruments and telescopes that can sample unprecedented volumes of the cosmos with unparalleled sensitivity out to great distances. Riding this wave, the field of galaxy formation and evolution has grown to become one of the most active research areas in astrophysics. Progress feeds off progress, where increasingly detailed observations of galaxies are used to build new theories, that in turn lead to predictions, which can direct and be tested against new observations. As the instruments have increased in sophistication, so have the amount of data they collect. Similarly, simulations of galaxies and the Universe have grown to keep pace. It is thus not surprising that data access has become a signature of this new era. Internet and cloud technologies allow scientists to store and retrieve large scientific datasets remotely. This is sometimes necessary since data volume and complexity often require resources beyond what is locally available. But even when not necessary it is frequently desired, as relocating storage and processing off-site reduces overheads, simplifies data management, and facilitates data sharing. Two notable examples are the Sloan Digital Sky Survey \citep[SDSS, ][]{Abazajian2003} ``SkyServer'', which hosts imaging, spectra, spectroscopic and photometric data; and the German Astrophysical Virtual Observatory \citep[GAVO, ][]{Lemson2006}, which houses the Millennium Simulation theoretical data products. Both on-line repositories are accessible by means of the Structured Query Language (SQL), and due to their accessibility, both have vastly increased the scientific value of the data they hold through data re-use. There are many ways this benefit can be measured, arguably the most important being an increased number of scientific publications. Such publications come predominantly from researchers who had nothing to do with the original data production. In large part due to this ease of access, the division between observer and theorist has faded somewhat. Observers now routinely use cutting edge theoretical models in their analysis, and theorists compare model predictions against observational data. This has all meant that the modern astronomer now routinely works across many traditional boundaries, often combining multiple disparate data products to undertake their science. The focus of the present work is on access to theoretical survey data, such as cosmological-scale dark matter simulations and galaxy formation models. Many groups around the world are currently producing state-of-the-art theory products whose value to the community is immense. However access from outside the group is often prohibitive, even when the authors are happy for others to use their work. Furthermore, comparing different simulations and models on an equal footing can be extremely problematic due to data size and transport barriers, data format differences, and complexity. This makes understanding how to correctly use the data challenging for the non-expert. Access is but one part of the puzzle however. To be compared fairly to observations, simulations must typically be modified to look more like the data being compared against. This can include: mapping the simulation cube into an observed light-cone where distance also equates to time evolution in the simulation, calculating absolute and apparent magnitudes for model galaxies in select filters from their star formation and metallicity histories, and ``observing'' mock galaxies to generate images similar to that which would be collected by a CCD. All are non-trivial tasks that require great care to implement correctly. Some effort has already gone in to producing such tools for the community. For example, the Mock Map Facility \citep[MoMAF, ][]{Blaizot2005} allows a user to build mock galaxy catalogues using the GALICS semi-analytic model \citep{Blaizot2004}. In a similar fashion, the Millennium Run Observatory \citep{MRO2012} provides a powerful set of tools to access and visualise mock catalogues based on the Millennium Run suite of dark matter simulations \citep{Springel2005GADGET}. In this paper we present a new online tool -- the Theoretical Astrophysical Observatory (TAO) -- that aims to further address the problem of community data access and, more specifically, simplifies the process of building mock galaxy catalogues to more individualised specifications. This paper is structured as follows: An introduction to TAO is presented in Section~\ref{TAO}. In the subsequent sections we then describe the first four TAO science modules: the basic galaxy and simulation selection tools (Section~\ref{galaxy-module}), the light-cone module (Section~\ref{Lightcones}), the spectral energy distribution (SED) module (Section~\ref{SEDs}), and the mock image generation module (Section~\ref{mockimage}). We then explore usage cases in Section~\ref{applications} that demonstrate the utility and functionality of TAO. Section~\ref{summary} concludes with a summary. For all results presented the cosmology of the simulation from which the result was drawn is assumed unless otherwise indicated, and we refer the reader to the associated reference for further details. | 14 | 3 | 1403.5270 |
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1403 | 1403.7934_arXiv.txt | {} { We present an 8-band ($u^{*}$, $g^{'}$, $r^{'}$, $i^{'}$, $z^{'}$, $Y$, $J$, $K_{\rm s}$) optical to near-infrared deep photometric catalogue based on the observations made with MegaCam and WIRCam at CFHT, and compute photometric redshifts, $z_{\rm p}$ in the North Ecliptic Pole (NEP) region. $AKARI$ infrared satellite carried out deep survey in the NEP region at near to mid infrared wavelength. Our optical to near-infrared catalogue provides us to identify the counterparts, and $z_{\rm p}$ for the $AKARI$ sources. } {We obtained seven ($g^{'}$, $r^{'}$, $i^{'}$, $z^{'}$, $Y$, $J$, $K_{\rm s}$) band imaging data, and we cross-matched them with existing $u^{*}$-band data (limiting magnitude = 24.6 mag [5$\sigma$; AB]) to design the band-merged catalogue. We included all $z^{'}$-band sources with counterparts in at least one of the other bands in the catalogue. We used a template-fitting methods to compute $z_{\rm p}$ for all the catalogued sources. } { The estimated 4$\sigma$ detection limits within an 1 arcsec aperture radius are 26.7, 25.9, 25.1, and 24.1 mag [AB] for the optical $g^{'}$, $r^{'}$, $i^{'}$, and $z^{'}$-bands and 23.4, 23.0, and 22.7 mag for the near-infrared $Y$, $J$, and $K_{\rm s}$-bands, respectively. There are a total of 85$\hspace{0.1em}$797 sources in the band-merged catalogue. An astrometric accuracy of this catalogue determined by examining coordinate offsets with regard to 2MASS is 0.013 arcsec with a root mean square (RMS) offset of 0.32 arcsec. We distinguish 5441 secure stars from extended sources using the $u^{*}-J$ versus $g^{'}-K_{\rm s}$ colours, combined with the SExtractor stellarity index of the images. Comparing with galaxy spectroscopic redshifts, we find a photometric redshift dispersion, $\sigma_{\Delta z/(1+z)}$, of 0.032 and catastrophic failure rate, $\frac{\Delta z}{1+z}>0.15$, of 5.8\% at $z<1$, while a dispersion of 0.117 and a catastrophic failures rate of 16.6\% at $z>1$. We extend estimate of the $z_{\rm p}$ uncertainty over the full magnitude/redshift space with a redshift probability distribution function and find that our redshift are highly accurate with $z^{'}<22$ at $z_{\rm p}<2.5$ and for fainter sources with $z^{'}<24$ at $z<1$. From the investigation of photometric properties of $AKARI$ infrared sources (23$\hspace{0.1em}$354 sources) using the $g^{'}z^{'}K_{\rm s}$ diagram, $<$ 5\% of $AKARI$ sources with optical counterparts are classified as high-$z$ ($1.4<z<2.5$) star-forming galaxies. Among the high-$z$ star-forming galaxies, $AKARI$ mid-infrared detected sources seem to be affected by stronger dust extinction compared with sources with non-detections in the AKARI MIR bands. The full, electronic version of our 8-band merged catalogue with $z_{\rm p}$ will be available at the CDS. } {} | An understanding of the cosmic history of star formation is one of the most important aspects in the study of galaxies. It has been shown that the star formation rate density derived from UV and optical wavelengths at $z\sim1$ is one order of magnitude higher than in the local Universe \citep{1995ApJ...441...18M, 2001AJ....122..288H, 1997ApJ...486L..11C, 1999ApJ...519....1S, 2007ApJ...657..738L}. These results highlight the importance of studying the cosmic star formation activity at high redshift ($z\sim1$). Studies of the extragalactic background have suggested at least one third (or half) of the luminous energy generated by stars has been reprocessed into the infrared by dust \citep{1999A&A...344..322L, 1996A&A...308L...5P, 2006ApJ...648..774S, 2008A&A...487..837F}, and that the contribution of infrared luminous sources to the cosmic infrared luminosity density increases with redshift, especially at $z>1$ \citep{2010A&A...514A...6G}. For luminous infrared galaxies ($L_{\rm IR}\hspace{0.3em}\raisebox{0.4ex}{$>$}\hspace{-0.65em}\raisebox{-.7ex}{$\sim$}\hspace{0.3em} 10^{11}L_{\odot}$), the SFR derived from UV continuum or optical diagnostics (H$\alpha$ emission line) is smaller than that inferred from the infrared or radio luminosity, which are free from dust extinction. The tendency becomes more conspicuous with increasing infrared luminosity. This suggests that more luminous galaxies, i.e., galaxies with larger SFR, are more heavily obscured by dust \citep{2001AJ....122..288H, 2001ApJ...558...72S, 2002ApJ...581..205H, 2006ApJ...637..227C, 2007ApJS..173..404B}. Therefore, to understand the star-formation history, it is essential to investigate star-formation in highly dust-obscured galaxies at high redshift ($z$\hspace{0.3em}\raisebox{0.4ex}{$>$}\hspace{-0.65em}\raisebox{-.7ex}{$\sim$}\hspace{0.3em}1) in the mid-infrared region where dust extinction is less severe. The infrared space telescope $AKARI$ \citep{2007PASJ...59S.369M} was launched in February 2006 and the $AKARI$/$IRC$ \cite[InfraRed Camera: ][]{2007PASJ...59S.401O} obtained higher quality near -- mid infrared data than the previous infrared space missions such as Infrared Astronomical Satellite \citep{1984ApJ...278L...1N} and Infrared Space Observatory \citep{1996A&A...315L..27K}. The $IRC$ has three channels (NIR, MIR-S, and MIR-L) with nine filters ($N2, N3, N4, S7, S9W, S11, L15, L18W$, and $L24$), and $AKARI$ carried out a deep survey program in the direction of North Ecliptic Pole (NEP), so-called $NEP$-$Deep$ $survey$ \citep[hereafter, NEP-Deep: ][]{2006PASJ...58..673M} with all the nine $IRC$ bands. Each single band observed $\sim$0.6 square degrees, and $\sim$ 0.5 square degrees circular area centered on $\alpha$ = 17$^h$55$^m$24$^s$, $\delta$ = $+$66$^{\circ}$37$^{'}$32$^{''}$ are covered by all the nine bands. The full width at half maximum (FWHM) of each IRC channel is $\sim$ 4 arcsec in NIR, $\sim$5 arcsec in MIR-S, and $\sim$6 arcsec in MIR-L. \cite{2013A&A...559A.132M} constructed a revised near to mid infrared catalogue of the $AKARI$ NEP-Deep. The 5$\sigma$ detection limits in the $AKARI$ NEP-Deep catalogue are 13, 10, 12, 34, 38, 64, 98, 105 and 266 $\mu$Jy at the $N2, N3, N4, S7, S9W, S11, L15, L18W$, and $L24$ bands, respectively. The real strength of the NEP-Deep survey lies in the unprecedented photometric coverage from 2 $\mu$m to 24 $\mu$m, critically including the wavelength domain between Spitzer$^{'}$s $IRAC$ \citep{2004ApJS..154...10F} and MIPS \citep{2004ApJS..154...25R} instruments from 8 $\mu$m to 24 $\mu$m, where only limited coverage is available from the peak-up camera on the IRS \citep{2004ApJS..154...18H}. Therefore, NEP-Deep survey has a great advantage to be able to study infrared galaxies without uncertainties of interpolation over the mid-infrared wavelength range. Furthermore, the NEP-Deep field is a unique region because many astronomical satellites have accumulated many deep exposures covering this location due to the nature of its position on the sky. X-ray observations by $Chandra$, UV observations by $GALEX$, and far-infrared observations by $Herschel$ were made toward the NEP-Deep field. In addition, sub-mm data from $SCUBA$-2 on the James Clerk Maxwell Telescope ($JCMT$) and radio data from Westerbork Synthesis Radio Telescope ($WSRT$) were also obtained in the NEP-Deep field \citep[see also][] {2008PASJ...60S.517W}. Thus this multi-band $AKARI$ NEP-Deep field data set provides a unique opportunity to study star formation of infrared luminous galaxies. Deep ancillary optical and near-infrared data covering the entire NEP-Deep region are essential for finding counterparts of sources detected with $AKARI$. In addition, multi-wavelength data are needed for accurate photometric redshift estimation, especially in covering the rest-frame wavelength range around the 4000$\AA$ break. Many studies have been made of the optical counterparts of the $AKARI$ sources. \cite{2012A&A...537A..24T} used the Subaru/Suprime cam (S-cam) to obtain deep optical images (28.4 mag for $B$-band, 28.0 mag for $V$, 27.4 mag for $R$, 27.0 mag for $i^{'}$, and 26.2 mag for $z^{'}$ in the AB magnitude system), but these data only cover one half of the NEP-Deep area. \cite{2007ApJS..172..583H} observed the entire NEP-Deep field with Canada France Hawaii Telescope (CFHT) in the $g^{'}$, $r^{'}$, $i^{'}$, and $z^{'}$-bands with limiting magnitudes of 26.1, 25.6, 24.7, and 24.0 mag (4$\sigma$) with 1 arcsec diameter apertures, however these images have insensitive areas resulting from gaps between CCD chips. \cite{2007AJ....133.2418I} observed the area with KPNO-2.1 m/FLAMINGOS in the $J$- and $K_{\rm s}$-bands, but the 3$\sigma$ detection limits were shallow (21.85 mag and 20.15 mag in the $J$ and $K_{\rm s}$-bands, respectively). Moreover, these data cover only about one third of the NEP-Deep field ($25^{'}\times30^{'}$). Figure \ref{fig:SEDexampleOptAKARI} is an example of SEDs for star-forming galaxies, Mrk231, M82, and Arp220 if their redshifts are at $z=0.5$ with infrared luminosity of 10$^{11}L_{\odot}$ (left) or $z=1.0$ with infrared luminosity of 2$\times$10$^{12}L_{\odot}$. In order to optically identify Arp220 at $z=1$ (blue SED) which can be detected by $AKARI$, 26 -- 23 mag [AB] for $g^{'}$--$z^{'}$ bands and 22 -- 23 mag [AB] for near-infrared bands are required. In this study, we present deep optical $g^{'}$, $r^{'}$, $i^{'}$, and $z^{'}$ (orange square in Figure \ref{fig:NEPD}) and near infrared $Y$, $J$, and $K_{\rm s}$ imaging data (red square in Figure \ref{fig:NEPD}) in the NEP-Deep field using MegaCam \citep{2003SPIE.4841...72B} and the Wide-field InfraRed Camera \citep[WIRCam;][]{2004SPIE.5492..978P} on the CFHT. We also combine existing $u^{*}$-band data \citep[purple square in Figure \ref{fig:NEPD}, PI: S. Serjeant; ][]{2012A&A...537A..24T} to provide a band-merged catalogue based on the $z^{'}$-band. The catalogue will be used to analyze the $AKARI$ NEP sources. This paper is organized as follows; we describe our observations and data reduction procedures in $\S$2, and source extraction in each band in $\S$3. We present our band-merged catalogue in $\S$4. In $\S$5, we describe our method of star-galaxy separation based on colour-colour-criteria and the SExtractor stellarity index. We calculate photometric redshifts for the sources in our catalogue by Spectral Energy Distribution (SED) fitting which is presented in $\S$6. $\S$7 provides properties of $AKARI$ sources identified their optical counterparts in our catalogue. We summarize our results in the final section. \begin{figure}[t] \begin{center} \includegraphics[width=90mm]{SEDexampleOptAKARI_z0.5_1_v2.ps} \caption{Example of galaxies SEDs. Left panel shows the SEDs with redshift of 0.5 with infrared luminosity of 10$^{11}L_{\odot}$, while right panel is for the SEDs with redshift of 1.0 with infrared luminosity of 2$\times$10$^{12}L_{\odot}$. Red, Green and Blue solid lines represent SEDs of Mrk231, M82, and Arp220. Thick horizontal lines in pink and sky blue show the 5$\sigma$ detection limits of $AKARI$ $N2$ -- $L24$ filters and ground based $g^{'}$ -- $K_{\rm s}$ band 4 $\sigma$ limiting magnitudes which we newly observed (see Table \ref{tb:photometry}). Filter response curves of CFHT/MegaCam, WIRCam, and $AKARI/IRC$ are shown at the bottom of the panels. Red, green, blue, pink, cyan, orange, and black dotted-lines represent $g^{'}$, $r^{'}$, $i^{'}$, $z^{'}$, $Y$, $J$, and $K_{\rm s}$, while red, green, blue, pink, cyan, yellow, black, orange, and gray solid lines are $AKARI/IRC$ $N2$ -- $L24$ bands, respectively.} \label{fig:SEDexampleOptAKARI} \end{center} \end{figure} \begin{figure}[htbp] \begin{center} \includegraphics[width=90mm]{NEPD.ps} \caption{Coverages of various surveys in the NEP-Deep field. The colour image in the middle is the three-colour near-infrared image made with the $IRC$ data (blue--2 $\mu$m, green--3 $\mu$m, red--4 $\mu$m). The orange box is the survey coverage of MegaCam $g^{'}$, $r^{'}$, $i^{'}$, and $z^{'}$, and the red box is that of WIRCam $Y$, $J$, and $K_{\rm s}$. The purple box represents the MegaCam $u^{*}$-band observation field \citep{2012A&A...537A..24T}.} \label{fig:NEPD} \end{center} \end{figure} | We obtained $g^{'}$, $r^{'}$, $i^{'}$, $z^{'}$, $Y$, $J$, and $K_{\rm s}$-band images with MegaCam and WIRCam at CFHT, and cross-matched each of all the band catalogues with existing $u^{*}$-band catalogue to construct an optical -- near infrared 8-band merged photometric catalogue covering the $AKARI$ NEP-Deep field. The 4$\sigma$ detection limits over an 1 arcsec radius aperture are 26.7, 25.9, 25.1, 24.1, 23.4, 23.0, and 22.7 AB mag for $g^{'}$, $r^{'}$, $i^{'}$, $z^{'}$, $Y$, $J$, and $K_{\rm s}$-bands, respectively. The astrometry of the band-merged catalogue is offset by 0.013 arcsec to the 2MASS with an RMS offset of 0.32 arcsec, while the RMS offsets between $z^{'}$-band and the other bands are 0.08--0.11 arcsec, but that between $z^{'}$ and $u^{*}$-bands is worse (0.18 arcsec) because of a slightly degraded PSF in $u^{*}$-band. We securely distinguished stars from galaxies with ($u^{*}-J$) versus ($g^{'}-K_{\rm s}$) colour-colour diagram with CLASS\_STAR of $<$ 0.8. We derived photometric redshifts based of a SED template fitting procedure using $LePhare$. The errors comparison with $z_{\rm s}$ for our spectroscopic sub-sample reveals the dispersion of $\sigma_{\Delta z/(1+z)}\sim0.032$ with $\eta=5.8$\% catastrophic failures at $z_{\rm p}<1$. We extrapolate this result to fainter magnitudes using the 1$\sigma$ uncertainties in the $z_{\rm p}$ probability distribution functions. At $z_{\rm p}<1$, we estimate a $z_{\rm p}$ accuracy of $\sigma_{\Delta z} = 0.7$ with $z^{'}<24$, while the accuracy is strongly degraded at $z_{\rm p}>1$ or $z^{'}>24$. We investigated properties of $AKARI$ sources with optical counterparts from our catalogue. We plotted the sources with $g^{'}z^{'}K_{\rm s}$ diagram and found that most of the $AKARI$ sources are located in the low-$z$ ($z<1.4$) and $<$ 5\% of them are classified as high-$z$ ($1.4<z<2.5$) star-forming galaxies. Among the high-$z$ star-forming galaxies, MIR detected sources seems to be affected stronger dust extinction compared with sources with non-detections in $AKARI$ MIR bands. Our final catalogue contains 85$\hspace{0.1em}$797 sources with $z_{\rm p}$, which are detected in $z^{'}$-band and at least one of the other bands. This optical to near-infrared photometric data with photometric redshift in the $AKARI$ NEP-Deep field derived here are crucial to study star-formation history at the era of active universe ($z\sim1$) using multi-wavelength data sets ($Chandra$, $GALEX$, $AKARI$, $Herschel$, $SCUBA$-2, and $WSRT$). | 14 | 3 | 1403.7934 |
1403 | 1403.5100_arXiv.txt | \noindent The discovery of B-modes, and their effect on the fit to inflationary parameters, opens a window to explore quantum gravity. In this paper we adopt an effective theory approach to study quantum gravity effects in inflation. We apply this approach to chaotic and $\lambda \phi^4$ inflation, and find that BICEP2 constrains these new operators to values which are consistent with the effective theory approach. This result opens the possibility to study quantum gravity in a systematic fashion, including its effect on Higgs inflation and other Starobisnky-like models. | The recent results from the BICEP2 experiment \cite{Ade:2014xna} and their discovery of B-modes in the cosmic microwave background (CMB) have profound consequences for cosmology and particle physics. The measurement of a tensor/scalar ratio $r=0.2^{+0.07}_{-0.05}$, if confirmed by future observations, is one of the most exciting results in physics since the discovery of the black body radiation about 100 years ago. More precisely, the question is truly whether the B-modes observed by BICEP2 are really of cosmological nature or whether they can be explained by a secondary source such as dust. In any case, if correct this result not only supports the hypothesis that our universe went through a period of cosmic inflation in the first few instants of its existence, but it also implies that the energy scale of inflation was very high and close to the Planck scale, around the typical scale for grand unification theories in supersymmetry \cite{Amaldi:1991cn}. Indeed, BICEP2 results imply that inflation took place at an energy scale of $10^{16}$ GeV which according to the Lyth bound \cite{Lyth:1996im} implies that the inflaton field took values much large than the Planck scale. Inflation is thus sensitive to quantum gravitational physics. We thus for the first time have a chance at probing quantum gravitational physics experimentally by studying the CMB. Since we are still very far away from a theory of quantum gravity, we have to rely on an effective theory approach, see e.g. \cite{Calmet:2013hfa,Donoghue:2012zc}. We shall consider the most generic effective theory for a scalar field coupled to gravity and use the recent data from BICEP2 and PLANCK to set limits on the parameters of this effective action for the inflaton $\phi$ \begin{eqnarray} S=\int d^x \sqrt{-g} \left (\frac{\bar M_P^2}{2} R + f(\phi) F(R,R_{\mu\nu}) + g^{\mu\nu} \partial_\mu \phi \partial^\nu \phi + V_{ren}(\phi)+ \sum_{n=5}^{\infty} c_n \frac{\phi^{n}}{\bar M_P^{n-4}} \right ) \end{eqnarray} where $\bar M_P$ is the reduced Planck, and $V_{ren}(\phi)$ contains all renormalizable terms up to dimension-four, for example $V_{ren} \supset v^3 \phi+ m^2 \phi^2 + \lambda_3 \phi^3 + \lambda_4 \phi^4$, and $c_n$ are Wilson coefficients of the higher-dimensional operators (HDO) to be discussed below. The generic term $f(\phi) F(R,R_{\mu\nu})$ stands for non-minimal couplings between the inflaton and the graviton. Via field redefinitions such terms could be shifted in the potential of the scalar field, potentially introducing new scalar degree of freedom as in the case of $R^2$. While these terms can be important for inflation, e.g. in the case of Higgs inflation, we shall ignore them as we wish to consider single field inflationary models. Note that we do not consider derivative terms of the type $(\partial^\mu \phi \partial_\mu \phi \phi^n)$ out of simplicity: we assume that the kinetic term of the graviton is canonically normalized. The validity of using effective theory techniques in inflation has recently been investigated \cite{Collins:2014yua,Agarwal:2013rva}. We are thus dealing with a potential of the form: \begin{eqnarray} V(\phi)=V_{ren} (\phi)+ \sum_{n=5}^{\infty} c_n \frac{\phi^{n}}{\bar M_P^{n-4}} \end{eqnarray} \begin{figure}[t!] \begin{minipage}{8in} \hspace*{-0.7in} \centerline{\includegraphics[height=9cm]{ns_r_noHDOs.pdf}} \label{fignoc} \hfill \end{minipage} \caption{ {\it Predictions for various polynomial forms of $V_{ren}$ with $N \in [50,60]$. The pink circle corresponds to the 95\% CL from BICEP2. } } \end{figure} In Fig.~\ref{fignoc} we show the predictions for various polynomial forms of $V_{ren}$. The areas correspond to $N \in [50,60]$. The pink circle corresponds to the 95\% CL from BICEP2. The models with potentials $\phi^{2-3}$ seem to be favoured, whereas other models with low degree polynomials, or Starobinsky-like seem to be ruled out at the 95\% CL. In this paper we study how the effect of the higher-dimensional operators changes these conclusions. In inflationary models, one often focusses on one specific term and one sets the remaining Wilson coefficients to zero. However in quantum field theory, with the exception of dimension three and four operators higher dimensional operators will be generated by quantum corrections. The reason why dimension three and four operators might in principle not be generated in the following. Let's imagine they are indeed generated by quantum gravity. In the limit where $M_P \to \infty$ these operators must go to zero. One thus expects an exponential suppression of such operators by $\exp(-M_P/\mu)$ where $\mu$ could be some low energy scale \cite{Calmet:2009uz,Holman:1992us}. This reasoning applies to $\phi^3$ and $\phi^4$, if they are not introduced in the action by hand, their Wilson coefficients are expected to be very tiny. On the contrary higher dimensional operators $c_n \frac{\phi^{n}}{\bar M_P^{n-4}}$ will be generated and one expects that their Wilson coefficients should be of order unity. The precise origin of these higher dimensional operators depends on the underlying theory of quantum gravity. In extra-dimensional theories they could arise from the exchange of super massive KK modes. In a generic theory of quantum gravity, one expects such operators to be generated by virtual and real quantum black holes \cite{Calmet:2011ta}. This is a well known problem for inflation \cite{Holman:1992us} and it has been argued that these Wilson coefficients should be of order $10^{-3}$ \cite{Kallosh:1995hi,Linde:2007fr} not to spoil the flatness of the potential. Here we study the implications of the current data on such higher dimensional terms generated by quantum gravity. | Our results have important implications for models of inflation. We have shown that quantum gravitational effects parametrized by higher dimensional operators have a significant impact in the interpretation of the data coming from observations of the PLANCK satellite or the BICEP2 experiment, even in a region of parameter space well within the validity of the effective theory approach. One possible interpretation is that quantum gravity effects make it very difficult to probe a specific model of inflation. This observation is similar to that made in the case of grand unified theories \cite{Calmet:2008df}. Another interpretation is that quantum gravitational effects can salvage models which seemed to be disfavoured by current data such as e.g. Higgs inflation \cite{Bezrukov:2007ep,Calmet:2013hia,Atkins:2010yg}. Within a specific models of inflation we can, as we have shown, derive bounds on higher dimensional operators and more specifically on the Wilson coefficients of these operators. In that sense the cosmic microwave background provides an ideal environment to probe quantum gravity effects. Indeed, we can now hope to probe the symmetries of quantum gravity. For example, we could answer questions such as: is there an approximate shift symmetry which prevents these higher dimensional operators? Are Lorentz invariance \cite{Colladay:1998fq} and CPT invariance \cite{Colladay:1996iz} valid symmetries at the Planck scale? Is space-time quantized and is there a minimal length in nature as expect from a unification of quantum mechanics and general relativity \cite{Calmet:2007vb} or is general relativity a purely classical theory \cite{Ashoorioon:2012kh}? Our results show that we will never be able to probe the potential of the inflaton without making assumptions about quantum gravity, or rather without assuming a specific framework for quantum gravity. Nevertheless, our results indicate that an effective theory approach is a valuable tool thanks to the outstanding degree of precision achieved by the experiments. Note that we focussed here on higher dimensional operators suppressed by the Planck scale, but if the inflaton is embedded into a grand unified theory, there is another natural scale below the Planck scale which would force any Wilson coefficient to be even tinier than the ones we discussed, namely the unification scale which at $10^{16}$ GeV coincides with the scale of inflation as mentioned earlier~\cite{Dimopoulos:1997fv}. Finally, this work can easily be extended to other models of inflations such as hybrid inflation and other higher dimensional operators. {\it Acknowledgments:} This work is supported in part by the European Cooperation in Science and Technology (COST) action MP0905 ``Black Holes in a Violent Universe" and by the Science and Technology Facilities Council (grant number ST/J000477/1). \bigskip{} \baselineskip=1.6pt | 14 | 3 | 1403.5100 |
1403 | 1403.1122_arXiv.txt | {A precise quantitative spectral analysis, encompassing atmospheric parameter and chemical elemental abundance determination, is time-consuming due to its iterative nature and the multi-parameter space to be explored, especially when done by the naked eye.} {A robust automated fitting technique that is as trustworthy as traditional methods would allow for large samples of stars to be analyzed in a consistent manner in reasonable time.} {We present a semi-automated quantitative spectral analysis technique for early-type stars based on the concept of $\chi^2$ min\-imization. The method's main features are as follows: far less subjectivity than the naked eye, correction for inaccurate continuum normalization, consideration of the whole useful spectral range, and simultaneous sampling of the entire multi-parameter space (effective temperature, surface gravity, microturbulence, macroturbulence, projected rotational velocity, radial velocity, and elemental abundances) to find the global best solution, which is also applicable to composite spectra.} {The method is fast, robust, and reliable as seen from formal tests and from a comparison with previous analyses.} {Consistent quantitative spectral analyses of large samples of early-type stars can be performed quickly with very high accuracy.} | The chemical evolution of galaxies is dominated by the evolution of early-type stars, since these objects are the progenitors of core-collapse supernovae, and therefore contribute to stellar nucleosynthesis in a pronounced way. In this context, important issues are the effects of rotation, especially for that of rotational mixing, on the evolution of massive stars \citep[e.g.,][]{rotation_heger,rotation_meynet}, as well as spatial and temporal variations of the chemical composition within the Galactic disk \citep[e.g.,][]{chemical_evolution_fuhrmann,chemical_evolution_przybilla}. Quantitative spectroscopic analyses of B- and late O-type stars allow for atmospheric parameters and chemical elemental surface abundances to be inferred with high precision, which directly addresses both of the aforementioned topics \citep[see][]{cas2}. Due to the high frequency of binary systems among early-type stars \citep[see, e.g.,][]{binaries_1,binaries_2}, analysis techniques, which are also able to deal with spectra of double-lined spectroscopic binary systems (SB2) are desirable. Quantitative spectroscopy is based on the comparison of synthetic and observed spectra. Owing to the multi-dimensionality of the parameter space involved (which include the following for B- and late O-type stars: effective temperature $T_{\mathrm{eff}}$, surface gravity $\log (g\,\mathrm{(cm\,s^{-2})})$, microturbulence $\xi$, macroturbulence $\zeta$, projected rotational velocity $\varv\,\sin(i)$, radial velocity $\varv_{\mathrm{rad}}$, metallicity $Z$, and elemental abundances $\{n(x)\}$), investigations are time-consuming since an iterative approach is required \citep[for details see][]{nieva_iterative}. Starting from initial estimates for the entire set of parameters, individual variables are refined by using spectral indicators that are sensitive to as few parameters as possible to reduce the complexity of the problem. In early-type stars of solar metallicity, for instance, Stark-broadened hydrogen and helium lines are primarily affected by changes in $T_{\mathrm{eff}}$, $\log(g)$, and $n(\mathrm{He})$ while they are comparatively insensitive to all others. Consequently, these features allow for the temperature, surface gravity, and helium abundance to be constrained. The use of multiple ionization equilibria, which requires that spectral lines of different ionization stages of the same element indicate equal abundances, yields further constraints on $T_{\mathrm{eff}}$ and $\log(g)$ but also on $\xi$ and $n(x)$. Matching the strength of spectral lines and their shape allows for $\zeta$ and $\varv\,\sin(i)$ to be derived. Because of the highly non-trivial coupling of different parameters, the adjustment of individual variables involves re-evaluation of most of the available indicators, leading to an iterative procedure. Although those iterative steps can be automated to speed up the investigation \citep[see][]{lefever_fitting}, the underlying strategy is still prone to miss the global best solution. On the one hand, not all parameters are varied at the same time but many of them separately so that correlations between them are neglected \citep[see][]{mokiem_fitting}. On the other hand, parameters are constrained from selected spectral indicators or windows instead of exploiting the information encoded in the entire spectrum. A global analysis method, which is a method simultaneously probing all parameters while considering the maximum useful spectral range, is therefore our goal. Automated fitting techniques are suitable for this purpose. Moreover, automation is far less subjective, since the matching of theory and observation is based on a mathematical measure, such as a $\chi^2$ criterion instead of visual inspection. This is particularly important when one wants to analyze larger samples in a homogeneous manner. The size of the corresponding multi-parameter space, however, requires calculations of numerous synthetic spectra, which is computationally expensive and, therefore, a major obstacle for automated fitting. To minimize the number of calculations involved, synthetic atmospheres may be computed on demand in the course of the fitting process, as realized by \citet{mokiem_fitting}. In this way, spectra are computed only if they are actually used. Nevertheless, even very efficient fitting algorithms can take from several dozens to hundreds of iterations to find the best solution, which implies a non-negligible run-time of the fitting process. This drawback can be overcome by making use of pre-calculated model grids in which interpolation between grid points can be used to evaluate the fitting function. Unfortunately, sufficient sampling of the whole multi-parameter space is typically not possible, given its large dimension. Consequently, grid-based fitting methods are usually restricted to small subspaces by either keeping some parameters fixed when computing tailored grids \citep[see][]{castro_fitting} or limiting the allowed parameter range, thus reducing the advantages of global automated fitting. However, due to some unique properties of spectra of early-type stars, such as the low density of spectral lines and the continuous opacity that is dominated by hydrogen and helium, many parameters --~in particular, the elemental abundances of the trace elements~-- are independent of each other. Exploiting this fact, it is possible to probe the entire parameter space by computing only a tiny fraction of it. Based on this idea, we have developed a grid-based global fitting method that facilitates quick and precise determinations of the atmospheric parameters of B- and late O-type stars, which takes non-local thermodynamic equilibrium (non-LTE) effects into consideration (Sect.~\ref{sec:setting_up}). Furthermore, it is shown that the accuracy of the analysis is generally not limited by statistics, such as the signal-to-noise ratio (S/N) of the observed spectrum, but rather by systematics, such as the uncertainties in atomic data (Sect.~\ref{sec:tests}). For demonstration purposes, the method is then applied to three well-studied early-type stars in Orion and to three SB2 systems yielding atmospheric and fundamental stellar parameters (Sect.~\ref{sec:analysis}). A discussion of the results obtained (Sect.~\ref{sec:discussion}) is rounded off by a summary (Sect.~\ref{sec:summary}). | \label{sec:tests} \subsection{Noise estimation}\label{subsection:noise_estimation} Calculating $\chi^2$ requires proper knowledge of the measurement uncertainties $\delta_i$, which either are systematic in nature and, for instance, caused by an incorrect continuum normalization, or, more importantly, have statistical fluctuations, such as noise $n_i$. The latter can be estimated from an observed spectrum, which does not need to be flux calibrated, in an easy, fast, and robust way when assuming that the noise $n_i$ of data point $i$ obeys a Gaussian probability distribution $p(n_i)$ with a mean value of zero and a priori unknown standard deviation $\sigma_i$: \begin{equation} p(n_i) = \frac{1}{\sqrt{2\pi}\sigma_i}\exp\left(-\frac{n_i^2}{2\sigma_i^2}\right)\, . \; \label{eq:noise_distribution} \end{equation} For small regions (several data points), the measured flux $f_i$ as a function of the wavelength $\lambda$ can be approximately written as the sum of a linear function $a + b \lambda_i$, which represents the first two terms in a Taylor expansion of the pure signal and a noise component $n_i$: \begin{equation} f_i = a + b \lambda_i + n_i\, . \; \end{equation} To estimate the noise level $\sigma_i$, consider the quantity $\Delta_i$ defined as \begin{eqnarray} \Delta_i & \equiv & f_i - (w_{i-2}f_{i-2} + w_{i+2}f_{i+2})\nonumber \\ & = & n_i - w_{i-2}n_{i-2} - w_{i+2}n_{i+2} + a + b \lambda_i \nonumber \\ & & - w_{i-2}(a + b \lambda_{i-2}) - w_{i+2}(a + b \lambda_{i+2})\label{eq:defining_iota}\, . \; \end{eqnarray} Here, $w_{i-2}$ and $w_{i+2}$ are weight factors and chosen such that only the noise terms in Eq.~(\ref{eq:defining_iota}) remain:\footnote{Note: $\lambda_{i+1} = \lambda_i + \Delta \lambda_i^{\mathrm{pixel}}/2 + \Delta \lambda_{i+1}^{\mathrm{pixel}}/2$ with $\Delta \lambda_i^{\mathrm{pixel}} = \Delta \lambda_i/2$ because of Nyquist's sampling theorem. For long-slit spectrographs, $\lambda / \Delta \lambda = R_{\mathrm{long-slit}} \propto \lambda$ so that $\Delta \lambda_i = \mathrm{constant}$ which implies $w_{i-2}=1-w_{i+2}=1/2$ to arrive at Eq.~(\ref{eq:defining_iota2}) from Eq.~(\ref{eq:defining_iota}). For Echelle spectrographs, $\lambda / \Delta \lambda = R_{\mathrm{Echelle}} = \mathrm{const.}$, which yields $\lambda_{i+1} = k \lambda_i$ with $k=(4 R_{\mathrm{Echelle}}+1)/(4 R_{\mathrm{Echelle}}-1)$ which leads to $w_{i-2}=1-w_{i+2}=(k^2-1)/(k^2-k^{-2}) \approx 0.5$.} \begin{equation} \Delta_i = n_i - w_{i-2}n_{i-2} - w_{i+2}n_{i+2}\, . \; \label{eq:defining_iota2} \end{equation} The reason for comparing $f_i$ to the (weighted) average of data points $i-2$ and $i+2$ instead of $i-1$ and $i+1$ is that adjacent pixels are likely correlated. For example, this is due to detector cross-talk or actions taken during data reduction like the wavelength calibration. Assuming that there is no correlation with the next neighbor but one implies that Eq.~(\ref{eq:noise_distribution}) is valid for points $i$, $i-2$, and $i+2$, and the probability distribution $p(\Delta_i)$ reads: \begin{eqnarray} p(\Delta_i) & = & \int\limits_{-\infty}^{\infty} \int\limits_{-\infty}^{\infty} \int\limits_{-\infty}^{\infty} p(n_i)p(n_{i-2})p(n_{i+2})\\ && \delta\left(\Delta_i - (n_i - w_{i-2}n_{i-2} - w_{i+2}n_{i+2}) \right)\mathrm{d} n_i \mathrm{d} n_{i-2}\mathrm{d} n_{i+2}\, . \; \nonumber \end{eqnarray} Here, $\delta$ is the dirac delta function. For adjacent data points, it is well justified to assume $\sigma_i = \sigma_{i-2} = \sigma_{i+2} \equiv \sigma$, so that $p(\Delta_i)$ simplifies to \begin{equation} p(\Delta_i) = \frac{1}{\sqrt{2\pi} \tilde{\sigma}}\exp\left(-\frac{\Delta_i^2}{2\tilde{\sigma}^2}\right), \quad \tilde{\sigma} = \sigma\sqrt{w^2_{i-2}+w^2_{i+2}+1}\, . \; \label{eq:iota_distribution} \end{equation} Consequently, the distribution of $\Delta_i = f_i - (w_{i-2}f_{i-2} + w_{i+2}f_{i+2})$ is a Gaussian with a standard deviation $\tilde{\sigma}$ defined by Eq.~(\ref{eq:iota_distribution}). Extending the assumption of a constant noise level $\sigma_i = \sigma$ to a statistically significant number of data points allows $\sigma$, which is the statistical component of the uncertainty $\delta_i$ in Eq.~(\ref{eq:chisqr}), to be derived from the measurable distribution of $\Delta_i$. If the reduced $\chi^2$ at the best fit is larger than $1$, it might also be necessary to consider a systematic component of $\delta_i$ (see footnote~\ref{footnote:chisqr}). \subsection{Performance and reliability of the method}\label{subsection:performance} Before fitting real spectra, several formal tests were carried out to examine the properties of the automated method. With this aim, mock spectra were constructed from synthetic ones by adding Gaussian-distributed noise that corresponded to different S/N. A spectral range $[3940\,\mathrm{\AA},7000\,\mathrm{\AA}]$ was chosen to match the minimum wavelength coverage of standard high-resolution spectrographs. Regions in that interval that are generally affected by telluric features were excluded. The spectral resolving power was set to $R = 45\,000$, which is very close to the resolution of the Echelle spectra which are analyzed in this study. Table~\ref{table:uncertainties} lists the results of this exercise for ten exemplary cases. The input parameters and, thus, the global minimum were recovered with excellent accuracy after only a run-time of few minutes on a standard $3.1$\,GHz single-core processor and independent of the choice of the starting parameters within the grid, which shows that our method is fast and reliable. It is important to stress here that all mock spectra were constructed from complete {\sc Surface} models, which, in contrast to the fitting function, treat every microscopic line blend correctly by simultaneously computing lines of all chemical species under consideration. Additionally, models off the grid points were chosen to check that our mesh is sufficiently spaced for the linear interpolation scheme applied. Because the differences of input and output values in Table~\ref{table:uncertainties} are often covered by the very small statistical uncertainties (see Sect.~\ref{subsection:uncertainties}) that result from the high S/N assigned to the mock spectra, we conclude that inaccuracies introduced by simplifications in our approach are negligible. In a second step, three mock composite spectra were created with the help of Eq.~(\ref{eq:composite}). The parameters chosen here are motivated by real SB2 systems and anticipate the results presented in Sect.~\ref{sec:analysis}. They cover a sharp-lined, well-separated and, thus, easy to analyze system and a very difficult configuration with heavily blended spectral features. Similar to the previous tests, most of the input parameters are recovered with very high precision or at least within the derived uncertainties, as seen in Table~\ref{table:uncertainties_binary}. In particular, the degree of accuracy in the inferred parameters of both components of the extremely blended composite spectrum is astonishing, hence, making us quite confident that our method is also highly suitable for investigations of SB2 systems. Although our method is able to model individual abundances if necessary, we generally prefer to assume an identical chemical composition for the two components within the binary system. In this way, the number of free parameters and, consequently, the numerical complexity of the problem is significantly reduced. In cases where the parameters of the secondary component are only poorly constrained due to their little impact on the composite spectrum, it is even necessary to impose these constraints, which compensate for the lack of spectral indicators to derive reasonable atmospheric parameters. Note that the assumption of an equal chemical composition is well justified for SB2 systems containing B-type or late O-type stars. On the one hand, the components of SB2 systems are in general similar regarding to their masses (Otherwise, the flux contribution of the fainter companion would not be visible in the spectrum.), ages (the whole system formed at once), and pristine chemical composition (both components formed from the same building material). On the other hand, processes causing chemical anomalies are rare among B- and late O-type stars and primarily affect helium \citep{helium_weak_rich}. Since chemical peculiarities are possibly even less frequent in detached binary systems \citep{pavlovski_southworth}, elemental abundances are expected to evolve in the same way in both components. To estimate the influence of this approximation on the spectral analysis, Table~\ref{table:uncertainties_binary} lists the results obtained from fitting the three mock composite spectra with adjustable abundances and an equal chemical composition. Even for the system with different individual abundances, the results derived by assuming an identical chemical composition are very satisfying. In particular, this is with respect to the primary component, which dominates the spectrum and in this way also the estimates for the system abundances and their respective confidence limits. As a consequence, the actual abundances of the secondary component may sometimes lie outside of the uncertainty intervals determined for the binary system as a whole. Nevertheless, it is obvious that the decision of whether or not to use separate abundances during the fitting process depends on the individual object and has to be checked, for example, a posteriori by inspecting the final match of the model to the observation. \begin{table*} \tiny \setlength{\tabcolsep}{0.15cm} \renewcommand{\arraystretch}{1.26} \caption{\label{table:uncertainties} Comparison of input parameters (\textit{``In'' row}) and corresponding parameters obtained from fits (\textit{``Out'' row}) for ten exemplary mock spectra computed from complete {\sc Surface} models, which simultaneously account for all lines considered in the fitting function.} \centering \begin{tabular}{lrrrrrrrrrrrrrrrrrrr} \hline\hline & S/N & $T_{\mathrm{eff}}$ & $\log(g)$ & $\varv_{\mathrm{rad}}$ & $\varv\,\sin(i)$ & $\zeta$ & $\xi$ & & \multicolumn{11}{c}{$\log(n(x))$} \\ \cline{5-8} \cline{10-20} & & (K) & (cgs) & \multicolumn{4}{c}{$(\mathrm{km\,s^{-1}})$} & & He & C & N & O & Ne & Mg & Al & Si & S & Ar & Fe\\ \hline In & $300$ & $15000$ & $3.750$ & $-18.0$ & $15.0$ & $7.0$ & $2.00$ & & $-1.06$ & $-3.70$ & $-4.30$ & $-3.20$ & $-4.00$ & $-4.70$ & $-5.60$ & $-4.60$ & $-4.80$ & $-5.60$ & $-4.60$ \\ Out & $305$ & $15000$ & $3.750$ & $-18.0$ & $14.8$ & $8.0$ & $2.10$ & & $-1.06$ & $-3.71$ & $-4.28$ & $-3.20$ & $-4.01$ & $-4.70$ & $-5.60$ & $-4.61$ & $-4.81$ & $-5.68$ & $-4.61$ \\ Stat. & $^{+3}_{-3}$ & $^{+20}_{-20}$ & $^{+0.003}_{-0.004}$ & $^{+0.1}_{-0.1}$ & $^{+0.1}_{-0.1}$ & $^{+0.2}_{-0.1}$ & $^{+0.04}_{-0.03}$ & & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.04}_{-0.04}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.01}$ & $^{+0.07}_{-0.08}$ & $^{+0.01}_{-0.01}$ \\ Sys. & \ldots & $^{+300}_{-300}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.2}_{-0.1}$ & $^{+0.7}_{-1.2}$ & $^{+0.79}_{-1.09}$ & & $^{+0.15}_{-0.09}$ & $^{+0.07}_{-0.09}$ & $^{+0.05}_{-0.08}$ & $^{+0.04}_{-0.08}$ & $^{+0.04}_{-0.02}$ & $^{+0.06}_{-0.07}$ & $^{+0.02}_{-0.02}$ & $^{+0.12}_{-0.18}$ & $^{+0.04}_{-0.04}$ & $^{+0.08}_{-0.14}$ & $^{+0.06}_{-0.10}$ \\ Start & \ldots & $19000$ & $3.700$ & $-15.0$ & $10.0$ & $10.0$ & $3.00$ & & $-0.85$ & $-3.60$ & $-4.20$ & $-3.20$ & $-4.00$ & $-4.60$ & $-5.80$ & $-4.40$ & $-4.90$ & $-5.60$ & $-4.60$ \\ \hline In & $300$ & $15000$ & $4.250$ & $36.0$ & $17.0$ & $16.0$ & $2.00$ & & $-1.06$ & $-3.70$ & $-4.30$ & $-3.20$ & $-4.00$ & $-4.70$ & $-5.60$ & $-4.60$ & $-4.80$ & $-5.60$ & $-4.60$ \\ Out & $295$ & $14860$ & $4.215$ & $36.0$ & $17.0$ & $16.1$ & $1.90$ & & $-1.04$ & $-3.68$ & $-4.32$ & $-3.22$ & $-4.00$ & $-4.72$ & $-5.60$ & $-4.61$ & $-4.80$ & $-5.50$ & $-4.65$ \\ Stat. & $^{+2}_{-2}$ & $^{+30}_{-20}$ & $^{+0.008}_{-0.006}$ & $^{+0.1}_{-0.1}$ & $^{+0.1}_{-0.1}$ & $^{+0.3}_{-0.2}$ & $^{+0.07}_{-0.03}$ & & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.01}$ & $^{+0.07}_{-0.07}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.10}_{-0.11}$ & $^{+0.01}_{-0.01}$ \\ Sys. & \ldots & $^{+300}_{-300}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.1}_{-0.1}$ & $^{+0.2}_{-0.3}$ & $^{+0.62}_{-0.86}$ & & $^{+0.15}_{-0.12}$ & $^{+0.07}_{-0.08}$ & $^{+0.06}_{-0.09}$ & $^{+0.07}_{-0.07}$ & $^{+0.06}_{-0.04}$ & $^{+0.06}_{-0.06}$ & $^{+0.02}_{-0.02}$ & $^{+0.11}_{-0.11}$ & $^{+0.04}_{-0.04}$ & $^{+0.08}_{-0.14}$ & $^{+0.08}_{-0.10}$ \\ Start & \ldots & $19000$ & $3.700$ & $35.0$ & $10.0$ & $10.0$ & $3.00$ & & $-0.85$ & $-3.60$ & $-4.20$ & $-3.20$ & $-4.00$ & $-4.60$ & $-5.80$ & $-4.40$ & $-4.90$ & $-5.60$ & $-4.60$ \\ \hline In & $100$ & $20000$ & $3.750$ & $19.0$ & $25.0$ & $18.0$ & $2.0$ & & $-1.06$ & $-3.70$ & $-4.30$ & $-3.20$ & $-4.00$ & $-4.70$ & $-5.60$ & $-4.60$ & $-4.80$ & $-5.60$ & $-4.60$ \\ Out & $100$ & $19960$ & $3.734$ & $18.9$ & $23.5$ & $22.0$ & $1.94$ & & $-1.05$ & $-3.68$ & $-4.28$ & $-3.19$ & $-4.02$ & $-4.71$ & $-5.56$ & $-4.57$ & $-4.78$ & $-5.59$ & $-4.59$ \\ Stat. & $^{+1}_{-1}$ & $^{+120}_{-120}$ & $^{+0.015}_{-0.017}$ & $^{+0.3}_{-0.3}$ & $^{+1.1}_{-1.1}$ & $^{+1.7}_{-0.9}$ & $^{+0.3}_{-0.7}$ & & $^{+0.02}_{-0.02}$ & $^{+0.04}_{-0.03}$ & $^{+0.04}_{-0.04}$ & $^{+0.04}_{-0.03}$ & $^{+0.04}_{-0.04}$ & $^{+0.06}_{-0.05}$ & $^{+0.05}_{-0.04}$ & $^{+0.07}_{-0.05}$ & $^{+0.03}_{-0.03}$ & $^{+0.06}_{-0.08}$ & $^{+0.05}_{-0.04}$ \\ Sys. & \ldots & $^{+400}_{-400}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.2}_{-0.2}$ & $^{+0.7}_{-0.7}$ & $^{+0.8}_{-1.7}$ & & $^{+0.09}_{-0.07}$ & $^{+0.08}_{-0.06}$ & $^{+0.08}_{-0.07}$ & $^{+0.11}_{-0.11}$ & $^{+0.04}_{-0.04}$ & $^{+0.11}_{-0.09}$ & $^{+0.08}_{-0.07}$ & $^{+0.14}_{-0.12}$ & $^{+0.05}_{-0.05}$ & $^{+0.05}_{-0.05}$ & $^{+0.05}_{-0.05}$ \\ Start & \ldots & $19000$ & $3.700$ & $10.0$ & $10.0$ & $10.0$ & $3.0$ & & $-0.85$ & $-3.40$ & $-4.10$ & $-3.10$ & $-4.20$ & $-4.80$ & $-5.60$ & $-4.20$ & $-4.70$ & $-5.70$ & $-4.50$ \\ \hline In & $250$ & $20000$ & $4.250$ & $25.0$ & $5.0$ & $26.0$ & $2.00$ & & $-1.06$ & $-3.70$ & $-4.30$ & $-3.20$ & $-4.00$ & $-4.70$ & $-5.60$ & $-4.60$ & $-4.80$ & $-5.60$ & $-4.60$ \\ Out & $254$ & $19990$ & $4.251$ & $25.0$ & $0.0$ & $26.9$ & $2.26$ & & $-1.07$ & $-3.73$ & $-4.31$ & $-3.22$ & $-4.02$ & $-4.72$ & $-5.58$ & $-4.64$ & $-4.81$ & $-5.61$ & $-4.60$ \\ Stat. & $^{+2}_{-2}$ & $^{+20}_{-20}$ & $^{+0.003}_{-0.004}$ & $^{+0.1}_{-0.1}$ & $^{+1.8}_{-0.0}$ & $^{+0.1}_{-0.1}$ & $^{+0.12}_{-0.07}$ & & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.01}$ & $^{+0.03}_{-0.04}$ & $^{+0.02}_{-0.02}$ \\ Sys. & \ldots & $^{+400}_{-400}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+3.4}_{-0.0}$ & $^{+0.1}_{-0.1}$ & $^{+1.04}_{-1.66}$ & & $^{+0.08}_{-0.06}$ & $^{+0.09}_{-0.07}$ & $^{+0.07}_{-0.07}$ & $^{+0.11}_{-0.12}$ & $^{+0.04}_{-0.03}$ & $^{+0.12}_{-0.13}$ & $^{+0.06}_{-0.06}$ & $^{+0.13}_{-0.11}$ & $^{+0.06}_{-0.05}$ & $^{+0.05}_{-0.05}$ & $^{+0.01}_{-0.03}$ \\ Start & \ldots & $17000$ & $4.000$ & $20.0$ & $10.0$ & $10.0$ & $3.00$ & & $-0.85$ & $-3.40$ & $-4.10$ & $-3.10$ & $-3.80$ & $-4.40$ & $-5.90$ & $-4.70$ & $-4.80$ & $-5.50$ & $-4.70$ \\ \hline In & $400$ & $25000$ & $3.750$ & $-25.0$ & $40.0$ & $28.0$ & $2.00$ & & $-1.06$ & $-3.70$ & $-4.30$ & $-3.20$ & $-4.00$ & $-4.70$ & $-5.60$ & $-4.60$ & $-4.80$ & $-5.60$ & $-4.60$ \\ Out & $396$ & $24930$ & $3.738$ & $-25.0$ & $39.7$ & $28.5$ & $2.02$ & & $-1.07$ & $-3.72$ & $-4.31$ & $-3.21$ & $-4.00$ & $-4.70$ & $-5.61$ & $-4.61$ & $-4.81$ & $-5.63$ & $-4.61$ \\ Stat. & $^{+2}_{-2}$ & $^{+20}_{-20}$ & $^{+0.002}_{-0.003}$ & $^{+0.1}_{-0.1}$ & $^{+0.1}_{-0.1}$ & $^{+0.1}_{-0.3}$ & $^{+0.04}_{-0.04}$ & & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.02}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.04}_{-0.04}$ & $^{+0.01}_{-0.01}$ \\ Sys. & \ldots & $^{+500}_{-500}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.3}_{-0.1}$ & $^{+1.3}_{-1.5}$ & $^{+0.71}_{-0.02}$ & & $^{+0.06}_{-0.07}$ & $^{+0.01}_{-0.06}$ & $^{+0.03}_{-0.03}$ & $^{+0.07}_{-0.08}$ & $^{+0.01}_{-0.02}$ & $^{+0.05}_{-0.08}$ & $^{+0.04}_{-0.06}$ & $^{+0.02}_{-0.06}$ & $^{+0.02}_{-0.03}$ & $^{+0.10}_{-0.12}$ & $^{+0.03}_{-0.03}$ \\ Start & \ldots & $23500$ & $3.800$ & $-20.0$ & $10.0$ & $10.0$ & $8.00$ & & $-1.10$ & $-3.50$ & $-4.10$ & $-3.30$ & $-4.10$ & $-4.50$ & $-6.00$ & $-4.20$ & $-4.70$ & $-5.40$ & $-4.30$ \\ \hline In & $275$ & $25000$ & $4.250$ & $25.0$ & $70.0$ & $0.0$ & $2.00$ & & $-1.06$ & $-3.70$ & $-4.30$ & $-3.20$ & $-4.00$ & $-4.70$ & $-5.60$ & $-4.60$ & $-4.80$ & $-5.60$ & $-4.60$ \\ Out & $274$ & $25010$ & $4.259$ & $25.0$ & $69.8$ & $3.6$ & $2.00$ & & $-1.05$ & $-3.71$ & $-4.29$ & $-3.21$ & $-3.99$ & $-4.68$ & $-5.60$ & $-4.61$ & $-4.82$ & $-5.59$ & $-4.61$ \\ Stat. & $^{+1}_{-1}$ & $^{+30}_{-30}$ & $^{+0.003}_{-0.003}$ & $^{+0.2}_{-0.1}$ & $^{+0.1}_{-0.1}$ & $^{+3.7}_{-2.8}$ & $^{+0.06}_{-0.11}$ & & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.03}_{-0.03}$ & $^{+0.03}_{-0.03}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.05}_{-0.07}$ & $^{+0.02}_{-0.02}$ \\ Sys. & \ldots & $^{+500}_{-500}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.5}_{-0.1}$ & $^{+3.5}_{-3.6}$ & $^{+1.41}_{-2.00}$ & & $^{+0.06}_{-0.06}$ & $^{+0.08}_{-0.10}$ & $^{+0.03}_{-0.03}$ & $^{+0.12}_{-0.11}$ & $^{+0.02}_{-0.04}$ & $^{+0.09}_{-0.10}$ & $^{+0.04}_{-0.04}$ & $^{+0.12}_{-0.11}$ & $^{+0.07}_{-0.06}$ & $^{+0.12}_{-0.15}$ & $^{+0.05}_{-0.04}$ \\ Start & \ldots & $19000$ & $3.700$ & $30.0$ & $10.0$ & $10.0$ & $3.00$ & & $-0.85$ & $-3.80$ & $-4.40$ & $-3.40$ & $-4.20$ & $-4.80$ & $-5.90$ & $-4.50$ & $-4.70$ & $-5.80$ & $-4.90$ \\ \hline In & $125$ & $30000$ & $4.250$ & $-15.0$ & $0.0$ & $18.0$ & $2.00$ & & $-1.06$ & $-3.70$ & $-4.30$ & $-3.20$ & $-4.00$ & $-4.70$ & $-5.60$ & $-4.60$ & $-4.80$ & $-5.60$ & $-4.60$ \\ Out & $120$ & $30110$ & $4.259$ & $-15.0$ & $5.8$ & $16.4$ & $1.84$ & & $-1.04$ & $-3.72$ & $-4.31$ & $-3.21$ & $-4.02$ & $-4.69$ & $-5.61$ & $-4.61$ & $-4.81$ & $-5.47$ & $-4.60$ \\ Stat. & $^{+2}_{-2}$ & $^{+40}_{-60}$ & $^{+0.007}_{-0.013}$ & $^{+0.1}_{-0.1}$ & $^{+0.4}_{-0.5}$ & $^{+0.4}_{-0.4}$ & $^{+0.17}_{-0.14}$ & & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.02}$ & $^{+0.03}_{-0.03}$ & $^{+0.04}_{-0.04}$ & $^{+0.03}_{-0.03}$ & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.03}$ & $^{+0.15}_{-0.24}$ & $^{+0.02}_{-0.02}$ \\ Sys. & \ldots & $^{+610}_{-610}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+1.1}_{-1.2}$ & $^{+0.1}_{-0.1}$ & $^{+0.36}_{-0.32}$ & & $^{+0.03}_{-0.03}$ & $^{+0.05}_{-0.06}$ & $^{+0.05}_{-0.05}$ & $^{+0.05}_{-0.03}$ & $^{+0.03}_{-0.02}$ & $^{+0.04}_{-0.04}$ & $^{+0.06}_{-0.06}$ & $^{+0.03}_{-0.03}$ & $^{+0.07}_{-0.06}$ & $^{+0.15}_{-0.17}$ & $^{+0.08}_{-0.08}$ \\ Start & \ldots & $32000$ & $4.400$ & $-15.0$ & $1.0$ & $0.0$ & $7.00$ & & $-1.15$ & $-3.70$ & $-4.10$ & $-3.10$ & $-4.20$ & $-4.70$ & $-5.90$ & $-4.70$ & $-4.60$ & $-5.40$ & $-4.80$ \\ \hline \multicolumn{20}{l}{Mock spectrum as a proxy to the observed spectrum of object \#1 in Table~\ref{table:program_stars}:}\\ In & $250$ & $23880$ & $4.127$ & $23.0$ & $5.0$ & $4.0$ & $2.00$ & & $-0.99$ & $-3.73$ & $-4.30$ & $-3.29$ & $-4.00$ & $-4.57$ & $-5.79$ & $-4.66$ & $-4.88$ & $-5.49$ & $-4.71$ \\ Out & $232$ & $23800$ & $4.109$ & $23.0$ & $4.7$ & $4.0$ & $2.02$ & & $-0.99$ & $-3.74$ & $-4.30$ & $-3.30$ & $-4.02$ & $-4.57$ & $-5.80$ & $-4.66$ & $-4.90$ & $-5.51$ & $-4.73$ \\ Stat. & $^{+2}_{-2}$ & $^{+50}_{-50}$ & $^{+0.006}_{-0.007}$ & $^{+0.1}_{-0.1}$ & $^{+0.5}_{-2.9}$ & $^{+2.2}_{-0.4}$ & $^{+0.08}_{-0.11}$ & & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.01}$ \\ Sys. & \ldots & $^{+480}_{-480}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.4}_{-0.6}$ & $^{+1.3}_{-1.5}$ & $^{+0.43}_{-0.90}$ & & $^{+0.05}_{-0.05}$ & $^{+0.04}_{-0.03}$ & $^{+0.03}_{-0.02}$ & $^{+0.08}_{-0.08}$ & $^{+0.04}_{-0.04}$ & $^{+0.08}_{-0.07}$ & $^{+0.01}_{-0.02}$ & $^{+0.06}_{-0.05}$ & $^{+0.02}_{-0.03}$ & $^{+0.06}_{-0.06}$ & $^{+0.02}_{-0.02}$ \\ Start & \ldots & $19000$ & $3.700$ & $20.0$ & $10.0$ & $10.0$ & $3.00$ & & $-0.90$ & $-3.50$ & $-4.30$ & $-3.30$ & $-4.20$ & $-4.50$ & $-5.80$ & $-4.50$ & $-4.90$ & $-5.50$ & $-4.70$ \\ \hline \multicolumn{20}{l}{Mock spectrum as a proxy to the observed spectrum of object \#2 in Table~\ref{table:program_stars}:}\\ In & $250$ & $19250$ & $4.052$ & $31.0$ & $7.0$ & $17.0$ & $2.00$ & & $-1.00$ & $-3.64$ & $-4.23$ & $-3.21$ & $-4.06$ & $-4.60$ & $-5.71$ & $-4.48$ & $-4.89$ & $-5.57$ & $-4.63$ \\ Out & $242$ & $19240$ & $4.058$ & $31.0$ & $4.8$ & $18.0$ & $2.07$ & & $-1.00$ & $-3.64$ & $-4.23$ & $-3.22$ & $-4.06$ & $-4.62$ & $-5.70$ & $-4.51$ & $-4.89$ & $-5.57$ & $-4.65$ \\ Stat. & $^{+2}_{-2}$ & $^{+20}_{-20}$ & $^{+0.005}_{-0.005}$ & $^{+0.1}_{-0.1}$ & $^{+0.4}_{-0.5}$ & $^{+0.1}_{-0.1}$ & $^{+0.05}_{-0.07}$ & & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.01}$ & $^{+0.03}_{-0.03}$ & $^{+0.02}_{-0.02}$ \\ Sys. & \ldots & $^{+390}_{-390}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.9}_{-3.2}$ & $^{+0.1}_{-0.1}$ & $^{+0.84}_{-1.43}$ & & $^{+0.08}_{-0.08}$ & $^{+0.08}_{-0.09}$ & $^{+0.08}_{-0.08}$ & $^{+0.11}_{-0.11}$ & $^{+0.03}_{-0.03}$ & $^{+0.10}_{-0.11}$ & $^{+0.05}_{-0.06}$ & $^{+0.13}_{-0.12}$ & $^{+0.04}_{-0.05}$ & $^{+0.05}_{-0.05}$ & $^{+0.01}_{-0.03}$ \\ Start & \ldots & $17000$ & $3.700$ & $20.0$ & $10.0$ & $10.0$ & $3.00$ & & $-0.85$ & $-3.50$ & $-3.90$ & $-3.40$ & $-3.80$ & $-4.40$ & $-5.40$ & $-4.00$ & $-4.70$ & $-5.40$ & $-4.80$ \\ \hline \multicolumn{20}{l}{Mock spectrum as a proxy to the observed spectrum of object \#3 in Table~\ref{table:program_stars}:}\\ In & $200$ & $29210$ & $4.284$ & $30.0$ & $31.0$ & $0.0$ & $3.20$ & & $-1.05$ & $-3.71$ & $-4.13$ & $-3.40$ & $-4.01$ & $-4.58$ & $-5.73$ & $-4.66$ & $-4.97$ & $-5.83$ & $-4.62$ \\ Out & $197$ & $29190$ & $4.273$ & $30.1$ & $30.8$ & $0.0$ & $3.12$ & & $-1.04$ & $-3.74$ & $-4.13$ & $-3.41$ & $-4.04$ & $-4.63$ & $-5.76$ & $-4.66$ & $-5.00$ & $-5.87$ & $-4.62$ \\ Stat. & $^{+1}_{-1}$ & $^{+30}_{-30}$ & $^{+0.005}_{-0.005}$ & $^{+0.1}_{-0.1}$ & $^{+0.1}_{-0.1}$ & $^{+1.8}_{-0.0}$ & $^{+0.08}_{-0.08}$ & & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.03}_{-0.03}$ & $^{+0.03}_{-0.03}$ & $^{+0.03}_{-0.03}$ & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.02}$ & $^{+0.21}_{-0.13}$ & $^{+0.02}_{-0.02}$ \\ Sys. & \ldots & $^{+590}_{-590}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.1}_{-0.1}$ & $^{+4.6}_{-0.0}$ & $^{+0.50}_{-0.57}$ & & $^{+0.04}_{-0.03}$ & $^{+0.03}_{-0.04}$ & $^{+0.05}_{-0.05}$ & $^{+0.04}_{-0.03}$ & $^{+0.04}_{-0.03}$ & $^{+0.05}_{-0.05}$ & $^{+0.06}_{-0.05}$ & $^{+0.04}_{-0.04}$ & $^{+0.06}_{-0.05}$ & $^{+0.32}_{-0.13}$ & $^{+0.09}_{-0.07}$ \\ Start & \ldots & $31000$ & $4.300$ & $20.0$ & $10.0$ & $10.0$ & $7.00$ & & $-1.05$ & $-3.60$ & $-4.20$ & $-3.20$ & $-4.10$ & $-4.60$ & $-5.80$ & $-4.40$ & $-4.90$ & $-5.60$ & $-4.60$ \\ \hline \end{tabular} \tablefoot{Starting parameters for the fitting algorithm are given as well (\textit{``Start'' row}). See Sect.~\ref{subsection:performance} for details. The S/N estimates in the \textit{``Out'' row} are based on the method outlined in Sect.~\ref{subsection:noise_estimation}. The abundance $n(x)$ is given as fractional particle number of species $x$ with respect to all elements. Statistical uncertainties (\textit{``Stat.'' row}) correspond to $\Delta \chi^2 = 6.63$ and are 99\%-confidence limits. Systematic uncertainties (\textit{``Sys.'' row}) cover only the effects induced by additional variations of $2\%$ in $T_{\mathrm{eff}}$ and $0.1\,\mathrm{dex}$ in $\log(g)$ (see Sect.~\ref{subsection:uncertainties} for details) and are formally taken to be 99\%-confidence limits.} \end{table*} \begin{table*} \begin{center} \tiny \setlength{\tabcolsep}{0.115cm} \renewcommand{\arraystretch}{1.3} \caption{\label{table:uncertainties_binary} Same as Table~\ref{table:uncertainties} but for three exemplary mock composite spectra.} \begin{tabular}{lrrrrrrrrrrrrrrrrrrr} \hline\hline & S/N & $T_{\mathrm{eff}}$ & $\log(g)$ & $\varv_{\mathrm{rad}}$ & $\varv\,\sin(i)$ & $\zeta$ & $\xi$ & $A_{\mathrm{eff,s}}/A_{\mathrm{eff,p}}$ & \multicolumn{11}{c}{$\log(n(x))$} \\ \cline{5-8} \cline{10-20} & & (K) & (cgs) & \multicolumn{4}{c}{$(\mathrm{km\,s^{-1}})$} & & He & C & N & O & Ne & Mg & Al & Si & S & Ar & Fe\\ \hline \multicolumn{20}{l}{Mock spectrum as a proxy to the observed spectrum of object \#5 in Table~\ref{table:program_stars} (sharp and well-separated features):}\\ In p & $220$ & $16680$ & $4.098$ & $-84.7$ & $7.9$ & $11.4$ & $2.10$ & \ldots & $-0.96$ & $-3.55$ & $-4.16$ & $-3.25$ & $-4.04$ & $-4.73$ & $-5.86$ & $-4.45$ & $-4.91$ & $-5.58$ & $-4.66$ \\ Out f & $215$ & $16680$ & $4.098$ & $-84.7$ & $6.9$ & $12.2$ & $2.17$ & \ldots & $-0.97$ & $-3.56$ & $-4.19$ & $-3.25$ & $-4.03$ & $-4.74$ & $-5.91$ & $-4.47$ & $-4.91$ & $-5.60$ & $-4.68$ \\ Stat. & $^{+1}_{-1}$ & $^{+80}_{-90}$ & $^{+0.023}_{-0.020}$ & $^{+0.1}_{-0.1}$ & $^{+1.4}_{-1.1}$ & $^{+0.7}_{-1.3}$ & $^{+0.14}_{-0.16}$ & \ldots & $^{+0.02}_{-0.03}$ & $^{+0.03}_{-0.03}$ & $^{+0.04}_{-0.04}$ & $^{+0.02}_{-0.03}$ & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.03}$ & $^{+0.04}_{-0.06}$ & $^{+0.03}_{-0.03}$ & $^{+0.02}_{-0.02}$ & $^{+0.07}_{-0.10}$ & $^{+0.02}_{-0.03}$ \\ Sys. & \ldots & $^{+340}_{-340}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.7}_{-0.6}$ & $^{+0.8}_{-0.8}$ & $^{+0.27}_{-0.29}$ & \ldots & $^{+0.06}_{-0.07}$ & $ ^{+0.07}_{-0.07}$ & $^{+0.06}_{-0.07}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.03}$ & $^{+0.02}_{-0.03}$ & $^{+0.02}_{-0.03}$ & $^{+0.02}_{-0.03}$ & $^{+0.05}_{-0.06}$ & $^{+0.06}_{-0.06}$ \\ Out i & \ldots & $16660$ & $4.096$ & $-84.7$ & $6.6$ & $12.4$ & $2.20$ & \ldots & $-0.97$ & $-3.56$ & $-4.18$ & $-3.26$ & $-4.03$ & $-4.75$ & $-5.90$ & $-4.47$ & $-4.91$ & $-5.60$ & $-4.68$ \\ Stat. & \ldots & $^{+70}_{-70}$ & $^{+0.017}_{-0.022}$ & $^{+0.1}_{-0.1}$ & $^{+1.4}_{-1.0}$ & $^{+0.9}_{-1.3}$ & $^{+0.13}_{-0.15}$ & \ldots & $^{+0.02}_{-0.02}$ & $ ^{+0.03}_{-0.03}$ & $^{+0.03}_{-0.04}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.03}$ & $ ^{+0.04}_{-0.05}$ & $^{+0.03}_{-0.03}$ & $^{+0.02}_{-0.02}$ & $^{+0.07}_{-0.11}$ & $^{+0.02}_{-0.03}$ \\ Sys. & \ldots & $^{+340}_{-340}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.6}_{-0.5}$ & $^{+0.4}_{-0.8}$ & $^{+0.27}_{-0.26}$ & \ldots & $^{+0.05}_{-0.06}$ & $^{+0.06}_{-0.06}$ & $^{+0.05}_{-0.06}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.03}_{-0.03}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.04}_{-0.06}$ & $^{+0.05}_{-0.05}$ \\ Start & \ldots & $15000$ & $4.100$ & $-80.0$ & $10.0$ & $10.0$ & $3.00$ & \ldots & $-0.85$ & $-3.60$ & $-4.20$ & $-3.20$ & $-4.00$ & $-4.60$ & $-5.80$ & $-4.40$ & $-4.90$ & $-5.60$ & $-4.60$ \\ In s & \ldots & $13490$ & $4.274$ & $125.0$ & $28.3$ & $15.6$ & $0.79$ & $0.642$ & $-0.96$ & $-3.55$ & $-4.16$ & $-3.25$ & $-4.04$ & $-4.73$ & $-5.86$ & $-4.45$ & $-4.91$ & $-5.58$ & $-4.66$ \\ Out f & \ldots & $13200$ & $4.210$ & $125.3$ & $ 29.3$ & $14.2$ & $0.30$ & $0.662$ & $-0.91$ & $-3.46$ & $-4.21$ & $-3.29$ & $-4.12$ & $-4.79$ & $-5.73$ & $-4.50$ & $-4.97$ & \ldots & $-4.76$ \\ Stat. & \ldots & $^{+200}_{-250}$ & $^{+0.050}_{-0.070}$ & $^{+0.5}_{-0.5}$ & $^{+0.8}_{-1.3}$ & $^{+1.7}_{-2.9}$ & $^{+0.33}_{-0.30}$ & $^{+0.020}_{-0.018}$ & $^{+0.10}_{-0.07}$ & $^{+0.13}_{-0.12}$ & $^{+0.26}_{-0.52}$ & $^{+0.06}_{-0.08}$ & $^{+0.13}_{-0.14}$ & $^{+0.06}_{-0.06}$ & $^{+0.13}_{-0.16}$ & $^{+0.05}_{-0.06}$ & $^{+0.11}_{-0.10}$ & \ldots & $^{+0.07}_{-0.09}$ \\ Sys. & \ldots & $^{+260}_{-360}$ & $^{+0.100}_{-0.100}$ & $^{+0.2}_{-0.2}$ & $^{+0.2}_{-0.6}$ & $^{+0.9}_{-1.2}$ & $^{+0.15}_{-0.22}$ & $^{+0.036}_{-0.033}$ & $^{+0.19}_{-0.17}$ & $^{+0.12}_{-0.12}$ & $^{+0.01}_{-0.06}$ & $^{+0.04}_{-0.07}$ & $^{+0.10}_{-0.11}$ & $^{+0.03}_{-0.04}$ & $^{+0.03}_{-0.04}$ & $^{+0.02}_{-0.02}$ & $^{+0.10}_{-0.09}$ & \ldots & $^{+0.09}_{-0.13}$ \\ Out i & \ldots & $13360$ & $4.258$ & $125.3$ & $28.7$ & $15.1$ & $0.15$ & $0.650$ & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ Stat. & \ldots & $^{+80}_{-90}$ & $^{+0.028}_{-0.029}$ & $^{+0.5}_{-0.5}$ & $^{+1.3}_{-1.1}$ & $^{+2.1}_{-2.5}$ & $^{+0.34}_{-0.15}$ & $^{+0.015}_{-0.014}$ & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ Sys. & \ldots & $^{+270}_{-270}$ & $^{+0.100}_{-0.113}$ & $^{+0.2}_{-0.3}$ & $^{+0.3}_{-0.3}$ & $^{+1.6}_{-1.3}$ & $^{+0.29}_{-0.15}$ & $^{+0.031}_{-0.032}$ & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ Start & \ldots & $15000$ & $4.100$ & $120.0$ & $10.0$ & $10.0$ & $3.00$ & $0.800$ & $-0.85$ & $-3.60$ & $-4.20$ & $-3.20$ & $-4.00$ & $-4.60$ & $-5.80$ & $-4.40$ & $-4.90$ & $-5.60$ & $-4.60$ \\ \hline \multicolumn{20}{l}{Mock spectrum as a proxy to the observed spectrum of object \#6 in Table~\ref{table:program_stars} (extremely blended features):}\\ In p & $350$ & $20600$ & $3.485$ & $-11.2$ & $54.2$ & $9.4$ & $6.04$ & \ldots & $-1.02$ & $-3.79$ & $-4.38$ & $-3.39$ & $-4.02$ & $-4.74$ & $-5.87$ & $-4.66$ & $-4.99$ & $-5.59$ & $-4.79$ \\ Out f & $350$ & $20740$ & $3.502$ & $-11.3$ & $54.4$ & $1.9$ & $5.80$ & \ldots & $-1.02$ & $-3.76$ & $-4.37$ & $-3.39$ & $-4.03$ & $-4.74$ & $-5.87$ & $-4.68$ & $-5.02$ & $-5.57$ & $-4.76$ \\ Stat. & $^{+2}_{-2}$ & $^{+30}_{-20}$ & $^{+0.005}_{-0.003}$ & $^{+0.2}_{-0.2}$ & $^{+0.2}_{-0.2}$ & $^{+4.4}_{-1.9}$ & $^{+0.07}_{-0.12}$ & \ldots & $^{+0.02}_{-0.03}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.03}$ & $^{+0.04}_{-0.02}$ & $^{+0.01}_{-0.02}$ & $^{+0.02}_{-0.01}$ & $^{+0.01}_{-0.04}$ & $^{+0.03}_{-0.04}$ & $^{+0.01}_{-0.01}$ \\ Sys. & \ldots & $^{+420}_{-420}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.3}_{-0.1}$ & $^{+3.1}_{-1.9}$ & $^{+0.24}_{-0.49}$ & \ldots & $^{+0.03}_{-0.04}$ & $^{+0.02}_{-0.02}$ & $^{+0.05}_{-0.05}$ & $^{+0.09}_{-0.07}$ & $^{+0.03}_{-0.04}$ & $^{+0.05}_{-0.05}$ & $^{+0.03}_{-0.03}$ & $^{+0.03}_{-0.03}$ & $^{+0.02}_{-0.05}$ & $^{+0.03}_{-0.04}$ & $^{+0.04}_{-0.04}$ \\ Out i & \ldots & $20790$ & $3.506$ & $-11.3$ & $54.4$ & $3.1$ & $5.74$ & \ldots & $-1.01$ & $-3.79$ & $-4.38$ & $-3.41$ & $-4.03$ & $-4.74$ & $-5.87$ & $-4.68$ & $-5.01$ & $-5.59$ & $-4.79$ \\ Stat. & \ldots & $^{+30}_{-30}$ & $^{+0.004}_{-0.004}$ & $^{+0.1}_{-0.1}$ & $^{+0.1}_{-0.1}$ & $^{+0.1}_{-3.1}$ & $^{+0.05}_{-0.02}$ & \ldots & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.03}$ & $^{+0.02}_{-0.02}$ \\ Sys. & \ldots & $^{+420}_{-420}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.4}_{-0.1}$ & $^{+2.8}_{-3.1}$ & $^{+0.46}_{-0.46}$ & \ldots & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.04}_{-0.04}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $ ^{+0.02}_{-0.02}$ \\ Start & \ldots & $20000$ & $3.500$ & $-10.0$ & $50.0$ & $10.0$ & $8.00$ & \ldots & $-1.05$ & $-3.60$ & $-4.20$ & $-3.20$ & $-4.00$ & $-4.60$ & $-5.80$ & $-4.40$ & $-4.90$ & $-5.60$ & $-4.60$ \\ In s & \ldots & $18610$ & $3.227$ & $-9.1$ & $134.0$ & $59.5$ & $2.90$ & $0.936$ & $-1.02$ & $-3.79$ & $-4.38$ & $-3.39$ & $-4.02$ & $-4.74$ & $-5.87$ & $-4.66$ & $-4.99$ & $-5.59$ & $-4.79$ \\ Out f & \ldots & $18520$ & $3.200$ & $-9.6$ & $118.0$ & $87.0$ & $3.82$ & $1.085$ & $-1.00$ & $-3.89$ & $-4.40$ & $-3.46$ & $-4.05$ & $-4.75$ & $-5.86$ & $-4.68$ & $ -5.01$ & $-5.68$ & $-4.89$ \\ Stat. & \ldots & $^{+60}_{-40}$ & $^{+0.003}_{-0.002}$ & $^{+0.4}_{-0.7}$ & $^{+1.6}_{-0.5}$ & $^{+0.5}_{-3.0}$ & $^{+0.16}_{-0.12}$ & $^{+0.008}_{-0.005}$ & $^{+0.02}_{-0.02}$ & $^{+0.04}_{-0.04}$ & $^{+0.03}_{-0.05}$ & $^{+0.04}_{-0.05}$ & $^{+0.04}_{-0.02}$ & $ ^{+0.05}_{-0.05}$ & $^{+0.03}_{-0.06}$ & $^{+0.03}_{-0.04}$ & $^{+0.03}_{-0.03}$ & $^{+0.06}_{-0.05}$ & $^{+0.04}_{-0.05}$ \\ Sys. & \ldots & $^{+580}_{-500}$ & $^{+0.124}_{-0.124}$ & $^{+0.3}_{-0.1}$ & $^{+1.3}_{-0.8}$ & $^{+2.0}_{-1.6}$ & $^{+0.52}_{-0.36}$ & $^{+0.069}_{-0.131}$ & $^{+0.06}_{-0.03}$ & $^{+0.07}_{-0.06}$ & $^{+0.09}_{-0.10}$ & $^{+0.11}_{-0.13}$ & $^{+0.06}_{-0.03}$ & $^{+0.10}_{-0.06}$ & $^{+0.06}_{-0.05}$ & $^{+0.04}_{-0.04}$ & $^{+0.07}_{-0.03}$ & $^{+0.04}_{-0.04}$ & $^{+0.06}_{-0.07}$ \\ Out i & \ldots & $18410$ & $3.197$ & $-9.9$ & $120.3$ & $84.9$ & $3.71$ & $1.066$ & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ Stat. & \ldots & $^{+70}_{-20}$ & $^{+0.010}_{-0.005}$ & $^{+0.7}_{-0.7}$ & $^{+4.8}_{-0.5}$ & $^{+3.0}_{-3.3}$ & $^{+0.15}_{-0.09}$ & $^{+0.015}_{-0.008}$ & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ Sys. & \ldots & $^{+410}_{-390}$ & $^{+0.119}_{-0.111}$ & $^{+0.2}_{-0.2}$ & $^{+0.7}_{-0.6}$ & $^{+1.4}_{-1.5}$ & $^{+0.62}_{-0.71}$ & $^{+0.054}_{-0.061}$ & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ Start & \ldots & $20000$ & $3.500$ & $-10.0$ & $100.0$ & $50.0$ & $8.00$ & $1.000$ & $-1.05$ & $-3.60$ & $-4.20$ & $-3.20$ & $-4.00$ & $-4.60$ & $-5.80$ & $-4.40$ & $-4.90$ & $-5.60$ & $-4.60$ \\ \hline \multicolumn{20}{l}{Mock spectrum as a proxy to the observed spectrum of object \#4 b in Table~\ref{table:program_stars} (but with individual metal abundances for the two components):}\\ In p & $340$ & $29710$ & $3.669$ & $104.0$ & $23.7$ & $41.2$ & $14.92$ & \ldots & $-1.17$ & $-3.79$ & $-4.38$ & $-3.39$ & $-4.02$ & $-4.74$ & $-5.87$ & $-4.66$ & $-4.99$ & $-5.59$ & $-4.79$ \\ Out f & $353$ & $29730$ & $3.678$ & $103.9$ & $24.9$ & $39.3$ & $15.02$ & \ldots & $-1.17$ & $-3.81$ & $-4.39$ & $-3.41$ & $-4.03$ & $-4.75$ & $-5.88$ & $-4.68$ & $-5.00$ & \ldots & $-4.86$ \\ Stat. & $^{+3}_{-2}$ & $^{+20}_{-40}$ & $^{+0.003}_{-0.003}$ & $^{+0.1}_{-0.1}$ & $^{+0.3}_{-0.3}$ & $^{+0.1}_{-0.1}$ & $^{+0.12}_{-0.09}$ & \ldots & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.03}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & \ldots & $^{+0.05}_{-0.04}$ \\ Sys. & \ldots & $^{+600}_{-600}$ & $ ^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.9}_{-1.0}$ & $^{+0.3}_{-0.1}$ & $^{+0.48}_{-0.61}$ & \ldots & $^{+0.04}_{-0.04}$ & $^{+0.02}_{-0.01}$ & $^{+0.04}_{-0.04}$ & $^{+0.05}_{-0.05}$ & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.03}$ & $^{+0.04}_{-0.03}$ & $^{+0.04}_{-0.04}$ & $^{+0.07}_{-0.06}$ & \ldots & $^{+0.07}_{-0.06}$ \\ Out i & \ldots & $29700$ & $3.673$ & $103.9$ & $24.7$ & $39.6$ & $14.98$ & \ldots & $ -1.17$ & $-3.81$ & $-4.39$ & $-3.41$ & $-4.04$ & $-4.74$ & $-5.86$ & $-4.68$ & $-5.00$ & \ldots & $-4.80$ \\ Stat. & \ldots & $^{+10}_{-20}$ & $^{+0.004}_{-0.003}$ & $^{+0.1}_{-0.1}$ & $^{+0.2}_{-0.1}$ & $^{+0.1}_{-0.1}$ & $^{+0.08}_{-0.05}$ & \ldots & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.03}$ & $^{+0.01}_{-0.01}$ & $^{+0.02}_{-0.02}$ & \ldots & $^{+0.04}_{-0.04}$ \\ Sys. & \ldots & $^{+600}_{-600}$ & $^{+0.100}_{-0.100}$ & $^{+0.1}_{-0.1}$ & $^{+0.8}_{-1.2}$ & $^{+0.3}_{-0.1}$ & $^{+0.50}_{-0.63}$ & \ldots & $^{+0.04}_{-0.03}$ & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.04}$ & $^{+0.05}_{-0.05}$ & $^{+0.02}_{-0.02}$ & $^{+0.03}_{-0.03}$ & $^{+0.03}_{-0.03}$ & $^{+0.04}_{-0.04}$ & $^{+0.07}_{-0.06}$ & \ldots & $^{+0.03}_{-0.02}$ \\ Start & \ldots & $31000$ & $3.800$ & $100.0$ & $40.0$ & $10.0$ & $9.00$ & \ldots & $-1.05$ & $-3.60$ & $-4.20$ & $-3.20$ & $-4.10$ & $-4.60$ & $-5.80$ & $-4.40$ & $-4.90$ & $-5.60$ & $-4.60$ \\ In s & \ldots & $28070$ & $4.343$ & $-110.9$ & $35.5$ & $62.6$ & $6.04$ & $0.218$ & $-1.17$ & $-3.76$ & $-4.50$ & $-3.59$ & $-4.07$ & $-4.61$ & $-5.70$ & $-4.71$ & $-4.94$ & $-5.60$ & $-4.69$ \\ Out f & \ldots & $27740$ & $4.253$ & $-110.2$ & $28.2$ & $67.7$ & $6.50$ & $0.221$ & $-1.23$ & $-3.86$ & $-4.50$ & $-3.64$ & $-4.28$ & $-4.45$ & $-5.73$ & $-4.85$ & $-4.96$ & \ldots & $-4.64$ \\ Stat. & \ldots & $^{+120}_{-{\color{white}0}80}$ & $^{+0.019}_{-0.019}$ & $^{+1.0}_{-0.9}$ & $^{+3.0}_{-3.3}$ & $^{+3.0}_{-5.9}$ & $^{+0.70}_{-0.40}$ & $^{+0.001}_{-0.002}$ & $^{+0.05}_{-0.04}$ & $^{+0.08}_{-0.07}$ & $^{+0.05}_{-0.05}$ & $^{+0.03}_{-0.03}$ & $^{+0.20}_{-0.18}$ & $^{+0.31}_{-0.60}$ & $^{+0.09}_{-0.09}$ & $^{+0.06}_{-0.06}$ & $^{+0.08}_{-0.08}$ & \ldots & $^{+0.05}_{-0.05}$ \\ Sys. & \ldots & $^{+710}_{-880}$ & $^{+0.334}_{-0.523}$ & $^{+1.3}_{-0.6}$ & $^{+4.0}_{-2.5}$ & $^{+0.6}_{-0.2}$ & $^{+1.10}_{-2.00}$ & $^{+0.022}_{-0.012}$ & $^{+0.14}_{-0.11}$ & $^{+0.06}_{-0.05}$ & $^{+0.05}_{-0.07}$ & $^{+0.08}_{-0.03}$ & $^{+0.04}_{-0.03}$ & $^{+0.17}_{-0.26}$ & $^{+0.06}_{-0.05}$ & $^{+0.07}_{-0.03}$ & $^{+0.04}_{-0.03}$ & \ldots & $^{+0.11}_{-0.07}$ \\ Out i & \ldots & $26870$ & $4.220$ & $-110.7$ & $33.5$ & $65.0$ & $4.74$ & $0.231$ & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ Stat. & \ldots & $^{+120}_{-140}$ & $^{+0.015}_{-0.018}$ & $^{+0.8}_{-1.0}$ & $^{+2.5}_{-2.7}$ & $^{+2.3}_{-2.9}$ & $^{+0.29}_{-0.30}$ & $^{+0.001}_{-0.002}$ & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ Sys. & \ldots & $^{+870}_{-850}$ & $^{+0.366}_{-0.526}$ & $^{+1.3}_{-0.9}$ & $^{+3.8}_{-2.7}$ & $^{+0.6}_{-0.5}$ & $^{+0.74}_{-1.76}$ & $^{+0.016}_{-0.010}$ & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ Start & \ldots & $23500$ & $3.800$ & $-100.0$ & $30.0$ & $10.0$ & $8.00$ & $0.300$ & $-1.05$ & $-3.60$ & $-4.20$ & $-3.20$ & $-4.10$ & $-4.60$ & $-5.80$ & $-4.40$ & $-4.90$ & $-5.60$ & $-4.60$ \\ \hline \end{tabular} \tablefoot{Same as Table~\ref{table:uncertainties}. The letter ``p'' denotes the primary and ``s'' the secondary component. The letter ``f'' indicates that all abundances were allowed to vary freely during the fitting process, whereas ``i'' denotes the assumption of an identical chemical composition of both components. Argon lines are not visible for all temperatures.} \end{center} \end{table*} \subsection{Discussion of statistical and systematic uncertainties}\label{subsection:uncertainties} \begin{figure*} \centering \includegraphics[width=0.49\textwidth]{teff_logg_confmap_chisqr.pdf} \includegraphics[width=0.49\textwidth]{teff_logg_confmap_chisqr_SB2.pdf} \caption{Examples of a color coded $\Delta \chi^2$ map as a function of effective temperature and surface gravity for the single star HD\,37042 (\textit{left}) and for the primary component of the SB2 system HD\,119109 (\textit{right}). The magenta line is the $\Delta \chi^2 = 6.63$ contour line, therefore, indicating the statistical (single parameter) 99\%-confidence interval for abscissa and ordinate. The four corners of the black dashed-dotted rectangle are defined by the four combinations that result from adding or subtracting the respective total uncertainty, which is a quadratic sum of statistical and systematic uncertainty, to each coordinate of the best fit location. The point of minimum $\Delta \chi^2$ on each edge of the rectangle is marked by a gray cross. The solid black line surrounds the region within the rectangle with $\Delta \chi^2$ values lower or equal the maximum of the four $\Delta \chi^2$ values given by the gray crosses. In this way, areas within the rectangle where the models fit the observation worst are excluded, while it is ensured that each edge of the rectangle contributes at least one point to the solid line at the same time. This construction is our approach to combine statistical and systematic uncertainties.} \label{fig:teff_logg_confmap_chisqr} \end{figure*} The accuracy of spectral analyses is generally limited by the quality of the obtained data and the ability of the model to reproduce the observation. As shown in this subsection, shortcomings in the model, which may be due to inaccurate atomic data or deficient line broadening theory, are the main obstacles to overcome to perform more precise investigations. Statistical uncertainties result from the noise in the observed spectrum and can be deduced from the $\chi^2$ statistics in the standard way: starting from the best fit with a reduced $\chi^2$ of about one\footnote{\label{footnote:chisqr}This condition is generally not met because there are always some lines that our models still cannot reproduce on the small scales given by the high S/N of the available observations. In that case, the $\delta_i$ values corresponding to these lines are increased until their $\chi_i$ values (see Eq.~(\ref{eq:chisqr})) approach $\pm 1$ at the best fit eventually yielding a reduced $\chi^2$ of about $1$.}, the parameter under consideration is increased/decreased, while all remaining parameters are fitted, until a certain increment $\Delta \chi^2$ from the minimum $\chi^2$ is reached \citep[for details, see][]{bevrob}. Here, each $\Delta \chi^2$ corresponds to a confidence level; for example, $\Delta \chi^2 = 6.63$ is equivalent to the 99\%-confidence interval (see the magenta line in Fig.~\ref{fig:teff_logg_confmap_chisqr} for an illustration). The resulting uncertainties are, of course, only trustworthy if the $\delta_i$ of Eq.~(\ref{eq:chisqr}) are reasonably estimated. The method outlined in Sect.~\ref{subsection:noise_estimation} can do so, as shown by the tests with mock spectra with known noise level (see Tables~\ref{table:uncertainties} and \ref{table:uncertainties_binary}). Moreover, those tests, which use the same models as the fitting routine and, thus, exclude all sources of systematic errors apart from microscopic line blends, give an estimate of the statistical uncertainties that can be expected in real data with a similar S/N. Systematic uncertainties are much harder to cope with. Sources of systematic errors occur almost everywhere in the course of the analysis \citep[see the discussion in][]{nieva_iterative}. At the same time, their effects are by no means trivial, and it is extremely difficult and sometimes even impossible to quantify them. In particular, this is true for atomic data (such as energy levels, oscillator strengths, and photo-ionization cross sections), which affect individual spectral lines and the atmospheric structure. Monte Carlo simulations in the style of \citet{sigut,sigut2} offer the possibility of estimating the effects on spectra caused by variations in these input data. However, a thorough error analysis has to take all sources of systematic errors into consideration at the same time to account for correlations as well, which is an unfeasible task. Our analysis strategy is designed to keep systematic uncertainties as small as possible. For instance, an inaccurate local continuum definition can introduce considerable uncertainties to the determination of metal abundances, especially in fast-rotating stars or low-resolution spectra where metal line blends lower the actual continuum. In our routine, these effects are allowed by re-normalizing the observed spectrum with the help of the synthetic ones. Here, the latter are used to properly locate the continuum regions, which are sufficiently frequent in optical spectra of early-type stars. For these, a correction factor is obtained by dividing the (smoothed) observed data with the model data. Interpolating this factor to the whole wavelength grid gives the local continuum correction term for all spectral lines. For this approach to work, a high degree of completeness in terms of modeled lines is necessary, which is verified by high-resolution, high S/N spectra of slow rotators, as seen in Figs.~\ref{fig:spectra_1}--\ref{fig:spectra_9} (available online only). Another crucial part of our strategy is that we are simultaneously fitting the maximum useful range of the optical spectrum. In this way, parameters are determined not just from one or two spectral indicators but from all available ones. As the systematic errors of the individual indicators are typically independent of each other, which can be exemplified by ionization equilibria of different metals or oscillator strengths of various multiplets, there is a good chance that their effects on the parameter determination average out because some lines systematically give higher and others lower abundances, thus reducing the impact of systematics. To crudely estimate the systematic uncertainties, we start from the assumption that they mainly appear as inaccuracies in the determination of effective temperature and surface gravity. From our extensive experience with the applied synthetic spectra, we find it realistic but conservative to assign errors of $\pm 2\%$ in $T_{\mathrm{eff}}$ and $\pm 0.1\,\mathrm{dex}$ in $\log(g)$. The ranges given by these errors are formally treated as 99\%-confidence intervals. The precision in fixing the microturbulence and the abundances of the chemical elements is then estimated from propagating the errors in $T_{\mathrm{eff}}$ and $\log(g)$. Here, a fit of all remaining parameters is performed for each pixel (that is for each combination of temperature and surface gravity) surrounded by the solid black line in Fig.~\ref{fig:teff_logg_confmap_chisqr}. In the case of a binary system, this procedure is carried out for the secondary component as well. The resulting (combined) ranges of parameter values are then taken to be 99\%-confidence intervals. This approach is valid as long as uncertainties induced by variations in $T_{\mathrm{eff}}$ and $\log(g)$ dominate other sources of systematic errors. While this is likely to be true for $\xi$ and $n(x)$, it is clearly not the case for $\varv_{\mathrm{rad}}$, $\varv\,\sin(i)$, and $\zeta$. Determination of radial velocities is generally limited by the accuracy of the wavelength calibration and ranges between $0.1$-$2\,\mathrm{km\,s^{-1}}$ for common spectrographs. Projected rotational velocity and macroturbulence are incorporated via convolution with corresponding profile functions. Because of simplifications (for example in the treatment of limb-darkening or the assumption of radial-tangential macroturbulence) during the derivation of the latter \citep[see][]{gray}, their validity may be limited to a few $\mathrm{km\,s^{-1}}$. The comparison of statistical and systematic uncertainties, as listed in Table~\ref{table:uncertainties}, shows that our method's total uncertainty is dominated by systematic effects down to at least a S/N of $100$. However, this by no means implies that high S/N data are an unnecessary luxury. They are indispensable to detect weak features, such as contributions from a faint companion star, which would otherwise be hidden by noise. Moreover, shortcomings in the models are much more likely to remain unrecognized in low S/N spectra. This is particularly true if they can be partly compensated by tuning some fitting parameters, which, in turn, would cause erroneous results. Instead, this comparison shows that the accuracy of the presented spectral analysis technique is currently limited by modeling and not by observation. \label{sec:discussion} \subsection{Single B- and late O-type stars in Orion}\label{subsection:singlestars} Focusing on a wide range of effective temperatures, we have selected three slow rotators (HD\,35299, HD\,35912, and HD\,37042) from the sample of \citet{orion_composition} to check our method against previous studies. As shown in Table~\ref{table:atmospheric_parameters}, our atmospheric parameters have excellent agreement with those derived by \citeauthor{orion_composition}. Similarly, the results for the abundances of helium, carbon, and nitrogen are perfectly consistent with each other within the error bars, even though helium was kept fixed at the solar value in the study of \citeauthor{orion_composition}. The same applies to oxygen and silicon abundances by \citet{orion_fies}. On the other hand, there are systematic discrepancies apparent for neon, magnesium, and iron that can be attributed either to differences in the synthetic models or in the analysis strategy. For instance, several \ion{Mg}{ii} lines, such as $\lambda 4481$\,\AA\ have shown to be very sensitive to the replacement of pre-calculated opacity distribution functions, as used by \citeauthor{orion_composition}, with the more flexible concept of opacity sampling that is coherently used here throughout all computational steps, which explains the deviations in magnesium. The disagreements in neon and iron presumably arise from the underlying analysis techniques and in particular from how the microturbulence parameter is constrained. Nevertheless, it is extremely satisfying to see that the results of the two approaches match so well despite being based on contrary conceptional designs. \subsection{Spectroscopic binaries} As a first application to SB2 systems, we have analyzed the composite spectra of three binary systems. While the lines of the two components are sharp and very well separated in our spectrum of HD\,119109, the opposite is true for HD\,213420 (see Figs.~\ref{fig:binary_spectra_1}--\ref{fig:binary_spectra_9}). In the case of HD\,75821, we have further derived parameters from spectra taken at three distinct orbital phases to investigate its influence on the results. \paragraph*{HD\,119109 (\#5):} to our knowledge, there is no hint for binarity in the literature for this system so far. Nevertheless, our spectrum shows that this is doubtlessly a SB2 system owing to the many lines that appear twice in the spectrum (see Figs.~\ref{fig:binary_spectra_1}--\ref{fig:binary_spectra_9}). Given the high quality of our observation and the opportune orbital phase, parameters of both components can be reliably deduced. The system turns out to be composed of two relatively unevolved (see Fig.~\ref{fig:evolution_tracks}), coeval ($\tau_{\mathrm{p}}=48^{+10}_{-16}\,\mathrm{Myr}$, $\tau_{\mathrm{s}}=49^{+47}_{-48}\,\mathrm{Myr}$) late-type B-stars of masses $M_{\mathrm{p}} = 5.2 \pm 0.2\,M_{\sun}$ and $M_{\mathrm{s}} = 3.5^{+0.4}_{-0.2} \,M_{\sun}$ when using single-star evolutionary tracks. The corresponding squared ratio of radii, $(R_{\star,\mathrm{s}} / R_{\star,\mathrm{p}})^2 = 0.45^{+0.29}_{-0.18}$, is consistent with the surface ratio $A_{\mathrm{eff,s}}/A_{\mathrm{eff,p}} = 0.642^{+0.015\mathrm{(stat.)}+0.027\mathrm{(sys.)}}_{-0.013\mathrm{(stat.)}-0.028\mathrm{(sys.)}}$, as is the spectroscopic distance, $d = 470^{+70}_{-60}\,\mathrm{pc}$, with the parallax, $\Pi^{-1} = 550^{+1700}_{-{\color{white}0}240}\,\mathrm{pc}$. The chemical composition resembles that of the single stars studied in Sect.~\ref{subsection:singlestars}. Using published radial velocity measurements, \citet{runaway_catalog} have proposed that this object is a runaway star with high probability based on its peculiar space motion. This conclusion should be considered as uncertain as long as the actual system velocity of this binary is unknown. \paragraph*{HD\,213420 (\#6):} this well-known binary system with a period of about $880$\,days and a radial velocity semi-amplitude of $9\,\mathrm{km\,s^{-1}}$ \citep{SB9} is a clear SB2 system, given the broad absorption features superimposed to He\,{\sc i} $\lambda 4438$\,\AA, $\lambda 6678$\,\AA, C\,{\sc ii} $\lambda 4267$\,\AA, Mg\,{\sc ii} $\lambda 4481$\,\AA, Si\,{\sc iii} $\lambda 4553$\,\AA, $\lambda 4568$\,\AA, and S\,{\sc ii} $\lambda 5454$\,\AA\ (see Figs.~\ref{fig:binary_spectra_1}--\ref{fig:binary_spectra_9}). Although the signatures of the secondary component are weak and thus only detectable in the case of a high S/N, they are apparently sufficient to determine reasonable atmospheric parameters for the companion because the resulting stellar parameters paint a consistent physical picture: In addition to the finding that the ages of both components (with masses $M_{\mathrm{p}} = 10.4^{+1.3}_{-1.2}\,M_{\sun}$, $M_{\mathrm{s}} = 11.1^{+0.5}_{-2.1} \,M_{\sun}$) are in perfect agreement ($\tau_{\mathrm{s}}=20^{+10}_{-{\color{white}0}4}\,\mathrm{Myr}$, $\tau_{\mathrm{p}}=18^{+14}_{-{\color{white}0}2}\,\mathrm{Myr}$), the spectroscopic parameter $A_{\mathrm{eff,s}}/A_{\mathrm{eff,p}} = 0.936^{+0.014+0.069}_{-0.015-0.060}$ lies within the uncertainty interval of the squared ratio of the evolutionary-track radii, $(R_{\star,\mathrm{s}} / R_{\star,\mathrm{p}})^2 = 1.9^{+1.9}_{-1.1}$. The spectroscopic distance of the system, $d = 510^{+110}_{-100}\,\mathrm{pc}$, finally fits to its parallax, $\Pi^{-1} = 530^{+210}_{-120}\,\mathrm{pc}$. Apart from a slight tendency to a lower metallicity (see Table~\ref{table:stellar_parameters}), the chemical composition agrees with the reference stars of Sect.~\ref{subsection:singlestars}. \paragraph*{HD\,75821 (\#4):} this eclipsing binary has a period of about $26.3$\,days and a radial velocity semi-amplitude of $92\,\mathrm{km\,s^{-1}}$ \citep{KXVel}. The spectrum best suited for the spectral analysis is the second one (b) in Table~\ref{table:atmospheric_parameters}, since the spectral line separation is largest in this case, which reveals several pure and unblended features of the companion (see Figs.~\ref{fig:binary_spectra_1}--\ref{fig:binary_spectra_9}). Reliable atmospheric and stellar parameters for both components are, hence, determinable whereby the latter assume that single-star evolutionary tracks are appropriate. Starting from this premise, the system consists of two coeval components ($\tau_{\mathrm{p}}=7^{+1}_{-1}\,\mathrm{Myr}$, $\tau_{\mathrm{s}}\leq 10\,\mathrm{Myr}$): a massive primary ($M_{\mathrm{p}} = 20.2^{+1.8}_{-1.5}\,M_{\sun}$), which is slightly evolved, and a less massive secondary ($M_{\mathrm{s}} = 11.5^{+2.0}_{-0.5}\,M_{\sun}$), which is almost unevolved (see Fig.~\ref{fig:evolution_tracks}). The spectroscopic distance $d = 960^{+240}_{-200}\,\mathrm{pc}$ lies well within the 99\%-uncertainty range of the parallax, $\Pi^{-1} = 1000^{+2300}_{-{\color{white}0}500}\,\mathrm{pc}$. Finally, the spectroscopically deduced effective surface ratio $A_{\mathrm{eff,s}}/A_{\mathrm{eff,p}} = 0.218^{+0.003+0.014}_{-0.002-0.011}$ agrees well with the squared ratio of the evolutionary-track radii, $(R_{\star,\mathrm{s}} / R_{\star,\mathrm{p}})^2 = 0.13^{+0.41}_{-0.04}$, and is further consistent with the photometric light curve \citep{KXVel2}. The elemental abundances of the system are in line with the single stars except for the relatively low helium, nitrogen, and oxygen content (see Table~\ref{table:atmospheric_parameters}). The heavily blended and, hence, almost vanishing imprints of the companion on the first (a) and third (c) spectrum are insufficient to properly constrain the secondary component's atmospheric parameters. Instead, unphysical values and large systematic uncertainties, which are induced by variations of $T_{\mathrm{eff}}$ and $\log(g)$ of the primary, are derived for the secondary's $T_{\mathrm{eff}}$ and $\log(g)$. These error margins are, on the one hand, a direct consequence of strong correlations among certain parameters and, on the other hand, related to the fact that contributions of the secondary component barely affect the spectrum at the corresponding orbital phases. In a simplified picture, increasing the primary's $T_{\mathrm{eff}}$ and decreasing its $\log(g)$ at the same time causes the \ion{He}{ii} lines to become considerably deeper than actually observed, while the \ion{He}{i} lines still fit nicely. To compensate for this, $A_{\mathrm{eff,s}}/A_{\mathrm{eff,p}}$ and, hence, the influence of the secondary component, has to be significantly increased to fill the \ion{He}{ii} lines with the continuum which thus weakens them again. However, this makes some spectral lines of the secondary component substantially too strong, which, in turn, is corrected for by smearing them out via a larger $\varv\,\sin(i)$ or $\zeta$ that finally leads to a more uncertain determination of $\varv_{\mathrm{rad}}$, given the high degree of line blending at these particular orbital phases. However, the primary's properties and the surface ratio $A_{\mathrm{eff,s}}/A_{\mathrm{eff,p}}$ are nicely recovered in all three orbital phases, which gives us confidence that the presented method is generally able to determine them from one single spectrum. In this paper, a novel objective method to analyze single or composite spectra of early-type stars is presented. It is based on fitting synthetic spectra to observation by using the standard concept of $\chi^2$ minimization, which requires the wavelength-dependent noise of the spectrum to be known. Therefore, a simple but precise way of estimating the local noise has been developed (see Sect.~\ref{subsection:noise_estimation}). To facilitate fast and efficient analyses, we make use of pre-calculated grids of synthetic spectra, instead of computing them on demand during the fitting procedure. To sample the entire multi-dimensional parameter space at once, we exploit the unique spectral properties of early-type stars, such as the low density of lines, which reduces the number of models required by several orders of magnitude. In this way, a simultaneous fit of all parameters is possible which has the great advantage that cumbersome iterations by hand or the risk of missing the global best solution are avoided. Moreover, parameters are not only constrained from a subset of available lines but from all useful features in the spectrum. The extension to composite spectra of double-lined binary systems proves extremely valuable in the future, given the high frequency of SB2 systems among early-type stars \citep[see][]{binaries_1,binaries_2}. In contrast to spectral disentangling techniques like those of \citet{spectral_disentangling_1} or \citet{spectral_disentangling_2}, the method presented here allows for --~at least~-- parameters of the primary and the components' effective surface ratio to be inferred from single-epoch spectra alone. Statistical and systematic uncertainties of our method are discussed (see Sect.~\ref{subsection:uncertainties}). The former are based here on a clearly defined mathematical measure, namely the $\chi^2$ statistics, while the latter on experience. We show that systematic effects generally dominate in the high-quality regime of our observations. The analysis of a larger sample of stars thus enables us to identify possible shortcomings in our models and to derive results with significantly reduced statistical scatter. As a case study, we have determined parameters of three well-known stars in the Orion region that turn out to be in excellent agreement with previous studies. Additionally, three binary systems have been analyzed with all of them yielding very conclusive results. Consequently, we are now in a position to homogeneously analyze large samples of early-type stars in relatively short times. The results of a comprehensive investigation of $63$ nearby mid B-type to late O-type stars will be published in a forthcoming paper. | 14 | 3 | 1403.1122 |
1403 | 1403.4707_arXiv.txt | The southern Galactic high mass star-forming region, G351.63-1.25, is a H\,{\sc ii}~region-molecular cloud complex with a luminosity of $\sim 2.0\times10^5$~L$_\odot$, located at a distance of 2.4 kpc from the Sun. In this paper, we focus on the investigation of the associated H\,{\sc ii}~region, embedded cluster and the interstellar medium in the vicinity of G351.63-1.25. We address the identification of exciting source(s) as well as the census of the stellar populations, in an attempt to unfold star formation activity in this region. The ionised gas distribution has been mapped using the Giant Metrewave Radio Telescope (GMRT), India at three frequencies: 1280, 610 and 325 MHz. The \hii~region shows an elongated morphology and the 1280 MHz map comprises six resolved high density regions encompassed by diffuse emission spanning 1.4$\times$1.0~pc$^2$. Based on measurements of flux densities at multiple radio frequencies, the brightest ultracompact core has electron temperature $T_e\sim7647\pm 153$~K and emission measure, $EM\sim2.0\pm0.8\times10^7$~cm$^{-6}$pc. The zero age main-sequence (ZAMS) spectral type of the brightest radio core is O7.5. We have carried out near-infrared observations in the JHK$_s$ bands using the SIRIUS instrument on the 1.4 m Infrared Survey Facility (IRSF) telescope. The near-infrared images reveal the presence of a cluster embedded in nebulous fan-shaped emission. The log-normal slope of the K-band luminosity function of the embedded cluster is found to be $\sim0.27 \pm0.03$ and the fraction of the near-infrared excess stars is estimated to be 43\%. These indicate that the age of the cluster is consistent with $\sim 1$~Myr. Other available data of this region show that the warm (mid-infrared) and cold (millimetre) dust emission peak at different locations indicating progressive stages of star formation process. The champagne flow model from a flat, thin molecular cloud is used to explain the morphology of radio emission with respect to the millimetre cloud and infrared brightness. | Our understanding of the formation of massive stars is poor relative to that of low-mass stars \citep{1987ARA&A..25...23S} although considerable progress is being made \citep{1999PASP..111.1049G, 2007prpl.conf..165B}. This is because the formation and early evolution of stars progress deep within the parental molecular cloud of gas and dust. Further adding to the difficulty, is the fast pre-main-sequence evolution of massive stars, their rarity as well as large distances (kpc scale or larger) as compared to their low mass counterparts. In addition, it has been observed that massive stars usually form in clusters or complexes, i.e. accompanied by swarms of stars of different masses \citep{1997A&A...320..159T}. The detailed study of massive star-forming complexes necessitates an investigation in different wavelength bands, in order to probe the distinct characteristics of the star formation process. Multiwavelength observations, therefore, hold the key to unraveling the least understood facets of high-mass star formation. Star forming complexes in the southern sky have been relatively less studied compared to the northern regions and in this paper we investigate one such star forming region in detail. The massive star-forming region, G351.63-1.25, (associated with IRAS 17258-3637) is a \hii~region-molecular cloud complex with a luminosity of $1.9\times10^5$~L$_\odot$ \citep{2004A&A...426...97F}. We have adopted a distance of 2.4 kpc based on the studies by \citet{2000MNRAS.317..315V}, \citet{2004A&A...426...97F}, and \citet{2005A&A...440..121B}. Millimetre continuum emission from cold dust in this region at 1.2 mm \citep{2004A&A...426...97F} shows the presence of a single dust core with total mass of $\sim1400$ M$_\odot$. \citet{2011ApJS..195....8C} have detected emission towards G351.63-1.25 at 2 and 3 mm and this is included in their QUaD Galactic Plane survey catalog. Molecular line investigation of this region has revealed a HC$_3$N core with tentative CO and SiO outflows \citep{2004AJ....128.2374S}. In the radio continuum, G351.63-1.25 has a very compact source \citep[FWHM$\sim6''$ at 3.7 cm;][]{1974ApJ...192..343B} which is surrounded by a more extended source \citep{1987A&A...171..261C}. More recent high resolution radio continuum observations at 8.7 GHz \citep{1998MNRAS.301..640W} reveal the central region ($6''\sim0.07$~pc) to be irregular shaped with local peaks. \citet{1990ApJ...353..564G} have presented far-infrared observations of this region in the 120-300 $\mu$m band using the Tata Institute of Fundamental Research (TIFR) 100 cm balloon borne telescope. They have constructed a spectral energy distribution from 2 $\mu$m to 1 mm and carried out simple radiative transfer calculations using a spherically symmetric dust shell, for an assumed distance of 5 kpc. An infrared cluster located in this region has been discovered by \citet{2003A&A...404..223B} % using the Two-Micron All Sky Survey (2MASS) survey. Further, high resolution K-band spectra of three young stellar objects located in this region have been obtained by \citet{2005A&A...440..121B, 2006A&A...455..561B} as a part of their survey to study massive young stellar objects. Methanol maser emission \citep{1994MNRAS.268..464S, 2000MNRAS.317..315V}, one of the signposts of massive star formation, has also been detected in this region. While few studies have looked at this massive star-forming region in general, there is no study focussing on the associated embedded cluster. Some of the questions that we aim to address relate to the identification of exciting source(s), census of the stellar populations, and compilation of the available observations to construct a picture of the star formation activity in this region. To carry out this investigation, we have used a combination of infrared and radio wavebands. We probe the young cluster using deeper and high resolution near-infrared (NIR) observations as compared to the previous studies (eg. based on 2MASS). Our new low frequency radio observations of this \hii~region have the advantage that we can simultaneously image the compact as well as diffuse emission with moderate to high angular resolution. The layout of the paper is as follows. In Sect. 2, we present the radio and NIR observations as well as a description of other available data-sets used in this study. Sections 3-6 describe the results and in Sect. 7, we discuss the multiwavelength scenario for star formation in the light of various observational results. The conclusions are presented in Sect. 8. | Based on the multiwavelength (radio, infrared and millimetre) investigation of the star-forming region associated with G351.63-1.25 presented here, we come to the following conclusions. \begin{enumerate} \item The radio map of the \hii~region at 1280 MHz comprises of six high density ionised clumps embedded in diffuse emission. The brightest clump at S2 is an ultracompact \hii~region with the electron temperature $\sim 7647\pm153$ K and emission measure $\sim 2.0\pm0.8\times10^7$~cm$^{-6}$pc. The equivalent ZAMS spectral type is estimated to be O7.5. \item The NIR broad band images in J, H and K$_s$ reveal the presence of fan-shaped nebulous emission as well as high extinction filamentary structures. The stellar component is probed using colour-magnitude and colour-colour diagrams. These have been used to find the infrared excess sources, associated with the embedded cluster. The log-normal slope of the KLF of the embedded cluster after removing the contamination due to foreground and background sources is $\sim 0.27\pm0.03$, indicating the youth of the cluster. The fraction of the NIR excess stars is estimated to be 43\% indicating an upper age limit of 1 - 2 Myr. Based on KLF as well as NIR excess fraction, we believe that age of the cluster is compatible with $\sim1$ Myr. \item The MIR images from WISE and MSX show diffuse emission that matches the ionised gas distribution very well. \item The ultracompact component S2, does not have an infrared counterpart within $3\arcsec$ of the radio peak at 1280 MHz. Further, based on the morphology of S2 (not point-like), the presence of other young stellar objects within the nebulosity of S2, the detection of dense molecular gas core close to it, the presence of Class I methanol maser as well as tentative evidence of SiO outflows, it is very likely that S2 is ionised by a group of massive embedded sources rather than a single source. \item The ionised clumps seen in the 1280 MHz map are likely to be externally ionised by the central cluster associated with S2 due to absence of NIR counterparts, less compact morphology, and optical depth effects at 1280 and 610 MHz. \item The warm and cold dust distributions (from MIR and millimetre emission) peak at different locations. The ionised emission is elongated indicating ionisation bounds on either side. The elongation is perpendicular to the direction of the line joining the peak brightness of ionised gas and cold dust. This is explained using the champagne flow model where star formation occurs in a thin, flat molecular cloud and the expansion of the \hii~region happens away from the cloud leading to a bipolar-type morphology of extended emission. \end{enumerate} | 14 | 3 | 1403.4707 |
1403 | 1403.1587_arXiv.txt | {The growth of dust particles into planet embryos needs to circumvent the ``radial-drift barrier'', \emph{i.e.} the accretion of dust particles onto the central star by radial migration. The outcome of the dust radial migration is governed by simple criteria between the dust-to-gas ratio and the exponents $p$ and $q$ of the surface density and temperature power laws. The transfer of radiation provides an additional constraint between these quantities because the disc thermal structure is fixed by the dust spatial distribution. To assess which discs are primarily affected by the radial-drift barrier, we used the radiative transfer code \mcfost\ to compute the temperature structure of a wide range of disc models, stressing the particular effects of grain size distributions and vertical settling. We find that the outcome of the dust migration process is very sensitive to the physical conditions within the disc. For high dust-to-gas ratios ($\gtrsim 0.01$) and/or flattened disc structures ($H/R \lesssim 0.05$), growing dust grains can efficiently decouple from the gas, leading to a high concentration of grains at a critical radius of a few AU. Decoupling of grains from gas can occur at a large fraction ($> 0.1$) of the initial radius of the particle, for a dust-to-gas ratio greater than $\approx$ 0.05. Dust grains that experience migration without significant growth (millimetre and centimetre-sized) are efficiently accreted for discs with flat surface density profiles ($p<0.7$) while they always remain in the disc if the surface density is steep enough ($p>1.2$). Between ($0.7<p<1.2$), both behaviours may occur depending on the exact density and temperature structures of the disc. Both the presence of large grains and vertical settling tend to favour the accretion of non-growing dust grains onto the central object, but it slows down the migration of growing dust grains. If the disc has evolved into a self-shadowed structure, the required dust-to-gas ratio for dust grains to stop their migration at large radius become much smaller, of the order of 0.01. All the disc configurations are found to have favourable temperature profiles over most of the disc to retain their planetesimals. } | \label{sec:intro} \begin{figure} \includegraphics[width = \hsize]{f1} \caption{Temperature exponent $q$ as a function of the surface density exponent $p_\mathrm{dust}$. Large bullets show the median values, smaller bullets the $1^\mathrm{st}$ and $2^\mathrm{nd}$ quartiles, and vertical bars the complete distribution of models; \emph{i.e.}, the horizontal ticks on each bar represent the minimum and maximum values reached in the whole set of models. Models with maximum grain sizes ranging from $1\,\mu$m to $10\,\mu$m are shown in red, while models with $a_\mathrm{max}$ ranging from $100\,\mu$m to $10$\,mm are shown in blue. The different models are slightly shifted along the $p$ axis for clarity. The plane is divided by the stability criteria for dust grains: $q = 1$ with growth, $-p_\mathrm{gas}+q+1/2 = 0$ (assuming $p_\mathrm{gas} = p_\mathrm{dust}$, black dashed line) without growth and for planetesimals: $q = 2/3$ (black dot-dashed lines). The thick gray line indicates the location of steady-state, constant $\alpha$ viscous disc models $p_{\rm gas} = 3/2 - q$. \label{fig:grain_size} } \end{figure} \defcitealias{Laibe08}{LGFM08} \defcitealias{Laibe2012}{LGM12} \defcitealias{Laibe2014b}{L14} The evolution of dust particles embedded in circumstellar discs constitutes the first step towards planet formation \citep{bw08,Chiang2010}. Micrometre-sized dust grains collide and grow by coagulation, forming larger pebbles (millimetre- and centimetre-sized, \citealt{Beckwith00,Dominik06PPV} and references therein) that may ultimately give birth to kilometre-sized planetesimals. Dust grains also settle towards the disc midplane and migrate inwards as a result of the conjugate actions of stellar gravity, gas drag, and radial pressure gradient \citep[e.g.][herafter \citetalias{Laibe2012}]{Weidendust1977,Nakagawa86,Fromang06,Laibe2012}. This results in a stratified disc structure with a population of small (micrometre-sized) grains remaining close to the surface and larger grains located deeper in the disc \citep[e.g.][]{Dullemond04,Duchene04,DAlessio06,Pinte07,Pinte08b}. However, the interplay between these two mechanisms remains unclear. For instance, how dust grains overcome the ``radial-drift barrier'' --- \emph{i.e.} the accretion of dust grains onto the central star on timescales shorter than the disc's lifetime. Several mechanisms have been invoked to overcome this barrier, such as grain growth (\citealp[e.g.\ ][hereafter \citetalias{Laibe08}]{Laibe08}, \citealp{Brauer08,Okuzumi2009,Birnstiel09,Zsom2010,Windmark2012,Garaud2013}) or trapping in pressure maxima \citep[e.g.\ ][]{Pinilla2012,Gibbons2012}. Another mechanism has been studied by \cite{Stepinski97,Youdin2002} and \cite{Youdin2004} and revived by \citetalias{Laibe2012}, \cite{Laibe2014a}, and \citet[][hereafter \citetalias{Laibe2014b}]{Laibe2014b} for growing dust grains. As the grains move inward, their radial motion is affected by the increasing drag force, the increasing pressure gradient, and eventually a larger size due to grain growth. The combination of these effects can lead to a variety of outcomes. In particular, for specific values of the exponents of the gas surface density ($\Sigma(r) \propto r^{-p}$) and midplane temperature ($T(r) \propto r^{-q}$), the time required for grains to reach smaller and smaller radii increases drastically\footnote{in the case where the gas accretion velocity is neglected}. This causes dust grains to decouple from the gas phase and ``pile-up'' in the dense, inner regions of the disc: the migration timescale becomes so long that dust particles are virtually stopped and never end up accreted onto the central object. Growing grains may also break through the drift barrier because of the transition from Epstein to Stokes drag at high gas densities \citep[][see their Fig. 11]{Birnstiel10}. Although the kinematics of the radial motion of the grains depends on the grain size, the outcome of the radial drift motion essentially depends on the values of $p$ and $q$. \citetalias{Laibe2012} and \citetalias{Laibe2014b} derived three analytic criteria that predict whether dust grains are ultimately accreted onto the central star or not. In order for dust to pile up, the criteria are (i) $q < 1$ and $\Lambda (r) > 1-q$ for growing grains, where \begin{equation} \Lambda (r) = \frac{\epsilon_{0}}{\left( p + q/2 + 3/2\right)\left(H(r)/r \right)^{2} } \end{equation} measures the relative efficiency between growth and migration, and $\epsilon_{0}$ is the disc's initial dust-to-gas ratio. (ii) $-p+q+1/2<0$ for non-growing grains in the Epstein drag regime (which corresponds to dust grains of size smaller than $\approx$\,10\,cm for density conditions encountered in protoplanetary discs), and (iii) $q<2/3$ for planetesimals ($>\,1$\,m) in the Stokes drag regime.\\ In the following, we use the terms ``growing grains'', ``non-growing grains'', and ``planetesimals'' to refer to these three cases. \begin{figure*} \includegraphics[width = 0.49\hsize]{f2} \hfill \includegraphics[width = 0.49\hsize]{f3} \caption{Stability criteria $\Lambda(r) + q - 1 > 0$ for the growing grains as a function of the surface density exponent for $r = 10\,$AU (left panel) and $r = 100\,$AU (right panel) and an initial dust-to-gas ratio $\epsilon_{0} = 0.01$ in both cases. Models with scale height of 5, 10, and 15\,AU at a radius of 100\,AU are shown in blue, black, and red respectively. The vertical axes are different in both panels. The second part of the stability criteria for growing grains : $q < 1$ is always satisfied in the disc models we have explored, see Fig~\ref{fig:grain_size}. \label{fig:Lambda}} \end{figure*} \begin{figure*} \includegraphics[width = 0.49\hsize]{f4} \hfill \includegraphics[width = 0.49\hsize]{f5} \caption{Relative decoupling radius for growing dust grains (\emph{i.e.} decoupling radius divided by initial radius of the grains in the disc) as a function of $\Lambda$ for various values of $p$ (left) and $q$ (right). The red thick solid line shows a typical Classical T Tauri Star disc with $p = 1$, $q = 0.5$. \label{fig:Rdec}} \end{figure*} In these former studies, $p$ and $q$ were considered to be independent parameters that could take any value. However, the radial temperature profile of the disc is set by the transfer of radiation, which depends on both the dust properties and the disc geometry. The $q$ parameter therefore depends on the dust surface density profile $p_\mathrm{dust}$ and can only take a limited range of values. Furthermore, the grain size distribution (which affects the wavelength dependence of the opacity) and vertical settling (which lowers the $\tau=1$ surface, changing the amount of stellar light intercepted by the disc as a function of the radius) are expected to affect the value of $q$ and, in turn, the outcome of the radial migration. In this paper, we present the first results of the effect of radiative transfer on the radial-drift barrier in both the Epstein and Stokes regimes. Specifically, we determine i) which parts of the ($p$, $q$) diagram are populated with physical models, ii) whether these discs are strongly affected by the radial-drift barrier process, and iii) the key parameters that affect the stability of the dust particles with respect to radial migration. \begin{table} \begin{center} \begin{tabular}{lcc} \hline Parameter & Range of values explored & Step \\ \hline $p_\mathrm{dust}$ & 0 -- 1.5 & 0.25 \\ $H_0$ (gas) [AU] at 50\,AU & 5 -- 15 & 5\\ $\beta$ (gas) & 1.0 -- 1.35 & 0.05 \\ $a_{\rm max}$ [$\mu$m]& 1 -- 10\,000 & factor 10\\ $\alpha_\mathrm{SS}$ & $10^{-4}$ -- $10^{-1}$ + (no settling) & factor 10\\ \hline \end{tabular} \end{center} \caption{Range of values explored for the various parameters in the grid of models computed with \mcfost. \label{Tab:param} } \end{table} | \label{Sec:conclu} Based on analytical calculations of the dust evolution in discs (we highlight the limitations in section~\ref{sec:limitation}), we have investigated the effects of a complete treatment of radiative transfer on the stability of dust grains and planetesimals relative to radial migration within protoplanetary discs. We find that for a significant fraction of the discs we considered, the dust particles pile up in the disc, potentially providing material for the formation of planetary cores. Excluding the first few central tenths of AU, all the disc configurations we explored lead to favourable temperature profiles ($q<2/3$) for the discs to retain their planetesimals. The necessary criterion $q<1$ for discs to retain their growing grains is also always fulfilled. In most of the disc configurations, the conditions are met for dust grains to decouple at a radius larger than 1\,\% if the initial dust-to-gas ratio is higher than 0.03. In the case of a flat surface density, lower initial dust-to-gas ratios, around 0.01, are enough. In those cases, dust grains starting at a few hundred AU will pile up and stop migrating in the regions where telluric planets are formed. If the initial dust-to-gas ratio is higher, between 0.05 and 0.1, dust grains pile up at a radius larger than 10\,\% of their initial radius and could provide the material for forming the cores of massive planets. Three classes of discs can be distinguished with respect to the outcome of the radial motion of non-growing grains. Discs with steep density profiles ($p_{\rm dust}>1.2$) will retain their grains, whereas dust migration will be very efficient for flat surface densities ($p_{\rm dust}<0.7$). For intermediate cases ($0.7<p_{\rm dust}<1.2$), significant migration of dust grains can occur, but its outcome needs to be studied via case-by-case detailed simulations coupling hydrodynamics and radiative transfer. Interestingly, this includes the case $p_{\rm dust} \simeq 1$, which corresponds to the peak of the distribution of the observed disc profiles. The presence of large grains and vertical settling steepens the temperature profile and tends to enhance the radial migration of the non-growing grains, favouring accretion onto the central object. For growing dust grains, however, the reduced temperature in presence of large grains and/or settling will slow down the migration and result in pile-up for almost all the disc configurations. If the settling and/or grain growth increases, the disc structure can become self-shadowed, resulting in much lower gas temperature and sound speed. In this case, the conditions become much more favorable for dust grains piling up and dust-to-gas ratios over around 0.01 are enough to stop the migration of the grains coming from 100\,AU at distances over a few AU. In the central regions of the disc where the stellar radiation can penetrate directly or accretion heating can contribute, the temperature profile is so steep ($q\gg1$) that both the dust grains, whether they are still growing or not, and planetesimals are rapidly accreted in all cases. This will also be the case if accretion heating becomes significant and results in a steep temperature profile in these central regions. Understanding the detailed outcome of the radial migration in protoplanetary discs requires numerical simulations to catch the complexity of all the processes at play (\citetalias[e.g.][]{Laibe08}, \citealp{Birnstiel09, Birnstiel10}). Ideally, these simulations should be coupling radiative transfer and dynamics, since the conditions for the migration or pile-up of the dust grains are strongly affected by the thermal structure of the disc. In this simple study, we performed an exhaustive exploration of the parameter space and, based on analytical criteria, we give the main results of the migration outcome. These results can provide valuable help in tailoring the input parameters of the dust evolution codes used to understand the now growing evidence of dust radial segregation in discs. | 14 | 3 | 1403.1587 |
1403 | 1403.0254_arXiv.txt | { We study the capture of galactic dark matter particles (DMP) in two-body and few-body systems with a symplectic map description. This approach allows modeling the scattering of $10^{16}$ DMPs after following the time evolution of the captured particle on about $10^9$ orbital periods of the binary system. We obtain the DMP density distribution inside such systems and determine the enhancement factor of their density in a center vicinity compared to its galactic value as a function of the mass ratio of the bodies and the ratio of the body velocity to the velocity of the galactic DMP wind. We find that the enhancement factor can be on the order of tens of thousands.} | In 1890, Henri Poincar\'e proved that the dynamics of the three-body gravitational problem is generally non-integrable \citep{poincare}. Even 125 years later, many aspects of this problem remain unsolved. Thus the capture cross-section $\sigma$ of a particle that scatters on the binary system of Sun and Jupiter has only recently been determined, and it has been shown that $\sigma$ is much larger than the area of the Jupiter orbit \citep{khriplovich2009,lages}. The capture mechanism is described by a symplectic dynamical map that generates a chaotic dynamics of a particle. The scattering, capture, and dynamics of a particle in a binary system recently regained interest with the search for dark matter particles (DMP) in the solar system and the Universe \citep{bertone2005,garrett,merritt}. Thus it is important to analyze the capture and ejection mechanisms of a DMP by a binary system. Such a system can be viewed as a binary system with a massive star and a light body orbiting it. This can be the Sun and Jupiter, a star and a giant planet, or a super massive black hole (SMBH) and a light star or black hole (BH). In this work we analyze the scattering process of DMP galactic flow, with a constant space density, in a binary system. One of the main questions here is whether the density of captured DMPs in a binary system can be enhanced compared to the DMP density of the scattering flow. The results obtained by \cite{lages} show that a volume density of captured DMPs at a distance of the Jupiter radius $r<r_p=r_J $ is enhanced by a factor $\zeta \approx 4000$ compared to the density of Galactic DMPs which are captured after one one orbital period around the Sun and which have an energy corresponding to velocities $v < v_{cap} \sim v_p \sqrt{m_p/M} \sim 1$km.s$^{-1} \ll u$. Here, $m_p, M$ are the masses of the light and massive bodies, respectively, $u \approx 220$km.s$^{-1}$ is the average velocity of a Galactic DMP wind for which, following \cite{bertone2005}, we assume a Maxwell velocity distribution: $f(v) dv = \sqrt{54/\pi} v^2/u^3 \exp(-3v^2/2u^2) dv$. Our results presented below show that for an SMBH binary system with $v_{cap} > u$ there is a large enhancement factor $\zeta_g \sim 10^4$ of the captured DMP volume density, taken at a distance of about a binary system size, compared to its galactic value for all scattering energies (and not only for the DMP volume density at low velocities $v < v_{cap} \ll u,$ as discussed by \cite{lages}). We note that the Galactic DMP density is estimated at $\rho_g \sim 4 \times 10^{-25}$g.cm$^{-3}$ , while the typical intergalactic DMP density is estimated to be $\rho_{g0} \sim 2.5 \times 10^{-30}$g.cm$^{-3}$ \citep{garrett,merritt}. At first glance, this high enhancement factor $\zeta_g \sim 10^4$ seems to be rather unexpected because it apparently contradicts Liouville's theorem, according to which the phase space density is conserved during a Hamiltonian evolution. Because of this, it is often assumed \citep{gould,edsjo1} that the volume (or space) DMP density cannot be enhanced for DMPs captured by a binary system, and thus $\zeta_g \sim 1$. Below we show that this restriction is not valid for the following reasons: first, we have an open system where DMPs can escape to infinity, being ejected from the binary system by a time-dependent force induced by binary rotation. This means that the dynamics is not completely Hamiltonian. Second, DMPs are captured (or they linger, or are trapped) and are accumulated from continuum at negative coupled energies near the binary during a certain capture lifetime (although not forever). Thus, the longer the capture lifetime, the higher the accumulated density. Third, we obtain the enhancement for the volume density and not for the density in the phase space, for which the enhancement is indeed restricted by Liouville's theorem. We discuss the details of this enhancement effect in the next sections. The scattering and capture process of a DMP in a binary system can be an important element of galaxy formation. This process can also be useful to analyze cosmic dust and DMP interaction with a supermassive black hole binary. This is expected to play a prominent role in galaxy formation, see \cite{nature2015}. Thus we hope that analyzing this process will be useful for understanding the properties of velocity curves in galaxies, which was started by \cite{zwicky} and \cite{rubin}. We note that the velocity curves of captured DMPs in our binary system have certain similarities with those found in real galaxies. | Our results show that DMP capture and dynamics inside two-body and few-body systems can be efficiently described by symplectic maps. The numerical simulations and analytical analysis show that in the center of these systems the DMP volume density can be enhanced by a factor $\zeta_g \sim 10^4$ compared to its galactic value. The values of $\zeta_g$ are highest for a high velocity $v_p $ of a planet or star rotating around the system center. We note that our approach based on a symplectic map description of the restricted three-body problem is rather generic. Thus it can also be used to analyze comet dynamics, cosmic dust, and free-floating constituents of the Galaxy. | 14 | 3 | 1403.0254 |
1403 | 1403.0853_arXiv.txt | {Understanding the relationship between the formation and evolution of galaxies and their central super massive black holes (SMBH) is one of the main topics in extragalactic astrophysics. Links and feedback may reciprocally affect both black hole and galaxy growth.} {Observations of the CO line at redshifts of 2-4 are crucial to investigate the gas mass, star formation activity and accretion onto SMBHs, as well as the effect of AGN feedback. Potential correlations between AGN and host galaxy properties can be highlighted by observing extreme objects. Despite their luminosity, hyper-luminous QSOs at z$=2-4$ are still little studied at mm wavelengths.} {We targeted CO(3-2) in ULAS J1539+0557, an hyper-luminos QSO ($\rm L_{bol}> 10^{48} erg/s$) at $\rm z=2.658$, selected through its unusual red colors in the UKIDSS Large Area Survey (ULAS).} {We find a molecular gas mass of $\rm 4.1\pm0.8 \times10^{10}~ M_{\odot}$, and a gas fraction of $\sim$0.4-0.1, depending mostly on the assumed source inclination. We also find a robust lower limit to the star-formation rate (SFR$=$250-1600 M$_\odot$/yr) and star-formation efficiency (SFE$=$25-350 L$_\odot$/(K km s$^{-1}$ pc$^{2}$) by comparing the observed optical-near-infrared spectral energy distribution with AGN and galaxy templates. The black hole gas consumption timescale, $\rm M(H_2)/\dot M_{acc}$, is $\sim 160$ Myr, similar or higher than the gas consumption timescale.} {The gas content and the star formation efficiency are similar to those of other high-luminosity, highly obscured QSOs, and at the lower end of the star-formation efficiency of unobscured QSOs, in line with predictions from AGN-galaxy co-evolutionary scenarios. Further measurements of the (sub)-mm continuum in this and similar sources are mandatory to obtain a robust observational picture of the AGN evolutionary sequence.} | Understanding the relations between the formation and evolution of galaxies and their central super massive black holes (SMBH) is a major challenge of present-day astronomy. Most of galaxy assembly and accretion activity occur at $\rm z=2-4$, so it is crucial to study SMBH-galaxy relationships at this epoch. The two main open questions are: a) what is the mechanism triggering nuclear accretion and star-formation? and b) are AGN outflows truly able to regulate star-formation in their host galaxies? Observations of molecular gas are useful to address both questions. So far, molecular gas has been detected in a few tens of $\rm z>2$ QSOs, with typical masses $1-10\times10^{10}$ M$_\odot$, indicating gas-rich hosts. However, most of these observations have been done either on lensed object (where the intrinsic luminosity is magnified up to 1000 times), or on z$=5-6$ QSOs (Riechers 2011 and references therein). There is a growing evidence for two modes of star-formation which may also be relevant for triggering nuclear activity: a quiescent one, taking place in most star-forming galaxies, with gas conversion time scales of $\sim1$ Gyr, and a less common {\it star-burst} mode, acting on much shorter time scales ($\sim10^7-10^8$ yr, see e.g. Rodighiero et al. 2011, Lamastra et al. 2013a and references therein). The latter mode is likely related to the powering of high luminosity QSOs. In fact, bolometric luminosities of the order of $10^{47}-10^{48}$ ergs/s imply mass accretion rates of tens to hundreds $\rm M_\odot$/yr onto $10^9-10^{10}~\rm M_\odot$ SMBHs (assuming a radiative efficiency of 0.1). If the accretion lasts for a few tens Myr (Salpeter timescale), this in turn implies gas reservoirs of $10^9-10^{10}$ M$_\odot$ even if the fraction of the gas that can reach the nucleus is high ($\Delta$M$_{gas}\sim $M$_{gas}/5$). At present, galaxy interactions seem to be the best (if not the only) mechanism capable of destabilizing such huge gas masses on short time scales. This naturally produces powerful AGN hosted in star-burst galaxies (Lamastra et al 2013b). In principle, from the gas consumption timescale (or its inverse, the so-called star formation efficiency, SFE, i.e. the ratio between the star-formation rate and the gas mass), one can directly derive information on the AGN and star-formation triggering mechanisms. The SFE depends also on the SMBH gas consumption time scales and on the energy injected in the ISM by the AGN ({\it feedback}). High SFE may be the outcome of a small cold gas reservoir which was reduced by on-going SMBH accretion and consequent AGN feedback. For this reason, to have information on AGN feedback is crucial for addressing both questions. There is both theoretical and observational evidence that high luminosity QSOs drive powerful outflows. On the theoretical ground, physically-motivated models predict strong winds from AGN with SMBH larger than $10^8$ M$_\odot$(Zubovas \& King 2014 and references therein). These models in general predict mass flows proportional to the AGN bolometric luminosity to some power (e.g. M$_{out}\propto$ L$_{Bol}^{1/2}$ in the Menci et al. 2008 model). For these reasons, the most luminous QSOs in the Universe are ideal and unique targets to study AGN/galaxy feedback mechanisms regulated by powerful outflows. Powerful and massive AGN driven outflows of molecular gas were recently discovered in luminous QSOs (Maiolino et al. 2012, Feruglio et al. 2010, Cicone et al. 2013). Broad Absorption Lines (BAL) with outflow velocities up to several thousands km/s are common in high-luminosity QSOs (Borguet et al. 2013). BALs are found in 40\% of mid-infrared selected QSOs (Dai et al. 2008) and in 40\% of the {\it WISE} selected luminous QSOs (Bongiorno et al. 2014, in prep.). Powerful, galaxy wide outflows have also been found in ionized gas using the broad [OIII] emission line (Cano-Diaz et al. 2012). In this paper we present results from the first Plateau de Bure Interferometer (PdBI) observation of an hyper-luminous QSO, selected from the UKIDSS Large Area Survey (ULAS) and the VISTA (J, K bands) Hemisphere Survey: ULAS J1539+0557 at $\rm z=2.658$ (ra:15:39:10.2, dec: 05:57:50.0, Banerji et al. 2012). ULAS J1539+0557 is heavily reddened (rest frame $\rm A_V\sim4$) and has a bright 22 $\mu$m flux of 19 mJy in the{\it WISE} all-sky survey, corresponding to $\lambda L_{\lambda}(7.8~ \mu$m)$=10^{47}$ ergs/s, and a bolometric luminosity of $\rm L_{bol}\sim10^{48}$ erg/s. The black hole mass is as large as $7.4\times10^{9}~\rm M_{\odot}$. As detailed in Banerji et al. (2012a), these hyper-luminous QSOs are unlikely to be lensed, therefore they truly trace an extremely luminous population. In the following we present the results of 3 mm observations of ULAS J1539+0557, targeting the CO(3-2) transition. We derive the gas mass, dynamical mass, and star-formation rate (SFR) of the host galaxy through the comparison of the observed UV-MIR Spectral Energy Distribution (SED) with galaxy templates. We compare the observed gas masses, gas fraction and gas consumption timescale with those of the other QSOs and galaxies at similar redshift. We finally discuss future desirable developments in this topic. A $H_0=70$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_M$=0.3, $\Omega_{\Lambda}=0.7$ cosmology is adopted throughout. | We detected CO(3-2) in the hyper-luminous QSO ULAS J1539+0557 at $\rm z=2.658$, a source selected by extremely red colors in the UKIDSS Large Area Survey (ULAS) and bright at 22 micron in the {\it WISE} survey. We find a molecular gas reservoir of $\rm 4.1\pm0.8 ~10^{10}~ M_{\odot}$. The dynamical mass is not well constrained but it could be 2-10 times higher, depending mostly on the gas disk size and inclination. In any case, the host galaxy does not appear deprived from cold gas, suggesting that it is still forming stars actively. From fitting of the UV to mid-IR SED, we derived a robust lower limit to the SFR and gas consumption time scale. The ratio of SMBH accretion to star-formation rate, $\rm \dot M_{acc}/SFR$, is significantly higher than that found by Mullaney et al. (2012) for AGN with star-forming hosts. The SFE is similar to that of highly obscured, high luminosity QSOs. This class of QSOs is believed to witness the brief evolutionary phase that traces the transition from a heavily enshrouded ULIRG-like phase of black-hole growth to the blue unobscured quasars. Due to their high luminosity these exceptional objects are ideal laboratories to investigate the physics of the feedback phenomenon with in situ observations at the peak of galaxy and SMBH assembly. The high luminosity allows highlighting the correlation between SFE and other parameters (e.g. obscuration, AGN luminosity). Both the {\it WISE} all sky survey and the UKIDSS and VISTA hemisphere Surveys have revealed a population of hyper-luminous QSOs in near and mid infrared. These selections have already produced reasonably large hyper-luminous QSO samples at z$\sim1.5-4$, the main epoch of galaxy formation and accretion activity in the Universe. Recently, Banerji et al. (2014) presented IR and X-ray observations of a similar source from the same parent sample, ULAS J1234+0907 at redshift 2.5, finding high SFR ($\gs 2000\rm M_\odot/yr$) and high X-ray luminosity ($\gs 10^{45}$ergs/s), thus confirming that infrared selection is efficient in discovering a population of hyper-luminous QSOs in the {\it blowout} phase. It is urgent to increase the sample of hyper-luminous QSOs with good estimates of both gas mass, dynamical mass, L$_{FIR}$, and X-ray luminosity, including both unobscured and highly obscured QSOs. These goals can be achieved with the present and future generation of millimeter interferometers, such as the PdBI, NOEMA and ALMA. | 14 | 3 | 1403.0853 |
1403 | 1403.5471_arXiv.txt | {The intense radiation flux of Type I X-ray bursts is expected to interact with the accretion flow around neutron stars. High frequency quasiperiodic oscillations (kHz QPOs), observed at frequencies matching orbital frequencies at tens of gravitational radii, offer a unique probe of the innermost disk regions. In this paper, we follow the lower kHz QPOs, in response to Type I X-ray bursts, in two prototypical QPO sources, namely 4U 1636-536 and 4U 1608-522, as observed by the Proportional Counter Array of the \emph{Rossi} X-ray Timing Explorer. We have selected a sample of 15 bursts for which the kHz QPO frequency can be tracked on timescales commensurable with the burst durations (tens of seconds). We find evidence that the QPOs are affected for over $\sim$200 s during one exceptionally long burst and $\sim$100 s during two others (although at a less significant level), while the burst emission has already decayed to a level that would enable the pre-burst QPO to be detected. On the other hand, for most of our burst-kHz QPO sample, we show that the QPO is detected as soon as the statistics allow and in the best cases, we are able to set an upper limit of $\sim$20 s on the recovery time of the QPO. This diversity of behavior cannot be related to differences in burst peak luminosity. We discuss these results in the framework of recent findings that accretion onto the neutron star may be enhanced during Type I X-ray bursts. The subsequent disk depletion could explain the disappearance of the QPO for $\sim$100 s, as possibly observed in two events. However, alternative scenarios would have to be invoked for explaining the short recovery timescales inferred from most bursts. Heating of the innermost disk regions would be a possibility, although we cannot exclude that the burst does not affect the QPO emission at all. Clearly the combination of fast timing and spectral information of Type I X-ray bursts holds great potential in the study of the dynamics of the inner accretion flow around neutron stars. However, as we show, breakthrough observations will require a timing instrument providing at least ten times the effective area of the RXTE/PCA.} | Illumination of accreting disks during Type I X-ray bursts gives us the opportunity to study the innermost regions of the accretion flow around neutron stars \citep{Galloway:2008, Strohmayer:2003aa,Cumming:2004aa}. Evidence of an interaction between the burst emission and the inner disk has been reported in a few individual bursts \citep{Yu:1999,Kuulkers:2003,Chen:2011,int-Zand:2011,Serino:2012,Degenaar:2013}. Disk depletion through radiation drag, heating of the inner disk, and even radiatively or thermally powered winds were discussed by \citet{Ballantyne:2004} and \citet{Ballantyne:2005}, who attempted to explain the time evolution of the properties of the \emph{superburst} of \object{4U\,1820-303}. More recently, \citet{Worpel:2013aa}, fitting the spectra of all photospheric radius expansion (PRE) bursts observed with the \emph{Rossi} X-ray Timing Explorer (RXTE) as the sum of a blackbody and a scalable continuum having the shape of the pre-burst persistent emission, reported a systematic increase of the persistent emission during the burst. They interpreted this result as evidence of an accretion rate enhancement due to a rapid increase of the radiation torque on a thin accretion disk, as formalized early on by \citet{Walker:1992}. A similar finding was reported by \citet{int-Zand:2013aa} for a burst observed simultaneously by \emph{Chandra} and RXTE, although disk reprocessing of the burst emission was preferred as an alternative explanation. \begin{table*} \caption{Principal characteristics of the selected X-ray bursts.} \label{tab:liste_bursts} \centering \begin{tabular}{c c c c c c c c c} \hline\hline Source & Burst ID & Obs ID & Start time & $L_{\text{peak}}$\tablefootmark{a} & $E_{\text{tot}}$\tablefootmark{a} & $\tau$\tablefootmark{a} & $C_{\text{pers}}$ & $C_{\text{peak}}$\\ & & & (RXTE time) & (10$^{38}$ ergs/s) & (10$^{39}$ ergs) & (s) & (cts/s) & (cts/s)\\ \hline 4U 1636-536 & 4 & 10088-01-08-030 & 94671416 & 2.68 & 5.54 & 20.7 & 788 & 9931\\ & 6 & 30053-02-02-02 & 146144682 & 2.89 & 1.78 & 6.2 & 679 & 9740\\ & 9 & 40028-01-02-00 & 162722852 & 2.94 & 1.84 & 6.3 & 569 & 9927\\ & 21 & 40028-01-18-000 & 208401523 & 2.79 & 2.35 & 7.0 & 737 & 9916\\ & 22 & 40028-01-18-00 & 208429016 & 2.76 & 1.85 & 6.7 & 574 & 10000\\ & 23 & 40028-01-19-00 & 208740744 & 2.79 & 2.13 & 7.6 & 541 & 10116\\ & 39 & 60032-01-09-00 & 242286131 & 1.46 & 1.33 & 9.1 & 417 & 7089\\ & 40 & 60032-01-09-01 & 242295310 & 1.06 & 1.14 & 10.9 & 425 & 5355\\ & 41 & 60032-01-10-00 & 242708641 & 2.00 & 1.50 & 7.5 & 428 & 9611\\ & 168 & 91024-01-30-10 & 374626248 & 2.98 & 2.06 & 6.9 & 473 & 9604\\ \hline 4U 1608-522 & 4 & 30062-02-01-000 & 133389809 & 1.43 & 1.35 & 9.1 & 643 & 9004\\ & 5 & 30062-01-01-00 & 133625123 & 2.34 & 2.32 & 9.9 & 543 & 10339\\ & 21 & 70059-01-20-00 & 273983179 & 2.33 & 1.93 & 8.3 & 617 & 10562\\ & 23 & 70059-03-01-000 & 274421898 & 2.39 & 3.16 & 13.2 & 517 & 10549\\ & 24 & 70059-03-01-000 & 274434678 & 1.08 & 1.1 & 10.2 & 510 & 9528\\ \hline \end{tabular} \tablefoot{Burst ID corresponds to the burst number in the \citet{Galloway:2008} burst catalog, Obs ID to the identification number of the RXTE observation in which the burst can be found, Start time to the RXTE time of the burst peak used to define the date $t = 0$ in Sect.~\ref{data_analysis}, $L_{\text{peak}}$ to the peak luminosity, $E_{\text{tot}}$ to the total energy, $\tau$ to the decay time constant, $C_{\text{pers}}$ to the raw persistent count rate before the burst, and $C_{\text{peak}}$ to its value at burst peak. \tablefoottext{a}{Values taken from \citet{Galloway:2008}. Distances of 6 and 3.6~kpc were taken to compute the peak luminosity $L_{\text{peak}}$ and total energy} $E_{\text{tot}}$ for 4U 1636-536 and 4U 1608-522, respectively \citep{Pandel:2008,Nakamura:1989}. } \end{table*} In this paper, we follow a different path and look at kilohertz quasiperiodic oscillations (kHz QPOs) in response to Type I X-ray bursts (see \citealt{van-der-Klis:2006} for a review of kHz QPOs). Although there is not yet a consensus on the origin of kHz QPOs, it is generally agreed that they arise from the vicinity of the neutron star \citep[e.g.,][]{Barret:2013}, most likely in a region to be exposed to the burst emission. It is therefore worth investigating how the QPO properties react to X-ray bursts. For this purpose, we use the RXTE archival data of \object{4U 1636-536} and \object{4U 1608-522}, known as frequent bursters \citep{Galloway:2008} and whose lower kHz QPOs can be detected and followed on the burst duration timescales of tens of seconds \citep{Mendez:1999,Barret:2005,Barret:2006}. | \label{discussion} High frequency QPOs are commonly believed to be generated close to the neutron star surface or in the innermost parts of the accretion disk. Similarly, Type I X-ray bursts are produced on the neutron star surface and radiate away enough energy to change the proprieties of the accretion flow. It is therefore natural to investigate the impact of a Type I X-ray burst on kHz QPOs. Our finding that there may be cases where the QPO is affected by the bursts on timescales of hundreds of seconds and cases where the QPO does not suffer from the bursts down to the shortest timescales that can be investigated by current data ($\sim$20~s) is clearly puzzling, especially because these two behaviors cannot be irrefutably connected in our limited sample to different properties of the bursts, such as the burst peak luminosity. We now discuss our results in the framework of the recent work by \citet{Worpel:2013aa}, claiming that the accretion rate is enhanced during Type I X-ray bursts. \subsection{A disk recession?} As accretion disks are optically thick in the radial direction, an enhanced accretion rate due to radiation torque can only be attained through disk depletion: $f_a > 1$ implies a receding disk. The Eddington-scaled accretion rate in our data sets is $\sim$0.12 and 0.04~$\dot{M}_{\text{Edd}}$ for 4U 1636-536 and 4U 1608-522, respectively, using a neutron star mass of 1.4~M$_{\odot}$. If we take conservative values for the mean $f_a$ measured during the 20~s following the burst onset of 1.5 and 2 for the two sources, this gives depleted masses of at least $\sim3\times10^{18}$ and $2\times10^{18}$~g. Using standard accretion disks as described in \citet{Shakura:1973} to model the mass distribution in the inner parts of the disk with an $\alpha$-parameter of 0.1, these masses correspond approximately to the mass contained between 7--50~$R_g$ for 4U 1636-536, and 7--30~$R_g$ for 4U 1608-522. It is important to note that the disk surface density scales as 1/$\alpha$ which is poorly constrained and that these masses are only rough estimates. An estimate of the timescale at which the disk recovers its former geometry is given by the viscous time \citep[][Eq. 5.69]{Frank:2002}, \begin{equation} t_{\text{visc}} \sim 3 \times 10^5 \alpha^{-4/5} \left(\dfrac{\dot{M}}{10^{16}\text{g/s}}\right)^{-3/10}\left(\dfrac{M}{\text{M}_{\odot}}\right)^{1/4}\left(\dfrac{R}{10^{10}\text{cm}}\right)^{5/4}~s, \end{equation} with $R$ the distance to the neutron star center, $\dot{M}$ the accretion rate, and $M$ the neutron star mass. For $M = 1.4$ M$_{\odot}$, $\alpha = 0.1$, and with the appropriate accretion rates, we find $t_{\text{visc}} \sim 130$~s at 50~$r_g$ for 4U 1636-536 and $t_{\text{visc}} \sim 100$~s at 30~$r_g$ for 4U 1608-522. It is worth noting that increasing $\alpha$ gives shorter viscous times, but it also increases the radius matching the loss of mass and similar timescales are found. Within all the caveats of the above assumptions, it is interesting to note that these timescales match the nondetection gap of the two shorter bursts from 4U 1636-536, shown in Fig. \ref{fig:4_22_23}. We note however that for the longer burst of 4U 1636-536, $f_a$ is still above 1 while the QPO reappears (see Fig. \ref{fig:fa_profiles}), which argues against the idea that the disk is still truncated through depletion. This clearly suggests that caution should be used when using $f_a$ to derive the accretion rate during the burst. Some refinements in the \citet{Worpel:2013aa} model might be necessary such as considering modifications of the spectral shape of the persistent emission during the burst. If such high levels of disk depletion occur, one would expect at least the disk emission to be modified; for example, a change in the disk inner radius from 7~$r_g$ to 50~$r_g$ would decrease its inner temperature by a factor of 4.4, assuming a dependency of $\propto R^{-3/4}$ as in \citet{Shakura:1973}. The timescales found are also a factor of 5-10 longer than the recovery time we inferred from 4U 1608-522, thus suggesting that an alternative to disk depletion should be considered. \begin{figure}[!t] \resizebox{\hsize}{!}{\includegraphics{pds_vs_cld_LOFT_2.pdf}} \centering \caption{Simulated dynamical PDS containing a QPO at 800 Hz and a smooth frequency jump of 10 Hz initiated at the burst peak (the dashed green line gives the QPO frequency as a function of time). The QPO rms amplitude is 8\% and the QPO width is 3 Hz. The LOFT/LAD 3--30\,keV light curve of the Type I X-ray burst (peak at 18 times the persistent emission level, rise time of 2\,s, and decay time of 7\,s) is overplotted with a white line. The persistent count rate was estimated using 4U 1608-522 as the source. The image corresponds to a series of 1 s PDS plotted as a function of time, convolved with a 6 Hz and 2 s averaging kernel. Power is color coded. We note that the color scale is different from the one used for RXTE data: it saturates at a power level of 8 instead of 3.} \label{fig:LOFT} \end{figure} \subsection{Heating of the inner region?} To reduce the viscous disk recovery time, only the innermost part of the accretion disk should be affected. At 10~$R_g$, the viscous time $\sim$18~s for 4U 1636-536 and $\sim$25~s for 4U 1608-522 with an $\alpha$-parameter of 0.1. One possibility could thus be disk irradiation by the burst photons, which is expected to produce significant heating, and might cause the disk to puff up \citep{Ballantyne:2005}. Leaving aside the two shorter bursts of 4U 1636-536 for which the QPO disappearance is marginally significant, such a mechanism could be consistent with the late reappearance of the QPO in the longer one (while the burst is still ongoing), but also with the short recovery times of the QPOs in 4U 1608-522. This might indicate that the modulated emission reappears only when the level of heating is sufficiently low. Unfortunately, current data cannot tell us what happens to the QPO within the first 20~s in 4U 1608-522, e.g., whether its amplitude drops or its coherence decreases. Hence, although that seems unlikely, we also cannot exclude that there is no effect of the burst on the QPO in this source. Existing data are therefore insufficient to access timescales shorter than 20~s, while we would like to measure the QPO parameters as close as possible to the burst peak. Assuming that the QPO amplitude and width remain constant within the burst and only the QPO frequency varies, in Fig. \ref{fig:LOFT} we show that a new generation timing instrument like the LOFT/LAD \citep{Feroci:2012} would allow us to track the QPO frequency, even at the burst peak. Tracking the QPO frequency along the frequency drift assumed in the simulation requires an increase in effective area by at least one order of magnitude (15 in the case considered here\footnote{LOFT/LAD response files were downloaded from \url{http: //www.isdc.unige.ch/loft} for the simulation. We have assumed the goal effective area of 12~m$^2$ at 8~keV for the LAD. }). This simulation illustrates how such a large area timing instrument could deliver breakthrough observations on the burst-QPO interaction, providing at the same time insights on the location of the QPO modulated emission. \subsection{Conclusions} The interaction between the kHz QPO signals and Type-I X-ray bursts has been studied in two LMXBs: 4U 1636-536 and 4U 1608-522. Two types of behaviors of different timescales have been identified. We have found clear evidence of an interaction of the burst with the QPO emission during an exceptionally long burst (and a possible indication for two others) while for most of them, within the current data, the QPO does not seem to be affected by the burst. We have set an upper limit of 20~s for the recovery time of the QPO in 4U 1608-522. We have shown that a next generation timing mission providing an increase in effective area of at least an order of magnitude, such as LOFT, would be able to detect the QPO throughout the bursts and hence provide better constraints on the physics of the interaction of the burst emission and its surroundings. This would need to be complemented by theoretical work aimed at a better modeling of the burst-disk interaction. | 14 | 3 | 1403.5471 |
1403 | 1403.6122_arXiv.txt | {Stellar convection is customarily described by Mixing-Length Theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and at all evolutionary phases. } {The aim of this study is to present a new theory of stellar convection that does not require the mixing length parameter. We present a self-consistent analytical formulation of stellar convection that determines the properties of stellar convection as a function of the physical behaviour of the convective elements themselves and of the surrounding medium.} {This new theory is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism the motion of stellar convective cells inside convectively-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism. } {We obtain an analytical, non-local, time-dependent sub-sonic solution for the convective energy transport that does not depend on any free parameter. The theory is suitable for the outer convective zones of solar type stars and stars of all mass on the main sequence band. The predictions of the new theory are compared with those from the standard mixing-length paradigm for the most accurate calibrator, the Sun, with very satisfactory results. } {} | In stellar interiors convection plays an important role: together with radiation and conduction, it transports energy throughout a star, and it chemically homogenizes the regions affected by convective instability. Therefore convection significantly affects the structures and evolutionary histories of stars. For example, the centre of main sequence stars slightly more massive than the Sun and above is dominated by convective transport of energy. In stars less massive than about 0.3 $M_\odot$ the whole structure becomes fully convective. The outer layers of stars of any mass are convective toward the surface. Very extended convective envelopes exist in red-giant-branch (RGB) and asymptotic-giant-branch (AGB) stars. Pre-main sequence stars are fully convective along the Hayashi-line. Finally convection is present in the pre-supernova stages of type I and II supernovae, and even during the collapse phase of type II supernovae \citep[e.g.][]{2014AIPA....4d1010A, 2014ApJ...785...82S, 2011ApJ...741...33A, 2007ApJ...667..448M}. In most cases, convection in the cores and inner shells does not pose serious difficulties to our understanding of the structure of the stars because the large thermal capacity of convective elements results in the degree of ``super-adiabaticity'' being so small that for any practical purpose the temperature gradient of the medium in the presence of convection can be set equal to the adiabatic value, unless evaluations of the velocities and distances traveled by convective elements are required, e.g. in presence of convective overshooting \citep[see for instance the early studies by][]{1975A&A....40..303M,1975A&A....43...61M,1981A&A...102...25B}. Describing convection in the outer layers of a star is by far more difficult and uncertain. Convective elements in this region have low thermal capacity, so that the super-adiabatic approximation can no longer be applied, and the temperature gradient of the elements and surrounding medium must be determined separately to exactly know the amount of energy carried by convection and radiation \citep[e.g.][]{ 2013sse..book.....K, 2004cgps.book.....W}. A suitable description of convection is therefore essential to determine stellar structure. The universally adopted solution is the Mixing-Length Theory (MLT) of convection, a simplified analytical formulation of the problem. Unfortunately, a more satisfactory analytical treatment of stellar convection is still missing and open to debate \citep[e.g.][]{2011A&A...528A..76C}. The MLT stands on the works of \citet[][]{1951ZA.....28..304B} and \citet[][]{1958ZA.....46..108B} which are based on earlier works on the concept of convective motion by \citet{Prandtl}. In this standard approach, the motion of convective elements is related to the mean-free-path $l_m$ that a generic element is \textit{supposed} to travel at any given depth inside the convectively unstable regions of a star \citep[e.g.][Chapter 7]{ 1994sse..book.....K}. The mean free path $l_m$ is assumed to be proportional to the natural distance scale $h_P$ given by the pressure stratification of the star. The proportionality factor is however poorly known and constrained. The mixing-length (ML) parameter $\Lambda _m$, defined by $l_m \equiv {\Lambda _m}{h_P}$, must be empirically determined. Nevertheless, the knowledge of this parameter is of paramount importance in correctly determining the convective energy transport, and hence the radius and effective temperature of a star. This critical situation explains the many versions of convection theory that can be found when investigated in different regions and evolutionary phases of a star such as the overshooting from core or envelopes zones \citep[e.g.][]{ 2008MNRAS.386.1979D, 2007A&A...475.1019C,1981A&A...102...25B}, the helium semi-convection in low and intermediate mass stars $m < 5{M_ \odot }$ \citep[e.g.][]{ 1993A&AS..100..647B, 1985ApJ...296..204C}, the time-dependent convection in the carbon deflagration process in Type I supernovae \citep[e.g.][]{ 1976Ap&SS..39L..37N}, the studies on the efficiency of convective overshooting \citep[e.g.][]{ 2013arXiv1301.7687B}, and the effects of rotation \citep[e.g.][]{2008A&A...479L..37M} to mention just a few. Examining the classical formulation of the MLT presented in any textbook, see for instance \citet[][]{Hofmeister1964}, \citet[][]{1968pss..book.....C} and their modern versions \citep[][respectively]{2013sse..book.....K,2004cgps.book.....W}, we note that the MLT reduces to the energy conservation principle supplemented by an estimate of the mean velocity of convective elements. In a convective region the total energy flux ($\varphi$) is the sum of the convective flux ($\varphi_{\rm{cnv}}$) and the radiative flux ($\varphi_{\rm{rad}}$); the total flux is set proportional to a fictitious radiative gradient $\nabla_{\rm{rad}}$ \footnote{Throughout the paper, we will introduce several logarithmic temperature gradients with respect to pressure $\frac{{d\log T}}{{d\log P}}$, shortly indicated as $\nabla$. Each of these gradients is also identified by a subscript such as ${\nabla _e}$, ${\nabla _{\bm{\xi }}}$, ${\nabla _{{\rm{ad}}}}$, $\nabla_{\rm{rad}}$ depending of the circumstances. Finally, the symbol $\nabla$ with no subscript is reserved for the ambient temperature gradient with respect to pressure across a star. } (which is always known once the total flux coming from inside is assigned, typically case in stellar interiors); the true radiative flux $\varphi_{\rm{rad}}$ is proportional to the real gradient of the medium $\nabla$; and the convective flux $\varphi_{\rm{cnv}}$ is proportional to the difference between the gradient of the convective elements and the gradient of the medium ($\nabla_e - \nabla$). By construction, the convective flux is also proportional to the mass of an ideal convective element, i.e., the amount of matter crossing the unit area per unit time with the mean velocity of convective elements. These elements may have any shape, mass, velocity and lifetime, and may travel different distances before dissolving into the surrounding medium, releasing their energy excess and inducing mixing in the fluid. However all this ample variety of possibilities is simplified to an ideal element of averaged dimensions, lifetime, mean velocity and distance travelled before dissolving: the so-called mixing-length $l_m$ (and associated mixing-length parameter $\Lambda_m$). As far as the velocity is concerned, this is estimated from the work done by the buoyancy force over the distance $l_m$, a fraction of which is supposed to go into kinetic energy of the convective elements. Since in this problem the number of unknowns exceeds the number of equations (flux conservation and velocity), two more suitable relations are usually added. These are firstly the ratio between the excess of energy in the bubble just before dissolving, to the energy radiated away (lost) during the lifetime, and secondly the excess rate of energy generation minus the excess rate of energy loss by radiation in the element relative to the surroundings. These are all functions of $\nabla$, $\nabla_e$ and $\nabla_{\rm{ad}}$, see e.g. \citet[][]{1968pss..book.....C}. Now the number of unknowns, i.e. $\varphi_{\rm{rad}}$, $\varphi_{\rm{cnv}}$, $\nabla$, $\nabla_e$, is equal to the number of equations and the problem can be solved once $l_m$ or $\Lambda_m$ are assigned. \textit{In this way the complex fluid-dynamic situation is reduced to an estimate of the mean element velocity simply derived from the sole buoyancy force, neglecting other fluid-dynamic forces that can shape the motion of convective elements as function of time and surrounding medium}. We present here a new description of stellar convection that provides a simple and yet dynamically complete fully analytical integration of the hydrodynamic equations, matching the existing literature results based on the classical MLT, but without making use of any mixing-length parameter ${\Lambda _m}$. The plan of the paper is as follows. In Section \ref{probIntro2} we formulate the problem within the mathematical framework we intend to adopt. In Section \ref{Velpot} we define the concept of a scalar field of the velocity potential for expanding/contracting convective elements. In Section \ref{EqcnvQ} and \ref{Accele} we formulate the equation governing the two degrees of freedom of our dynamical system: In Section \ref{EqcnvQ} formulates the equation of motion for a convective element as seen by a non-inertial frame of reference co-moving with it, and presents two lemmas that are functional to our aim; in Section \ref{Accele} we solve the equation of motion of a convective element expressed in the co-moving frame of reference. In Section \ref{Results} we present the predictions of our theory. First, we formulate the basic equations of stellar convection showing that the mixing-length parameter is no longer required. Then we apply the new formalism to the case of the Sun. Finally in Section \ref{Conc} we present some concluding remarks highlighting the novelty and the power of the new theory. | \label{Conc} It has taken almost one century to develop a theory for stellar convection and energy transport without the mixing-length parameter. In this first study we have presented a new simple theory of stellar convection that does not contain adjustable parameters such as the mixing-length. The whole solution (temperature gradients of the medium and convective elements, the distances travelled by typical elements, their velocities and lifetimes, the convective flux etc.) are all determined by the physical conditions inside the stars. We consider this to be a significant advance. We have formulated the equations of fluid dynamics in the potential-flow approximation. A posteriori it is evident that this is advantageous, simply because for a body rapidly expanding from rest it is a good approximation every time the inertia forces are larger than the viscous ones (at least on a time-scale of the order of $\tau \sim \textrm{O}\left( {\frac{{\Delta z}}{{\dot \xi }}} \right)$). This justifies this approximation and the description of the mechanics of the convective elements that follows. We summarise here the major features and the major achievements of our theory. The approach is based on the addition of an equation for the motion of the convective elements to the classical system of algebraic equations for the convective energy transport. The motion of a convective element is described by the vertical displacement of its barycenter and relative expansion (contraction) of its radius, and the inertia of the fluid mass displaced by the convective element is accounted for. Consequently the acceleration imparted to the convective elements in addition to the buoyancy force takes into account effects that in the standard MLT are neglected, i.e. the inertial term of the fluid displaced by the movement and expansion (contraction) of the convective cell, and an extra term arising from the changing size of the convective element (the larger the convective element the stronger is the buoyancy effect and the larger the acquired velocity and vice versa). This results in a new and more complicated term of the acceleration $\propto \frac{{\nabla - {\nabla _e}}}{{\nabla + 2\nabla }} \propto \nabla - {\nabla _e}$, agreeing with the Schwarzschild criterion. It is found that the best reference frame to describe the system is the one comoving with the element. Our treatment of the fluid-dynamics governing the motion of the convective elements allows us to remove any preliminary assumptions about the size and path of the convective elements and these now arise as natural outputs of our theory. No external calibration of parameters is required: the solution of the equations governing stellar convection is unique, in the sense that it is fully determined by physical properties of the medium. This is best shown in our Fig.\ref{Fig4_bis} which represents the numerical and graphical visualization of the Theorem of Uniqueness. The solution of the system we build up behaves asymptotically, so no mixing-length/time is required. It is required only to wait that amount of time for which, within a given layer, the solution becomes stable to the required precision (in our case the yellow strip of Fig.\ref{Fig4_bis}). The whole system of ADEs is further simplified to an algebraic system by decoupling the evolution of the generalized coordinates of the radius and position of a convective element. This result is achieved by means of a series of theorems, corollaries and lemmas that permit the analysis of the different mathematical and physical aspects of the problem, always retaining the necessary rigour to trace progress to the final result. The new theory applied to the external convection in the Sun has been proven to yield results (convective fluxes, temperature gradients $\nabla$ and $\nabla_e$, velocity and size of the convective elements) as good as those that are currently obtained with the standard MLT upon having calibrated the mixing-length parameter. The size and path of a convective element will change with the position inside the convective region, the evolution of the star, i.e. the particular phase under consideration, and finally the stellar mass itself. We have two final comments. First we comment briefly on the reasons why it was necessary to develop the theory in the non-inertial reference frame ${S_1}$ co-moving with the convective element instead of the more natural frame ${S_0}$ co-moving with the star. The flow past a sphere is indeed a well-studied topic of fluid dynamics (too large to be reviewed here!) and recently the Lagrange formalism has become particularly suitable to address this kind of problem: see e.g. \citet[][and references therein]{Tuteja2010} for a recent review and discussion. Unfortunately, this approach does not yield Eq.(\ref{Eq010}) and Eq.(\ref{Eq018}), in the Theorem and companion Corollary discussed in Section \ref{EqcnvQ} which are required to derive the acceleration term in which the properties of the convection element are related to the depth inside the star. To compute the kinetic term of the energy we would require to evaluate the integral $T = \frac{1}{2}\rho \int_{}^{} {\left\| {{{\bm{v}}_0}} \right\|{d^3}{\bm{x}}} $ which for the potential flow of Eq.(\ref{Eq004}) turns out to diverge. This would force us to work at the limit condition $\mathop {\lim }\limits_{\xi \to \infty } {{\bm{v}}_0} = 0$ for Eq.(\ref{Eq005}) and with a suitable potential energy ${E_P} = {E_P}\left( {z,R} \right)$ in the two generalized coordinates $z$ and $R$ as defined above in ${S_0}$. The resulting Lagrange equations under the approximation of Eq.(\ref{Eq011}) reduce to a system of decoupled equations instead of Eq.(\ref{Eq018}) which in contrast retains the desired coupling between the generalized coordinates. At this point the only viable solution is instead to write a Lagrangian for the non-inertial system, and this is indeed what was derived in \citet{2009A&A...499..385P} (their section 3.1), which represents our starting point. Second, we compare the new theory with recent statistical analyses of turbulent convection in stars by \citet[][and references therein]{2014arXiv1401.5176M}. In brief, adopting the so-called Reynolds-Averaged Navier Stokes (RANS) framework in spherical geometry, developed by the authors over the years \citep[e.g.][]{2014arXiv1401.5176M} they present results for convection occurring in the stellar interiors and evolutionary phases of typical stars. These works represent an ideal tool to set up \textit{numerical } experiments of stellar convection (from 1D to 3D models). However an \textit{analytical }approach provides an understanding of the process in a way that a numerical one does not. In a forthcoming study we will present an extended survey of the impact on stellar models and a direct integration of the ADE system composed by Eq.(\ref{Eq056}) with Eq.(\ref{Eq018}) to extend the present formalism and theory to the case of overshooting, where the path travelled by the convective element has specifically to be computed \citep[][in preparation]{Pasetto14}. \begin{appendix} | 14 | 3 | 1403.6122 |
1403 | 1403.6408_arXiv.txt | Observations of protoplanetary disks show that some characteristics seem recurrent, even in star formation regions that are physically distant such as surface mass density profiles varying as $r^{-1}$, or aspect ratios about 0.03 to 0.23. Accretion rates are also recurrently found around $10^{-8} - 10^{-6}~\mathrm{M_{\odot}~yr^{-1}}$ for disks already evolved (\cite{isella09,andrews09,andrews10}). Several models have been developed in order to recover these properties. However, most of them usually simplify the disk geometry if not its mid-plane temperature. This has major consequences for modeling the disk evolution over million years and consequently planet migration. In the present paper, we develop a viscous evolution hydrodynamical numerical code that determines simultaneously the disk photosphere geometry and the mid-plane temperature. We then compare our results of long-term simulations with similar simulations of disks with a constrained geometry along the \cite{chiang97} prescription (dlnH/dlnr = 9/7). We find that the constrained geometry models provide a good approximation of the disk surface density evolution. However, they differ significantly regarding the temperature time evolution. In addition, we find that shadowed regions naturally appear at the transition between viscously dominated and radiation dominated regions that falls in the region of planetary formation. We show that $\chi$ (photosphere height to pressure scale height ratio) cannot be considered as a constant, consistently with \cite{watanabe08}. Comparisons with observations show that all disk naturally evolve toward a shallow surface density disk ($\Sigma \propto r^{-1}$). The mass flux across the disk stabilizes in about 1 million year typically. | \label{intro} Observations of gas-rich circumstellar disks enable to constrain the outer regions of these disks whereas the inner regions remain more cryptic. In particular, the latest observations of the Taurus \citep{isella09} and Ophiuchus \citep{andrews09,andrews10} young stars provided details about the large scale morphology of protoplanetary disks: surface mass densities, temperatures, photosphere heights, accretion rates... Among the recurrent characteristics, \cite{mundy00} and \cite{garaud07} report shallower surface mass density profiles than the usual Minimum Mass Solar Nebula \citep{weiden77, hayashi81}, while measured flaring angles of 0.03 to 0.23 (and up to 0.26 from the \cite{lagage06} VISIR observation of HD97048) may provide additional constraints for the photosphere height of the disks. The accretion rates are also recurrently found around $10^{-8} - 10^{-6}~\mathrm{M_{\odot}~yr^{-1}}$ providing upper values on the age of the disks. The purpose of the present paper is to establish the importance of a realistic protoplanetary disk geometry in order to calculate its thermodynamics and dynamical evolution. Its temperature will actually govern how the disk will spread and therefore its mass distribution. We will thus detail a numerical model for the dynamical and thermodynamical evolution of a disk around a classical T Tauri type star over timescales about the same order of magnitude as the disk lifetime, while taking into account the coupling between the disk photosphere geometry and its temperature profile. Numerous previous studies tried to approach the problem using different approximations. For example, some studies neglect some of the viscous effects: \cite{dullemond01}, \cite{jc04} and \cite{jc08} modeled passive disks while \cite{dalessio98}, \cite{hughes10} and \cite{bitsch12} neglected only the viscous spreading and kept the viscous heating contribution. Other very constraining hypotheses set surface mass density profiles \citep{calvet91} or mid-plane temperature profiles \citep{hughes10}. Neglecting the disk irradiation by the star simplifies also the problem as the viscous heating only depends on the surface mass density and the viscosity, and not on the disk shape. However, this approximation is only valid in the case of a dominating viscous heating \citep{hueso05}. Actually, most observational constraints on the physical properties of the disks are provided by the study of the outer regions, where the viscous heating is negligible compared to the irradiation heating. It is therefore necessary to consider both the viscous heating and the irradiation heating. Numerous studies impose a uniform and constant grazing angle (as in \cite{ciesla09} and \cite{zhu08} using the 0.05 rad value derived by \cite{brauer08}) or assume a photosphere height profile in $r^{9/7}$ \citep{hueso05,birnstiel10} as derived by \cite{chiang97} in the case of a steady state with a surface mass density in $r^{-3/2}$. While these models provide a good knowledge of the outermost regions having reached their steady state, the viscous evolution timescales suggest that such a steady state is maintained only for a short period of time before the disk gets photo-evaporated in a few million years. It is then necessary to focus on the transitory evolution of the disk before it reaches the steady state since it appears that the planet cores will accrete very quickly in the early evolution of the disk. The numerical code we detail in this paper does not rely on any steady state analytical equation and sets free a number of parameters such as the geometric structure by coupling it to the thermodynamical structure on one hand and coupling the thermodynamical evolution to the dynamical evolution on the other hand. Comparisons of the obtained steady state asymptotic behavior with analytical developments and actual observations will provide validation of that code in order to further study the formation of the first solids in future papers: \cite{hasegawa112} showed for example that planetary traps can be generated from irregularities in temperature or density radial distributions. In the present paper, we calculate the disk photosphere and pressure scale heights jointly with its mid-plane temperature at every time step. We can therefore study the transitions between zones dominated by viscous heating and stellar irradiation. Using pre-existing semi-analytical models, we have built a hydrodynamical evolution code that properly includes the disk geometry and eliminates some assumptions and fixed parameters, allowing to derive self-consistently the disk structure. The dynamical and thermodynamical parameters are coupled through the turbulent viscosity that drives the viscous heating and the viscous spreading. We will confront the observational data with our numerical models and show the convergence toward a steady state with a surface-mass density decreasing as $r^{-1}$ independently from the initial density profile. Of course, the present model makes numerous approximations of some of the disk aspects but a special effort has been made for a consistent coupling of the dynamical and thermodynamical evolutions. We present the physical model and the numerical code in Section \ref{methods}. We apply our numerical evolution to a standard protoplanetary disk model, the Minimum Mass Solar Nebula (MMSN) from \cite{weiden77} around a typical T Tauri type star in Section \ref{mmsn} and the sensitivity to the initial conditions in Section \ref{ini}. We discuss the importance of calculating self-consistently the geometric structure of the disk in Section \ref{geo}. We then compare our simulated disks to analytical asymptotic solutions on one hand and observations from \cite{isella09}, \cite{andrews09} and \cite{andrews10} on the other before discussing the consequences on the disk properties in Section \ref{obs}. | Using a 1D viscous hydrodynamical code of disk viscous evolution coupled with a thermodynamical model of viscous and radiative heating, we have studied the evolution of a protoplanetary disk around a T Tauri type star. Special care was given to enforcing a consistency between the photosphere geometry and the disk thermal structure. Applying this code to a disk surrounding a young solar type star, we were able to retrieve the main characteristics of observed protoplanetary disks as reported in \cite{andrews09} and \cite{isella09}, thus validating our numerical code for further developments. We were able to characterize the steady state that appears in a few million years and retrieve its properties: a radially uniform mass flux with values matching the observed mass accretion rates. This steady state is observed despite a wide range of initial conditions and systematically tends to a surface-mass density profile varying as $r^{-1}$, no matter the initial power-law index of the density distribution. This power-law index is reached in a time that can be compared to the disk lifetime between 10 and 100 AU and in a few million years beyond 100 AU. This slower evolution in the outer regions may actually allow to trace the initial conditions as they are relaxed much later at the outer edge. Another important result is that the disk is not always fully irradiated: shadowing can occur in the transition zone. However, after a few 100,000 years of evolution, the disk is fully irradiated, leading to a photosphere profile varying as $r^{1.1}$. This asymptotic state is a consequence of the balance between energy input due to stellar irradiation and energy loss due to viscous dissipation, resulting in a simple relation between the temperature and surface mass density power-law index (see Equation \ref{steady2}). This work also focused on the differences with the simple geometric models inherited from \cite{chiang97}. This geometry in $H_{photo} \propto r^{9/7}$ is actually a reliable approximation if one only focuses on the evolution of the surface mass density on a large scale. However, when interested in smaller structures, we must investigate the local geometry: we showed the importance of calculating self-consistently the geometry of the disk in agreement with its temperature. We also invalidated the approximation of a constant and uniform ratio of photosphere to pressure scale height. While investigating the possibility to form the first solids in a protoplanetary disk, it is important to have a realistic model for the disk geometry as it will drive the temperature and surface mass density evolution. Indeed, shadowing or changes of state might create irregularities in temperature or density that are thought to be a favorable terrain to generate outward migration and therefore make planetary traps \citep{hasegawa112}. While this study validates the detailed numerical code, we now have a precious tool to explore a huge variety of initial conditions and configurations: it is necessary to explore the stellar diversity in order to reproduce these observations individually. Our numerical model may also be improved in its physics by taking into account the feeding of the disk by the collapse of the molecular cloud for instance \citep{yang12}, improving the disk chemistry \citep{tscharnuter07}, or its dissipation by the photo-evaporation \citep{font04, alexander07, alexander09, owen10}. The internal structure may also be refined by considering the variations of the opacities with the temperature, implementing shadowing effects and variable opacities \citep{bitsch12}, or using a better Magneto-Rotational Instability model in order to add variations of the turbulent viscosity parameter and define dead-zones \citep{charnoz12,zhu101}. The stellar model may also be improved by inputing the young Sun evolution from \cite{piau11}. Understanding how the disk scales with the protostar will certainly help targeting future ALMA and JWST observations. | 14 | 3 | 1403.6408 |
1403 | 1403.3531_arXiv.txt | {} {To observe molecular absorption from diffuse clouds across 3mm receiver band.} {We used the EMIR receiver and FTS spectrometer at the IRAM 30m telescope to construct absorption spectra toward bright extra-galactic background sources at 195 kHz spectral resolution ($\approx$ 0.6 \kms). We used the IRAM Plateau de Bure interferometer to synthesize absorption spectra of \hthcop\ and HCO toward the galactic HII region W49.} {HCO, \cc3h\ and CF\p\ were detected toward the blazars \bll\ and 3C111 having \EBV\ = 0.32 and 1.65 mag. HCO was observed in absorption from ``spiral-arm'' clouds in the galactic plane occulting W49. The complement of detectable molecular species in the 85 - 110 GHz absorption spectrum of diffuse/translucent gas is now fully determined at rms noise level $\delta_\tau \approx 0.002$ at \EBV\ = 0.32 mag (\AV\ = 1 mag) and $\delta_\tau$/\EBV\ $\approx\ 0.003$ mag$^{-1}$ overall. } {As with OH, \hcop\ and \cch, the relative abundance of \cc3h\ varies little between diffuse and dense molecular gas, with N(\cc3h)/N({\it o-c}-\c3h2) $\approx$ 0.1. We find N(CF\p)/N(H$^{13}$CO\p) $\approx 5$, N(CF\p)/N(\cch) $\approx$ 0.005-0.01 and because N(CF\p) increases with \EBV\ and with the column densities of other molecules we infer that fluorine remains in the gas phase as HF well beyond \AV\ = 1 mag. We find N(HCO)/N(H$^{13}$CO\p) = 16 toward \bll, 3C111 and the 40 km/s spiral arm cloud toward W49, implying X(HCO) $\approx 10^{-9}$, about 10 times higher than in dark clouds. The behaviour of HCO is consistent with previous suggestions that it forms from C\p\ and \HH, even when \AV\ is well above 1 mag. The survey can be used to place useful upper limits on some species, for instance N(\hhco)/N(\HH CS) $>$ 32 toward 3C111, compared to 7 toward TMC-1, confirming the possibility of a gas phase formation route to \hhco. In general, however, the hunt for new species will probably be more fruitful at cm- and sub-mm wavelengths for the near future. } | Microwave and sub-mm absorption-line spectroscopy have greatly extended the inventory of molecules known to exist in diffuse molecular interstellar clouds, that is, clouds with appreciable \HH\ content but \AV $\la 1$ mag. Just in the past few years, sub-mm observations from the PRISMAS project using the HIFI instrument on HERSCHEL, from the APEX telescope in the Atacama and the GREAT instrument on SOFIA have more than doubled the number of known species following observation of the hydrides and hydride ions of oxygen, nitrogen, sulfur, fluorine and chlorine \citep{GerLev+12,NeuFal+12}. Sub-mm observations of the familiar species CH \citep{GerdeL+10} and \chp\ \citep{FalGod+10,GodFal+12} have allowed these species, previously seen only in the optical absorption spectra of relatively nearby stars, to be tracked across the disk of the Milky Way. Even so, the search for new molecules and the overall effort to systematize the diffuse cloud chemistry have been seriously hindered by the narrow bandwidths that were available for high sensitivity observations of heavier polyatomic species in the microwave (cm-wave and mm-wave) domain. This impediment is gradually being overcome by new technology such as the WIDAR correlator at the Karl Guthe Jansky VLA that we used to detect {\it l}-\c3h2\ and survey the abundance of several small hydrocarbons \citep{LisSon+12}. An even larger development is the advent of the very wide-band EMIR receivers at the IRAM 30m Telescope on Pico de Veleta, which produced the recent 1-3 mm WHISPER surveys of emission from the Horsehead nebula \citep{GuzRou+12,PetGra+12,GraPet+13}. Here we describe a 3mm band survey of absorption from the galactic diffuse and translucent clouds seen toward the mm-bright blazars \bll\ (\EBV\ = 0.32 mag) and 3C111 (\EBV\ = 1.65 mag). As a result of this work the mm-wave absorption spectrum is now known at a detection level of 1\% absorption or better over the 3mm band and this paper reports the detection of three new species HCO, \cc3h\ and CF\p, toward both objects. \begin{figure} \includegraphics[height=15.5cm]{SweepF1.eps} \caption[]{Properties of the spectral sweep. Top: Line profile integrals (equivalent widths) for the spectral sweep plotted against those previously obtained by synthesis at the Plateau de Bure Interferometer in our prior work. Bottom: 8-channel running mean channel-channel rms in the line/continuum ratio at 0-absorption for 3C111 and \bll. The points labelled SO in the upper panel represent the 3$_2$-2$_1$ line at 99.3 GHz as discussed in Sect 2.1 of the text. } \end{figure} The plan of this work is as follows. The observations are described in Sect. 2. In Sections 3-5 we discuss the detection and chemistry of HCO, \cc3h\ and CF\p, respectively. Section 6 is the briefest of summaries. | We surveyed the 84 - 116 GHz 3mm spectrum in absorption against the compact extragalactic mm-continuum sources \bll\ and 3C111 as noted in Table 1 at 195 kHz spectral resolution (0.6 \kms\ at 100 GHz), achieving an rms noise level $\delta_\tau \approx 0.002$ at \EBV\ = 0.32 mag (\AV\ = 1 mag) toward \bll\ and $\delta_\tau$/\EBV\ $\approx\ 0.003$ mag$^{-1}$ overall. HCO, \cc3h\ and CF\p\ were detected in absorption toward both sources and HCO was also found in the diffuse ``spiral-arm'' clouds in the galactic plane in front of W49. We discussed observational aspects of their chemistry in Sections 3-5. \cc3h\ is notable for having a nearly fixed abundance with respect to \hcop, \cch\ and c-\c3h2\ over a wide range of column density, even across the divide between the diffuse and dark or giant molecular clouds. The increase in N(CF\p) beyond \AV\ = 1 mag shows that both fluorine and C\p\ are abundant in the gas phase at such extinctions but conclusions about the depletion of fluorine are sensitive to assumptions about the temperature profile. The relative abundance ratio N(HCO)/N(\HH) is higher in diffuse than dark or dense molecular gas, consistent with its prior interpretation as a species requiring both C\p\ and \HH\ for its formation via the reaction O + C\HH\ $\rightarrow$ HCO + H. No other new species are present in the spectra toward \bll\ (\AV = 1 mag) at a 5-sigma optical depth limit of 0.01 in any single feature, suggesting that the hunt for new species in diffuse clouds in the radio domain will be most profitably conducted in the cm-wave region below 30 GHz where the more heavily-populated lower-lying energy levels of heavier polyatomic molecules are most readily accessible. \begin{figure} \includegraphics[height=7cm]{SweepF7.eps} \caption[]{CF\p\ spectra toward \bll\ (upper) and 3C111 (lower). The velocity axis corresponds to the mean LTE intensity-weighted centroid of the two hyperfine components noted in Table 4. Shown for comparison are scaled spectra of the 18.3 GHz transition of c-\c3h2\ from \cite{LisSon+12}. For spectroscopic data, see Table 4.} \end{figure} \begin{figure} \includegraphics[height=6.6cm]{SweepF8.eps} \caption[]{Column density of CF\p\ vs. \hthcop\ (at left) and \cch\ (right). Data for the Horsehead nebula (TdC) are from \cite{GuzPet+12}. The prediction N(CF\p) $\approx 4.5 \times 10^{11}\pcc$ at \AV\ $\ga$ 1 mag of \cite{NeuWol09} is shown as a blue dashed horizontal line. The power law slopes of the best-fit lines (0.59, 0.38) are noted.} \end{figure} \begin{table} \caption[]{CF\p\ transitions observed and column density-optical depth conversions$^a$} { \small \begin{tabular}{lcccc} \hline Frequency &F$^\prime$ - F & J$^\prime$ - J & \AF & N(X)/$\int\tau dv^b $ \\ MHz & & & 10$^{-6}$\ps & $\pcc (\kms)^{-1}$ \\ \hline 102587.189 & 1/2-1/2 & 1-0 & 4.82 & $4.04\times10^{13} $ \\ 102587.533 & 3/2-1/2 & 1-0 & 4.82 & $2.02\times10^{13} $ \\ \hline \end{tabular}} \\ $^a$ Spectroscopic data from \cite{GuzRou+12} and {\tt www.splatalogue.net}\\ $^b$ Assuming excitation in equilibrium with the cosmic microwave background \\ \end{table} \begin{appendix} | 14 | 3 | 1403.3531 |
1403 | 1403.6314_arXiv.txt | All articles {\it must} contain an abstract. This document describes the preparation of a conference paper to be published in \jpcs\ using \LaTeXe\ and the \cls\ class file. The abstract text should be formatted using 10 point font and indented 25 mm from the left margin. Leave 10 mm space after the abstract before you begin the main text of your article. The text of your article should start on the same page as the abstract. The abstract follows the addresses and should give readers concise information about the content of the article and indicate the main results obtained and conclusions drawn. As the abstract is not part of the text it should be complete in itself; no table numbers, figure numbers, references or displayed mathematical expressions should be included. It should be suitable for direct inclusion in abstracting services and should not normally exceed 200 words. The abstract should generally be restricted to a single paragraph. Since contemporary information-retrieval systems rely heavily on the content of titles and abstracts to identify relevant articles in literature searches, great care should be taken in constructing both. " followed by the text of the abstract. The abstract should normally be restricted to a single paragraph and is terminated by the command \verb" The abstract appears here. | These guidelines show how to prepare articles for publication in \jpcs\ using \LaTeX\ so they can be published quickly and accurately. Articles will be refereed by the \corg s but the accepted PDF will be published with no editing, proofreading or changes to layout. It is, therefore, the author's responsibility to ensure that the content and layout are correct. This document has been prepared using \cls\ so serves as a sample document. The class file and accompanying documentation are available from \verb"http://jpcs.iop.org". The text of the article should should be produced using standard \LaTeX\ formatting. Articles may be divided into sections and subsections, but the length limit provided by the \corg\ should be adhered to. \subsection{Acknowledgments} Authors wishing to acknowledge assistance or encouragement from colleagues, special work by technical staff or financial support from organizations should do so in an unnumbered Acknowledgments section immediately following the last numbered section of the paper. The command \verb"\ack" sets the acknowledgments heading as an unnumbered section. \subsection{Appendices} Technical detail that it is necessary to include, but that interrupts the flow of the article, may be consigned to an appendix. Any appendices should be included at the end of the main text of the paper, after the acknowledgments section (if any) but before the reference list. If there are two or more appendices they will be called Appendix A, Appendix B, etc. Numbered equations will be in the form (A.1), (A.2), etc, figures will appear as figure A1, figure B1, etc and tables as table A1, table B1, etc. The command \verb"\appendix" is used to signify the start of the appendixes. Thereafter \verb"\section", \verb"\subsection", etc, will give headings appropriate for an appendix. To obtain a simple heading of `Appendix' use the code \verb"\section*{Appendix}". If it contains numbered equations, figures or tables the command \verb"\appendix" should precede it and \verb"\setcounter{section}{1}" must follow it. | 14 | 3 | 1403.6314 |
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1403 | 1403.3477_arXiv.txt | We describe a new paradigm for understanding both relativistic motions and particle acceleration in the M87 jet: a magnetically dominated relativistic flow that naturally produces four relativistic magnetohydrodynamic (MHD) shocks (forward/reverse fast and slow modes). We apply this model to a set of optical super- and subluminal motions discovered by Biretta and coworkers with the {\em Hubble Space Telescope} during 1994 -- 1998. The model concept consists of ejection of a {\em single} relativistic Poynting jet, which possesses a coherent helical (poloidal + toroidal) magnetic component, at the remarkably flaring point HST-1. We are able to reproduce quantitatively proper motions of components seen in the {\em optical} observations of HST-1 with the same model we used previously to describe similar features in radio VLBI observations in 2005 -- 2006. This indicates that the quad relativistic MHD shock model can be applied generally to recurring pairs of super/subluminal knots ejected from the upstream edge of the HST-1 complex as observed from radio to optical wavelengths, with forward/reverse fast-mode MHD shocks then responsible for observed moving features. Moreover, we identify such intrinsic properties as the shock compression ratio, degree of magnetization, and magnetic obliquity and show that they are suitable to mediate diffusive shock acceleration of relativistic particles via the first-order Fermi process. We suggest that relativistic MHD shocks in Poynting-flux dominated helical jets may play a role in explaining observed emission and proper motions in many AGNs. | \label{sec:int} In this paper we apply our previous relativistic MHD shock model for the 2005 M87 radio jet \citep[hereafter Paper I]{N10} to the {\em optical} super/subluminal knots discovered by \citet[]{B99} using the {\em Hubble Space Telescope} ({\em HST}) at five epochs between 1994 and 1998. These observations reveal superluminal features in the range $5c$ -- $6c$ with some subluminal components located around 0$\farcs$8--1.6$\arcsec$ (projected) from the core (or $\sim260$ -- 520 pc de-projected for a viewing angle of $\sim 14^{\circ}$; Wang \& Zhou 2009). This region has been named as the ``HST-1'' complex. So far HST-1 is one of the most energetic elements of the M87 jet, exhibiting both fast and slow (super/subluminal) motions as well as the birth of new components and the fading of older ones \citep[]{B99, C07}. The global structure of the jet is characterized as a parabolic stream on the sub-arcsecond scale, which changes into a conical stream beyond one arcsecond; HST-1 is indeed the narrow ``neck'' in the jet, indicating an over-collimated focal point (or ``recollimation shock'') \citep[]{AN12, NA13}. Multi-band light curves of HST-1 reveal an impulsive flare event that had a peak in 2005 \citep[]{H06, C07, M09}. As reported in \citet[]{C07}, between 2005 December and 2006 February, the component HST-1c, which had been ejected during 2004 -- 2005 from HST-1d (the upstream edge in the HST-1 complex), {\em split into two bright features}: a faster moving component (c1: $4.3c \pm 0.7c$) and a slower moving one (c2: $0.47c \pm 0.39c$). The ejection of these components is believed to be associated with the HST-1 flare occurring in 2005. The simultaneous rise and fall of light curves at all wavelengths (radio, optical, NUV, and X-ray bands) indicate that the flare was a local event caused by a simple compression at HST-1 \citep[]{H06, H09}, which created an increase of the synchrotron particle energy at all wavelengths equally and a fractional polarization in the optical band at a level from 20\% to 40\% \citep[]{P11}. Furthermore, the very high energy (VHE) $\gamma$-ray emission in the TeV band that occurred in 2005 \citep[]{A06} may be associated with contemporaneous radio-to-X-ray flaring of HST-1, while the nucleus itself was in a {\em quiescent} phase from radio to X-ray bands during the $\gamma$-ray flare event \citep[]{A12}. The VLBA monitoring at 22/43 GHz of EGRET blazars has established a statistical association that $\gamma$-ray flares at high levels occur shortly after ejections of new superluminal components of parsec-scale jets in nearby VLBI cores \citep[]{J01}. Thus, we suggest that the VHE flare associated with the superluminal knot ejection in M87 is intrinsically similar to events seen in other blazars. Paper I proposed a model to explain the ejected super/subluminal VLBA knots from HST-1d in 2005 -- 2006 \citep[]{C07} as a pair of forward/reverse fast-mode MHD shocks in a strongly magnetized relativistic flow that possesses an ordered helical field component. A simple test of this model would be to find another appropriate candidate quad shock complex in the M87 jet. Here, we seek it in the earlier HST observations of 1994 -- 1998 \citep[]{B99}, and we suggest that HST-1$\epsilon$ ($6.00c \pm 0.48c$) / HST-1 East ($0.84c \pm 0.11c$) in their observations are a similar pair to HST-1c2/c1. With several moderate changes in model parameters, we then reproduce the component motions with our quad MHD shock model and show that the shock conditions there are ideal for particle acceleration. This paper is organized as follows. In \S 2, we outline the numerical model. In \S 3, we describe our numerical results. Discussions and conclusions are given in \S 4. | \label{sec:Dis-Con} The basic assumption of our model posits ejection of a {\em single} relativistic jet, which naturally produces four MHD shocks, from a stationary feature (standing over-collimation Mach disk / oblique shock system) in compact radio sources that produce a pair of super/subluminal knots. In M87, we believe that the HST-1 complex is the place where these events occur \citep[]{B99,C07}. Very recently, \citet[]{G12} reported two superluminal components ejected from HST-1 after 2007 (component 2 in 2008 and component 3 in 2010). In their analysis, component 2 is identified as being similar to HST-1c (seen in \citet[]{C07}); it eventually splits into two sub-components, although the authors argue that the slow sub-component may be an underlying, standing or very slowly moving feature (a detailed proper motion analysis was not conducted for this sub-component). {\em However}, we suggest that component 2 may represent the ejection of a third quad relativistic shock system in the M87 jet, which possesses both sub- (reverse) and superluminal (forward) features. \citet[]{G12} also pointed out simultaneous timings between the superluminal component ejections and VHE flares in 2008 and 2010 \citep[]{A12}, suggesting that structural changes at the upstream edge of HST-1 are related to these flares. Very recently, \citet[]{M13} studied proper motions of the M87 jet on arcsecond (kiloparsec) scales by using more than a decade of {\em HST} archival imaging. Significant new apparent motions $\gtrsim c$ have been found at the knot A/B/C complex. Furthermore, knots C and A move in opposite directions {\em transverse} to the jet axis with $V \gtrsim 0.1c$ in projection. This may indicate a counter-rotational motion around the jet axis as expected for a pair of fast-mode shocks (FF/RF) in an older (and now much larger) quad MHD shock system. (Such motions occur in our current simulation of the much smaller HST-1 complex, as seen in (d) of Fig. \ref{fig: f1} and also in Paper I.) Overall velocity profiles along the jet axis, as well as transverse to that axis, may be explained as embedded flow trajectories within systematic helical magnetic fields \citep[]{M13}. Velocity components that lie upstream of knot A are observed to still have highly relativistic, and thus one-sided (i.e., {\em negative}), transverse motions (Doppler boosted towards us). Once the jet becomes mildly relativistic, however, we are able to track the full (i.e., both {\em positive} and {\em negative}) transverse motions of the helical pattern in projection. Furthermore, there is a conspicuous ``tip-to-tail'' alignment of almost all the velocity vectors within the knot A/B/C complex, strongly suggesting a flattened view of a helical motion which might result in such a ``zig-zag'' pattern. In the framework of a quad MHD shock system, a pair of fast-mode shocks (FF/RF), corresponding to the knots C/A, may be responsible for driving the helical distortion near the postshock region of B via the current-driven helical kink ($m=1$) instability \citep[]{NM04}. Thus, we propose that the region A/B/C may be a good example (on the kiloparsec scale) of the interplay between the MHD shocks and current-driven instability, where the magnetic field plays a fundamental role in the M87 jet dynamics, as originally suggested in Paper I. It is widely believed that moving shocks in jets (``shock-in-jet'' model) are responsible for the synchrotron emission in blazars \citep[{\em e.g.},][]{BK79, M80}. A subset of the preceding, superluminal (forward shock) and the following, stationary/subluminal (reverse shock) features are frequently seen in VLBI observations \citep[]{J05, L09}. Among shock-in-jet models, the following two major scenarios have been discussed in a non-MHD framework: (1) a collision of the faster shock with either the preceding slowly moving shock \citep[''internal shock'' model: {\em e.g.},][]{S01} or (2) a standing shock complex \citep[{\em e.g.},][]{DM88, S04}. Note that both forward and reverse sonic shocks are expected in these models. An extension of the internal shock model with a perpendicular MHD forward/reverse shocks has been performed by \citet[]{M07}. As mentioned in \S \ref{sec:int}, strong $\gamma$-ray flares occur after ejections of new superluminal components from parsec-scale regions of jets in nearby VLBI cores \citep[]{J01}. Instead of an internal shock scenario, we suggest here that there is a {\em standing} shock at HST-1 based on the observational aspects. Furthermore, because of the strong polarization associated with the knots in M87, as well as the superluminal motion, we must model these shocks using special relativistic magnetohydrodynamic simulations. In this paper, we investigate a pair of super/subluminal motions in the M87 jet based on the quad relativistic MHD shock model \citep[]{N10}. The model concept consists of ejection at HST-1 of a {\em single} relativistic Poynting jet, which possesses a coherent helical (poloidal + toroidal) magnetic component that naturally produces such features, as a counterpart to the hydrodynamic Mach disk - oblique shock system. HST-1$\epsilon$/East, which were identified in HST observations \citep[]{B99}, are modeled quantitatively with one-dimensional axisymmetric SRMHD simulations. We conclude that forward/reverse fast-mode MHD shocks are a promising explanation for the observed features, not only with regard to their intrinsic motions, but also in the efficiency of the diffusive shock acceleration (through the first-order Fermi process) of non-thermal particle accelerations at the shock fronts. Three fundamentals at the fast-mode MHD shocks derived from the simulations (shock compression ratio, degree of magnetization, and magnetic obliquity (magnetic pitch angle)) are suitable to mediate a Fermi-I process. While we do not yet fully investigate the hypothesis that ``all relativistic jets are dominated by the toroidal magnetic field component in the observer's frame'', $B_{\phi}/B_{z} \sim \gamma$ \citep[]{LPG05} certainly holds in the interknot (intershock) region of the M87 jet as we found ($B_{\phi}/\gamma/B_{z} \sim 1$ in the fluid frame). Therefore, we suggest our model may be applicable to many super/subluminal features of AGN jets in general. M.N. acknowledges part of this research was carried out under supported by the Allan C. Davis fellowship jointly awarded by the Department of Physics and Astronomy at Johns Hopkins University and the Space Telescope Science Institute. Part of this research also was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. | 14 | 3 | 1403.3477 |
1403 | 1403.1644_arXiv.txt | The cosmic age is an important physical quantity in cosmology. Based on the radiometric method, a reliable lower limit of the cosmic age is derived to be $15.68\pm 1.95$ Gyr by using the $r$-process abundances inferred for the solar system and observations in metal-poor stars. This value is larger than the latest cosmic age $13.813\pm 0.058$ Gyr from Planck 2013 results, while they still agree with each other within the uncertainties. The uncertainty of $1.95$ Gyr mainly originates from the error on thorium abundance observed in metal-poor star CS 22892-052, so future high-precision abundance observations on CS 22892-052 are needed to understand this age deviation. | 14 | 3 | 1403.1644 |
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1403 | 1403.5298_arXiv.txt | Three Luminous Blue Variables (LBVs) are located in and near the Quintuplet Cluster at the Galactic Center: the Pistol star, G0.120-0.048, and qF362. We present imaging at 19, 25, 31, and 37 $\mu$m of the region containing these three LBVs, obtained with SOFIA using FORCAST. We argue that the Pistol and G0.120-0.048 are identical ``twins" that exhibit contrasting nebulae due to the external influence of their different environments. Our images reveal the asymmetric, compressed shell of hot dust surrounding the Pistol Star and provide the first detection of the thermal emission from the symmetric, hot dust envelope surrounding G0.120-0.048. However, no detection of hot dust associated with qF362 is made. Dust and gas composing the Pistol nebula are primarily heated and ionized by the nearby Quintuplet Cluster stars. The northern region of the Pistol nebula is decelerated due to the interaction with the high-velocity (2000 km/s) winds from adjacent Wolf-Rayet Carbon (WC) stars. From fits to the spectral energy distribution (SED) of the Pistol nebula with the DustEM code we determine that the Pistol nebula is composed of a distribution of very small, transiently-heated grains ($10-\sim35$ $\AA$) having a total dust mass of $0.03$ $M_\odot$, and that it exhibits a gradient of decreasing grain size from the south to the north due to differential sputtering by the winds from the WC stars. The total IR luminosity of the Pistol nebula is $5.2\times10^5\,L_\odot$. Dust in the G0.120-0.048 nebula is primarily heated by the central star; however, the nebular gas is ionized externally by the Arches Cluster. Unlike the Pistol nebula, the G0.120-0.048 nebula is freely expanding into the surrounding medium. A grain size distribution identical to that of the non-sputtered region of the Pistol nebula satisfies the constraints placed on the G0.120-0.048 nebula from DustEM model fits to its SED and implies a total dust mass of $0.021$ $M_\odot$. The total IR luminosity of the G0.120-0.048 nebula is $\sim10^5\,L_\odot$. From Paschen-$\alpha$ and 6 cm observations we determine a total gas mass of 9.3 $M_\odot$ and 6.2 $M_\odot$ for the Pistol and G0.120-0.048 nebulae, respectively. Given the independent dust and gas mass estimates we find that the Pistol and G0.120-0.048 nebulae exhibit similar gas-to-dust mass ratios of $310^{+77}_{-52}$ and $293^{+73}_{-101}$, respectively. Both nebulae share identical size scales ($\sim 0.7$ pc) which suggests that they have similar dynamical timescales of $\sim10^4$ yrs, assuming a shell expansion velocity of $v_\mathrm{exp}=60$ km/s. | Stars classified as Luminous Blue Variables (LBVs) exist in a very brief ($<10^5$ yrs) and extreme evolutionary phase nearing the end of their lifetimes. Given the brevity of their lifetimes, LBVs are extremely rare and only $\sim10$ have been confirmed within the Milky Way (Clark et al. 2005). Of the known Galactic LBVs, only a few have been found to be associated with their birth-cluster (Pasquali et al. 2006). Remarkably, three LBVs are located in the vicinity of the "Quintuplet" Cluster in the Galactic Center, a site of recent massive star formation (Mauerhan et al. 2010; Figer, McLean \& Morris 1999). The Quintuplet Cluster also hosts several Wolf-Rayet and dozens of O and B stars, all of which are believed to have formed coevally (Figer, McLean \& Morris 1999). Since LBVs are thought to be the intermediate link between massive O stars and Wolf-Rayet stars (Langer et al. 1994), studying these three LBVs in the context of the Quintuplet Cluster provides unique insight into the evolution of massive stars. The three LBVs in the $3' \times 3'$ vicinity of the Quintuplet Cluster are qF362 (Figer, McLean \& Morris 1999; Geballe et al. 2000), the Pistol Star (Figer et al. 1998), and G0.120-0.048 (Mauerhan et al. 2010) (hereafter referred to as LBV3). Although these LBVs exhibit similar luminosities ($\sim10^6\,L_\odot$) and wind velocities ($\sim 100$ km/s) the nature of their outflows varies drastically. LBVs are typically surrounded by nebulae composed of material from their outflows (Nota et al. 1995); however, qF362 exhibits no observable nebular emission from gas or dust whereas the Pistol Star and LBV3 have surrounding shells of gas and dust (Yusef-Zadeh \& Morris 1987; Figer et al. 1999b; Mauerhan et al. 2010). The morphology and flux observed from the ionized gas emission in the nebulae surrounding the Pistol Star and LBV3 are notably dissimilar: the Pistol nebula appears compressed and asymmetric about the Pistol Star and shows strong emission from ionized gas at its northern edge while the LBV3 nebula is circularly symmetric about LBV3 and appears to have a uniform emission measure (Mauerhan et al. 2010). From Paschen-$\alpha$ observations, Figer et al. (1999) argue that the preferential ionization of the Pistol nebula is due to the proximity of the hot O and B stars of the Quintuplet Cluster located to the north of the nebula, and that the Pistol Star itself contributes less than $8\%$ of the total ionizing flux to the nebula. The compression of the Pistol nebula at the northern edge and the northern displacement of the Pistol Star from the center of the nebula are attributed to the interaction with the winds of the Wolf-Rayet Carbon (WC) stars in the Quintuplet Cluster. Figer et al. (1999) also confirm from radial velocity observations of the Pistol nebula that it was formed from material in the outflows from the Pistol star. LBV3 and its nebula are located approximately $\sim2.8'$ south-west of the Pistol Star and the Quintuplet Cluster. The LBV3 nebula was recently discovered by Mauerhan et al. (2010) from the HST/NICMOS Paschen-$\alpha$ survey of the Galactic Center (Dong et al. 2011; Wang et al. 2010). K-band spectroscopy of LBV3 revealed its spectral similarities to the Pistol Star and qF362 and confirmed its nature as a true LBV. The spherical symmetry and uniform ionization of the LBV3 nebula strongly suggests that it is composed of material from its outflow. Like the Pistol nebula, LBV3 does not produce enough Lyman-continuum photons to ionize the nebula and is likely externally ionized primarily by the hot stars in the Arches Cluster. Although the LBV3 and Pistol nebulae exhibit different morphologies and fluxes in Paschen-$\alpha$ emission their near-identical size scale (r$\sim200''$) and wind velocities indicate that their nebular ages are very similar ($\sim10^4$ yrs). The thermal infrared dust emission from the Pistol and LBV3 nebulae provide important insight into the differences and similarities between the two sources. From observations with ISOCAM-CVF Moneti et al. (1999) first characterized the thermal mid-IR emission from the dust composing the Pistol nebula. The dust in the Pistol nebula appeared much more uniformly illuminated than the ionized gas; it more closely resembles a compressed sphere than the shape of a ``pistol." Spitzer/IRAC 8 $\mu$m observations of the Pistol nebula (Stolovy et al. 2006) revealed a morphology identical to that found by Moneti et al. (1999). In the case of LBV3, no detection was made of the nebular dust component with Spitzer/IRAC (and no observations were made with ISOCAM-CVF). This non-detection of the dust in the LBV3 nebula at 8 $\mu$m presents an interesting dichotomy in the dust properties of the two LBV nebulae in this region. Coupled with the absence of any form of nebular emission from qF362, the differences between the two LBV nebulae can be attributed to the impact of the influence of the hot Quintuplet Cluster stars and/or differences in the local ambient medium. In this paper we present 19.7, 25.2, 31.5, and 37.1 $\mu$m observations tracing the warm dust emission of the Pistol nebula and the first detection of the warm dust emission of the LBV3 nebula taken by FORCAST aboard the Stratospheric Observatory for Infrared Astronomy (SOFIA). We compare and contrast the dust properties, morphology, and energetics of the nebulae and address the cause of the apparent differences between the three LBVs in this $3' \times 3'$ region of the Galactic Center. | We have presented imaging of the Pistol and LBV3 nebulae at 19.7, 25.2, 31.5, and 37.1 $\mu$m, tracing the warm dust emission. Our conclusions on the properties and evolution of the LBV3 and Pistol nebulae are summarized in Tab.~\ref{tab:CC}. The analysis suggests that both nebulae formed under very similar stellar conditions; however, the differences in their surrounding environments have differentiated their morphologies. Due to its proximity to the Quintuplet Cluster, the dust in the Pistol nebula is luminous, compressed, and externally heated while the dust in the LBV3 nebula is dim, symmetric, and centrally heated. Interestingly, the gas in the LBV3 nebula is externally ionized by the Arches Cluster and possibly the Quintuplet Cluster, while the gas in the Pistol nebula is externally ionized by the Quintuplet Cluster. Both nebulae share identical size scales, gas-to-dust mass ratios, as well as total gas masses. We hypothesize that the Pistol nebula is composed of a population of very small, transiently-heated grains that are preferentially sputtered at the northern region of the nebula where it is colliding with the high-velocity winds from the nearby WC stars. Although the grain composition is not as well determined for the LBV3 nebula as for the Pistol, we find that the non-sputtered southern grain distribution of the Pistol appears to resemble that of LBV3, and thereby supports our interpretation of LBV3 as a twin of the Pistol nebula. The non-detection of any emission surrounding qF362 in any the FORCAST wavebands suggests that it is the only one of the three LBVs in the region to not have undergone a dust-forming outburst phase. Any dust that might have been produced by qF362 in sufficient quantities to enshroud the star would have easily been observed by either FORCAST or IRAC. \emph | 14 | 3 | 1403.5298 |
1403 | 1403.5067_arXiv.txt | {We present a generic inference method for inflation models from observational data by the usage of higher-order statistics of the curvature perturbation on uniform density hypersurfaces. This method is based on the calculation of the posterior for the primordial non-Gaussianity parameters $f_\text{NL}$ and $g_\text{NL}$, which in general depend on specific parameters of inflation and reheating models, and enables to discriminate among the still viable inflation models. To keep analyticity as far as possible to dispense with numerically expensive sampling techniques a saddle-point approximation is introduced, whose precision is validated for a numerical toy example. The mathematical formulation is done in a generic way so that the approach remains applicable to cosmic microwave background data as well as to large scale structure data. Additionally, we review a few currently interesting inflation models and present numerical toy examples thereof in two and three dimensions to demonstrate the efficiency of the higher-order statistics method. A second quantity of interest is the primordial power spectrum. Here, we present two Bayesian methods to infer it from observational data, the so called critical filter and an extension thereof with smoothness prior, both allowing for a non-parametric spectrum reconstruction. These methods are able to reconstruct the spectra of the observed perturbations and the primordial ones of curvature perturbation even in case of non-Gaussianity and partial sky coverage. We argue that observables like $T-$ and $B-$modes permit to measure both spectra. This also allows to infer the level of non-Gaussianity generated since inflation.} | \subsection{Motivation} By precision measurements of the cosmic microwave background (CMB) \cite{2012arXiv1212.5225B,2013arXiv1303.5076P} it has become possible to determine the exact statistics of its temperature anisotropies. These anisotropies are strongly connected to the curvature perturbations on uniform density hypersurfaces $\zeta$, predicted by inflationary models, with the result that the zoo of models can be constrained by exploiting observational data, e.g., by the usage of Gaussian statistics \cite{2006JCAP...08..009M,2013arXiv1303.3787M,2013arXiv1312.2347R,2013arXiv1312.3529M,2013arXiv1303.5082P}. The viable models that are compatible with current \textit{Planck} constraints on primordial non-Gaussianity, often represented by the $f_\text{NL}$ parameter, are given by $-3.1 \leq f_\text{NL} \leq 8.5~(68\%$C.L. statistical$)$ \cite{2013arXiv1303.5084P} for the local type of non-Gaussianity. In particular, a value of $|f_\text{NL}|\propto \mathcal{O}(1)$ is in agreement with the data. Such a low value of non-Gaussianity opens the possibility to include the effect of primordial non-Gaussianity when performing routine cosmological parameter estimates in order to maximally exploit the data, since it permits approximations which prevent the computations from becoming numerically too expensive. The contributions from higher-order statistics can in many cases (see Sec.\ \ref{sec:special_models}) be parametrized by the local non-Gaussianity parameter $f_\text{NL}$ and $g_\text{NL}$ \cite{2006PhRvD..74j3003S}, \begin{equation} \label{deffnl} \zeta = \zeta_1 + \frac{3}{5}f_\text{NL}\zeta_1^2 +\frac{9}{25}g_\text{NL}\zeta_1^3 +\mathcal{O}(\zeta_1^4), \end{equation} where $\zeta_1$ is the Gaussian curvature perturbation. $f_\text{NL}$ contributes to the bi- and trispectrum, while $g_\text{NL}$ contributes only to the trispectrum of the curvature perturbation. As things turned out, there are inflation models among the ones, which are favored by current data, e.g., stated in Ref.\ \cite{2013arXiv1312.3529M} (AI, BI, ESI, HI, LI, MHI, RGI, SBI, SFI )\footnote{Terminology according to Ref.\ \cite{2006JCAP...08..009M}: AI = Arctan Inflation, BI = Brane Inflation, ESI = Exponential SUSY Inflation, HI = Higgs Inflation, LI = Loop Inflation, MHI = Mutated Hilltop Inflation, RGI = Radiation Gauge Inflation, SBI = Supergravity Brane Inflation, SFI = Small Field Inflation.} or Ref.\ \cite{2013arXiv1303.5082P}, predicting values of $|f_\text{NL}|\propto\mathcal{O}(1)$ and distinctly deviate from $g_\text{NL}=0$ if the possibility of non-Gaussianity is taken into account. It is crucial to realize that it is less likely for (at least) two disjunct inflation models to predict the same combination $(f_\text{NL},g_\text{NL})$ than only the same value of $f_\text{NL}$ or $g_\text{NL}$. In other words, if we would be able to infer these two non-Gaussianity parameters simultaneously from CMB or large scale structure (LSS) data, we had a powerful tool to distinguish between the remaining inflation models. This requires to derive a posterior probability density function (pdf) for $(f_\text{NL},g_\text{NL})$ within a Bayesian framework. How this can be done analytically is presented in the first part of this paper. Additionally, we show how this method can be recast to infer parameters specific to inflationary models, e.g., shape parameters of inflationary potentials, or the presence of an additional bosonic field, directly from data. We also provide a validation of our approach to show its precision despite using an approximation. The second quantity of interest here is the primordial power spectrum, $P_\zeta(k)$ or $P_{\zeta_1}(k)$, in particular due to its constraining character with respect to inflationary scenarios. The \textit{Planck} collaboration might have seen some features within the primordial power spectrum which in turn would indicate non-linear physics and thus could point to inflation models beyond single-field slow-roll inflation \cite{2013arXiv1303.5082P}. Additionally, these types of deviations are well motivated by, e.g., implications of the recent BICEP2 data \cite{2014arXiv1403.3985B,2014arXiv1403.7786H,2014arXiv1404.3690H,2014arXiv1405.2012H}, or special features of the inflaton potential \cite{2014arXiv1404.2985E,2014arXiv1404.6093M}. However, for the detection of such features one has to appropriately reconstruct the power spectrum from observational data. For this purpose we suggest two non-parametric spectral inference methods in Sec.\ \ref{sec:pps}. \subsection{Previous Bayesian work} The majority of publications \cite{2007JCAP...03..019C,2011PhRvD..84f3013S,2010ApJ...724.1262E,2010A&A...513A..59E,2009PhRvD..80j5005E,PhysRevD.87.063003, KSW}, which are dealing with Bayesian reconstructions of non-Gaussian quantities from CMB have their focus only on estimators or the pdf of the $f_\text{NL}$ or $g_\text{NL}$ parameter. They usually require computationally expensive calculations like Monte Carlo sampling except for some, e.g.\ Refs.\ \cite{paper1, 2013JCAP...06..023V}, which derive analytic expressions by performing approximations. High precision CMB measurements of the \textit{WMAP} and \textit{Planck} satellites have opened a new window to the physics of the early Universe and have thus improved the constraints on some parameters of non-Gaussianity \cite{2013arXiv1303.5084P} and on many inflation models \cite{2013arXiv1303.5082P} based on the two-point function, but have not connected the inflationary parameters directly to higher-order statistics. A way of direct inference of single-field slow-roll inflation models from CMB data of the \textit{Planck} satellite was recently presented by Refs.\ \cite{2013arXiv1303.3787M,2013arXiv1312.2347R,2013arXiv1312.3529M}. Here, the CMB power spectrum was analyzed already ruling out a huge amount of inflation models. We, however, go beyond Gaussian and three-point statistics to achieve tighter constraints on reasonable, not necessarily single-field slow-roll inflation models given the \textit{Planck} and future data. An independent cross-check of CMB results is the analysis of the LSS data. Current results for non-Gaussianity values, e.g.\ Refs. \cite{2013arXiv1303.1349G,2013arXiv1309.5381A,2008PhRvD..77l3514D,2008JCAP...08..031S,2012MNRAS.422.2854G,2011JCAP...08..033X,2013MNRAS.428.1116R} and forwarding references thereof, are consistent with CMB constraints. Thus, the LSS provides also a natural data set to infer inflation models. The inference approach presented in this paper is in principle able to deal with this type of data sets as well (see Sec.\ \ref{sec:validation}). According to the reconstruction of the primordial power spectrum, there exist a huge amount of approaches and an overview of the literature can be found in section 7 of Ref.\ \cite{2013arXiv1303.5082P} and in Ref.\ \cite{ 2014arXiv1402.1983P}. Within this work we exclusively focus on the approach of Refs.\ \cite{2011PhRvD..83j5014E} and \cite{2013PhRvE..87c2136O}, which developed approximative, but inexpensive Bayesian inference schemes for spectra within the framework of information field theory. For a brief review on inferring primordial non-Gaussianities in the CMB beyond Bayesian techniques (e.g., bi- and trispectrum estimators, Minkowski Functionals, wavelets, needlets, etc.) we want to point to Ref.\ \cite{2010AdAst2010E..71Y} and forwarding references thereof. \subsection{Structure of the work} The remainder of this work is organized as follows. In Sec.\ \ref{sec:ift} we describe the considered data model and introduce the generic method of inferring inflation models postulating $f_\text{NL}$, $g_\text{NL}$. In Sec.\ \ref{sec:special_models} we review a few inflation models that are not ruled out by current \textit{Planck} data and quote corresponding expressions for $f_\text{NL}$ and $g_\text{NL}$. Additionally, we show where the specific models are localized in the $f_\text{NL}$-$g_\text{NL}$-plane. The Bayesian posterior for special inflationary parameters is shown in Sec.\ \ref{sec:validation} as well as a numerical implementation (toy case) of the also pedagogically important curvaton scenario in the Sachs-Wolfe limit and its validation by the Diagnostics of Insufficiencies of Posterior distribution (DIP) test \cite{paper2}. In Sec. \ref{sec:pps} we introduce a method to reconstruct the primordial power spectrum of $\zeta$ and $\zeta_1$. We summarize our findings in Sec.\ \ref{sec:conclusion}. Being at the interface of statistical analysis and physical cosmology, it seems appropriate to guide the reader by giving some reading instructions. For a reader who is rather interested in the statistical analysis, i.e.\ how to infer (inflationary) parameters from CMB data and how to reconstruct a power spectrum in a non-parametric way in general, paragraphs starting with symbol $\blacktriangleright$ and ending with symbol $\blacktriangleleft$ might be skipped. For a reader rather interested in physical cosmology these symbols might mark paragraphs of special interest. | \label{sec:conclusion} We have presented a novel and generic method to infer inflation models from observations by the non-Gaussianity parameters $f_\text{NL}$ and $g_\text{NL}$ and how to reformulate this method to infer specific parameters of inflation models, $p$, directly (see especially Secs.\ \ref{sec:ift} and \ref{sec:special_models}). This approach, i.e.\ the analytical derivation of a posterior for $f_\text{NL}$ and $g_\text{NL}$ as well as for $p$ can be used to further distinguish between the already restricted amount of inflation models. It is formulated in a generic manner in the framework of information field theory, so that it is applicable to CMB data as well as to LSS data (see especially the three dimensional example of Sec.\ \ref{sec:scmexp}) by tuning the response appropriately. The analyticity of the method, achieved by a saddle-point approximation, allows to dispense with numerically expensive sampling techniques like the commonly used Monte Carlo method. The analytic approximation we introduced has been validated successfully by the DIP test \cite{paper2}. The second quantity of interest here is the primordial power spectrum due to its farreaching implications for inflationary cosmology. We have presented two computationally inexpensive, approximative Bayesian methods to infer the primordial power spectrum from CMB data, the so called critical filter, Eq.\ (\ref{crit}), and an extension thereof with smoothness prior, Eq.\ (\ref{smooth}). Both methods allow a non-parametric reconstruction of the power spectrum including the reconstruction of possible features on specific scales. Additionally, both methods are able to perform this inference process even in the case of partial sky coverage and non-Gaussianity. We have argued that this property would allow to infer the level of non-Gaussianity of a field if one could measure both, the power spectrum of the non-Gaussian and Gaussian curvature perturbations. These spectra might be inferred from, e.g., $T-$ and $B-$modes due to the fact that $B-$ modes might be less non-Gaussian than $T-$ modes \cite{2010PhRvD..82j3505S}. A fully quantitative analysis thereof, however, is left for future work. | 14 | 3 | 1403.5067 |
1403 | 1403.0474_arXiv.txt | We report on XMM-Newton and Chandra observations of the Galactic supernova remnant candidate \snr, together with complementary radio, infrared, and $\gamma$-ray data. An approximately elliptical X-ray structure is found to be well correlated with radio shell as seen by the Very Large Array. The X-ray spectrum of \snr\ can be well-described by an absorbed collisional ionization equilibrium plasma model, which suggests the plasma is shock heated. Based on the morphology and the spectral behaviour, we suggest that \snr\ is indeed a supernova remnant belongs to a mix-morphology category. | Supernovae (SNe) and their remnants play a crucial role in driving the dynamical and chemical evolution of galaxies (Woosley \& Weaver 1995). Each SN produces bulks of heavy elements and disperses them throughout the interstellar medium (ISM) (e.g. Thielemann et al. 1996; Chieffi \& Limongi 2004). The shock waves from the SN explosions may also trigger star formation in molecular clouds (Boss 1995). In addition, the blast waves in supernova remnants (SNRs) can accelerate particles to relativistic energies via Fermi-I acceleration (Reynolds 2008), which has long been suggested as a promising acceleration mechanism for Galactic cosmic rays (GCRs). For investigating the role of SNRs as GCR accelerators, it is necessary to ask whether they can account for the entire energy density of CRs in the Milky Way. This is related to the mechanical power provided by the SNe, which in turn is associated with their event rate. In our Milky Way, the currently known SNR population is far below the expectation based on a event rate of 2 SNe/century (Tammann et al. 1994) and a typical evolution timescale of $\sim10^{5}$~yrs (see Hui et al. 2012; Hui 2013). Therefore, deeper searches for Galactic SNRs are certainly needed. \\[-2ex] With the much improved spatial and spectral resolution and enlarged effective area, state-of-the-art X-ray observatories like Chandra and XMM-Newton provide powerful tools for studying the shock-heated plasma and the non-thermal emission from the leptonic acceleration in SNRs (Hui 2013; Kang 2013). However, the number of X-ray detected SNRs is still significantly smaller than the corresponding number of detections in the radio. Until now there are 302 SNRs that have been uncovered in the Milky Way: 274 objects recorded in Green (2009) plus 28 objects reported in Ferrand \& Safi-Harb (2012), while the number of Galactic SNRs detected in X-rays is about 100\footnote{http://www.physics.umanitoba.ca/snr/SNRcat/}. Therefore, enlarging the sample of the X-ray detected SNRs would be valuable. Recently, we have initiated an observational campaign for searching and identifying new Galactic SNRs with X-ray telescopes (Hui et al. 2012). Here we report our detailed X-ray analysis of the another SNR candidate \snr. \\[-2ex] \snr\ was first detected as an unidentified object in ROSAT All-Sky Survey (RASS) with an extent of about $12' \times 8'$. This object has a centrally-peaked morphology in X-rays. Cross-correlating with the Effelsberg Galactic Plane 11~cm survey data, \snr\ is found to positionally coincide with an incomplete radio shell (cf. Figure~1d in Schaudel et al. 2002). A follow-up observation with the Effelsberg telescope at a wavelength of 6~cm revealed a non-thermal radio emission with a spectral index of $\alpha =-0.79\pm0.23$. Furthermore, the existence of polarization in the radio shell was reported by Schaudel et al. (2002). All these evidences suggest that \snr\ is very likely to be a SNR with center-filled X-ray (mixed) morphology. However, the poor spatial resolution ($\sim96$") and the limited photon statistic ($\sim50$ source counts) of RASS data do not allow one to unambiguously confirm its physical nature. Furthermore, the limited energy bandwidth of ROSAT (0.1-2.4~keV) does not allow one to determine whether a possible hard X-ray ($>$2~keV) component, arising from the interactions of the reflected shocks with the dense ambient medium or alternatively from the synchrotron emission radiated by relativistic leptons, is present in the hard X-ray band. This motivates us to carry out a detailed X-ray studies of \snr\ with XMM-Newton and Chandra. \\[-2ex] Considering the composition of GCRs, leptons only constitute a small proportion. A large fraction of the observed GCRs are hadrons (i.e proton and heavy ions; cf. Sinnis et al. 2009). Due to the large masses of hadrons, they are not efficient synchrotron emitters. X-ray and radio observations are generally difficult to constrain their presence. On the other hand, the collision of relativistic hadrons can lead to the production of neutral pions which can subsequently decay into $\gamma-$rays (Caprioli 2011). For complementing the aforementioned X-ray investigation of \snr\ as a possible acceleration site of GCRs, we have also conducted a search for $\gamma-$ray emission at the location of \snr\ wtih the Large Area Telescope (LAT) on board the Fermi Gamma-Ray Space Telescope. \\[-2ex] In this paper, we report a detailed high energy investigation of \snr. The observations and the data reduction of XMM-Newton and Chandra observatories are described in section 2. Sections 3 and 4 present the results of the X-ray spatial and spectral analysis respectively. In section 5, we describe a deep search of $\gamma-$ray emission with Fermi. Finally, we discuss the physical implications of the results and summarize our conclusions in sections 6 and 7 respectively. | We have performed a detailed spectro-imaging X-ray study of the supernova remnant candidate \snr\ with XMM-Newton and Chandra. A central-filled X-ray structure correlated with an incomplete radio shell has been revealed. Its X-ray spectrum is thermal dominated and has shown the presence of a hot plasma accompanied with metallic emission lines. These observed properties indicate that \snr\ is a SNR belong to a mix-morphology category. The enhanced abundances of O and Ne suggest \snr\ might be resulted from a core-collapsed SN. We have also searched for the possible $\gamma$-ray emission from \snr\ with \emph{Fermi} LAT data. With the adopted $\sim4.3$~yrs data span in this study, we report a non-detection of any $\gamma-$ray emission in the energy range of $0.2-300$~GeV. | 14 | 3 | 1403.0474 |
1403 | 1403.5838.txt | Stellar distance is an important basic parameter in stellar astrophysics. Stars in a cluster are thought to be formed coevally from the same interstellar cloud of gas and dust. They are therefore expected to have common properties. These common properties strengthen our ability to constrain theoretical models and/or to determine fundamental parameters, such as stellar mass, metal fraction, and distance when tested against an ensemble of cluster stars. Here we derive a new relation based on solar-like oscillations, photometric observations, and the theory of stellar structure and evolution of red giant branch stars to determine cluster distance moduli through the global oscillation parameters \dnu\ and \numax\, and photometric data \textit{V}. The values of \dnu\ and \numax\ are derived from \kepler\ observations. At the same time, it is used to interpret the trends between \textit{V} and \dnu. From the analyses of this newly derived relation and observational data of NGC~6791 and NGC~6819 we devise a method in which all stars in a cluster are regarded as one entity to determine the cluster distance modulus. This approach fully reflects the characteristic of member stars in a cluster as a natural sample. From this method we derive true distance moduli of $13.09\pm0.10$ mag for NGC~6791 and $11.88\pm0.14$ mag for NGC~6819. Additionally, we find that the distance modulus only slightly depends on the metallicity [Fe/H] in the new relation. A change of 0.1 dex in [Fe/H] will lead to a change of 0.06 mag in the distance modulus. | \label{sec1} %Asteroseismology Asteroseismology provides a powerful tool to probe detailed information regarding the internal structure and evolutionary state of stars. Many stars with solar-like oscillation have been observed with space-based instruments, such as \textit{WIRE} \citep[e.g.][]{Hacking99,Buzasi00}, \textit{MOST} \citep[e.g.][]{Walker03,Matthews04}, \textit{CoRoT} \citep[e.g.][]{Baglin06}, and \kepler\ \citep[e.g.][]{Koch10,Gilliland10}. These missions have provided precise near-uninterrupted photometric timeseries data which allows for asteroseismic analyses of many stars. This opens the possibility to study large samples of stars, i.e., to perform so-called ``ensemble asteroseismology'' \citep{Chaplin11}. The observed oscillation parameters can be used to determine the stellar fundamental parameters (mass $M$, radius $R$, surface gravity $g$, mean density $\rho$, etc.). The members of a cluster constitute a natural sample, as stars in a cluster are assumed to be formed coevally from the same interstellar cloud of gas and dust. Therefore, they are expected to have common properties, such as element composition, distance, age, etc. For this reason, ensemble asteroseismology is very suitable for cluster stars, for examples, see \citet{Stello10,Stello11a,Stello11b}, \citet{Hekker11b}, \citet{basu11}, \citet{Miglio12}, \citet{Corsaro12}, and \citet[][]{Wu13}. %cluster distance Distance is a fundamental parameter in astrophysics. The \textit{Hipparcos} satellite \citep[e.g.][]{Perryman_ESA97} provided parallax measurements of a large number of stars to obtain their distances. For clusters, there are many methods to obtain the cluster distance modulus or distance. For example, isochrone fitting \citep[e.g.][]{Chaboyer99,Stetson03,Bedin05,Bedin08,Hole09,Wu13}, or using red-clump stars as ``standard candles'' \citep[e.g.][]{Garnavich94,Gao12}. Additionally, the cluster distance can be derived from a detailed analysis of binary systems \citep[e.g.][]{Brogaard11,Jeffries13,Sandquist13}, from the period-luminosity relation of pulsating stars \citep[e.g.][]{Soszynski08,Soszynski10}, or from direct estimates \citep[e.g.][]{basu11,Miglio12,Balona13}, and so on. %\subsection{NGC~6791} \renewcommand{\arraystretch}{1.} \begin{deluxetable*}{lccccccr} \tablewidth{\textwidth}%{0pt} \tablecaption{Literature overview of cluster distance moduli of NGC~6791 and NGC~6819.\label{table_liter}} \tablehead{ \colhead{${\rm (m-M)_{0}}$} & \colhead{${\rm (m-M)_{V}}$} & \colhead{$E(B-V)$} & \colhead{$A_{V}$} & \colhead{Metallicity\tablenotemark{a,b}} & \colhead{Age} & \colhead{Methods} & \colhead{Ref.} \\ \colhead{[mag]} & \colhead{[mag]} & \colhead{[mag]} & \colhead{[mag]} & \colhead{$Z$\tablenotemark{a} or [Fe/H]\tablenotemark{b}}& \colhead{[Gyr]}& & } \startdata \multicolumn{8}{c}{NGC 6791} \\ \hline 13.55 & 14.21\tablenotemark{aa} & 0.22$\pm$0.02 & 0.66 & 0.01\tablenotemark{a} & \nodata & main-sequence stars & \citet[][]{Kinman65} \\ %(1) \\ 12.88$\pm$0.6\tablenotemark{aa} & 13.3$\pm$0.6 & 0.13 & 0.42 & \nodata & \nodata & spectroscopic parallaxes & \citet[][]{Harris_Canterna81} \\ %(2) \\ 13.48$\pm$0.35\tablenotemark{aa} & 13.9$\pm$0.35 & 0.13 & 0.42 & \nodata & \nodata & sed-clump stars & \citet[][]{Harris_Canterna81} \\ %(2) \\ 13.58$\pm$0.2\tablenotemark{aa} & 14.0$\pm$0.2 & 0.13 & 0.42 & 0.02\tablenotemark{a,c} & $\sim$7 & isochrone & \citet[][]{Harris_Canterna81} \\ %(2) \\ 13.25 & \nodata & \nodata & \nodata & \nodata & \nodata & red-clump stars & \citet[][]{Anthony-Twarog84} \\ 12.8\tablenotemark{d} & 13.5 & 0.20 & 0.70 & 0.019\tablenotemark{a,c} & 6.0$\pm$0.7& isochrone & \citet[][]{Anthony-Twarog_Twarog85} \\ %(3) \\ 12.5\tablenotemark{e} & 13.2 & 0.20 & 0.70 & 0.0169\tablenotemark{a,c}& 12.0 & isochrone & \citet[][]{Anthony-Twarog_Twarog85} \\ %(3) \\ 12.75\tablenotemark{aa,e} & 13.45 & 0.225 & 0.70\tablenotemark{aa} & 0.0169\tablenotemark{a,c}& 10$\sim$12.5 & isochrone & \citet[][]{Kaluzny90} \\ %(4) \\ \nodata & 13.65 & \nodata & \nodata & 0.0\tablenotemark{b,c}& $\sim$9 & red-clump stars & \citet[][]{Zurek93} \\ %(5) \\ \nodata & 13.6& \nodata & \nodata & $-$0.04$\pm$0.12\tablenotemark{b} & $\sim$9 & red-clump stars & \citet[][]{Garnavich94} \\ %(13) \\ \nodata & 13.55& 0.19$\pm$0.03 & \nodata & 0.03\tablenotemark{a} & $\sim$9 & isochrone & \citet[][]{Garnavich94} \\ %(13) \\ 12.66 & 12.96 & 0.10$\pm$0.02 & \nodata & $+$0.19\tablenotemark{b}& 10 & isochrone & \citet[][]{Montgomery94} \\ %(5) \\ 12.97 & 13.52& 0.17 & \nodata & $+$0.3\tablenotemark{b} & 7.2 & red-clump stars & \citet[][]{Kaluzny95} \\ %(14) \\ 12.75$\sim$12.82 & 13.30$\sim$13.37& 0.17 &\nodata & $+$0.2\tablenotemark{b} & 7.2 & main-sequence stars & \citet[][]{Kaluzny95} \\ %(14) \\ 12.86$\sim$12.93 & 13.41$\sim$13.48& 0.17 &\nodata & $+$0.3\tablenotemark{b} & 7.2 & main-sequence stars & \citet[][]{Kaluzny95} \\ %(14) \\ \nodata & 13.49$\sim$13.70 & 0.19$\sim$0.24 & \nodata &$+$0.35\tablenotemark{b} &10$\pm$0.5 & red-clump stars & \citet[][]{Tripicco95} \\ %(6) \\ \nodata & 13.49$\sim$13.52 & 0.20$\sim$0.23 & \nodata &$+$0.15\tablenotemark{b} &10 & isochrone & \citet[][]{Tripicco95} \\ %(6) \\ \nodata & 13.30$\sim$13.45 & 0.08$\sim$0.13 & \nodata & $+$0.4\tablenotemark{b}&8$\pm$0.5 & isochrone & \citet[][]{Chaboyer99} \\ %(7) \\ \nodata & 13.42 & 0.10$\sim$0.11 & \nodata & $+$0.4\tablenotemark{b}&8 & isochrone & \citet[][]{Liebert99} \\ %(7) \\ \nodata & $\sim$13.0 & 0.1 & \nodata & \nodata & \nodata & binaries & \citet[][]{Mochejska03} \\ %(17) \\ 12.79 & \nodata & 0.09 & \nodata & $+$0.3\tablenotemark{b} & 12 & isochrone & \citet[][]{Stetson03} \\ %(8) \\ 13.0 & 13.5 & 0.15 & \nodata & 0.03\tablenotemark{a} & 9 & isochrone & \citet[][]{King05} \\ %(9) \\ 13.07$\pm$0.04 & \nodata & 0.14$\pm$0.04 & \nodata & $+$0.4$\pm$0.01\tablenotemark{b} & 8 & red-clump stars & \citet[][]{Carney05} \\ % (10) \\ 12.93 & \nodata & 0.17 & \nodata & $+$0.3\tablenotemark{b} & 8 & isochrone & \citet[][]{Carney05} \\ % (10) \\ 12.96 & \nodata & 0.13 & \nodata & $+$0.4\tablenotemark{b} & 8 & isochrone & \citet[][]{Carney05} \\ % (10) \\ 13.11 & \nodata & 0.11 & \nodata & $+$0.5\tablenotemark{b} & 7.5 & isochrone & \citet[][]{Carney05} \\ % (10) \\ 13.07$\pm$0.05 & 13.45 & 0.09$\pm$0.01 & \nodata & 0.046\tablenotemark{a} & 8.0$\pm$1.0 & isochrone & \citet[][]{Carraro06} \\ %(11) \\ \nodata & 13.35 & 0.13 & \nodata & 0.04\tablenotemark{a} & 8$\sim$9 & isochrone & \citet[][]{Carraro06} \\ %(11) \\ 13.14$\pm$0.15\tablenotemark{aa}& 13.60$\pm$0.15& 0.15 & 0.46\tablenotemark{aa} & $+$0.45\tablenotemark{b} & 7.0$\pm$1.0 & isochrone & \citet[][]{Anthony-Twarog07} \\ %(12) \\ 13.0 & \nodata& 0.14 & \nodata & $+$0.37\tablenotemark{b} & 8.5 & isochrone & \citet[][]{Kalirai07} \\ %(12) \\ \nodata & 13.30$\pm$0.2 & 0.09 & \nodata & \nodata & \nodata & binaries & \citet[][]{de-Marchi07} \\ %(15) \\ 13.0 & \nodata & 0.15$\pm$0.02 & \nodata & $+$0.40$\pm$0.10\tablenotemark{b} & 6.2$\sim$9.0 & binary & \citet[][]{Grundahl08} \\ %(16) \\ \nodata & 13.46 & 0.15 & \nodata & $+$0.40\tablenotemark{b} & 7.7$\sim$9.0 & isochrone & \citet[][]{Grundahl08} \\ %(16) \\ \nodata & 13.51$\pm$0.06 & 0.160$\pm$0.025 & \nodata & $+$0.29$\pm$0.10\tablenotemark{b} & \nodata & binaries & \citet[][]{Brogaard11} \\ %(17) \\ 13.11$\pm$0.06 &13.61$\pm$0.06\tablenotemark{aa} & 0.16 & 0.50\tablenotemark{aa} & $+$0.29\tablenotemark{b} & 6.8$\sim$8.6 & asteroseismology & \citet[][]{basu11} \\ %(18) \\ 13.01$\pm$0.07\tablenotemark{aa} & 13.51$\pm$0.02 & 0.16$\pm$0.02 & 0.50$\pm$0.06\tablenotemark{aa} & $+$0.3\tablenotemark{b} & \nodata & asteroseismology & \citet[][]{Miglio12} \\ %(19) \\ 12.97$\pm$0.05\tablenotemark{aa} & 13.36$\pm$0.04 & 0.14$\pm$0.01 & 0.43$\pm$0.03\tablenotemark{aa} & 0.04$\pm$0.005\tablenotemark{a} & 8.0$\pm$0.4 & isochrone & \citet[][]{Wu13} \\ %(20) \\ \textbf{13.08$\pm$0.08} & \textbf{13.58$\pm$0.03} & \textbf{0.16$\pm$0.025} & \textbf{\nodata} & \textbf{$+$0.29$\pm$0.10\tablenotemark{b}} & \textbf{\nodata} & \textbf{asteroseismology} & \textbf{The present work\tablenotemark{bb}} \\ \textbf{13.09$\pm$0.10} & \textbf{13.59$\pm$0.06} & \textbf{0.16$\pm$0.025} & \textbf{\nodata} & \textbf{$+$0.29$\pm$0.10\tablenotemark{b}} & \textbf{\nodata} & \textbf{asteroseismology} & \textbf{The present work\tablenotemark{cc}} \\ \hline %\hline \multicolumn{8}{c}{NGC 6819} \\ \hline 11.54 & 11.9 & 0.12 & 0.36 & \nodata & \nodata & main-sequence turnoff & \citet[][]{Burkhead71} \\ %(21) \\ 11.5 & 12.6 & 0.3 & 0.9 & \nodata & 2 & main-sequence stars & \citet[][]{Lindoff72} \\ %(1) \\ 11.76 & 12.50 & 0.28 & \nodata & \nodata & \nodata & main-sequence stars & \citet[][]{Auner74} \\ %(1) \\ \nodata & 12.35& 0.16 & \nodata & -0.10$\sim$0.0\tablenotemark{b} & 2.4 & isochrone/ZAHB & \citet[][]{rv98} \\ %(21) \\ \nodata & 12.30$\pm$0.12& 0.10 & \nodata & 0.02\tablenotemark{a} & 2.5 & isochrone & \citet[][]{Kalirai01} \\ %(22) \\ \nodata & 12.30& 0.10 & \nodata & 0.019\tablenotemark{a,c} & 2.4 & isochrone & \citet[][]{Hole09} \\ %(23) \\ \nodata & 12.38& \nodata & \nodata & \nodata & \nodata & binary & \citet[][]{Talamantes10} \\ %(25) \\ 11.85$\pm$0.05& 12.31$\pm$0.05\tablenotemark{aa} & 0.15 & 0.46\tablenotemark{aa} & $+$0.09\tablenotemark{b} & 2$\sim$2.4 & asteroseismology & \citet[][]{basu11} \\ %(18) \\ 11.34$\pm$0.02\tablenotemark{aa}& 11.80$\pm$0.02 & 0.15 & 0.46\tablenotemark{aa} & 0.0\tablenotemark{b} & \nodata & asteroseismology & \citet[][]{Miglio12} \\ %(19) \\ \nodata & 12.50& 0.14 & \nodata & $+$0.09\tablenotemark{b} & 2.25 & isochrone & \citet[][]{Anthony-Twarog13} \\ %(24) \\ \nodata & 12.39$\pm$0.08 & \nodata & \nodata & $+$0.09\tablenotemark{b} & 2.65$\pm$0.25 & binaries & \citet[][]{Sandquist13} \\ %(26) \\ 12.00$\pm$0.05 & 12.37$\pm$0.10 & 0.12$\pm$0.03 & \nodata & \nodata & \nodata & dwarf stars near the turnoff & \citet[][]{Jeffries13} \\ %(27) \\ \nodata & 12.28$\sim$12.40 & 0.12$\pm$0.03 & \nodata & $+$0.06$\sim$$+$0.13\tablenotemark{b} & 2.1$\sim$2.5 & isochrone & \citet[][]{Jeffries13} \\ %(27) \\ \nodata& 12.44$\pm$0.07 & \nodata & \nodata & $+$0.09$\pm$0.03\tablenotemark{b} & 2.2$\sim$3.7 & binaries & \citet[][]{Jeffries13} \\ %(27) \\ 11.88$\pm$0.08 & 12.34$\pm$0.08\tablenotemark{aa} & 0.15 & 0.46\tablenotemark{aa} & & \nodata & asteroseismology & \citet[][]{Balona13} \\ % (28) \\ 11.94$\pm$0.04 & 12.40$\pm$0.04\tablenotemark{aa} & 0.15 & 0.46\tablenotemark{aa} & 0.02\tablenotemark{a} & 2.5 & isochrone & \citet[][]{Balona13} \\ % (28) \\ 12.00$\pm$0.06\tablenotemark{aa} & 12.40$\pm$0.05 & 0.13$\pm$0.01 & 0.40$\pm$0.03\tablenotemark{aa} & 0.022$\pm$0.004\tablenotemark{a} & 1.9$\pm$0.1 & isochrone & \citet[][]{Wu13} \\ %(20) \\ \textbf{11.83$\pm$0.14} & \textbf{12.27$\pm$0.02} & \textbf{0.142$\pm$0.044} & \textbf{\nodata} & \textbf{$+$0.09$\pm$0.03\tablenotemark{b}} & \textbf{\nodata} & \textbf{asteroseismology} & \textbf{The present work\tablenotemark{bb}}\\ \textbf{11.88$\pm$0.14} & \textbf{12.32$\pm$0.03} & \textbf{0.142$\pm$0.044} & \textbf{\nodata} & \textbf{$+$0.09$\pm$0.03\tablenotemark{b}} & \textbf{\nodata} & \textbf{asteroseismology} & \textbf{The present work\tablenotemark{cc}} \enddata \tablenotetext{a}{Metal fraction $Z$.} \tablenotetext{b}{Metallicity [Fe/H].} \tablenotetext{c}{Solar metallicity, corresponding [Fe/H]=0.0.} \tablenotetext{d}{Based on Yale isochrone models.} \tablenotetext{e}{Based on VandenBerg isochrone models.} \tablenotetext{aa}{Calculated with Equations \eqref{eq_dm-a} and/or \eqref{eq_extinction}.} \tablenotetext{bb}{Based on classical relation (Equation \eqref{eq-log2}).} \tablenotetext{cc}{Based on new relation (Equation \eqref{eq-log3}).} \tablecomments{Column 1---True distance modulus (${\rm (m-M)_{0}}$); Column 2---Apparent distance modulus (${\rm (m-M)_{V}}$); Column 3---Interstellar reddening ($E(B-V)$); Column 4---Interstellar extinction ($A_{V}$); Column 5---Metallicity ($Z$ (metal fraction) or [Fe/H]); Column 6---Cluster ages; Column 7---Methods used to determine distance modulus; Column 8---Reference.} %\tablerefs{ %(1) \citet[][]{Kinman65}; %(2) \citet[][]{Harris_Canterna81}; %(3) \citet[][]{Anthony-Twarog_Twarog85}; %(4) \citet[][]{Kaluzny90}; %(5) \citet[][]{Montgomery94}; %(6) \citet[][]{Tripicco95}; %(7) \citet[][]{Chaboyer99}; %(8) \citet[][]{Stetson03}; %(9) \citet[][]{King05}; %(10) \citet[][]{Carney05}; %(11) \citet[][]{Carraro06}; %(12) \citet[][]{Anthony-Twarog07}; %(13) \citet[][]{Garnavich94}; %(14) \citet[][]{Kaluzny95}; %(15) \citet[][]{de-Marchi07}; %(16) \citet[][]{Grundahl08}; %(17) \citet[][]{Brogaard12}; %(18) \citet[][]{basu11}; %(19) \citet[][]{Miglio12}; %(20) \citet[][]{Wu13}; %(21) \citet[][]{rv98}; %(22) \citet[][]{Kalirai01}; %(23) \citet[][]{Hole09}; %(24) \citet[][]{Anthony-Twarog13}; %(25) \citet[][]{Talamantes10}; %(26) \citet[][]{Sandquist13}; %(27) \citet[][]{Jeffries13}; %(28) \citet[][]{Balona13}.} \end{deluxetable*} \renewcommand{\arraystretch}{1} In the \textit{Kepler} field of view there are two open clusters NGC~6791 and NGC~6819 in which solar-like oscillations have been observed for a number of red-giant stars \citep{Stello10,Stello11a,Stello11b,Hekker11b,basu11,Miglio12,Corsaro12,Balona13,Wu13}. An overview of earlier work regarding distance moduli, interstellar extinctions/reddenings, ages and metallicities presented in the literature for these clusters is provided in Table~\ref{table_liter}. In short: NGC~6791 is one of the oldest \citep[$6\sim8$ Gyr, e.g.][]{Harris_Canterna81,Wu13} clusters with super-solar metallicity \citep[${\rm[Fe/H]}\approx0.3\sim0.4$ dex, e.g.][]{Carraro06,Brogaard11,Wu13}, with a true distance modulus in the range $12.9 \sim 13.1$ mag \citep{basu11,Miglio12,Wu13}. NGC~6819 is an intermediate-age cluster \citep[$1.6\sim2.5$ Gyr, e.g.][]{rv98,Kalirai01,basu11,Wu13} with near-solar or slightly super-solar metallicity \citep[e.g.][]{Bragaglia01,Hole09,Warren&Cole09,Wu13}. The true distance modulus of this cluster is of the order of $11.8 \sim 12.0$ \citep[e.g.][]{basu11,Jeffries13,Balona13,Wu13}. In this paper, we propose a new method to estimate the cluster distance modulus from global oscillation parameters (\dnu\ and \numax) and V photometry of cluster members of NGC~6791 and NGC~6819. This method is based on a relation between the frequency of maximum oscillation power \numax, the large frequency separation \dnu, the apparent magnitude $V$, the metallicity $Z$, and the distance modulus ${\rm (m-M)_{0}}$. | \label{sec_summary} From the global oscillation parameters (large frequency separation \dnu\ and frequency of maximum oscillation power \numax) and photometry data (apparent magnitude \textit{V}), we have determined the distance moduli for clusters NGC~6791 and NGC~6819, applying a new method, which regards all stars in a cluster as one entity and determine a mean value of the distance modulus but do not calculated individual distance moduli for the stars. This fully reflects the characteristic of member stars in a cluster as a natural sample. From this investigation we conclude the following: \rmnum{1}: Based on the solar-like oscillations and photometric observations, we have derived relation $6\log\nu_{\rm{max}}+15\log T_{\rm eff}=12\log\Delta\nu+1.2(4.75-V-BC)+1.2{\rm (m-M)_{0}}+1.2A_{\rm V}$. We then verified this relation using observational data, and determined the cluster distance moduli of NGC~6791 and NGC~6819. \rmnum{2}: Based on the solar-like oscillations, photometric observations, and the theory of stellar structure and evolution of red giant stars, we have obtained a new relation $9.482\log\nu_{\rm{max}}=15.549\log\Delta\nu- 1.2(V+BC)+0.737\log Z+1.2{\rm (m-M)_{0}}+1.2A_{\rm V}+5.968$. We have verified this relation using observational data. \rmnum{3}: Based on the new relations, we have interpreted the trends between the apparent magnitude and larger frequency separation. At the same time, we have determined the cluster apparent distance moduli to be $13.59\pm0.06$ mag for NGC~6791 and $12.32\pm0.03$ mag for NGC~6819, respectively. Accordingly the corresponding true distance modulus is $13.09\pm0.10$ mag for NGC~6791 and $11.88\pm0.14$ mag for NGC~6819, respectively. \rmnum{4}: We have found that the influence of $E(B-V)$ for the distance modulus is very complicated and can not be neglected for the classical relation. The change of 0.01 mag in $E(B-V)$ will lead to an uncertainty of at least 0.04 mag in \dm. The contribution of \teff\ to the uncertainty is considerable in the classical relation, while it is not present in the new relation. Additionally, we have found that the distance modulus only slightly depends on the metallicity in the new relation. \rmnum{5}: The new method presented here could be used as a discrimination tool to determine the membership of cluster stars in the same way as the asteroseismic method of \citet{Stello11b}. | 14 | 3 | 1403.5838 |
1403 | 1403.7901_arXiv.txt | Lie-integration is one of the most efficient algorithms for numerical integration of ordinary differential equations if \dm{high precision is needed for longer terms}. The method is based on the computation of the Taylor-coefficients of the solution as a set of recurrence relations. In this paper we present these recurrence formulae for orbital elements and other integrals of motion for the planar $N$-body problem. We show that if the reference frame is fixed to one of the bodies -- for instance to the Sun in the case of the Solar System --, the higher order coefficients for all orbital elements and integrals of motion depend only on the mutual terms corresponding to the orbiting bodies. | \label{sec:introduction} Due to the lack of analytical solutions, numerical integration is required to solve the equations of motion of the gravitational $N$-body problem for almost any initial conditions for $3\le N$. There are many textbooks with algorithms related to general purpose numerical integration of ordinary differential equations \citep[ODEs, see e.g.][for an introduction]{press2002}. \dm{In principle, if we have to solve the equation $\dot x_i=f_i(\mathbf{x})$, where $\mathbf{x}=(x_1,\dots,x_N)$, then the respective Lie-operator is defined as \begin{equation} L=\sum\limits_{i=1}^Nf_i\frac{\partial}{\partial x_i}. \end{equation} The solution of the equation after time $\Delta t$ is then written in the form \begin{equation} x(t+\Delta t)=\exp\left(\Delta t\cdot L\right)x(t)=\sum\limits_{k=0}^{\infty}\frac{\Delta t^k}{k!}L^kx(t). \end{equation} The finite approximation of the above sum is called Lie-integration \citep[see also][]{grobner1967}. The higher order derivatives can efficiently be computed using recurrence relations where the derivatives $L^{k+1}x(t)$ are expressed as functions of $L^{\ell}x(t)$, where $0\le\ell\le k$.} The method has many advantages: it is one of the most efficient methods if we consider long-term and high precision computations, adaptive forms can be implemented without losing computation time, roundoff errors are smaller than other algorithms, etc. \citep[see e.g.][]{pal2007,hanslmeier1984}. However, the need of derivations of the respective recurrence series for any new problem is a major drawback. First, \cite{hanslmeier1984} have obtained the recurrence relations for the $N$-body problem, taking into account mutual and purely Newtonian gravitational forces. Soon after, the relations have been derived for the restricted three-body problem \citep{delva1984}. Many methods for stability analysis require the computation of linearized equations. The relations for the linearized $N$-body problem -- including the equations where one of the bodies is fixed -- have been presented by \cite{pal2007}. The algorithm of Lie-integration has widely been applied for stability studies related to known planetary systems \citep[see e.g.][]{asghari2004} or special resonant systems \citep[see e.g.][]{funk2013}. In addition, more sophisticated semi-numerical methods can be based on the Lie-series \citep[see e.g.][about the numerical computation of partial derivatives of coordinates and velocities with respect to the initial conditions and the direct applications for exoplanetary analysis]{pal2010}. \dm{Recently, \cite{bancelin2012} published the relations extended with relativistic effects and some non-gravitational forces. It should be noted that Lie-integration does not handle regularization, i.e., equations are integrated in proper time by default. However, the method itself could be applied for regularized forms of the perturbed two-body problem \citep[see e.g.][for a review about recent methods]{bau2013}. Due to its properties and implementation techniques, close encounters can be handled easily with Lie-series \citep[see also][]{funk2013}.} The aim of this paper is to present the recurrence relations for the osculating orbital elements and the mean longitude in the case of the planar $N$-body problem. Here we employ a reference frame where one of the bodies (i.e., the central body) has been fixed. Choosing this reference frame has the advantage that all of the bodies orbiting the center have constant osculating orbital elements \emph{if} we neglect mutual interactions. As we show later on, all of the non-trivial terms depend purely on the mutual terms between the orbiting bodies. \dm{In other words, trivial cases yield constantly zero series for the Lie-coefficients. In Sec.~\ref{sec:lienbody} we summarize the relations for the fixed-center reference frame, following the notations of \cite{hanslmeier1984} and \cite{pal2007}. } The recurrence equations for constants of motion are derived in Sec.~\ref{sec:lieorbitals} while the relations for the mean longitude are obtained in Sec.~\ref{sec:liemeanlongitude}. Our results and conclusions are summarized in Sec.~\ref{sec:summary}. | \label{sec:summary} In this paper we presented recurrence formulae of the orbital elements related to the planar $N$-body problem. As we showed, the structure of these formulae depends only on the terms related to the mutual interactions. Therefore, the relations for the two-body problem reduces to a constant motion that can be integrated with arbitrary step size. \dm{It should be noted that although the presented procedure still requires the computation of higher order derivatives of coordinates and velocities, these relations are exploited as auxiliary equations for computing the mutual terms and these are not integrated directly. } \dm{In order to estimate the merits of using the orbital elements instead of the coordinates and velocities, we can compare, for instance, the magnitude of the terms $L^kC_i$ when these are computed using equation (\ref{eq:lbci}) or equation (\ref{eq:lcchigher}). In the unperturbed case, the latter one yields exactly zero while roundoff errors initiate an exponential growth in the higher order derivatives yielded by naive computation. Using double-precision arithmetic and bootstrapping with unity specific mass and angular momentum, the roundoff errors accumulate to unity around the order of $k\approx 19\dots 21$, depending on the initial eccentricity and orbital phase. In addition, for a given step size and desired precision, employing orbital elements instead of coordinate components decrease the integration order $n_{\rm max}$. For weakly perturbed systems (like the inner Solar System), this decrement can be a factor of $\sim 2$. This would naively yield a gain of $\sim 4$ in computing time due its $\mathcal{O}(n_{\rm max}^2)$ dependence. However, the additional computations needed by the orbital elements make a practical implementation less efficient. Our initial analysis also showed that the higher the perturbations, the less the gain in the integration order. In the case of the outer Solar System (where $m_i/M \lesssim 10^{-3}$), this gain in the decrease of the maximum of derivative order is less prominent.} Following studies could investigate the relations for the spatial problem. In some cases, this extension could be straightforward for scalar quantities like the specific energy. \dm{Care must be taken in the cases where pseudo-scalars (like $C_i$) or explicit coordinates occur.} Another interesting point can be the elimination of the need for computing the recurrence formulae for coordinates and velocities and employ directly the orbital elements. \vspace*{1ex} \noindent \textbf{Acknowledgments.} The author would like to thank the anonymous referees for their valuable comments. The author also thanks L\'aszl\'o Szabados for the careful proofreading. This work has been supported by the Hungarian Academy of Sciences via the grant LP2012-31. | 14 | 3 | 1403.7901 |
1403 | 1403.5559_arXiv.txt | We investigate the extent and the properties of the \mgii\ cool, low--density absorbing gas located in the halo and in the circum--galactic environment of quasars, using a sample of 31 projected quasar pairs with impact parameter $\pd<200 $\,kpc in the redshift range $0.5\lsim\z\lsim1.6$. In the transverse direction, we detect 18 \mgii\ absorbers associated with the foreground quasars, while no absorption system originated by the gas surrounding the quasar itself is found along the line--of--sight. This suggests that the quasar emission induces an anisotropy in the absorbing gas distribution. Our observations indicate that the covering fraction ($\fc$) of \mgii\ absorption systems with rest frame equivalent width $\ewr(\lambda2796)>0.3$\,\AA\ ranges from $\fc\sim1.0$ at $\pd\lsim65$\,kpc to $\fc\sim0.2$ at \mbox{$\pd\gsim150$\,kpc}, and appears to be higher than for galaxies. Our findings support a scenario where the luminosity/mass of the host galaxies affect the extent and the richness of the absorbing \mgii\ circum--galactic medium. | 14 | 3 | 1403.5559 |
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1403 | 1403.2379_arXiv.txt | We present the results of a survey aimed at discovering and studying transiting planets with orbital periods shorter than one day (ultra--short-period, or USP, planets), using data from the {\em Kepler} spacecraft. We computed Fourier transforms of the photometric time series for all 200,000 target stars, and detected transit signals based on the presence of regularly spaced sharp peaks in the Fourier spectrum. We present a list of 106 USP candidates, of which 18 have not previously been described in the literature. In addition, among the objects we studied, there are 26 USP candidates that had been previously reported in the literature which do {\em not} pass our various tests. All 106 of our candidates have passed several standard tests to rule out false positives due to eclipsing stellar systems. A low false positive rate is also implied by the relatively high fraction of candidates for which more than one transiting planet signal was detected. By assuming these multi-transit candidates represent coplanar multi-planet systems, we are able to infer that the USP planets are typically accompanied by other planets with periods in the range 1-50~days, in contrast with hot Jupiters which very rarely have companions in that same period range. Another clear pattern is that almost all USP planets are smaller than 2~$R_\oplus$, possibly because gas giants in very tight orbits would lose their atmospheres by photoevaporation when subject to extremely strong stellar irradiation. Based on our survey statistics, USP planets exist around approximately $(0.51\pm 0.07)\%$ of G-dwarf stars, and $(0.83\pm 0.18)\%$ of K-dwarf stars. | The field of exoplanetary science rapidly accelerated after the discovery of hot Jupiters with orbital periods of a few days (Mayor et al.~1995; Marcy \& Butler 1996). More recently, another stimulus was provided by the discovery of terrestrial-sized planets with periods shorter than one day. These objects, which we will refer to as ultra-short period or USP planets, have many interesting properties. They are so close to their host stars that the geometric probability for transits can be as large as 40\%. The expected surface temperatures can reach thousands of kelvins, allowing the detection of thermal emission from the planets' surfaces (Rouan et al.~2011; Demory et al.~2012; Sanchis-Ojeda et al.~2013a). The induced stellar orbital velocities can be as high as a few m~s$^{-1}$, allowing the planet masses to be measured with current technology even for stars as faint as $V=12$ (Howard et al.\ 2013; Pepe et al.\ 2013). Among the best known USP planets are 55~Cnc~e (Dawson \& Fabrycky 2010; Winn et al.~2011; Demory et al.~2011a), CoRoT-7b (L{\'e}ger et al.~2009; Queloz et al.~2009), and Kepler-10b (Batalha et al.~2011). The NASA {\em Kepler} space telescope (Borucki et al.~2010) monitored the brightness of about 200,000 stars for 4 years, long enough to observe thousands of transits of a typical USP planet. Along with Kepler-10b, some of the more prominent discoveries have been the innermost planets of Kepler-42 (Muirhead et al.\ 2012) and Kepler-32 (Fabrycky et al.~2012; Swift et al.~2013) and the system Kepler-70, where two very short period planets were inferred by means of the light reflected by their surfaces (Charpinet et al.\ 2011). However, since it was not clear that the official lists of {\em Kepler} USP planet candidates were complete, we and several other groups have performed independent searches. One object that emerged from our search was the Earth-sized planet Kepler-78b (Sanchis-Ojeda et al.~2013a), which has an orbital period of 8.5 hours and is currently the smallest exoplanet for which measurements of the mass and radius are both available (Howard et al.~2013; Pepe et al.~2013). Jackson et al.~(2013) performed an independent search for planets with periods $P<0.5$~day, finding several new candidates. More general surveys for {\em Kepler} planets have also found USP planets (Huang et al.~2013; Ofir \& Dreizler~2013). Particularly interesting is the discovery of KOI 1843.03 (Ofir \& Dreizler~2013), a planet with an orbital period of only 0.18~days or 4.25~hr. Rappaport et al.~(2013a) demonstrated that in order to survive tidal disruption, the composition of this Mars-sized planet must be dominated by iron as opposed to rock. In this paper we describe a survey to detect USP planets using the entire {\em Kepler} dataset. Section \ref{sec:obs} describes the data that we utilized in our study. Our Fourier-based transit search technique is explained in Section \ref{sec:search}, along with the steps that were used to winnow down thousands of candidates into a final list of 106 likely USP planets. Section \ref{sec:trans} presents the properties of the candidates. The issue of false positives within the USP list is examined in Section \ref{sec:multi}, with the conclusion that the false-positive probability is likely to be low. As a corollary we infer that most USP planets are accompanied by somewhat more distant planets. Section \ref{sec:occur} gives estimates for the occurrence rate of USP planets, and its dependence upon period, radius, and the type of host star. Finally, Section \ref{sec:disc} provides a summary of our findings and some remarks about the relevance of USP planets within the field of exoplanets. \vspace{0.5cm} | \label{sec:disc} In this work we have performed a systematic search of the entire {\em Kepler} database for ultra-short period (USP) planet candidates, defined as those having orbital periods $< 1$~day. We utilized a standard Fourier transform algorithm to search for periodic signals in the data, and found it to be quite efficient at finding short-period periodicities. An automated pipeline selected several thousand objects for further investigation including the analysis of transit-profile shapes in the folded light curves. The folded light curves for these candidates were also inspected by eye to yield a first-cut set of 375 interesting candidates. These objects were combined with 127 USP planet candidates from the KOI list, as well as other objects found in the literature, resulting in a set of 471 distinct candidates worthy of detailed study. These 471 initially selected candidates were then subjected to a number of standard tests, including examination of shifts in the light centroid during transits/eclipses, symmetry between odd and even transits/eclipses, shape of transits, etc. The final result is a set of 106 USP planet candidates that have passed a set of very restrictive tests. Eight of these objects are completely new, while another 10 were KOIs that had been rejected, largely because their orbital period had been incorrectly identified by the {\em Kepler} pipeline. Our final set of 106 USP candidates, and their properties, are summarized in Table 1. In the process we also eliminated some 26 USP candidates from the KOI list and others that were found in the literature. These are listed, along with reasons for rejection, and 8 more USP candidates not considered in this study due to low SNR, in Table 2. The USP planets are inferred to occur around one out of every 200 stars, on average. This makes them nearly as abundant as hot Jupiters. We also infer that the USPs nearly always have companion planets with $P<50$~days unlike hot Jupiters, which rarely have such companions. The occurrence rate of USP planets rises with period from 0.2 to 1~day, and there is evidence that the occurrence rate is higher for cooler stars than for hotter stars. The population of USP planets offers a number of opportunities for follow-up ground-based observations, as has already been illustrated by the examples of Kepler-10b (Batalha et al.\ 2011) and Kepler-78b (Sanchis-Ojeda et al.\ 2013a). A key finding was the relative scarcity of USP planets with radius $>2~R_\oplus$. It is worth noting that the well-known USP planet 55~Cnc~e has a radius very near the top end of the range of planet sizes in our catalog; its radius has been estimated as 2.0~$R_\oplus$ (Winn et al.\ 2011) or 2.2~$R_\oplus$ (Gillon et al.\ 2012). The results of our survey would seem to imply that the discovery of an USP planet as large as 55~Cnc~e was unlikely. However, it is difficult to assess the significance of this ``fluke'' given that the mass and radius of 55~Cnc~e were determined after a process of discovery with important and complicated selection effects. The relative scarcity of planets with $>2~R_\oplus$ could be naturally interpreted as a consequence of the strong illumination in the tight orbits. It is possible that a large fraction of the Earth-sized planets in our sample were formerly sub-Neptunes (see Owen \& Wu~2013 and references therein). There might be other observational signatures of this phenomenon, such as enhanced densities or other compositional properties, that are worth exploring. It is also worth continuing the exploration of planets with slightly longer orbital periods to determine at what distance sub-Neptunes start to become common (see Figure~\ref{fig:fressin}), and to study those systems in detail to understand the speed and efficiency of the mass-loss mechanism. It is unclear how the USP planets attained such tight orbits, although there is little doubt that they formed further away from their host stars. The relation between the USPs and the first discovered family of close-in planets---the hot Jupiters---is also not clear. For hot Jupiters, the formation problem is more difficult, in a sense, because they are supposed to have migrated from beyond the snow line, whereas current planet formation theories can accommodate the formation of smaller planets closer to the star. A full comparison between the properties of both families of planets could reveal more differences that might help us understand how the close-in small planets evolve into their current stage. In particular, it would be interesting to test whether the host stars of USP planets are preferentially metal-rich, as is well known to be the case for hot Jupiters (Santos et al.\ 2004). Studies of small planets at somewhat longer periods have not found such a metallicity effect in systems with G and K host stars (Schlaufman \& Laughlin 2011; Buchhave et al.\ 2012). It would also be interesting to measure the obliquities of the host stars to see if their rotation axes are frequently misaligned with the planetary orbits, as is the case with hot Jupiters (see, e.g., Winn et al.\ 2010; Triaud et al.\ 2010; Albrecht et al.\ 2012), or whether they have low obliquities similar to many of the multi-transit host stars that have been measured (Sanchis-Ojeda et al.\ 2012; Hirano et al.\ 2012b; Albrecht et al.\ 2013; Van Eylen et al.\ 2014). Such measurements might be challenging for small planets, but could be achievable with techniques that do not depend critically on transit observations, such as asteroseismology (Chaplin et al.\ 2013). Given a large sample of obserations, the $v \sin{i}$ technique can also be used to constrain the statistical properties of the distribution of obliquities for a given family of planets (Schlaufman 2010; Hirano et al.\ 2012a; Hirano et al.\ 2014). A large fraction of our planet candidates should induce radial velocity changes in their host stars at levels of a few meters per second. Measuring the masses of these planets, or constraining them, may be achievable with high-precision radial velocity instruments on large telescopes, at least for the brightest host stars. This would increase our knowledge of the compositions of Earth-size planets. | 14 | 3 | 1403.2379 |
1403 | 1403.4243_arXiv.txt | {We explore the possibility of emergent cosmology using the {\em effective potential} formalism. We discover new models of emergent cosmology which satisfy the constraints posed by the cosmic microwave background (CMB). We demonstrate that, within the framework of modified gravity, the emergent scenario can arise in a universe which is spatially open/closed. By contrast, in general relativity (GR) emergent cosmology arises from a spatially closed past-eternal Einstein Static Universe (ESU). In GR the ESU is unstable, which creates fine tuning problems for emergent cosmology. However, modified gravity models including Braneworld models, Loop Quantum Cosmology (LQC) and Asymptotically Free Gravity result in a stable ESU. Consequently, in these models emergent cosmology arises from a larger class of initial conditions including those in which the universe eternally oscillates about the ESU fixed point. We demonstrate that such an oscillating universe is necessarily accompanied by {\em graviton production}. For a large region in parameter space graviton production is enhanced through a parametric resonance, casting serious doubts as to whether this emergent scenario can be past-eternal. } | \label{sec: intro} The inflationary scenario has proved to be successful in describing a universe which is remarkably similar to the one which we inhabit. Indeed, one of the central aims of the ongoing effort in the study of cosmic microwave background (CMB) observations is to converge on the correct model describing inflation \cite{Ade:2013uln}. However, despite its very impressive achievements, the inflationary paradigm leaves some questions unanswered. These pertain both to the nature of the inflaton field and to the state of the universe prior to the commencement of inflation. Indeed, as originally pointed out in \cite{Borde:2001nh}, inflation (within a general relativistic setting) could not have been past eternal. This might be seen to imply one of several alternative possibilities including the following: \begin{enumerate} \item The universe quantum mechanically tunnelled into an inflationary phase. \item The universe was dominated by radiation (or some other form of matter) prior to inflation and might therefore have encountered a singularity in its past. \item The universe underwent a non-singular bounce prior to inflation. Before the bounce the universe was contracting. \item The universe existed `eternally' in a quasi-static state, out of which inflationary expansion emerged. \end{enumerate} One should point out that, at the time of writing, none of the above possibilities is entirely problem free. Nevertheless, our focus in this paper will be on the last option, namely that of an {\em Emergent Cosmology}. The idea of an emergent universe is not new and an early semblance of this concept can be traced back to the seminal work of Eddington \cite{Eddington:1930zz} and Lema\^{\i}tre \cite{Lemaitre:1927zz}, which was based on the Einstein Static Universe \cite{Einstein:1917ce}. Indeed, in 1917, Einstein introduced the idea of a closed and static universe sourced by a cosmological constant and matter. Subsequently it was found that: (a) the observed universe was expanding \cite{Hubble:1929ig}, (b) the Einstein Static Universe (ESU) was unstable. It therefore became unlikely that ESU could describe the present universe but allowed for our universe to have emerged from a static ESU-phase in the past. With the discovery of cosmic expansion Einstein distanced himself from his own early ideas referring to them, years later, as his biggest blunder \cite{Pais:1982up}. Interest in the ESU subsequently waned, although models in which the ESU featured as an intermediate stage --- called {\em loitering\/} --- received a short-lived burst of attention in the late 1960's, when it was felt that a universe which loitered at $z \simeq 2$ might account for the abundance of QSO's at that redshift; an observation that inspired Zeldovich to write his famous review on the cosmological constant \cite{Zel'dovich:1968zz}. The present resurgence of interest in ESU and emergent cosmology owes much to the CMB observations favouring an early inflationary stage, supplemented by the fact that an inflationary universe is geodesically incomplete \cite{Borde:2001nh} and might therefore have had a beginning. This paper commences with a discussion of emergent cosmology in the context of general relativity in section \ref{sec:emergent_GR}. Since GR-based ESU is unstable, this scenario suffers from severe fine-tuning problems, as originally pointed out in \cite{Ellis:2002we,Ellis:2003qz}. One can construct stable ESUs in the context of the Braneworld scenario \cite{Shtanov:2002mb}, Loop Quantum Cosmology (LQC) \cite{Ashtekar:2006uz} and Asymptotically Free Gravity. This is the focus of section \ref{sec:emergent_grav}. When viewed in the classical context, a stable ESU allows the universe to oscillate `eternally' about the ESU fixed point \cite{Mulryne:2005ef,Parisi:2007kv}. If the universe is filled with a scalar field, then these oscillations can end, giving rise to inflation. However, this scenario is feasible only for an appropriate choice of the inflaton potential. Equally important is the fact that an oscillating universe generically gives rise to graviton production, which forms the focus of section \ref{sec:graviton}. For a large region in parameter space, the production of gravitons proceeds through a parametric resonance, which seems to question the possibility of whether a universe could have oscillated `eternally' about the ESU fixed point. Our conclusions are drawn in section \ref{sec:conclusions}. Our main results seem to suggest that, while emergent cosmology (EC) can be constructed on the basis of both GR and modified gravity, the restrictions faced by working EC models are many. Consequently, realistic EC is possible to construct only in a small region of parameter space, and that too for a rather restrictive class of inflationary potentials. | \label{sec:conclusions} In this paper we have shown how the effective potential formalism can be used to study the dynamical properties of the emergent universe scenario. Within the GR setting, the effective potential has a single extreme point, a maximum, which corresponds to the {\em unstable} Einstein Static Universe (ESU). Extending our analysis to modified gravity theories we find that a new {\em minimum} in the effective potential appears corresponding to a {\em stable} ESU. These results are in broad agreement with earlier studies which also pointed out the appearance of an ESU in the context of extensions to GR \cite{Mulryne:2005ef,Parisi:2007kv,Boehmer:2007tr}; also see \cite{Mukherjee:2006ds}. While in GR, the emergent scenario can only occur if the universe is closed, we show that this restriction does not apply to certain modified gravity models in which the emergent scenario can occur in spatially closed as well as open cosmologies. The appearance of a stable minimum in the effective potential considerably enlarges the initial data set from which the universe could have `emerged'. In this case, in addition to being precisely located at the minimum (ESU) -- which requires considerable fine tuning of initial conditions, the universe can oscillate about it. Furthermore, we show that the existence of an ESU, while being conducive for emergent cosmology, is not essential for it. In section \ref{sec:LQC} this is demonstrated for LQC for which a stable ESU exists only for $\Lambda>\kappa \rho_c$ \cite{Parisi:2007kv}. We demonstrate that even for $\Lambda\ll \kappa \rho_c$, when a stable ESU no longer exists, the universe can still oscillate about the minimum of its effective potential allowing an emergent scenario to be constructed. However an oscillating universe is always accompanied by graviton production. While the magnitude of this semi-classical effect depends upon parameters in the effective potential, % for a large region in parameter space this effect can be very large, casting doubts as to whether such an emergent scenario could have been past-eternal.\footnote{ Graviton production is small, and does not stand in the way of emergent cosmology being past eternal, only if the universe oscillates very near the minimum of its effective potential. (Naturally, there is no particle production for a universe located precisely at the minimum of $U(a)$, i.e. for the ESU.) But this situation might require considerable fine tuning of parameters.} (The instability of emergent cosmology to quantum effects has also been recently investigated in \cite{Mithani:2014jva}.) Although graviton production has been discussed in detail for an effective potential derived from the braneworld scenario, the effect itself is semi-classical and generic, and would be expected to accompany any emergent scenario in which the universe emerges from an oscillatory state. One might also note that in the emergent scenarios discussed in this paper, the post-emergent universe inflates by well over 60 e-folds. Consequently any feature associated with the transition from an ESU to inflation is pushed to scales much larger than the present horizon. However it could well be that in some emergent scenarios this is not the case, and the transition from the ESU to inflation takes place fewer than $\sim 60$ e-folds from the end of inflation. In this case the spectrum of inflationary perturbations would differ from those considered in this paper on large scales, and may contain a feature in the CMB anisotropy spectrum, $C_\ell$, at low values of $\ell$. \bigskip | 14 | 3 | 1403.4243 |
1403 | 1403.6841_arXiv.txt | We discuss the ongoing development of single-mode fiber Fabry-Perot (FFP) Interferometers as precise astro-photonic calibration sources for high precision radial velocity (RV) spectrographs. FFPs are simple, inexpensive, monolithic units that can yield a stable and repeatable output spectrum. An FFP is a unique alternative to a traditional etalon, as the interferometric cavity is made of single-mode fiber rather than an air-gap spacer. This design allows for excellent collimation, high spectral finesse, rigid mechanical stability, insensitivity to vibrations, and no need for vacuum operation. The device we have tested is a commercially available product from Micron Optics\footnotemark[0]\footnotetext[0]{Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.}. Our development path is targeted towards a calibration source for the Habitable-Zone Planet Finder (HPF), a near-infrared spectrograph designed to detect terrestrial-mass planets around low-mass stars, but this reference could also be used in many existing and planned fiber-fed spectrographs as we illustrate using the Apache Point Observatory Galactic Evolution Experiment (APOGEE) instrument. With precise temperature control of the fiber etalon, we achieve a thermal stability of 100 $\mu$K and associated velocity uncertainty of 22 cm s$^{-1}$. We achieve a precision of $\approx$2 m s$^{-1}$ in a single APOGEE fiber over 12 hours using this new photonic reference after removal of systematic correlations. This high precision (close to the expected photon-limited floor) is a testament to both the excellent intrinsic wavelength stability of the fiber interferometer and the stability of the APOGEE instrument design. Overall instrument velocity precision is 80 cm s$^{-1}$ over 12 hours when averaged over all 300 APOGEE fibers and after removal of known trends and pressure correlations, implying the fiber etalon is intrinsically stable to significantly higher precision. | Many hundreds of exoplanets have been discovered or confirmed using high precision Doppler radial velocity (RV) techniques. With high resolution spectrographs such as HIRES \citep{1994SPIE.2198..362V} on the Keck I telescope and HARPS \citep{2003Msngr.114...20M} on the ESO La Silla 3.6m telescope reaching long term precisions of 1 - 2 m s$^{-1}$ or better in the visible, detecting low mass planets around other stars has become a feasible endeavor. Utilizing precise calibration and novel data reduction methods, a wealth of low-mass planets are being discovered using these instruments. M-dwarfs are estimated to makeup the majority (over 70 percent) of stars in the Milky Way (RECONS\footnote{\url{http://www.chara.gsu.edu/RECONS/}}). These small stars have low masses, resulting in large Doppler reflex signals due to orbiting companions. Habitable-Zone (HZ) boundaries \citep{2013ApJ...765..131K} are also much closer to the host stars in M-dwarf systems than larger solar-type stars, making them ideal candidates for surveys designed to detect potentially habitable planets. Recently \cite{2013arXiv1302.1647D} used $Kepler$ data to estimate the frequency of terrestrial planets in the HZ of cool stars and arrive at a planetary occurrence rate of $0.15^{+0.13}_{-0.06}$ per star for Earth-size planets (0.5 - 1.4)$R_{\earth}$. \cite{2013ApJ...767L...8K} reanalyzed this data using new HZ boundaries and arrive at an even higher terrestrial planet frequency of $0.48^{+0.12}_{-0.24}$ per M-dwarf. These high occurrence rates imply the solar neighborhood is potentially teeming with terrestrial planets orbiting in the HZs of cool stars. This is an exciting region of exoplanet discovery space, and many dedicated instruments are being built specifically to observe these cool stars. Achieving 1 m s$^{-1}$ precision will allow for the robust detection of terrestrial-mass planets in the HZs of many nearby M-dwarfs systems. Instruments such as the Habitable-Zone Planet Finder (HPF, \cite{2012SPIE.8446E..1SM}) and the Calar Alto high-Resolution search for M dwarfs with Exoearths with Near-infrared and optical Echelle Spectrographs (CARMENES, \cite{2012SPIE.8446E..0RQ}) will be on the forefront of dedicated near-infrared (NIR) Doppler instruments, capable of achieving 1 - 3 m s$^{-1}$ measurement precision on low mass M-dwarfs. HPF consists of a stabilized, R $\approx$ 50 000 fiber-fed spectrograph enclosed in a large vacuum cryostat that is cooled to 180 K. The spectrograph simultaneously covers parts of the z (0.8 - 0.9 $\mu$m), Y (0.95 - 1.1 $\mu$m) and J (1.2 - 1.35 $\mu$m) NIR bands. For the next generation of stabilized NIR Doppler spectrographs to be able to achieve 1 m s$^{-1}$ precision or better on nearby stars, a highly stable calibration source must be used to accurately remove any instrumental drifts. Detection of low mass planets requires stable, accurate instruments for confident detections. Simultaneous wavelength calibration of starlight, either by imprinting spectral features directly onto the stellar spectrum or by having a dedicated calibration fiber with a stable reference is required to achieve the highest measurement precisions. Wavelength calibrators such as molecular iodine cells and Thorium-Argon (Th-Ar) lamps have been used to great success in the visible as references against which Doppler shifts are measured, but can be limiting factors in the push for increasing measurement precision. The limited wavelength coverage and non-uniform spectral features of these references places limits on high precision measurements. This is especially true in the NIR, where no precise wavelength calibrators have been traditionally available. Here we present test results of a commercially produced single-mode fiber (SMF) Fiber Fabry-Perot interferometer (FFP) as a precise calibration source in the H-band (1.5 - 1.7 $\mu$m). Tests with the Sloan Digital Sky Survey III (SDSS-III, \cite{2011AJ....142...72E}) APOGEE instrument demonstrate radial velocity precisions close to the expected photon-noise limit. This device represents one of the only \lq{}astro-photonic\rq{} devices being developed for high precision RV measurements. FFPs, like conventional Fabry-Perot cavities, create interference patterns by combining light traversing different delays. The interference creates a rich spectrum of narrow lines, ideal for use as a precise spectrograph reference. An FFP can produce a high density of clean lines over a wide bandwidth, greatly expanding the wavelength regions over which precise RV measurements are possible. The physical nature of Fabry-Perot cavities does not, by itself, enable absolute wavelength calibration but does provide a stable grid of lines to track instrument drift. | \label{sec:cals} \subsection{Molecular Absorption Cells} Simultaneous calibration using molecular Iodine (I$_2$) cells has achieved long-term RV precisions of 1$-3$ m s$^{-1}$\citep{1996PASP..108..500B, 2012ApJ...751L..16A} using the entire 500 - 620 nm bandwidth of the I$_2$ cell. Incident starlight is passed through a temperature controlled absorption cell which imprints the dense forest of I$_2$ molecular lines onto the stellar spectrum. This allows for precise correction of instrument point-spread function (PSF) changes and simultaneous wavelength calibration. The intrinsic I$_2$ spectrum must be measured to high accuracy in order to correctly model PSF variations and extract precise velocity measurements. No such absorption cell currently exists that covers major parts of the z/Y/J/H NIR bands, where the majority of the flux lies for a typical mid to late M-dwarf, though many development efforts are currently underway \citep{doi:10.1117/12.2023690}. \cite{2010ApJ...713..410B} achieved $\approx$3 m s$^{-1}$ RV precision on bright M-dwarfs in the $K$ band using simultaneous calibration with a NH$_3$ cell on the CRIRES \citep{2004SPIE.5492.1218K} instrument on VLT. The wavelength coverage of this method is narrow, spanning roughly 36 nm. This also required the high resolving power (R = 100 000) of CRIRES and bright (K$<$8 mag) targets, but is an interesting wavelength region as $K$ band is densely populated with telluric absorption features from H$_2$O and CH$_4$. \cite{2010ApJ...723..684B} utilized this stable forest of telluric H$_2$O and CH$_4$ bands near 2.3 $\mu$m to obtain RV precisions of $\approx$50 m s$^{-1}$ on ultracool dwarfs using the NIRSPEC instrument on the Keck II telescope. These telluric features are not static however, and require unique reduction methods and careful atmospheric monitoring to reach $<$10 m s$^{-1}$ precision. \cite{2009ApJ...692.1590M} explored using a number of commercially available molecular gas cell references and concluded that a combination of H$^{13}$C$^{14}$N, $^{12}$C$_2$H$_2$, $^{12}$CO, and $^{13}$CO cells, illuminated by a continuum source, could provide a dense enough set of features for precise calibration in the H-band. \cite{2012SPIE.8446E..8GR} discuss the plans to improve the measurement precision of CRIRES using these cells. \subsection{Emission Lamps} Hollow cathode lamps (HCLs) are widely used in high-resolution spectroscopy to derive precise wavelength solutions. These lamps produce a dense set of emission features to calibrate against, though the density and relative strength of these features can lead to a significant number of blends. Bright lines from the lighter fill gases of HCLs can be used for moderate precision wavelength calibration, but are a significant source of error in sensitive high-resolution instruments that require a high-precision calibration \citep{2006SPIE.6269E..23L}. The popular Thorium-Argon HCL has been used to attain sub m s$^{-1}$ long term precision on stable, inactive Solar-type stars with HARPS \citep{2011arXiv1109.2497M}. The wealth of available atomic $^{232}$Th transitions provide emission features spanning the UV to NIR regions, making the element ideal for use as a broadband wavelength reference. However Thorium does not contain sufficient bright lines beyond 1 $\mu$m to be the optimal wavelength calibration source in the NIR. Additionally, emission lines from the Ar fill gas in these lamps are bright in the NIR, and can saturate detector areas during typical exposure timescales. Ar lines are also susceptible to pressure shifts, making them highly sensitive to ambient conditions \citep{2006SPIE.6269E..23L}. Precise calibration using Uranium-Neon (U-Ne) hollow-cathode lamps has yielded RV precisions of $<$10 m s$^{-1}$ using the Pathfinder testbed instrument \citep{2010SPIE.7735E.231R} on bright RV standard stars. $^{238}$U, like $^{232}$Th, is a heavy element with a long half-life. This represents one of the few emission lamps tested specifically for use in NIR Doppler instruments. A high density of lines is present in all commonly used NIR bands \citep{2011ApJS..195...24R, 2012ApJS..199....2R}, making the lamp ideal for use as a precise reference source. The U-Ne lamp in the NIR does not suffer from the bright Ar lines, though the high density of Uranium lines results in many blended features even at the high resolution of astronomical spectrographs. Both Th-Ar and U-Ne lamps are routinely used in the SDSS/APOGEE instrument. \subsection{Laser Frequency Combs} Laser Frequency Combs (LFC) have also been tested in astronomical applications with success in recent years. LFCs represent the pinnacle for current astronomical wavelength references, producing sharp emission features at frequencies traceable to a stable atomic transition. Combs used in astronomical applications comb are generally frequency stabilized by locking both the offset frequency and laser repetition rate to a global positioning system-stabilized atomic clock which can yield absolute precisions better than $10^{-10}$\citep{2012OExpr..20.6631Y}. Despite the high cost and complexity in design, LFC development is a high priority in the spectroscopic community due to the desire to increase RV precision in order to detect Earth-like planets. The difficulty lies in creating a LFC that both spans the entire optical or NIR regions, and is stable over long intervals. LFCs have been shown to be stable to the cm s$^{-1}$ level \citep{2008Natur.452..610L}, but are not quite yet at the \lq{}turn-key\rq{} stage of use in astronomical instruments. While our group and other groups are actively pursuing this path \citep{2012OExpr..20.6631Y,2012OExpr..2013711P}, LFCs are currently expensive and are likely only a viable option for a limited number of high precision instruments on large telescopes. \subsection{Fabry-Perot References} Fabry-Perot interferometers (FPI) can yield high velocity precision with precise environmental control, though lack the innate absolute referencing of a frequency-locked LFC. To an astronomical spectrograph, the output spectrum of an FPI is quite similar to that of an LFC despite originating from very different physical properties. The intrinsic spectrum of the FPI is a picket fence of interferometric Airy peaks filtered from a broadband continuum source, rather than a discrete set of emission lines generated from a series of laser pulses. \cite{2012SPIE.8446E..8EW} tested custom air-gap FPIs for the HARPS and HARPS-N spectrographs, achieving 10 cm s$^{-1}$ stability over a nightly interval. In both instruments Zerodur was used as the cavity spacer material to minimize thermal sensitivity. Previous versions of the device were subject to large velocity drifts possibly due to varying collimation from the multi-mode fiber illumination \citep{2010SPIE.7735E.164W}. This was corrected by redesigning the interferometer housing to provide a more constant illumination incident on the cavity. Precise temperature and vacuum control are required to maintain the cavity length and density to the precision required. Night to night drift of the updated device is very low, averaging 10 cm s$^{-1}$ stability over one night and 1 m s$^{-1}$ stability over 60 days \citep{2012SPIE.8446E..8EW}. \subsection{Photon-Limited Precision Comparison of Sources} \label{sec:photon_limit} The ideal Doppler calibration spectrum is a picket fence of stable, sharp emission features. Spectral regions with large flux gradients have the highest information content, and therefore contribute the highest precision. Continuum regions, areas with low line density, and areas with many blended lines do little to increase Doppler measurement precision significantly. A high density of uniform and fairly evenly separated lines will therefore give the highest velocity measurement precision \citep{2007MNRAS.380..839M}. Fabry-Perots and frequency combs have both of these attributes. For a given velocity shift, as measured by pixel $i$ at wavelength $\lambda(i)$ with associated noise $\sigma_{F}(i)$ in an extracted spectrum $F(i)$, the limiting velocity precision, $\sigma_v(i)$, is (as described in \cite{2001A&A...374..733B}): \begin{equation} \frac{\sigma_{v}(i)}{c} = \frac{\sigma_{F}(i)}{\lambda(i)[{\partial F(i)}/{\partial \lambda(i)}]}. \label{eq:qfact} \end{equation} The total velocity precision, $\sigma_v$, from all pixels is then: \begin{equation} \sigma_v = \frac{1}{\sqrt{\sum_i \sigma_v(i)^{-2}}}. \end{equation} Figure~\ref{fig:photon_rv} shows the expected photon-limited velocity measurement precision for several calibration sources discussed in the text assuming a noiseless detector, $R\approx$50 000 instrument resolving power, maximum signal-to-noise of 200 per pixel in extracted spectrum, and three-pixel sampling of the resolution element. The LFC and FP references clearly enable higher measurement precision than typical atomic emission lamps. Atomic lamp spectra are generated from archival FTS line lists \citep{2011ApJS..195...24R,0067-0049-178-2-374}. The fill gas elements (Argon, Neon) were not included in the analysis as they are generally excluded for precise calibration work. Emission lines from the fill gases also tend to be much brighter, exacerbating extraction issues. \begin{figure} \begin{center} \includegraphics[width=3.5in]{f1-eps-converted-to.pdf} \caption{Theoretical photon-limited velocity precision of reference sources discussed in the text using the methods from \cite{2001A&A...374..733B}. Velocity errors were computed for 20 nm sections of model spectra assuming $R = $ 50 000 with three pixel sampling of the resolution element and maximum SNR of 200 in the extracted spectrum. The peak signals for the simulated LFC and FP spectra are assumed to be uniform for all lines. The squares are the total velocity precision in each NIR band. The LFC and FP references give significant precision advantages over classical emission lamps.} \label{fig:photon_rv} \end{center} \end{figure} We present a NIR H-band fiber Fabry-Perot interferometer as a precise spectrograph calibration device. This device is a commercially available product we are developing as a prototype for a similar calibration source being developed for the HPF instrument. An FFP is a unique alternative to traditional wavelength calibration systems, providing a dense set of stable spectral features across a wide wavelength range. A stabilized fiber etalon can yield high relative precisions at relatively low cost. Precise temperature control is essential for these devices, as the spectral output is sensitive to significant shifts even at moderately stable temperature control. With a benchtop controller, we are able to achieve a thermal control precision of 100 $\mu$K, corresponding to roughly 22 cm s$^{-1}$ velocity stability. Tests on the SDSS-III APOGEE spectrograph showed the FFP was able to track instrument drift at precisions close to the expected photon-limit of the instrument. An individual APOGEE fiber was tracked to better than $\approx$3 m s$^{-1}$. This represents nearly two orders of magnitude improvement in measurement sensitivity for the APOGEE instrument. When averaging over all fibers, our measurement precision improves to 80 cm s$^{-1}$ over 12 hours. Stress-induced birefringence of the SMF used in the FFP leads to a strong polarization dependence in the output spectrum. This effect was directly observed in the laboratory experiments using a polarized 1550 nm laser in data taken at the NIST 2.0 m FTS, though we do not believe this was an issue in the APOGEE data discussed here. We have significantly reduced this sensitivity by adding a high-contrast polarizer at the FFP input and shortening the amount of polarization-altering SMF-28 fiber prior to the interferometer cavity. The high RV precisions achieved here validate the design attributes of the APOGEE instrument as ideal fundamental traits for a highly stable Doppler velocimeter. Many of these ideas will be used on the HPF instrument to achieve better stability and overall velocity precision. These results also validate the fundamental soundness of the cryogenic enclosure design being adopted for precision RV instruments like HPF. | 14 | 3 | 1403.6841 |
1403 | 1403.4596_arXiv.txt | { The BICEP2 collaboration has reported a strong $B$ mode signal in the CMB polarization, which is well fit by a tensor-to-scalar ratio of $r\simeq 0.2$. This is greater than the upper limit $r < 0.11$ obtained from the temperature anisotropies under the assumption of a constant scalar spectral index $n_s$. This discrepancy can be reduced once the statistical error and the contamination from polarized dust are accounted for. If however a large value for $r$ will be confirmed, it will need to be reconciled with the temperature anisotropies data. The most advocated explanation involves a variation of $n_s$ with scales (denoted as running) that has a magnitude significantly greater than the generic slow roll predictions. We instead study the possibility that the large scale temperature anisotropies are not enhanced because of a suppression of the scalar power at large scales. Such a situation can be achieved for instance by a sudden change of the speed of the inflaton (by about $14\%$), and we show that it fits the temperature anisotropies and polarization data considerably better than a constant running (its $\chi^2$ improves by $\sim 7.5$ over that of the constant running, at the cost of one more parameter). We also consider the possibility that the large scale temperature fluctuations are suppressed by an anti-correlation between tensor and scalar modes. Unfortunately, while such effect does affect the temperature fluctuations at large scales, it does not affect the temperature power spectrum and cannot, therefore, help in reconciling a large value of $r$ with the limits from temperature fluctuations. } \begin{document} | The BICEP2 experiment \cite{Ade:2014xna} has observed a $B$-mode polarization of the Cosmic Microwave Background (CMB) that can be well fit by a lensed-$\Lambda$CDM + tensor theoretical model, with tensor-to-scalar ratio $r=0.2^{+0.07}_{-0.05}$, with $r=0$ disfavored at $7\sigma$. It is possible that the actual primordial component of the $B$-mode found by BICEP2 is smaller than $r=0.2$. A number of tests were performed on the BICEP2 data to ensure that the the observed value is not due to any instrumental effects. Moreover, the lensing contribution to $B$-modes does not appear to be sufficiently large to explain the measured value. The signal, observed by BICEP2, peaks at $\ell \approx 100$, where the primordial signal is expected to dominate, whilst the lensing signal peaks at $\ell \approx 1000$. Other potential contaminants are the Galactic synchrotron and polarized-dust emission. Whilst the former effect is negligible at the BICEP2 observing frequency, the polarized dust is a substantial contaminant. Although the area of sky probed by BICEP2 is very clean with respect to the total intensity emission by dust there is still much uncertainty in the level of polarised dust contamination due to the lack of observations. A number of models were considered by BICEP2 for the subtraction of the dust contamination which result in some shift in the maximum likelihood values in $r$. A further argument for the primordial nature of the signal is that cross-correlation between frequencies (specifically, the preliminary BICEP2 $\times$ Keck cross-correlation shown in \cite{Ade:2014xna}) displays little change in the observed amplitude. This appears to indicate that frequency dependent foregrounds are not the dominant contributor to the observed $B$-modes. On the other hand, more recent works \cite{antibicep} (appeared after the first version of this manuscript) argue that the polarized dust contamination is likely stronger than what assumed in \cite{Ade:2014xna}. This could invalidate BICEP2 claim of a primordial origin of the observed signal, or at least reconcile it with the Planck limit \cite{Ade:2013uln} $r < 0.11$. In this work we assume that the BICEP2 noise estimate is correct. The data already collected by Planck should have the sensitivity and frequency range to definitely confirm or rule out the primordial nature of such a large signal. If the primordial contribution to the $B$-modes is confirmed, it will represent the first detection of gravity waves from inflation \cite{Ade:2014xna}. This is of paramount importance, since - under the assumption that the observed gravity waves are those created by a period of quasi de-Sitter inflationary expansion (namely that $P_t \sim V/M_p^4$, where $P_t$ is the tensor power spectrum, $V^{1/4}$ is the energy scale of inflation, and $M_p \simeq 2.4 \times 10^{18} $ GeV is the reduced Planck mass) - it allows us, for the first time, to determine the energy scale of inflation. From the parametrization $r \equiv P_t/P_s$, and from the measured value of the scalar power spectrum, $P_s \simeq 2.45 \times 10^{-9}$, one obtains the well known relation \begin{equation} V^{1/4} \simeq 2.25 \cdot 10^{16} \, {\rm GeV} \; \left( \frac{r}{0.2} \right)^{1/4} \;. \end{equation} Therefore, if the $B$-mode signal observed by BICEP2 is due to inflationary vacuum modes, we have now learnt that inflation took place at the GUT scale. As we already mentioned, taken at face value, the BICEP2 value is in strong tension with the $2 \sigma$ limit $r<0.11$ obtained by the Planck inflation analysis \cite{Ade:2013uln}. Such a limit however relies on the scaling of the temperature anisotropy data (supplemented by the WMAP large-scale polarization likelihood), and not on the direct measurement of the $B$-mode polarization. The $r<0.11$ limit appears robust under the inclusion of several data sets (such as the ACT+SPT temperature data, BAO, and the Planck lensing \cite{Ade:2013uln}). However, it crucially relies in the assumption of a constant spectral tilt $n_s$. Specifically, it is obtained from the Planck+ACT+SPT temperature data (with the Planck data supplemented by the WMAP large-scale polarization likelihood), under the assumption of constant spectral tilt $n_s = 0.960 \pm 0.007$ \cite{Ade:2013uln}. As discussed in \cite{Ade:2013uln}, a more relaxed limit is obtained if $n_s$ is allowed to vary with scale $k$. Specifically, it is customary to parametrize the scalar power spectrum as \begin{equation} P_s \left( k \right) \equiv P \left( k_0 \right) \left( \frac{k}{k_0} \right)^{n_s - 1 + \frac{1}{2} \alpha_s \ln \frac{k}{k_0} } \;, \label{parametrizationP} \end{equation} where $k_0 = 0.05$ Mpc$^{-1}$, is the chosen pivot scale (this is the scale at which also $r$ is defined) and the parameter $\alpha_s$ denotes the running of the scalar spectral tilt \cite{Kosowsky:1995aa} with $\alpha_s = \frac{d \, n_s}{d \, {\rm ln } \, k}$. If $\alpha_s \neq 0$, the $r<0.11$ limit is relaxed to $r \la 0.25$. From Figure~5 of \cite{Ade:2013uln} we infer that a value $\alpha_s \sim - 0.02$ is required to reconcile the temperature data with $r =0.2$. Such a large value of $\vert \alpha_s \vert$ is not a generic prediction of slow roll inflationary models. Indeed, in terms of the slow roll parameters \begin{equation} \epsilon \equiv \frac{M_p^2}{2} \left( \frac{V_{,\phi}}{V} \right)^2 \;,\; \eta \equiv M_p^2 \frac{V_{,\phi\phi}}{V} \;,\; \xi^2 \equiv M_p^4 \frac{V_{,\phi} V_{,\phi\phi\phi}}{V^2} \;, \end{equation} where $V$ denotes the potential of the inflaton $\phi$ and comma denotes a derivative, we have the well known slow roll relations \begin{eqnarray} && r = 16 \, \epsilon \;\;\;,\;\;\; n_s - 1 = 2 \eta - 6 \epsilon\,, \nonumber\\ && \alpha_s = - 2 \xi^2 + \frac{r}{2} \left( n_s - 1 \right) + \frac{3}{32} r^2 \simeq - 2 \xi^2 - 0.00025\,, \nonumber\\ \label{slow-roll} \end{eqnarray} where $n_s = 0.96$, $r=0.2$ has been used in the final numerical estimate. This is typically much smaller than the required value, since, as evident in (\ref{slow-roll}), the running is generically of second order in slow roll. In principle, models can be constructed in which the third derivative term $\xi^2$ is ``anomalously large''. However, besides being hard to motivate, it is difficult to maintain a large third derivative, while the first two derivatives are small, for a sufficiently long duration of inflation, \cite{Chung:2003iu,Easther:2006tv}, so that the models in which a large running is achieved have potentials with some bump-like feature or superimposed oscillations \cite{Hannestad:2000tj,Chung:2003iu, Feng:2003mk,Kobayashi:2010pz,Takahashi:2013tj}, or possess some peculiar aspects beyond standard scenarios \cite{Kawasaki:2003zv,Huang:2003zp,BasteroGil:2003bv,Yamaguchi:2003fp,Ballesteros:2005eg}. In summary, it appears that $r=0.2$ can be reconciled with the limits from the temperature anisotropies through a negative running, which is however of substantially larger magnitude than the generic slow roll prediction. It is possible that the value of $r$ from the polarization will shift towards $r \sim 0.1$, in which case the tension with the temperature data can be relaxed (or disappear altogether). This can happen factoring in both the statistical uncertainty in the BICEP2 $r=0.2^{+0.07}_{-0.05}$ result, and the decrease of $r$ that appears in most of the model-dependent dust corrections \cite{Ade:2014xna}. Remarkably, $r$ close to $0.15$ appears as a prediction of the simplest models of inflation, such as chaotic inflation~\cite{Linde:1983gd} and natural inflation~\cite{Freese:1990rb}. Even if UV complete theories typically leads to a lower inflationary scale, it is possible to construct models that can evade the fundamental constraints which typically make high-scale inflation difficult to realize~\cite{Kim:2004rp,Kaloper:2008fb,Kaloper:2011jz,Pajer:2013fsa} and still display such simple potentials. However, from a theoretical point of view, it is interesting to understand the implications that a large measured value for $r$ from polarization would have for inflationary model building. In this work we discuss two additional possibilities (in addition to the already mentioned running of the spectral tilt) to suppress the large scale temperature signal in presence of a large $r\simeq 0.2$. The first mechanism relies on the presence of a large scale suppression in the scalar power. A similar idea was already explored in \cite{Contaldi:2003zv}, in order to address the suppressed power of the temperature anisotropies at the largest scales. The best fit to the first year WMAP data was obtained if the power drops to zero at scales $k \la 5 \times 10^{-4} \, {\rm Mpc}^{-1}$ \cite{Bennett:2003bz}. Such a strong suppression can for example occur if the universe is closed, with a curvature radius comparable to the horizon at the onset of inflation \cite{Linde:2003hc}, or if the inflaton was in fast roll at the beginning of the last $\sim 60$ $e$-folds of inflation~\cite{Contaldi:2003zv}. In this case, one also expects a suppression of the tensor signal at large scales, although this suppression is milder than that of the scalar power \cite{Nicholson:2007by}. Here, for simplicity, we only consider a simple model for suppression in order to explore the viability of such a model in explaining the surprisingly discrepancy between $TT$ and $BB$ spectra. We do not assume that the power drastically drops to $\simeq 0$ at large scales, but that it decreases by a factor $\left( 1 - \Delta \right)^2$ for $k$ smaller than a given scale $k_*$ (a similar analysis on Planck data only was performed in~\cite{Hazra:2013nca}). Our best fit is characterized by a $\sim 26\%$ drop in power that can be achieved for example by a change of slope of the inflaton potential, such that the inflaton goes slightly faster when the largest modes were generated. However, the system never leaves the slow-roll regime. Therefore, contrary to the situation studied in \cite{Contaldi:2003zv,Bennett:2003bz} there is no discontinuity in the tensor power. Specifically, we study the model originally proposed by Starobinsky \cite{Starobinsky:1992ts} for this change in slope (see also~\cite{Kaloper:2003nv}). Alternatively, a change in power can result from a change of the sound speed of the inflaton perturbations~\cite{Park:2012rh} (see also~\cite{Wu:2006xp,D'Amico:2013iaa} for other models leading to a similar effect). The second possibility that we discuss is a negative correlation between the scalar and tensor signal\footnote{In a previous version of this manuscript we reached a different conclusion. This section has been modified after the findings of~\cite{Zibin:2014iea,Emami:2014xga}, see also~\cite{Chen:2014eua}.}. This correlation will affect the sum of the scalar and tensor modes on the temperature anisotropy. Some degree of non-vanishing scalar-tensor correlation is expected in the presence of the breaking of Lorentz invariance, and for example it arises if the background expansion is anisotropic \cite{Gumrukcuoglu:2006xj,Pereira:2007yy,Gumrukcuoglu:2007bx,Pitrou:2008gk}. Unfortunately, we will see that such a correlation does not affect the temperature power spectrum, and will therefore not help reconcile the constraints on $r$ from $TT$ with those from $BB$ spectra. The plan of the paper is the following: In Section~\ref{cut-off} we discuss the effects of a large scale suppression of the scalar power. In Section~\ref{anti} we discuss the effects of an anti-correlation between scalar and tensor modes. In Section ~\ref{conclusions} we present our conclusions. Finally, in Appendix ~\ref{app} we study a parametrization of the scalar power spectrum characterized by a step function suppression. This parametrization lacks the ``ringing'' effect that is typically encountered in concrete models (see Figure \ref{fig:starob}). The comparison between the two analyses shows that the ringing present in the Starobinsky model has a minor impact on the data. | \label{conclusions} The BICEP2 experiment has detected a $B$-mode polarization signal in the CMB that can be explained by a lensed-$\Lambda$CDM + tensor theoretical model, with tensor/scalar ratio $r=0.2^{+0.07}_{-0.05}$. While keeping in mind that the central value can be reduced with more statistics or with the subtraction of the dust-polarized signal, we discussed some possible mechanism that may explain how $r=0.2$ can be reconciled with the upper limits on tensor modes from the temperature anisotropies measurements. A possible way to reconcile this discrepancy is already offered in the Planck \cite{Ade:2013uln} and the BICEP2 \cite{Ade:2014xna} analyses, where a running of the spectral tilt is advocated. However, if the central value $r=0.2$ will be confirmed, the required magnitude of the running is significantly greater than the generic slow-roll predictions. Motivated by this, we discussed two alternative possibilities for suppressing the large scales temperature anisotropies. The first possibility involves a large scale suppression in the scalar power. This can for instance be achieved if the inflaton zero mode has a greater speed, or if the inflaton perturbations have a larger speed of sound, when the largest observable scales are produced. This resembles the study of \cite{Contaldi:2003zv}, in which the power at very large drops to a negligible value due to a period of kinetic dominated regime at the beginning of the last $\sim 60 \, e$-folds of inflation. Contrary to that case, here we study the possibility that a partial drop of scalar power occurs at scales that are larger than but comparable to the first acoustic peak. The best fit to the temperature data is obtained for a transition scale $k_* \simeq 1.5 \times 10^{-3} \, {\rm Mpc}^{-1}$, with a $\simeq 26 \%$ decrease in power. This fit improves over the Planck ones with conventional models due to the suppression in power in the $10 \la \ell \la 30$ region. Moreover, the model easily fits the tensor-to-scalar ratio $r\sim 0.2$ observed by BICEP2. Quite interestingly, the $\chi^2$ of the fit of this model to the Planck+WP+BICEP2 data improves by about $\sim 7.5$ with respect to the fit of the same data of a model with constant running. This is a considerable improvement, given that the suppression model has only one more parameter than the model with a constant running. The significance of the improvement is supported by the Akaike Information Criterion, see Table \ref{tab:AIC}. A second possibility is a negative correlation between tensor and scalar modes. Such a correlation is expected to occur, to some degree, in models with broken rotational symmetry. Such a situation actually appears to be present in the WMAP \cite{Eriksen:2003db} and in the Planck \cite{Ade:2013nlj} temperature data. Unfortunately, a primordial tensor-scalar correlation does not affect the temperature power spectrum, that is used by Planck to set limits on the tensor-to-scalar ratio, and cannot therefore help reconcile the bounds on $r$ found from BICEP2 with those from Planck. It would be interesting to study whether, and under what conditions, such a conclusion might be avoided.\\ \appendix | 14 | 3 | 1403.4596 |
1403 | 1403.3239_arXiv.txt | The Apache Point Observatory Galactic Evolution Experiment (APOGEE) - one of the Sloan Digital Sky Survey III programs -- is using near-infrared spectra of $\sim 100,000$ red giant branch star candidates to study the structure of the Milky Way. In the course of the survey, APOGEE also acquires spectra of hot field stars to serve as telluric calibrators for the primary science targets. We report the serendipitous discovery of two rare, fast-rotating B stars of the $\sigma$ Ori E type among those blue field stars observed during the first year of APOGEE operations. Both of the discovered stars display the spectroscopic signatures of the rigidly rotating magnetospheres (RRM) common to this class of highly-magnetized ($B \sim 10$ kiloGauss) stars, increasing the number of known RRM stars by $\sim 10 \%$. One (HD 345439) is a main-sequence B star with unusually strong He absorption (similar to $\sigma$ Ori E), while the other (HD 23478) fits a ``He-normal'' B3IV classification. We combine the APOGEE discovery spectra with other optical and near-infrared spectra of these two stars, and of $\sigma$ Ori E itself, to show how near-infrared spectroscopy can be a uniquely powerful tool for discovering more of these rare objects, which may show little/no RRM signatures in their optical spectra. We discuss the potential for further discovery of $\sigma$ Ori E type stars, as well as the implications of our discoveries for the population of these objects and insights into their origin and evolution. | $\sigma$ Orionis E is the archetype of an unusual and rare class of helium-strong main sequence B stars \citep{Gray2009}, characterized by extremely large magnetic fields and fast rotation. $\sigma$ Ori E itself has a measured longitudinal magnetic field varying with an amplitude of $B_l \sim 2-3$ kG with an inferred polar magnetic strength of $\sim 10$ kG \citep{Townsend05, Kochukhov11, Oksala2012} a rotational velocity of $\vsini = 160 \ {\rm km \ s^{-1}}$, and a rotational period of $1.19 \ {\rm d}$ \citep{Townsend05}. The high magnetic field of the star is thought to form a Rigidly Rotating Magnetosphere (RRM) \citep{Townsend05} which traps circumstellar material in two co-rotating clouds at a distance of several stellar radii beyond the photospheric surface, producing an extremely broad, double-horned \halpha emission profile with velocity width $>1000 \ {\rm km \ s^{-1}}$ as well as periodic modulation of the star's light curve. The magnetic field also appears to be responsible for the enhanced He absorption via localized surface abundance anomalies it creates in the star. A more recently-discovered star in the same class, HR 7355 \citep{Riv2008, Riv2010, Oksala2010}, shows similarly He-strong absorption and polar field strength ($B \sim 11-12$ kG) to $\sigma$ Ori E, and corresponding \halpha emission profiles with velocity widths of $\sim 1300 \ {\rm km \ s^{-1}}$. HR 7355 shows exceptionally fast rotation ($P = 0.52$ d and $\vsini = 310 \ {\rm km \ s^{-1}}$); this star, along with HR5907 ($P = 0.51$d, $\vsini = 340 \ {\rm km \ s^{-1}}$), are the two fastest-rotating, non-degenerate magnetic stars known -- in fact, their speeds approach the rotational breakup velocity \citep{Riv2013, Grunhut}. The simultaneous presence of such extreme rotation and large magnetic field is somewhat surprising for massive B stars, and for HR 7355 the spindown timescale via magnetic braking should be much shorter than its estimated age \citep{Riv2013, Mikulasek10}. Thus, these stars provide a unique conundrum for theories of both star formation and magnetic field evolution. Increasing the known number of these objects will allow us to understand how common this phenomenon is for massive stars, and establish the range of properties they can exhibit. In this paper, we present the discovery of two additional members of this rare class of stars from the Sloan Digital Sky Survey III's Apache Point Observatory Galactic Evolution Experiment (SDSS-III/APOGEE) \citep{Gunn, Eisenstein11, Majewski2013, Wilson2012}. APOGEE is a near-infrared (NIR), H-band ($1.51-1.70 \ \mu$m), high-resolution ($R \simeq 22,500$), spectroscopic survey primarily targeting red giant stars in the Milky Way. As part of routine survey operation, APOGEE selects bright, hot, blue stars in each survey field for telluric correction of the red giant spectra. Below, we describe the serendipitous discovery of the two $\sigma$ Ori E type stars among these APOGEE telluric standards, identified via the unique magnetospheric signatures they produce in their Brackett series emission profiles. We next present optical spectra that confirm the He-strong classification of one star and the apparent ``He-normal'' nature of the other, allow measurements of $\vsini$, and show evidence of \halpha profiles matching the Brackett series RRM signatures. We also present Triplespec NIR spectra of these two stars and $\sigma$ Ori E itself, which confirm the similarities among all three stars and the ``smoking gun'' signature provided by the Brackett series line profiles created by the rigidly rotating magnetospheres in these stars. We conclude by discussing the potential for further discovery of $\sigma$ Ori E type stars during the APOGEE survey, and the implications they will have for understanding the breadth of characteristics in the population of these objects, their origin, and their evolution. | The $\sigma$ Ori E stars present a mystery for stellar evolution. B-stars should not have large convective zones, and thus are expected to possess relatively weak magnetic fields -- but typically measured field strengths for $\sigma$ Ori E analogs are $ \sim 10$kG and higher, in apparent (and strong) contradiction of this theoretical expectation. Furthermore, most theories predict that young B stars should spin down on a $ \sim 1$Myr timescale, but the $\sigma$ Ori E star HR7355 appears to be $15-25$Myr old \citep{Riv2013, Mikulasek10} and yet has a high rotational velocity. While we cannot measure the magnetic field from our current data, the unique RRM signature clearly indicates that HD 345439 and HD 23478 are also magnetized stars (which future spectropolarimetry observations could confirm), and they are both definitely fast rotators. While the RRM can theoretically arise in any star where the Alfven radius exceeds the Kelperian co-rotation radius \citep{ud1, ud2}, in which case fields as low as $\sim 1$ kGauss could suffice, the other resemblances between these stars and the $\sigma$ Ori E stars seem to imply that similar field strengths of $\sim 10$ kGauss are most likely. In the case of HD 23478, its sky position, parallax of 4.99 mas, and proper motion of $+8 {\rm mas/yr}$, $-8 {\rm mas/yr}$ \citep{vanleeuwen07} all match the members of the IC 348 young open cluster \citep{Scholz}. This result constrains the age of HD 23478 to match that of IC 348 -- previously estimated as $1.3-3$ Myr by \citet{Herbig1998}; \citet{Bell2013} however have recently derived an age closer to $\sim 5-6$ Myr based on current isochrone-fitting techniques. Future measurements of the magnetic field in this star can then provide an estimated spindown timescale, to see if this star matches expectations or, like HR 7355, seems to be spinning too fast for its age and magnetic field. As this work has shown, a particularly promising avenue for identifying more of these unusual stars is near-infrared spectroscopy. We believe the APOGEE spectra in Figure 1 to be the first published NIR spectra of $\sigma$ Ori E stars, and they are remarkable in the strength of the RRM signatures in the Brackett lines. Based on our sample of spectra (which are admittedly few in number and sparse in phase sampling), each individual Brackett transition shows stronger RRM signatures than \halpha for the same star, and the presence of $10$ transitions in just $2/3$ of the H-band makes the NIR an exceptionally powerful new diagnostic approach for identifying $\sigma$ Ori E stars. Our discoveries were entirely serendipitous, yet they have increased the known sample of these stars by $\sim 10$\%, and HD 345439 alone has enhanced the number of ``extreme'' (near-breakup velocity) rotators by 50\%. Furthermore, the optical spectra of these stars are much more ``normal'' than their NIR spectra - both HD 23478 and HD 345439 have previous optical observations and classifications that entirely missed their RRM nature. We can see in Figure 4 that the Brackett series RRM signatures are substantially stronger than even the NIR Paschen series, indicating that the NIR H-band may be a ``sweet spot'' for this diagnostic. The fact that HD 23478 is both nearby and bright in the optical, yet eluded RRM classification until now, further accentuates the diagnostic power of NIR spectroscopy for this work. Thus, with the advent of powerful IR spectrographs at many observatories, and of large-scale IR spectroscopic surveys such as APOGEE, we can speculate that the discovery of these previously-rare stars may accelerate quickly in the near future. | 14 | 3 | 1403.3239 |
1403 | 1403.7526_arXiv.txt | A number of planet-host stars have been observed to rotate with a period equal to an integer multiple of the orbital period of their close planet. We expand this list by analyzing \kepler{} data of \hatpeleven{} and finding a period ratio of 6:1. In particular, we present evidence for a long-lived spot on the stellar surface that is eclipsed by the planet in the same position four times, every sixth transit. We also identify minima in the out-of-transit lightcurve and confirm that their phase with respect to the stellar rotation is mostly stationary for the 48-month timeframe of the observations, confirming the proposed rotation period. For comparison, we apply our methods to \keplerseventeen{} and confirm the findings of \citet{2012A&A...547A..37B} that the period ratio is not exactly 8:1 in that system. Finally, we provide a hypothesis on how interactions between a star and its planet could possibly result in an observed commensurability for systems where the stellar differential rotation profile happens to include a period at some latitude which is commensurable to the planetary orbit. | \label{sec:introduction} \change{Many stars} have been observed to exhibit photometric variations synchronous to the orbit of their close planet. When these variations are attributed to photospheric features rotating with the stellar surface, this implies a synchronicity between stellar rotation and planetary orbit. One of the earliest robust detections of this phenomenon is by \citet{2008A&A...482..691W} in the system \tauboo{}. They report on periodic photometric variations of the host star with a period within 0.04\% of that of the planetary orbit, and attribute this to an active region on the surface of the star. Similarly, stellar photometric variations synchronous to the planetary orbit have been detected for the planetary systems CoRoT-2 \citep{2009EM&P..105..373P,2009A&A...493..193L} and CoRoT-4 \citep{2009A&A...506..255L}. For all three stars, the rotation period inferred from spectroscopy is consistent with the period of photometric variations, supporting that the variations are due to photospheric features stationary on the stellar surface. Another interesting example is \keplerthirteen{}. \citet{2012MNRAS.421L.122S} measure the rotational period of the star by frequency analysis of the spot-modulated lightcurve and find a 5:3 commensurability with the orbital period of the planet \keplerthirteenb{} at high significance. However, frequency analysis is not the only method suitable for measuring rotation rates of spots on the stellar surface. A transiting planet may eclipse spots on the surface of its host star, resulting in anomalies in the transit lightcurve. This phenomenon was observed, for example, in the systems \change{HD 209458 \citep{2003ApJ...585L.147S},} HD 189733 \citep{2007A&A...476.1347P}, TReS-1 \citep{2009A&A...494..391R}, and CoRoT-2 \citep{2009A&A...493..193L}. Repeated transit anomaly detections due to the same spot can be used to constrain the stellar rotation period. This method was first applied by \citet{2008ApJ...683L.179S} to HD 209458. \change{Another application of starspot-induced transit anomalies is to constrain the spin-orbit geometry, as was first mentioned by \citet{2010ApJ...723L.223W}.} This method was developed and applied independently by \citet{2011ApJ...740...33D} and \citet{2011ApJ...743...61S} to \hatpeleven{}, by \citet{2011ApJ...733..127S} to WASP-4, and by \citet{2011ApJ...740L..10N} to CoRoT-2. Independent measurements of the \rmeffect{} on \hatpeleven{} show that the planetary orbit normal is almost perpendicular to the projected stellar spin \citep[the projected obliquity is $\approx103\degree$, see][]{2010ApJ...723L.223W,2011PASJ...63S.531H}. Relying only on photometric data, \citet{2011ApJ...740...33D} and \citet{2011ApJ...743...61S} independently identify two active latitudes (where spots are most prevalent) on the surface of the star, which they assume to be symmetrical around the equator, to conclude that \hatpelevenb{} is on a nearly polar orbit in accordance with the spectroscopic results, and that the stellar spin axis of \hatpeleven{} is close to being in the plane of sky. \change{The transit lightcurve of \keplerseventeenb{} ($P=1.49\;\mathrm{days}$) also exhibits anomalies due to spots on the surface of its host star. In their discovery paper, \citet{2011ApJS..197...14D} analyze these anomalies to study both stellar rotation and orbital geometry. They observe that the transit anomaly pattern repeats every eighth planetary orbit, suggesting that the spots rotate once while the planet orbits eight times. They dub the phenomenon of the same spots reappearing periodically at the same phase in transit lightcurves---every eighth one in this case---the \strobo{}. As for the orbital geometry, they found that transit anomalies in successive orbits are consistent with being caused by the same spots that rotate one eighth of a full revolution on the stellar surface with each orbit of the planet. This implies a low projected obliquity of the planetary orbit, and also excludes frequency aliases (like the star rotating three or five times while the planet orbits eight times).} In this paper, we present evidence for a 6:1 period commensurability between the rotation of the star \hatpeleven{} and the orbit of its planet \hatpelevenb{} \citep[$P=4.89\;\mathrm{days}$,][]{2010ApJ...710.1724B}. The increasing number of systems known to exhibit such commensurability raises the question whether this is the result of an interaction between the planet and the star. Whenever studying stellar rotation, it is important to remember that stars with convective zones exhibit differential rotation. In this paper, the working definition of stellar rotation rate is that inferred through dominant spots on the stellar surface, either from the rotational modulation of the out-of-transit lightcurve or from transit anomalies. This way we measure the rotation rate of the stellar surface at the latitude of the spots or active regions. If spots from multiple latitudes with different rotational rates contribute significantly to the lightcurve, then we expect the inferred posterior distribution of the rotational period to have a broader profile. Despite their usefulness in confining planetary obliquity and mapping spots, transit anomalies due to the planet eclipsing spots can be a nuisance too: they contaminate the transit lightcurve, introducing biases in the detected transit depth \citep{2009A&A...505.1277C}, time, and duration. \citet{2010A&A...520A..66B} point out that in the particular case of stellar rotation-planetary orbit commensurability, activity-induced transit timing variations (TTVs) can be periodic, and thus can result in spurious planet detections. This further motivates the need for understanding stellar rotation--planetary orbit commensurability. In Section \ref{sec:acf}, we look at the periodogram and autocorrelation function of \hatpeleven{} and \keplerseventeen{} lightcurves to confine the rotational period. In Section \ref{sec:anomalies}, we present the case of a spot on \hatpeleven{} recurring multiple times due to the \strobo{}. In Section \ref{sec:macula}, we analyze all transit anomalies observed on \hatpeleven{} to feed the best-fit spot parameters into the rotational modulation model \macula{} \citep{2012MNRAS.427.2487K}, and compare the resulting model lightcurve to observations. In Section \ref{sec:recurrence}, we perform a statistical analysis of spot-induced anomalies in the transits of \hatpelevenb{} and \keplerseventeenb{}. In Section \ref{sec:flipflop}, we look for the periodicity of lightcurve minima for both stars. We show evidence for two spots or spot groups at opposite longitudes on both \hatpeleven{} and \keplerseventeen{}, and find that on the former, they seem to alternate in relative activity level, which is known as the ``flip-flop'' phenomenon \change{\citep{1991LNP...380..381J}}. In Section \ref{sec:interaction}, we state one possible hypothesis about stellar rotation--planetary orbit resonance, and discuss difficulties in proving it. Finally, we summarize our findings in Section \ref{sec:conclusion}. | \label{sec:conclusion} The main focus of this paper is to present evidence for the 6:1 commensurability between the planetary orbit and the stellar rotation in the \hatpeleven{} system. For reference, we perform the same analysis for \keplerseventeenb{}, for which \citet{2011ApJS..197...14D} observe an 8:1 commensurability based on transit anomalies. However, \citet{2012A&A...547A..37B} show that in fact, spots with a different rotational rate dominate the out-of-transit lightcurve. These results are not necessarily contradictory because of possible differential rotation: in case of \keplerseventeen{}, the spots dominating the lightcurve might lie at a different latitude that the ones observed via anomalies in the transits of the planet with a low projected obliquity. We calculate the autocorrelation function for the lightcurve of these two stars, and present a statistical analysis of possible spot-induced transit anomaly recurrence periods, which independently exclude frequency aliases of the proposed 6:1 and 8:1 commensurabilities. In case of \hatpeleven, the recurring transit anomalies imply a tight commensurability because of the polar orbit. We also present periodograms, and propose that the period discrepancy when looking at the FWHM of frequency peaks might be due to spot evolution causing the peaks to split. We also present evidence for a tight 6:1 commensurability for \hatpeleven{} in the form of four observed transit anomalies presumably due to the same spot. We fit for all observed transit anomalies of \hatpeleven{}, and feed the resulting spot parameters into \macula{}, to show that it is plausible that rotational modulation accounts for most of the out-of-transit lightcurve variation. Furthermore, we identify minima in the lightcurve of both stars, and conclude that in case of \hatpeleven{}, there is a tight 6:1 period commensurability, whereas for \keplerseventeen{}, we confirm the period of 12.01 found by the much more sophisticated analysis of \citet{2012A&A...547A..37B}, distinct from the 8:1 commensurability. We identify two active longitudes for both stars, and see indication for two flip-flop events between these active longitudes on \hatpeleven{}. Finally, we hypothesize that for stars with an intermediate latitude with a rotational period commensurable to the orbit of a close planet, star-planet interactions might induce spot formation preferentially at this latitude, which would show up as a resonance between the dominant period in the out-of-transit lightcurve and the planetary orbit, and also as the \strobo{} if the planet is transiting and the transit chord intersects this active latitude. However, proving this hypothesis might be difficult mostly because of the small number of bright targets and the uncertainties in differential rotation parameters. | 14 | 3 | 1403.7526 |
1403 | 1403.0595_arXiv.txt | We present the helium abundance of the two metal-poor clusters M30 and NGC6397. Helium estimates have been obtained by using the high-resolution spectrograph FLAMES at the ESO Very Large Telescope and by measuring the He~I line at 4471 $\mathring{A}$ in 24 and 35 horizontal branch stars in M30 and NGC6397, respectively. This sample represents the largest dataset of He abundances collected so far in metal-poor clusters. The He mass fraction turns out to be Y=0.252$\pm$0.003 ($\sigma$=0.021) for M30 and Y=0.241$\pm$0.004 ($\sigma$=0.023) NGC6397. These values are fully compatible with the cosmological abundance, thus suggesting that the horizontal branch stars are not strongly enriched in He. The small spread of the Y distributions are compatible with those expected from the observed main sequence splitting. Finally, we find an hint of a weak anticorrelation between Y and [O/Fe] in NGC6397 in agreement with the prediction that O-poor stars are formed by (He-enriched) gas polluted by the products of hot proton-capture reactions. | \label{intro} Helium is the most abundant among the few chemical elements ($^{3}$He, $^{4}$He, D, $^6$Li, $^7$Li, $^9$Be, $^{10}$B and $^{11}$B) synthesized directly in the primordial {\sl furnax} of the Big Bang. The most recent determination of the primordial He mass fraction provides an initial value $Y_{P}$=~0.254$\pm$0.003 \citep{izotov}. The study of the He content of stars in globular clusters (GCs) is still a challenging task but it is crucial for a number of aspects of the stellar astrophysics. First of all, the He content in Galactic GC stars is thought to be a good tracer of the primordial He abundance because these are among the first generations of stars formed in the Universe and the mixing episodes occurring during their evolution only marginally affect their surface He abundance \citep{sweigart97}. Moreover, the He content is usually invoked as one of the possible {\it second parameter} \citep[together with age, CNO/Fe ratio, stellar density; see e.g.][]{gratton10,dotter10,dalex13,milone13}, to explain the observed distribution of stars along the horizontal branch (HB), being the overall metallicity the first parameter. Finally, observational evidence reveal the presence of multiple stellar generations in GCs, formed in short timescales ($\sim$100 Myr) after the initial star-formation burst, from a pristine gas polluted by the products of hot proton-capture processes \citep[see e.g.][and references therein]{gratton12a}. Thus, these new stars are expected to be characterized by (mild or extreme) He enhancement with respect to the first ones, together with enhancement of Na and Al, and depletion of O and Mg. Despite such an importance, however, the intrinsic difficulties in the derivation of He abundances in low-mass stars have prevented a detailed and systematic investigation of He in GCs. Only few photospheric He transitions are available in the blue-optical spectral range ($<$5900 $\mathring{A}$) and they are visible only at high effective temperatures ($T_{eff}$). Therefore, He lines in GC stars can be detected only among the HB stars hotter than $\sim$9000 K (the precise boundary also depends on the available signal-to-noise ratio of the spectra, SNR). Instead, the measure of the He abundance in FGK-type stars is limited only to the use of the chromospheric line at 10830 $\mathring{A}$, while no photospheric He line is available in these stars. Unfortunately, this transition is extremely weak and very high SNR and spectral resolution are required for a proper measurement. Moreover, the precise He abundance heavily depends on the modeling of the chromosphere. However, this line can provide differential measures of the He abundance, as performed by \citet{pasquini11} in two giants in NGC2808, \citet{dupree11} in 12 giant in Omega Centauri and \citet{dupree13} in two giants in Omega Centauri. \citet{pasquini11} point out a Y difference of at least 0.17 between the two stars. A similar difference has been suggested by \citet{dupree13} for giants in Omega Centauri. A further complication in the measurement of the He abundance in HB stars is provided by diffusion processes, like radiative levitation and gravitational settling, occurring in the radiative atmospheres of HB stars hotter than $\sim$11000-12000 K, corresponding to the so-called {\it Grundahl Jump} \citep{grundahl99}. These phenomena lead to a substantial modification of the surface chemical composition, and in particular to a decrease of the He abundance \citep[see Fig.~22 in][]{behr03} and an enhancement of the iron-peak element abundances. As a consequence, only HB stars in the narrow $T_{eff}$ range between $\sim$9000 and $\sim$11000 K can be used as reliable diagnostics of the He content of the parent cluster. At present, determinations of the He mass fraction (Y) in GC HB stars not affected by diffusion processes have been obtained only for some metal-intermediate ([Fe/H]$\sim$--1.5/--1.1) GCs: NGC6752 \citep[][$<$Y$>$=~0.24$\pm$0.01, 4 stars]{villanova09}, M4 \citep[][$<$Y$>$=~0.29$\pm$0.01, 6 stars]{villanova12}, NGC1851 \citep[][$<$Y$>$=~0.29$\pm$0.05, 20 stars]{gratton12b}, M5 \citep[][$<$Y$>$=~0.22$\pm$0.03, 17 stars]{gratton13}, NGC2808 \citep[][$<$Y$>$=~0.34$\pm$0.01, 17 stars]{marino13} and M22 \citep[][$<$Y$>$=~0.34$\pm$0.01, 29 stars]{gratton14}. All these analyses are based on the photospheric He~I line at 5875 $\mathring{A}$. Some evidence suggest that the variation of He in GC stars is linked to different chemical compositions. The differential analysis performed by \citet{pasquini11} on two giants in NGC2808 with different Na content highlights that the Na-rich star is also He enriched at odds with the Na-poor one. \citet{villanova09} and \citet{villanova12} derived He, Na and O abundances for HB stars in NGC6752 and M4, respectively, finding that the stars along the reddest part of the HB of NGC6752 have a standard He content, as well as Na and O abundances compatible with the first generation, while the stars in the bluest part of the HB of M4 are slightly He-enhanced (by $\sim$0.05), with Na and O abundance ratios compatible with the second stellar generation. In a similar way, \citet{marino13} found a clear evidence of He enhancement (by $\sim$0.09) among the bluest HB stars in NGC2808, that are also all Na-rich. Further spectroscopic evidence (not including the measure of He abundances) strengthen the connection between the HB morphology and the chemical composition, pointing out that the bluest portion of the HB (before the onset of the radiative levitation) is populated mainly by second generation stars, while the reddest part of the sequence is dominated by first generation stars \citep[like in M4,][]{marino11} or by a mixture of first and second generation stars \citep[like in NGC2808,][]{marino13}. In this paper we present the first determination of the He abundance in HB stars of the metal-poor GCs M30 and NGC6397 ([Fe/H]=~--2.28$\pm$0.01 and [Fe/H]=~--2.12$\pm$0.01, \citet{lovisi12} and \citet{lovisi13}, respectively). | We have analysed the He mass fraction Y for a sample of 24 and 35 HB stars in M30 and NGC6397, respectively. The main results are: {\sl (i)} both clusters have an average He content compatible with the primordial He abundance ($<$Y$>$=0.252$\pm$0.003 for M30 and $<$Y$>$=0.241$\pm$0.004 for NGC6397) and they are not strongly enriched in He; {\sl (ii)} a weak (but statistically significant) anticorrelation between Y and [O/Fe] among the HB stars of NGC6397 does exist (but it is not detected in M30). We suggest that the O-poor, He-rich stars found in the HB of NGC6397 belong to the second stellar generation of the cluster. Unfortunately Na abundances are not available for these stars. In principle, Y-[O/Fe] anti-correlation is expected in all the GCs displaying the chemical signatures of the self-enrichment processes, even if its very small slope makes its detection very hard. The lack of Y-[O/Fe] anti-correlation for the stars in M30 can be due to several causes, mainly the size of our sample (three times smaller than that secured for NGC6397) and the SNR of the spectra (lower than that of the spectra of NGC6397). Also, we cannot rule out that M30 has undergone a self-enrichment process less efficient with respect to NGC6397, as suggested by their different [O/Fe] distributions (in fact M30 shows a lack of stars with [O/Fe]$<$0, instead detected among the stars of NGC6397). Thus, the internal variation of the He content in the stellar population of M30 could be smaller than 0.01. The Y-[O/Fe] anti-correlation observed in NGC6397 seems to confirm the theoretical expectations that the GC stars born after the first burst of star formation are both depleted in O and (mildly) enriched in He, demonstrating that the stars usually labelled as {\it second generation stars} show the signatures of hot-temperature proton-capture processes, with a simultaneous O-depletion and a weak He enrichment. \begin{figure} \epsscale{0.9} \plotone{helium_oxy.ps} \caption{Behavior of the Y abundance as a function of [O/Fe] for the stars in M30 (upper panel) and NGC6397 (lower panel). The arrows show the effects of a change in $T_{eff}$ and logg. Labelled are the values of the Spearman correlation coefficient. Solid lines are the best-fit straight lines. } \label{hox} \end{figure} | 14 | 3 | 1403.0595 |
1403 | 1403.3865.txt | We extend our earlier work on turbulence-induced relative velocity between equal-size particles (Pan \& Padoan, Paper I) to particles of arbitrarily different sizes. The Pan \& Padoan (PP10) model shows that the relative velocity between different particles has two contributions, named the generalized shear and acceleration terms, respectively. The generalized shear term represents the particlesÕ memory of the spatial flow velocity difference across the particle distance in the past, while the acceleration term is associated with the temporal flow velocity difference on individual particle trajectories. Using the simulation of Paper I, we compute the root-mean-square relative velocity, $\langle w^2 \rangle^{1/2}$, as a function of the friction times, $\tau_{\rm p1}$ and $\tau_{\rm p2}$, of the two particles, and show that the PP10 prediction is in satisfactory agreement with the data, confirming its physical picture. For a given $\tau_{\rm p1}$ below the Lagrangian correlation time of the flow, $T_{\rm L}$, $\langle w^2 \rangle^{1/2}$ as a function of $\tau_{\rm p2}$ shows a dip at $\tau_{\rm p2} \simeq \tau_{\rm p1}$, indicating tighter velocity correlation between similar particles. Defining a ratio $f\equiv \tau_{\rm p,l}/\tau_{\rm p,h}$, with $\tau_{\rm p,l}$ and $\tau_{\rm p,h}$ the friction times of the smaller and larger particles, we find that $\langle w^2 \rangle^{1/2}$ increases with decreasing $f$ due to the generalized acceleration contribution, which dominates at $f\lsim 1/4$. At a fixed $f$, our model predicts that $\langle w^2 \rangle^{1/2}$ scales as $\tau_{\rm p,h}^{1/2}$ for $\tau_{\rm p,h}$ in the inertial range of the flow, stays roughly constant for $T_{\rm L} \lsim \tau_{\rm p,h} \lsim T_{\rm L}/f$, and finally decreases as $\tau_{\rm p,h}^{-1/2}$ for $\tau_{\rm p,h} \gg T_{\rm L}/f$. The acceleration term is independent of the particle distance, $r$, and reduces the $r-$dependence of $\langle w^2 \rangle^{1/2}$ in the bidisperse case. %We investigate the relative velocity of inertial particles induced by turbulent %motions, extending our earlier work on equal-size particles (Pan \& Padoan, Paper I) to the %case of different particles of arbitrary sizes. The model of Pan \& Padoan (PP10) %shows that the relative velocity between different particles has two contributions, named the generalized %shear and acceleration terms, respectively. The generalized shear term %represents the particles' memory of the {\it spatial} flow velocity difference %across the particle distance at given times in the past, while the acceleration term is associated with the {\it temporal} %flow velocity difference on individual particle trajectories. The latter vanishes for equal-size particles. %Using the simulation of Paper I, we compute the root-mean-square (rms) relative velocity, $\langle w^2 \rangle^{1/2}$, %as a function of the friction times, $\tau_{\rm p1}$ and $\tau_{\rm p2}$, of any two particles, %and show that the prediction of the PP10 model is in satisfactory agreement with the %data, confirming the validity of its physical picture. For a given $\tau_{\rm p1}$ %below the Lagrangian correlation time of the flow, $T_{\rm L}$, the rms relative %velocity as a function of $\tau_{\rm p2}$ shows a dip at $\tau_{\rm p2} \simeq \tau_{\rm p1}$, %indicating tighter velocity correlation between similar particles. %The generalized shear term dominates for particles of similar sizes, while %Defining a friction time ratio as $f\equiv \tau_{\rm p,l}/\tau_{\rm p,h}$, with $\tau_{\rm p,l}$ and $\tau_{\rm p,h}$ %the friction times of the smaller and larger particles, respectively, %The acceleration term dominates when the particle friction times differ by %more than a factor of $\sim 4$. %we find that $\langle w^2 \rangle^{1/2}$ increases with decreasing %$f$ due to the generalized acceleration contribution, which starts to %dominate at $f\lsim 1/4$. %defined as the ratio of the friction time, %$\tau_{\rm pl}$, of the smaller particle to the larger one $\tau_{\rm ph}$. %At a fixed $f$, our model predicts %the rms relative velocity scales as $\tau_{\rm p,h}^{1/2}$ for $\tau_{\rm p,h}$ in the %inertial range of the flow, stays roughly constant for $T_{\rm L} \lsim \tau_{\rm p,h} \lsim T_{\rm L}/f$, %and finally decreases as $\tau_{\rm p,h}^{-1/2}$ for $\tau_{\rm p,h} \gg T_{\rm L}/f$ (or $\tau_{\rm p,l} \gg T_{\rm L}$). %This qualitative behavior is confirmed by the simulation data, although %The predicted inertial-range scaling, $\langle w^2 \rangle^{1/2} \propto \tau_{\rm p,h}^{1/2}$, at %any $f$ needs to be verified by simulations at high resolutions. %The acceleration term is independent of the particle distance, $r$, %and thus reduces the $r-$dependence of the relative velocity in the bidisperse case, %making it easier to achieve numerical convergence of the collision statistics. %for small particles of different sizes. %%The purpose of this theoretical study on the rms %%relative velocity is to fully understand the underlying physics, %%and other statistical measures more relevant for the application %%to dust particle collisions %, such the distribution of the collision velocity, %%will be examined in details in future works. %even though modeling the dust particle growth would require the more detailed statistical measures %such as the probability distribution function. %The physical picture provides insights for the probability distribution of the relative velocity. %because correctly modeling the rms relative velocity, %the simplest statical measure. %Using the simulation data of Paper I, we computed the probability %distribution function (PDF) of the relative velocity in the bidisperse case. %The trend of the PDF shape with varying friction times is successfully explained by %the physical picture of the PP10 model for the acceleration and shear effects. %Although the PDF in the bidisperse case is typically thinner than %the monodispsere case, significant non-Gaussianity still exists, %and the PDF becomes nearly Gaussian only when the friction time of the larger particle %is much larger the Lagrangian correlation timescale of the flow. %The non-Gaussianity of turbulence-induced relative velocity needs to be incorporated into %coagulation models for dust particle growth in protoplanetary disks. %as it determines the fractions of collisions leading to %sticking, bouncing or fragmentation. | This paper is a follow-up to our earlier work on turbulence-induced relative velocity of dust particles (Pan \& Padoan 2013; Paper I hereafter). The study is mainly motivated by the problem of dust particle growth and planetestimal formation in protoplanetary disks (e.g., Dullemond and Dominik 2005; Zsom et al.\ 2010, 2011; Birnstiel et al.\ 2011; Windmark et al.\ 2012; Garaud et al.\ 2013). In Paper I, we conducted an extensive statistical study of the relative velocity and the collision kernel of equal-size particles suspended in turbulent flows using both analytical and numerical methods. %In Paper I, we presented a detailed statistical %analysis of the relative velocity %including its probability distribution, %and explored the collision kernel as a function of the particle inertia in The case of equal-size particles, usually referred to as the monodisperse case, is of theoretical interest, but insufficient for astrophysical applications, as dust particles in protoplanetary disks have a size distribution. %Even if %all dust particles started from the same initial size, a size distribution would %have developed from collisional coagulation or fragmentation. %Therefore, modeling dust collisions requires the collision velocity %between different particles. The main goal of the current paper is to investigate turbulence-induced relative velocity in the general case of different particles of arbitrary sizes, known as the bidisperse case. %We refer the reader to Paper I for a more detailed discussion for the motivation of our study. Saffman and Turner (1956, hereafter S-T) derived a formula for the variance of the turbulence-induced relative velocity in the limit of small particles with friction time, $\tau_{\rm p}$, much smaller than the Kolmogorov timescale, $\tau_\eta$. This limit, known as the S-T limit, is usually expressed as $St \ll 1$, where the Stokes number, $St$, is defined as $St \equiv \tau_{\rm p}/\tau_{\rm \eta}$. The Saffman-Turner formula consists of two terms, named the shear and the acceleration term, respectively (e.g., Zhou et al.\ 2001). %In the S-T prediction, The shear term is determined solely by the flow velocity difference across the particle distance $r$. It is independent of $St$, but has a significant dependence on $r$ (see Paper I). %the relative velocity variance scales as $r^2$ for $r$ below the Kolmogorov %length scale, $\eta$. The name of the acceleration term originates from its dependence on the acceleration, ${\bs a}$, of the flow velocity, and it contributes a 1D variance of $a^2 (\tau_{\rm p2} -\tau_{\rm p1})^2$ to the relative velocity, where $\tau_{\rm p1}$ and $\tau_{\rm p2}$ are the friction times of the two particles, and $a$ is the 1D rms of the flow acceleration. This effect of the flow acceleration on the relative velocity of small particles of different sizes was also found by Weidenschilling (1984). %$\propto \frac{\bar{\epsilon}}{\nu} r^2$ where $\bar{\epsilon}$ and ${\nu}$ %and the average dissipation rate and the kinematic viscosity of the flow In the monodisperse case, the acceleration term vanishes and only the shear term contributes. The shear term in the S-T prediction for equal-size particles has been discussed in detail in Paper I. Its validity, accuracy and limitations have been systematically examined using a numerical simulation. %We refer the reader to Paper I for %the relative velocity at a small distance $r$. In the bidisperse case, the fundamental difference from the case of equal-size particles is the contribution of the acceleration term, which tends to increase the particle collision velocity. The dependence of the acceleration term on the friction time difference, $\tau_{\rm p2} -\tau_{\rm p1}$, corresponds to the fact that particles of different sizes have different responses to the flow velocities along their trajectories. Interestingly, unlike the shear term, the acceleration contribution in the S-T formula is independent of the particle distance, $r$. This observation is of particular importance for the application to dust particles in protoplanetary disks. Because the size of dust particles is typically much smaller than the Kolmogorov scale, $\simeq 1$ km, of protoplanetary turbulence, %and they should be viewed as nearly point particles (e.g., Hubbard 2012). one is required to examine the collisional statistics in the $r\to0$ limit (e.g., Hubbard 2012) that is not accessible to numerical simulations due to their limited resolution. Therefore, unless the measured statistics already converges at the resolution scale, an extrapolation to the $r\to 0$ limit is needed. %before applying it to dust particle collisions. Such an extrapolation was found to be challenging for small equal-size particles with $St\lsim 1$ due to the $r-$dependence of the shear effect\footnote{To evaluate the collision kernel of small equal-size particles in the $r\to 0$ limit, a method is developed in Paper I to isolate an $r-$independent contribution by splitting particle pairs at given distances into two types, named continuous (S-T) pairs and caustic (sling) pairs, respectively (Falkovich et al.\ 2002, Wilkson et al.\ 2006).}(Paper I). %As will be shown in this paper, In the bidisperse case, the presence of the %$r-$independent acceleration term reduces the $r-$dependence and makes it easier to achieve numerical convergence for the relative velocity between small particles of different sizes. %in simulations. %makes it easier to the extrapolate Pan and Padoan (2010, PP10) developed a model for the rms relative velocity in the general bidisperse case, for arbitrarily different particles of any size. It was shown that the model prediction is in good agreement with the simulation data of Zhou et al.\ (2001) at low resolutions. The PP10 formulation for the relative velocity also consists of two contributions, named as the generalized shear and acceleration terms, as they reduce, respectively, to the shear and acceleration terms in the S-T formula in the small particle limit. It can thus be viewed as a generalized formulation that extends the S-T limit ($St_{1,2} \ll 1$) to particles of arbitrary sizes. The generalized shear term has a similar form as the monodisperse model discussed in Paper I. It represents the particles' memory of the {\it spatial} flow velocity difference, $\Delta {\bs u} (R)$, across the separation, $R$, of the two particles at given times in the past. The physical meaning of the generalized acceleration term will be clarified in the present paper, and we will show its connection with the {\it temporal} flow velocity difference, $\Delta_{\rm T} {\bs u}$, along individual trajectories of the two particles. An approximate relation for the acceleration term will be established in terms of $\Delta_{\rm T} {\bs u}$ and the particle friction times. Using the simulation of Paper I, %at a moderate resolution, we will systematically test the PP10 model for the relative velocity between different particles. %A variety of theoretical models were constructed for relative velocity variances in %the general bidisperse case with $\tau_{\rm p1,2}$ covering the entire scale range of the flow. A variety of models have been developed to predict the relative velocity of particles of different sizes, covering the entire scale range of the turbulent flow (e.g., V\"olk et al.\ 1980; Yuu 1984; Kruis \& Kusters,1997; Zhou et al.\ 2001; Zaichik et al.\ 2006, 2008; see PP10 and references therein). In the astrophysics literature, the model of choice has been that by V\"olk et al.\ (1980) and its later refinements (e.g., Markiewicz, Mizuno \& V\"olk 1991, Cuzzi \& Hogan 2003, and Ormel \& Cuzzi 2007). %As discussed in PP10 and Paper I, the V\"olk et al.\ model has serious physical weaknesses and overestimates the %relative velocity of equal-size particles. To our knowledge, the accuracy of %the V\"olk et al.\ model has not been carefully tested in the bidisperse case. In this paper, we only test the PP10 model, in an effort of providing an improved physical insight. Other models, particularly V\"olk et et al.\ (1980) and Zaichik et al.\ (2008), will be tested and compared with PP10 in a separate work. Theoretical models only predict the rms or variance of the relative velocity, which, %As the simplest statistical measure, the rms however, is not sufficient to model collisions of dust particles (Paper I). In fact, the rms does not directly enter the estimate of the collision kernel, which is determined by the first-order moments, i.e., the average of the radial component or the mean 3D amplitude of the relative velocity (Wang et al.\ 2000). %$\langle |w_{\rm r}| \rangle$ (or $\langle |{\bs w}| \rangle$) rather than the rms, $\langle w_{\rm r}^2\rangle^{1/2}$. The variance of the relative velocity does not even represent the average collision energy per collision. Instead, using a collision-rate weighting, the average collision energy depends on the third-order moment of the collision velocity (e.g., Hubbard 2012). Furthermore, an accurate coagulation model for dust particles in protoplanetary disks requires the entire probability distribution of the collision velocity, as the outcome of each collision depends on the collision velocity (Windmark et al.\ 2012; Garaud et al.\ 2013). %We defer a systematic study of the PDF to a later work. Despite these limitations, the rms relative velocity still provides a rough approximation to the mean of the relative velocity, and it is therefore a useful tool to shed light on the physics of turbulence-induced particle collisions. The main purpose of the current work is to confirm the accuracy of the PP10 model for the rms relative velocity, and hence to validate the physical picture revealed by that model. We will show in a separate paper that this physical picture provides an understanding of the probability distribution of the collision velocity as well. In addition to turbulent motions, there are other effects, such as differential settling or radial drift, that can provide important contributions to the relative velocity between dust particles of different sizes in protoplanetary disks. In this work, we do not consider these contributions. The numerical experiment used here employs a statistically stationary and isotropic turbulent flow, which is a further idealization relative to realistic protoplanetary disks with Keplerian rotation, stratifications, etc. However, the highly idealized simulation provides a useful tool to study the role of turbulence-induced collisions. %The large-scale anisotropy may leave an imprint on the relative speed %of large particles whose memory covers the length scales at which the rotation effect is significant. In \S 2, we present a simple model for the relative velocity between inertial particles and the local flow velocity, a special bidisperse case that provides a clean comparison between our model and the simulation. The PP10 formulation for the bidisperse relative velocity is reviewed in \S 3. A brief presentation of our numerical simulation is given in \S 4. In \S 5, we examine the statistics of the particle-flow relative velocity. In \S 6, we show simulation results for the rms relative velocity, and test the prediction of the PP10 model. %The relative velocity PDF as a %function of the friction time or Stokes number pair is systematically explored and interpreted in %\S7. We summarize the main results and conclusions in \S 7. %For small particles, we expect our simulations and theoretical model to apply for the %turbulence-induced collision speed of small dust particles in protoplanetary disks, because %the statistical isotropy is likely to be restored the scale of the particle size, which is below the %Kolmogorov scale of the turbulent flow, Finally, the idealized sitation isolates various %complexities in a protoplanetary disk, and is thus a useful tool to reveal the fundamental %physics of turbulence-induced relative speed of inertial particles. | We have investigated the relative velocity of inertial particles suspended in turbulent flows, extending our earlier work on equal-size particles (Pan \& Padoan 2013; Paper I) to the general bidisperse case for different particles of arbitrary sizes. We have made use of the same numerical simulation presented in Paper I, which evolved 14 species of inertial particles in a simulated turbulent flow. % covering the entire scale range of the The particle friction time, $\tau_{\rm p}$, ranges from $0.1\tau_\eta$ ($St =0.1$) to $54T_{\rm L}$ ($St=795$), with $\tau_\eta$ and $T_{\rm L}$ the Kolmogorov timescale and the Lagrangian correlation time of the flow, respectively. We computed the rms relative velocity, $\langle w^2 \rangle ^{1/2}$, for all Stokes number pairs $(St_1, St_2)$ available in the simulation, and tested the PP10 model for the general bidisperse case. %We have also conducted a systematic analysis of the probability distribution function (PDF) of the relative velocity %as a function of the Stokes number pair. Here we list our main conclusions. \begin{enumerate} \item As a special bidisperse case, we examined the relative velocity, ${\bs w}_{\rm f}$, between inertial particles and the local flow velocity. We showed that ${\bs w}_{\rm f}$ can be roughly estimated as the {\it temporal} flow velocity difference, $\Delta {\bs u}_{\rm T}(\Delta \tau)$, along the particle trajectory at a time lag, $\Delta \tau$, close to the particle friction time $\tau_{\rm p}$. A simple model is developed for the rms of ${\bs w}_{\rm f}$, assuming that the temporal flow velocity correlation on the particle trajectory can be approximated by the Lagrangian correlation function, $\Phi_{\rm L}$. Adopting a bi-exponential form for $\Phi_{\rm L}$, our model is in good agreement with the simulation data. In particular, it predicts that the rms of ${\bs w}_{\rm f}$ increases linearly with $St$ for $St\ll1$, scales as $St^{1/2}$ in the inertial range, and finally approaches the flow rms velocity for $\tau_{\rm p} \gg T_{\rm L}$. %and approaches constant for $\tau_{\rm p} \gg T_{\rm L}$. %The PDF shape of ${\bs w}_{\rm f}$ becomes thinner with increasing $St$, %and approaches Gaussian for $\tau_{\rm p} \gsim 3.5-7 T_{\rm L}$. This behavior %corresponds to the thinning trend of the PDF of $\Delta {\bs u}_{\rm T}$ %with increasing time lag as inferred from the PDFs of the %Lagrangian and Eulerian temporal flow velocity differences. The particle-flow relative velocity is an interesting delimiter that helps confine the relative velocity behavior in the general bidisperse case. \item We introduced the general formulation of PP10 for the relative velocity of different particles of arbitrary sizes. The formulation shows that the relative velocity variance is contributed by two terms, named as the generalized acceleration and shear terms because they reduce to the acceleration and shear terms in the Saffman-Turner formula for small particles with $St \ll 1$. The generalized acceleration term originates from different responses of particles of different sizes to the flow velocities. We established an approximate relation between the generalized acceleration term and the {\it temporal} flow velocity difference, $\Delta {\bs u}_{\rm T}$, along the trajectory of the larger particle. On the other hand, the generalized shear term represents the contribution from the particles' memory of the {\it spatial} flow velocity difference, $\Delta {\bs u}$, across the distance of the two particles at given times in the past. %(see detailed discussions in Paper I). An analytical expression is derived for the generalized acceleration term, while the generalized shear term is modeled in a similar way as the mondispserse model presented in Paper I, accounting for the combined effects of the particle memory and the separation of particle pairs backward in time. For equal-size particles, the acceleration term vanishes, and only the shear term contributes. \item Using our simulation, we computed the rms relative velocity, $\langle w^2 \rangle ^{1/2}$, between particles of any different sizes. We first examined $\langle w^2 \rangle ^{1/2}$ as a function of $St_2$ at fixed values of $St_1$. If $\tau_{\rm p1} \lsim T_{\rm L}$, the relative velocity shows a dip around $St_2 \simeq St_1$, indicating that the velocities of nearby particles of similar sizes have a tighter correlation than particles of different sizes. The dip disappears for $\tau_{\rm p1} \gsim T_{\rm L}$. The generalized shear term dominates the contribution to the rms relative velocity for particles of similar sizes, while the acceleration term dominates if the Stokes numbers differ by more than a factor of $\simeq 4$. %In the limits $St_2 \to 0$ and $St_2 \to \infty$, $\langle w^2 \rangle ^{1/2}$ %approaches the particle-flow relative velocity and the 1-particle velocity of particles (1), respectively. Defining the ratio, $f\equiv St_{\ell}/St_{h}$, between the small ($St_{\ell}$) and large ($St_{h}$) Stokes numbers, we also considered $\langle w^2 \rangle ^{1/2}$ as a function of $St_{h}$ at fixed values of $0\le f\le 1$. The limits $f\to0$ and $f\to1$ correspond to the particle-flow relative velocity and the monodisperse case, respectively. At a fixed $f$, $\langle w^2 \rangle ^{1/2}$ increases with $St_{h}$ for $ \tau_{\rm ph} \lsim T_{\rm L}$, stays roughly constant for $T_{\rm L} \lsim \tau_{\rm ph} \lsim T_{\rm L}/f$ (or equivalently $f T_{\rm L} \lsim \tau_{\rm p l} \lsim T_{\rm L}$), and finally decreases as $St_{h}^{-1/2}$ for $\tau_{h} \gg T_{\rm L}/f$. For any value of $f$, a $St_{h}^{1/2}$ scaling is predicted, if the larger friction time, $\tau_{\rm p,h}$, is within the inertial range of the flow. This $St_{h}^{1/2}$ scaling will have to be verified in future simulations with higher resolutions. At a given $St_{h}$, $\langle w^2 \rangle ^{1/2}$ increases with decreasing $f$ due to the increase of the acceleration contribution, which starts to dominate at $f\lsim 1/4$. The generalized acceleration contribution is independent of the distance, $r$, %or the relative motions of the two particles, and provides equal contributions to %the radial and tangential components of the relative velocity, and thus reduces the $r-$dependence of the relative velocity between small, different particles, making it easier to achieve numerical convergence for the collision statistics of point-like particles at $r \to 0$. The prediction of the PP10 model is in good agreement with the simulation data. The largest discrepancy occurs for $f=\frac{1}{2}$ and $St_{h}$ in the inertial range, where the model underestimates the rms relative velocity by 15-20\%. At other values of $f$, the discrepancy between our model and the simulation is $<10\%$. This confirms the validity of the physical picture revealed by our model. %between different particles than equal-size particles in the Saffman-Turner limit. %the difference in the radial and tangential rms relative speeds, and the asymmetry between %approaching and separating pairs found in Paper I for identical particles all decrease when \end{enumerate} %Despite extensive conclusions drawn in the current work for the particle relative %velocity in the general bidisperse case, %e will focus on Future developments will be made to investigate more practical measures for the study %to dust particle collisions in protoplaneraty turbulence. We emphasize that the theoretical modeling of the rms relative velocity is important for understanding the fundamental physics, even though its practical use is limited. In future work, we will focus on establishing statistical measures or tools that can be applied to model dust particle collisions in protoplanetary turbulence. We have started an effort in an ongoing paper (Pan \& Padoan 2014) to explore the collision kernel %and the average collision velocity as a function of the Stokes number pair in the general bidisperse case, accounting for turbulence-induced collision velocity and the effect of turbulent clustering. In the next paper of this series, we will systematically examine the probability distribution of the collision velocity, which is needed to determine the fractions of collisions leading to sticking, bouncing or fragmentation. Due to the limited resolution, the simulated flow in the current work has only a short inertial range, and our model prediction for particles in the inertial range remains to be tested and validated. %Dust particles of sub-millimeter to meter size in protoplanetary turbulence belong %to the inertial range, and modeling the collisions of these particles is crucial to assessing the viability of the %planetesimal formation mechanism by particle coagulation. Future simulations at higher resolutions are being planned to obtain accurate measurements for the collision statistics of inertial-range particles. | 14 | 3 | 1403.3865 |
1403 | 1403.1888_arXiv.txt | We consider the observational signatures of giant impacts between planetary embryos. While the debris released in the impact remains in a clump for only a single orbit, there is a much longer lasting asymmetry caused by the fact that all debris must pass through the collision-point. The resulting asymmetry is stationary, it does not orbit the star. The debris is concentrated in a clump at the collision-point, with a more diffuse structure on the opposite side. The asymmetry lasts for typically around 1000 orbital periods of the progenitor, which can be several Myr at distances of $\sim$50~AU. We describe how the appearance of the asymmetric disc depends on the mass and eccentricity of the progenitor, as well as viewing orientation. The wavelength of observation, which determines the grain sizes probed, is also important. Notably, the increased collision rate of the debris at the collision-point makes this the dominant production site for any secondary dust and gas created. For dust small enough to be removed by radiation pressure, and gas with a short lifetime, this causes their distribution to resemble a jet emanating from the (stationary) collision-point. We suggest that the asymmetries seen at large separations in some debris discs, like Beta Pictoris, could be the result of giant impacts. If so this would indicate that planetary embryos are present and continuing to grow at several tens of AU at ages of up to tens of Myr. | \label{intro} The final stage of terrestrial planet formation is now widely believed to be one of chaotic growth, with the terrestrial planets built up through series of planetary scale impacts (commonly known as giant impacts) between planetary embryos \citep[e.g.][]{kenyon2006, raymond2009, kokubo2010}. While giant impacts are perhaps most frequently discussed in relation to terrestrial planet formation they are certainly not limited to the terrestrial zone of a planetary system. In our own solar system the Pluto-Charon system \citep{canup2005, canup2011, stern2006}, and Haumea and its collisional family \citep{brown2007}, are both proposed to have their origin in giant impacts. It has also long been suggested that a large impact could explain Uranus' large obliquity \citep[e.g.][]{benz1989, slattery1992}. Outside our own solar system there are numerous examples of planets and debris discs that can be found at substantial distances from their parent star. Examples are the HR8799 system with 4 massive gas giant planets, the outermost at 68AU and a debris disc at 90-300AU (e.g. \citealt{marois2008, soummer2011}; Matthews et al. in press), or Fomalhaut with a massive debris disc at 140 AU \citep[e.g.][]{stapelfeldt2004, boley2012}. Debris discs are belts of planetesimals and dust produced by destructive collisions amongst the larger planetesimals \citep[e.g.][]{wyatt2007, wyatt2007b, wyatt2008}. The outer regions of planetary systems thus clearly provide an environment in which giant impacts can occur. Indeed some extrasolar systems possess much more material at large distances than our solar system, such that more, and larger, impacts can be expected than in the solar system. An essential property of giant impacts, wherever they occur, is that they produce substantial quantities of debris. Giant impacts span a large range of collision scenarios and outcomes from catastrophic disruption to fairly efficient accretion dependent on impact velocity and geometry \citep[e.g.][]{leinhardt2012}. As a result the quantity of debris produced can vary greatly, but even impacts that are apparently efficient accretion events release $\ga$1 per cent of the mass of the colliding bodies in debris. Indeed it is such debris that is liberated from the progenitor but remains bound to it that is key to the models for the formation of our Moon \citep[e.g.][]{canup2004b} and Pluto-Charon \citep[e.g.][]{canup2005}, while models for the formation of Mercury require large quantities of unbound debris \citep{anic2006, benz2007}. Debris produced by giant impacts, its properties, evolution and detectability, remains an understudied topic in comparison to the giant impacts that produce it, and those studies that have been done have generally focussed on the terrestrial planet region. Previous work that has been conducted in this area include \citet{kenyon2004}, who investigated debris produced during terrestrial planet formation in a statistical way, and \citet{jackson2012} who studied the evolution of debris produced by the Moon-forming impact. Impacts occurring at large orbital distances emphasise different aspects of the debris evolution. In particular since orbital periods are longer and velocities are lower at larger distances the evolution of a debris disc is substantially slower, which means that features that are short-lived and thus unlikely to be seen in the terrestrial zone can be much longer lived and become important characteristics in the outer regions. Furthermore since a debris disc at a large orbital distance is, by definition, much larger in spatial extent, and also less likely to be hidden by the star, there is a much greater possibility of obtaining spatially resolved images to observe structure within the disc. Of particular interest are disc asymmetries. There are a growing number of young systems with resolved debris discs that display asymmetries and other as yet poorly understood features, such as HD15115 \citep[e.g.][]{kalas2007,rodigas2012} and HD32297 \citep[e.g.][]{kalas2005b, schneider2005, currie2012}, with the 12 million year old Beta Pictoris system \citep[e.g.][]{telesco2005, li2012} probably the best known example. If we believe that giant impacts are indeed common, particularly during the epoch of planet formation, then we might reasonably expect that some of these systems may have experienced a giant impact in the comparatively recent past. If this is the case a question that we should be asking is; can a giant impact explain some of the features of these discs? If giant impacts can explain some of these features, thus providing evidence for massive bodies at large orbital distances, this also provides us with important information about the process of planet formation. In this work we discuss the morphologies (\S~\ref{sec:obsdisc}) and detectability (\S\S~\ref{sec:detectability} and \S~\ref{sec:collevol}) of debris discs produced by giant impacts and how these vary with parameters such as the mass of the progenitor body. We also discuss the morphology of small dust grains influenced by radiation pressure (\S\S~\ref{sec:blowout}) and CO (\S\S~\ref{sec:CO}), created in the destruction of the collisional debris. Finally we apply our models of giant impact debris to the debris disc of Beta Pictoris (\S~\ref{sec:betapic}). First however we describe the analytics that underpin the determination of the orbits of the debris, and thus the shape, and features of the disc, in Section~\ref{orbeq}. | \label{conclusion} Planetary scale, giant, impacts have occurred in the outer reaches of our own solar system, and it is not unreasonable to expect similar impacts to occur in the outer reaches of other planetary systems. These large impacts release substantial quantities of debris that will go into orbit around the host star and produce an, initially, high asymmetric disc. The behaviour of this giant impact debris is governed by a set of equations that we described in Section~\ref{orbeq}. The key result of these equations is the existence of the collision-point, a fixed point in space at the location at which the originating giant impact takes place and through which all of the debris must pass. The collision-point is of paramount importance in determining the appearance and evolution of the debris disc, and is what produces the strong asymmetry in these discs. We have studied the morphologies of debris discs generated by giant impacts and shown how the character of the disc varies depending on the mass of the progenitor body (and its orbital distance). At the same orbital distance a debris disc produced by an impact involving a more massive progenitor is broader both radially on the side of the disc opposite the collision-point, and vertically. In addition a debris disc produced by an impact involving a more massive progenitor is more strongly dominated by the collision-point due to the effect that while all material must pass through the collision-point, elsewhere the material is more dispersed than in a disc originating from a less massive progenitor. The lifetime of the asymmetry due to the collision-point is determined by precession caused by other bodies in the system, a typical lifetime however is a few thousand orbits. The long orbital periods at large distances from the parent star translates this into timescales of $\sim$1Myr. The eccentricity of the orbit of the progenitor body interacts with the asymmetry present due to the collision-point. Depending on the location of the impact around the orbit this can enhance or reduce the asymmetries in the brightness and radial extent of the disc at the collision-point and opposite it. In general the complexity of the disc structure is increased for eccentric progenitors. We have also studied the collisional evolution of the asymmetric discs generated by giant impacts. In the second meaning of its name the collision-point dominates the collisional evolution of the disc. As such material whose distribution depends strongly on the location at which it is produced, such as small dust grains that are strongly influenced by radiation pressure, and CO, demonstrate even stronger asymmetries, focussed on the collision-point. In addition the highly asymmetric debris disc produced by a giant impact evolves much faster collisionally than an equivalent axisymmetric disc. Nonetheless for a disc that is detectable initially the expected detectable lifetime is typically at least as long as the lifetime of the asymmetry. As such it is reasonable to expect that we can observe asymmetric discs resulting from impacts between Moon-size and larger bodies at large distances ($\sim$50AU) from their host star. We applied our model of giant impact debris discs to the debris disc around the star Beta Pictoris and demonstrated that it is capable of broadly reproducing the asymmetry observed in the mid-infrared by \citet{telesco2005}, in CO/sub-mm by Dent et al. subm., and in scattered light by \citet{larwood2001}. A more detailed analysis would be required however to determine if this is the best model for the disc, and if so what the system parameters are. If debris discs generated by giant impacts are found in the outer reaches of extrasolar planetary systems, for example if this is shown to be the best model for Beta Pictoris, this has important implications for planet formation models. The occurrence of giant impacts could imply that rocky/icy bodies routinely grow to large, planetary, sizes at substantial distances from their host star. | 14 | 3 | 1403.1888 |
1403 | 1403.6185_arXiv.txt | {In this work we present simple, physics-based models for two effects that have been noted in the fully depleted CCDs that are presently used in the Dark Energy Survey Camera. The first effect is the observation that the point-spread function increases slightly with the signal level. This is explained by considering the effect on charge-carrier diffusion due to the reduction in the magnitude of the channel potential as collected signal charge acts to partially neutralize the fixed charge in the depleted channel. The resulting reduced voltage drop across the carrier drift region decreases the vertical electric field and increases the carrier transit time. The second effect is the observation of low-level, concentric ring patterns seen in uniformly illuminated images. This effect is shown to be most likely due to lateral deflection of charge during the transit of the photo-generated carriers to the potential wells as a result of lateral electric fields. The lateral fields are a result of space charge in the fully depleted substrates arising from resistivity variations inherent to the growth of the high-resistivity silicon used to fabricate the CCDs.} | \label{sec:intro} Fully depleted charge-coupled devices (CCDs) are presently in use in three major astronomical imaging cameras: the PAN-Starrs PS1 camera~\cite{panstarrs}, the HyperSuprime-Cam camera~\cite{hsuprime}, and the Dark Energy Survey Camera (DECam)~\cite{des}. The thicknesses of the CCDs are 75~\cite{panstarrs2}, 200~\cite{hsuprime2} and 250~$\mu$m~\cite{des2}, respectively. The primary advantages of the thick, fully depleted devices compared to thinned, conventional scientific CCDs are the enhanced quantum efficiency and reduced fringing at long wavelengths~\cite{groom1999}. The purpose of this work is to present first order, physics-based models to explain some of the low-level phenomena that have been observed during telescope operation with these thick, fully depleted CCDs. The effects of interest in this work are the dependence of the CCD point-spread function (PSF) on signal level, and the appearance of fixed-pattern, low-level variations in the CCD images seen during uniform illumination of the devices. For the former we present a first order theoretical model for the effect, while for the latter we include experimental results to assist in the understanding of the basic mechanisms involved. The CCDs described in this work are fabricated on high-resistivity silicon substrates that are manufactured using the float-zone refining technique~\cite{Ammon}. The resistivity is greater than 4000~$\Omega$-cm for the n-type substrates considered here, and the CCDs are operated with a substrate-bias voltage that fully depletes the high-resistivity substrate~\cite{Holland1}. As discussed in the remainder of the paper, the low-level effects that arise in these thick, fully depleted CCDs depend on the vertical electric fields in the device, and we show that the effects can be reduced by operating the CCDs with increased vertical fields. | \label{sec:summary} We have presented a simple, physics-based model to explain the dependence of the point-spread function on light level in fully depleted CCDs. Given that this work is part of the proceedings of a workshop, it is not intended that this model be considered a rigorous solution to the problem but rather a starting point for a more accurate model. We have also studied the low-level variations in signal level seen during uniform illumination of fully depleted CCDs, and have shown through a review of the literature that essentially all types of silicon imaging devices can exhibit similar effects. The physics of the observed effects for the various types of imagers differ, but in all cases the origin of the low-light variations is the resistivity striations that are inherent to the growth of the silicon crystals. We have presented a simple model based on the lateral displacement of charge due to lateral volume charge density variations arising from the resistivity striations, and have presented experimental evidence in support of the model. The operation of fully depleted CCDs at high vertical electric fields offers a means to minimize both effects considered in this paper. | 14 | 3 | 1403.6185 |
1403 | 1403.4850.txt | We present measurements of the star formation rate (SFR) in the early-type galaxies (ETGs) of the \atlas\ sample, based on \textit{Wide-field Infrared Survey Explorer} (\textit{WISE}) 22~\mum\ and \textit{Galaxy Evolution Explorer} far-ultraviolet emission. We combine these with gas masses estimated from $^{12}$CO and \hi\ data in order to investigate the star formation efficiency (SFE) in a larger sample of ETGs than previously available. We first recalibrate (based on \textit{WISE} data) the relation between old stellar populations (traced at $K_{\rm s}$-band) and 22~\mum\ luminosity, allowing us to remove the contribution of 22~\mum\ emission from circumstellar dust. We then go on to investigate the position of ETGs on the Kennicutt-Schmidt (KS) relation. Molecular gas-rich ETGs have comparable star formation surface densities to normal spiral galaxy centres, but they lie systematically offset from the KS relation, having lower star formation efficiencies by a factor of $\approx$2.5 (in agreement with other authors). This effect is driven by galaxies where a substantial fraction of the molecular material is in the rising part of the rotation curve, and shear is high. We show here for the first time that although the number of stars formed per unit gas mass per unit time is lower in ETGs, it seems that the amount of stars formed per free-fall time is approximately constant. The scatter around this dynamical relation still correlates with galaxy properties such as the shape of the potential in the inner regions. This leads us to suggest that dynamical properties (such as shear or the global stability of the gas) may be important second parameters that regulate star formation and cause much of the scatter around star-formation relations. | Star formation is a fundamental process, responsible for converting the soup of primordial elements present after the big bang into the universe we see around us today. Despite this, debate still rages about the way star formation proceeds, and the role (if any) that environment plays in its regulation. For instance, high-redshift starbursts seem to convert gas into stars much more efficiently than local disc galaxies \citep{2010ApJ...714L.118D,2010MNRAS.407.2091G}. This increased efficiency may be explained by a change in gas properties (e.g the high fraction of gas at high volume densities in starbursts), or may be an artefact of the imperfect methods we have of estimating star-formation rates, and tracing molecular hydrogen \citep{2012ApJ...746...69G}. Atomic gas is present in $\approx$32\% of early-type galaxies \citep[ETGs;][]{1977A&A....54..641B,1985AJ.....90..454K,2006MNRAS.371..157M,2007A&A...474..851D,2009A&A...498..407G,2010MNRAS.409..500O,2012MNRAS.422.1835S}, dust in $\approx$60\% \citep{2001AJ....121..808C,2012ApJ...748..123S,2013MNRAS.431.1929A}, and molecular gas in 22\% \citep[][hereafter Paper IV]{2007MNRAS.377.1795C,Welch:2010in,2011MNRAS.414..940Y}. Low level residual star formation has also been detected through studies of UV emission \citep[e.g.][]{2005ApJ...619L.111Y,2007ApJS..173..619K,2010ApJ...714L.290S,Wei:2010bt}, optical emission lines \citep[e.g.][]{Crocker:2011ic} and infra-red emission (e.g. \citealt{1989ApJS...70..329K,2007MNRAS.377.1795C,2009ApJ...695....1T}, hearafter T09; \citealt{2010MNRAS.402.2140S}). Typically ETGs have much smaller fraction of molecular gas to stellar mass than spirals. This average fraction appears to decrease with increasing galaxy bulge fraction (\citealt{2013MNRAS.432.1862C}, hereafter Paper XX; see also \citealt{2012ApJ...758...73S}). This suggests a connection between bulge formation and galaxy quenching, as also suggested by optical studies \citep{2012ApJ...753..167B}. However the decrease of the molecular gas fraction does not seem to be the only factor making ETGs red. In fact, even at fixed gas fraction, molecule-rich ETGs form stars less efficiently than normal spirals, and very much less efficiently than high-redshift starburst galaxies \citep[][hereafter Paper XXII]{2011MNRAS.415...61S,2012ApJ...758...73S,2013MNRAS.432.1914M}. Such a suppression would help explain how objects in the red sequence can harbour substantial cold gas reservoirs for a long period of time, without becoming significantly blue. A similar suppression of star formation may also be ongoing in the central parts of our own Milky Way \citep{2013MNRAS.429..987L}, suggesting this may be a general process in spheroids and/or dense stellar environments. The physics of whatever process is causing this suppression of star formation is, however, unknown. The deep potential wells of these objects could hold gas stable against collapse \citep[dubbed `morphological-quenching';][]{2009ApJ...707..250M}, or strong tidal fields and streaming motions could pull clouds apart \citep[e.g.][]{2013arXiv1304.7910M,2013arXiv1303.6286K}, lowering the observed SFE. In this work we use data from the \atlas\ project to investigate if local ETGs do display a lower SFE than local spirals, and if so what may be driving this suppression. \atlas\ is a complete, volume-limited exploration of local ($<$42 Mpc) ETGs \citep[][hereafter Paper I]{2011MNRAS.413..813C}. All 260 \atlas\ sample galaxies have measured total molecular gas masses (or upper limits; from IRAM 30m CO observations presented in Paper IV). \hi\ masses are also available for the northern targets (from Westerbork Synthesis Radio Telescope, WSRT, observations; \citealt{2012MNRAS.422.1835S}, hereafter Paper XIII). To estimate the SFR in these objects, we utilise data from the \textit{Wide-field Infrared Survey Explorer} \citep[\textit{WISE};][]{2010AJ....140.1868W} all sky survey at 22~\mum, and from the \textit{Galaxy Evolution Explorer} (\textit{GALEX}) in the far ultraviolet (FUV). Section 2 presents the data we use in this work, and describes how derived quantities are calculated. Section 3 presents our results, where we investigate the 22~\mum\ emission from CO non-detected ETGs, and the star formation activity in objects with a cold ISM. Section 4 discusses these results, and what we can learn about star formation and the evolution of ETGs. Section 5 presents our conclusions. | In this paper we presented star formation rates for the (fast-rotating) molecule-rich \atlas\ early-type galaxies, derived from \textit{WISE} 22~\mum\ and \textit{GALEX} FUV data. We first recalibrated the relation between $K_{\rm s}$-band luminosity and 22~\mum\ emission for our large sample of CO non-detected ETGs, to allow subtraction of 22~\mum\ emission from circumstellar material around old stars. The emission from CO non-detected galaxies can vary by almost half an order of magnitude between objects of the same stellar mass. AGN activity and galaxies with younger stellar populations ($<$4~Gyr) contribute to this scatter, but do not dominate it. We were unable to reproduce claimed correlations between stellar metallicity and the scatter in this relation, and thus the astrophysical driver of the majority of the scatter remains unknown. Once the contribution from old stars has been removed, we found SFRs between $\approx$0.01 and 3 $M_{\odot}$ yr$^{-1}$, and SFR surface densities ranging from $\approx$0.004 to 18.75 $M_{\odot}$ yr$^{-1}$ kpc$^{-2}$. The median SFR for our molecular gas-rich ETGs is $\approx$0.15 $M_{\odot}$ yr$^{-1}$, and the median SFR surface density is 0.06 $M_{\odot}$ yr$^{-1}$ kpc$^{-2}$. Almost all molecule-rich ETGs have higher SFR surface densities than the disk of the average spiral galaxy, but similar to spiral galaxy centres. This is depute many of the galaxies being bulge-dominated, and lying in the red-sequence on an optical colour magnitude diagram. It is thus clear that selecting early-type objects by morphology or optical colour is not a good way to build a sample free from star formation activity, as is often assumed by studies at higher redshifts. Using these SFRs, we showed that our ETGs fall below the canonical Kennicutt-Schmidt relation, forming on average a factor of $\approx$2.5 fewer stars per unit molecular gas mass than late-type and starburst galaxies (and a factor of $\approx$20 fewer than high-redshift starbursts). In our study, this difference is mainly driven by galaxies with SFRs below $\approx$0.3 $M_{\odot}$ yr$^{-1}$ kpc$^{-2}$ (or equivalently cold gas surface densities $<$300 $M_{\odot}$ pc$^{-2}$). These systems have the majority of their molecular gas concentrated in the inner regions of their host galaxy where the rotation curve is still rising, and shear is high. A local dynamical star-formation relation (taking into account the local free-fall time within the galaxy disc) reproduces well our observations. Using this relation one can obtain a single star-formation relation, that fits ETGs, Galactic clouds and spiral/starburst galaxies at all redshifts. Despite this, the residuals around the dynamical star-formation relation still correlate with galaxy properties such as the shape of the potential in the inner regions. We postulate that the dynamical stability of the gas may be an important second parameter, that suppresses star formation and causes much of the scatter around the best-fit dynamical star-formation relation. We discussed various mechanisms that can cause this effect, and more generally the difficulties inherent in estimating SFRs and molecular gas masses in these ETGs. A changing X$_{\rm CO}$ factor could potentially cause the low SFE we observe, but it can not explain why the SFE in our study depends so strongly on dynamical quantities. It is clear that further study will be required to fully determine the cause of the low SFE in ETGs. Ascertaining what is driving the residuals around the KS and KDM12 law will give us a direct way to probe the physics that regulates star formation. For instance, if variations in cloud properties and gas velocity dispersions are present in the central parts of ETGs, then they can potentially explain some of the SFE trends. Obtaining observational evidence for such variations will require high angular and spectral resolution observations, to resolve individual molecular clouds. Gas-phase metallicity estimates and observations of multiple spectral lines could also be used to determine if the X$_{\rm CO}$ factor in these objects is systematically different. In addition, studies of the stability of the gas, and comparison with spatially-resolved star-formation relations, will be crucial to determine how changes in galactic conditions affect the physics of star formation. \noindent \textbf | 14 | 3 | 1403.4850 |
1403 | 1403.4525_arXiv.txt | This paper introduces a new empirical model for the rotational evolution of Sun-like stars -- those with surface convection zones and non-convective interior regions. Previous models do not match the morphology of observed (rotation period)-color diagrams, notably the existence of a relatively long-lived ``$C$-sequence'' of fast rotators first identified by \citet{barnes2003}. This failure motivates the Metastable Dynamo Model (MDM) described here. The MDM posits that stars are born with their magnetic dynamos operating in a mode that couples very weakly to the stellar wind, so their (initially very short) rotation periods at first change little with time. At some point, this mode spontaneously and randomly changes to a strongly-coupled mode, the transition occurring with a mass-dependent lifetime that is of order 100 MYr. I show that with this assumption, one can obtain good fits to observations of young clusters, particularly for ages of 150 MYr to 200 MYr. Previous models and the MDM both give qualitative agreement with the morphology of the slower-rotating ``$I$-sequence'' stars, but none of them have been shown to accurately reproduce the stellar-mass-dependent evolution of the $I$-sequence stars, especially for clusters older than a few hundred MYr. I discuss observational experiments that can test aspects of the MDM, and speculate that the physics underlying the MDM may be related to other situations described in the literature, in which stellar dynamos may have a multi-modal character. | \subsection{Double Zone Model} The prevailing model of the evolution of stellar rotation is what I term (following \citet{spada2011}) the Double Zone Model (DZM). It has evolved over the last 25 years from the stellar wind torque law in the form written by \citet{kawaler1988}, with still earlier progenitors including \citet{weber1967, mestel1968} and \citet{belcher1976}. Since the early 1990s, the model has been extended and tested against successively improved observations in a series of papers, e.g. \citet{pinsonneault1990, macgregor1991, krishnamurthi1997, irwin2009, denissenkov2010, epstein2014}. It has recently been generalized in several ways, e.g. by \citet{reiners2012, spada2011} and \citet{gallet2013}. Stripped of most physical justification, the model may be summarized as follows: (1) The torque acting on a star because of its magnetized stellar wind is given by the bifurcated expression \begin{eqnarray} {dJ \over dt} \ = \ K_W \ \Omega^3 \ \left [ {R \over M} \right ]^{1/2}, \ \ \ \ \Omega \leq \Omega_{crit}, \\ \ \ \ \ \ \ \ \ \ = \ K_W \ \Omega \Omega_{crit}^2 \left [ {R \over M} \right ]^{1/2}, \ \ \ \Omega \geq \Omega_{crit}, \ \ \ \nonumber \end{eqnarray} where $J$ is the star's total angular momentum, $M$ and $R$ are the star's mass and radius (both in solar units), and $\Omega$ is the stellar rotation frequency, often expressed in units of the Sun's rotation frequency of about $3 \times 10^{-6}$ rad s$^{-1}$. The constant $K_W$ has the dimensions of a moment of inertia (g cm$^2$) and is chosen to give the solar rotation frequency at the solar age. This expression (with torque scaling as $\Omega^3$ for slow rotators) yields the \citet{skumanich1972} $\Omega \propto t^{-1/2}$ rotation law for old stars. (2) Initial conditions are applied at an age of 1 to 20 MYr counting from the birth line of \citet{palla1990}, corresponding to current estimates of the time during which contracting protostars are magnetically locked to their natal disks. Initial rotation periods $P_0$ are usually in the range 1 to 15 days, corresponding to the period distributions seen in the youngest open clusters (e.g., \citet{rebull2001, rebull2004}). (3) The dynamo saturation frequency $\Omega_{crit}$ is actually taken to be a function of stellar mass $M_*$ (or equivalently of $(B-V)$ color). Its effect in the model is to decrease the torque acting on fast-rotating (periods of a few days or less) stars, so their short rotation periods can survive long enough for us to see them in clusters with ages as great as 500 MYr. (4) The angular momentum in stellar convection zones is assumed to be weakly coupled to that in their radiative interiors. This allows the CZ to rotate more or less independently of the star's interior. The coupling is characterized by an equilibration timescale $\tau_c$, which is a function of stellar mass, increasing from 10 MYr for stars with more than solar mass, to greater than 100 MYr for early M-type stars. In addition, to avoid spoiling the fit to fast-rotating stars, $\tau_c$ must depend also on $\Omega$ itself, being 1 MYr or less for rapid rotators, and attaining the values just mentioned only for slow rotators \citep{denissenkov2010}. Thus $\tau_c$ is, in principle, a free function of mass and $\Omega$. As a simplification, \citet{denissenkov2010} took $\tau_C$ to be short (1 MYr) for stars rotating faster than a critical period $P_{crit}$; otherwise $\tau_C$ was taken to be long, of order 100 MYr. In either case, the equilibrium rotation frequency of the CZ is determined by balancing the angular momentum flux across the bottom of the CZ with that lost to the stellar wind. Recently \citet{reiners2012} and \citet{gallet2013} have proposed variants on the DZM, differing mainly in the torque laws assumed. \citet{reiners2012} argue that the relevant magnetic field quantity is the star's typical surface magnetic field strength, not its magnetic flux (as assumed by, e.g., \citet{kawaler1988}). This identification results in a strong $R^{16/3}$ dependence of the torque on the stellar radius, and leads to a time dependence of $P_{rot}$ that scales as $\Omega$ for $\Omega$ faster than some critical value, and as $\Omega^5$ if $\Omega$ is slower than that value. For a solar-mass star, this torque law generates an evolution of $P_{rot}$ that resembles the Skumanich $t^{1/2}$ law, but only in the sense of the average behavior over several GYr. For other masses and ages up to a few GYr, a Skumanich-like power law is not obtained. \citet{gallet2013} derive a torque law from numerical stellar wind simulations by \citet{matt2012}. Their torque law has no simple analytic form, but it does lead to a fairly strong dependence of the torque on $R$. In the limit of slowly-rotating stars its dependence on $\Omega$ is slightly stronger than $\Omega^3$, while the rapid-rotation limiting dependence is slightly weaker than $\Omega$. \subsection{Barnes's Symmetrical Empirical Model} \citet{barnes2010} and \citet{barneskim2010} sought to describe observed cluster $P_{rot}$-color diagrams empirically, connecting their expressions with astrophysical concepts only after obtaining a satisfactory fit to the observations. For purposes of this paper, I call their model the Symmetrical Empirical Model (SEM). Its logic runs as follows: (1) Stars on the $I$- and $C$-sequences obey different period-evolution equations, namely \begin{eqnarray} P_I(B-V, t) \ = \ f(B-V) g(t), \ \ (I-{\rm sequence}) \\ P_C(B-V, t) \ = \ P_0 e^{[t/T(B-V)]}. \ \ (C-{\rm sequence}) \nonumber \end{eqnarray} Here $g(t) \ = \ t^{-1/2}$, as in the Skumanich law, $P_0$ is a constant period, and the functions $f(B-V)$ and $T(B-V)$ are initially arbitrary functions that can be determined from fits to the observations. Both $T(B-V)$ and $f^2(B-V)$ have dimensions of time. \citet{barneskim2010} note that both these functions appear to be related in simple ways to a physically interesting quantity, namely the turnover time of the convection zone, denoted $\tau$. (2) Accepting this identification, the period evolution expressions can be combined into one period evolution equation that has the correct behavior both for large and small values of the period $P$: \begin{equation} {dP \over dt} \ = \ \left [ {k_I P \over \tau} \ + \ {\tau \over k_C P} \right ]^{-1} \ , \end{equation} where $k_I$ and $k_C$ are dimensionless constants determined from fits to the data. This equation gives the SEM its name. To parallel the development of the DZM, I transform the period evolution equation to a torque law, assuming solid-body rotation, so that the relevant moment of inertias for both sequences are equal to the total stellar value $I_*$. The resulting torque law is \begin{equation} {dJ \over dt} \ = \ - I_* {\Omega^2 \over 2 \pi } \left [ {{2 \pi k_I} \over {\tau \Omega}} \ + \ {{\tau \Omega} \over {2 \pi k_C}} \right ] ^{-1}. \end{equation} (3) Initial conditions may be applied as with the DZM, though \citet{barnes2010} prefers to set initial periods at the zero-age main sequence (ZAMS), roughly 50 MYr after the birth line. At this time the rotation periods are at their shortest, limited at the short-period end by the breakup equatorial speed of the star. The SEM is a descriptive, not explanatory model, as \citet{barneskim2010} take pains to point out. That is, the physical processes that determine the functions $f(B-V)$ and $T(B-V)$ are not specified. The possible connection between these functions and the convective turnover time $\tau$ is, however, suggestive. If the reality of this relationship can be verified, then it might place a useful constraint on more physics-based models of stellar magnetic fields. | \subsection{Summary of Conclusions} In the foregoing sections, I have described a modeling exercise in which I have tried to match observed $P_{rot}$-color diagrams using three different models of the stellar spindown process. In this attempt, I have assigned primary importance to the observed existence in fairly young clusters of two sequences of stars, first noted by \citet{barnes2003}: the $C$-sequence at $P_{rot}$ of about 2 days and less, separated by a poorly-populated gap from the $I$-sequence at longer periods. The principal conclusion of the current modeling study is that previous models (the double zone model, or DZM {\it e.g.} \citet{denissenkov2010}, and Barnes symmetrical empirical model, or SEM \citep{barnes2010, barneskim2010}) do not adequately represent the best recent open cluster observations. In particular, by virtue of the continuous way in which these models map initial conditions into the history of torque on a star, they appear unable to produce $C$-sequences that are as populous, well-defined, or at periods as short as those seen in the observational data. I propose the so-called Metastable Dynamo Model (MDM) as a solution to this problem. Its key hypothesis is that some or all stars go through an early phase in which magnetic activity is present, but the angular momentum coupling to the stellar wind is very small. It appears to be quite difficult to explain the properties of the $C$-sequence without invoking some such mechanism that decouples many young stars from the stellar wind torque, at least for a time. Fits of the MDM parameters to cluster data constrain the strength of the angular momentum coupling for the hypothetical weakly-coupled stars to be at least 300 times less than for $I$-sequence stars. The typical lifetime for the weakly-coupled phase is found to be about 80 MYr for stars of 1 $M_{\sun}$; the data are consistent with longer lifetimes of this phase for smaller-mass stars, but the form of this dependence is poorly constrained. All three model classes (DZM, SEM, MDM) have failings, notably inability to reproduce the time history of the color dependence of $P_{rot}$ on the $I$-sequence. For the MDM, these inaccuracies are smallest for the cluster M34 (age about 220 MYr), and are larger for both younger and older clusters. \subsection{Observational Tests} The foregoing analysis suggests a number of observational tests that may help choose among the various theories, test their premises, or refine their physical interpretations. The DZM makes the striking prediction that most relatively young stars (ages between 50 and 300 Myr, depending on mass) on the $I$-sequence should have markedly different rotation rates in their CZs and in their radiative interiors. In principle, the radial variation of $\Omega$ can be measured with asteroseismology. This has been done for many years with solar pulsations, and indeed, using photometric data from the $Kepler$ mission, recent analysis of pulsations in red giant stars has revealed large differences in rotation rate between the tiny degenerate core and the extensive convective envelope \citep{beck2012}. Asteroseismic measurements of rotation in young Sun-like stars have not yet been successful, however. (\citet{deheuvels2014} have measured rotational splitting in $Kepler$ data for several subgiant stars. But since the method used requires detection of mixed oscillation modes, having properties of both pressure- and gravity-modes, it is not applicable to the relatively young stars under discussion here.) Young, magnetically active stars display larger photometric noise than do their older, inactive brethren, and moreover magnetic activity suppresses the surface amplitudes of acoustic oscillations, making them more difficult to observe \citep{chaplin2011}. This unfortunate combination has so far prevented conclusive asteroseismic measurements of radial differential rotation in Sun-like stars. Analysis of longer (full mission length) time series from $Kepler$ may yet allow such measurements. Apart from reproducing the morphology of the $C$- and $I$-sequences, a successful model of rotational evolution should also give the observed distribution of stars in the gap between sequences. For a uniform distribution of initial rotation periods, the MDM's prediction in this respect is clear: Stars in the gap must have recently transitioned from weak- to strong-coupling modes, hence they are rapidly evolving to longer periods; as their periods increase, $dP_{rot}/dt$ decreases. Thus the star density should be lowest at periods just above those in the $C$-sequence and rise towards longer periods, up to the $I$-sequence. This behavior is clearly visible in the probability density distributions shown in Fig. 7. Predictions for the DZM and the SEM are slightly more complicated, and little work has been done concerning them, but there are no fundamental obstacles to doing so. The observational picture is more difficult, however. Star counts between the $C$- and $I$-sequences are small, and as yet data are too sparse to make strong tests of the models within the period gap. Further observations are essential for this purpose. Finally, if the MDM scenario is correct, then stars lying on the $C$-sequence must differ greatly from similar-mass stars in the period gap, having much weaker angular momentum coupling to the stellar wind. What could cause such a difference? Clearly there must be some difference in the wind, in the magnetic field that threads it, or both. Gross changes in the stellar wind seem implausible and in any case unobservable, given current techniques. If the difference is in the field, however, then diagnostics may be feasible. Observations of X-ray luminosity as a function of $P_{rot}$ show no obvious step across the period range occupied by the $C$-sequence \citep{pizzolato2003}. Therefore the hypothetical discontinuous change in coupling properties would likely be signalled not by a difference in the typical magnetic field strength, but rather by a change in its spatial organization. This idea is not new; it was suggested in \citet{barnes2003}, and has since been explored using X-ray data by, e.g., \citet{wright2011}, by \citet{gondoin2012, gondoin2013}, with spectropolarimetry by, e.g., \citet{morin2011, jeffers2011}, and by \citet{marsden2011a, marsden2011b}. and, in the context of ultra-cool dwarf stars, by combining X-ray and rotation data \citep{cook2013}. A related line of argument starts with the observed Vaughan-Preston gap in the distribution of stars in $P_{rot}$-$R_{HK}^{\prime}$ space, where $R_{HK}^{\prime}$ is the Mt. Wilson Ca II activity index \citep{vaughan1980}. This gap was quickly interpreted as evidence for a small discrete set of dynamo classes, most clearly seen as relations between $P_{rot}$ and the dynamo cycle period $P_{cyc}$ \citep{durney1981, brandenburg1998, bohm-vitense2007}. In the current context, perhaps the most intriguing result of these studies is the observation that some stars lie in a ``supersaturated dynamo'' state, described by \citet{saar1999}. Stars thus identified have short rotation and cycle periods, and the power-law relation between these periods has the opposite sign from that seen in stars with longer $P_{rot}$. Moreover, the transition between the supersaturated and other dynamo modes appears to be abrupt (because there are very few transitional objects seen), and involves a discontinuous change in the cycle period. The various lines of study just described involve a wide range of stellar circumstances and several different (and hypothetical) formulations of dynamo physics. So it is not clear that all of these studies relate to the same phenomena, or are governed by the same processes. Nevertheless, taken together they reinforce the idea that a variety of dynamo modes might exist, yielding (among other properties) different partitioning of power across large and small spatial scales. If almost all of the magnetic energy were found in small-scale strucures in which positive and negative field regions accurately cancel one another, then little field might penetrate to heights where the stellar wind expansion begins. The result would be an almost field-free wind, and only minimal torque on the star. Differences among photospheric spatial structures may be identifiable using Doppler imaging and spectropolarimetry, by comparing very rapid rotators against stars with similar activity diagnostics but slower rotation periods. Measuring the cycle periods of very fast rotators might also be revealing, as a probe of deeper-seated differences among the properties of stellar dynamos. \subsection{Final Considerations} It is worthwhile to reiterate a few points, and to raise some issues for further work. (1) The population synthesis calculations described above suggest that the MDM has some validity, but they are by no means conclusive evidence that it is correct, nor that the DZM or SEM are wrong. There may well be parameter choices for these latter models that will better reproduce the $C$-sequence population than the ones I have employed here. Better fitting of the $I$-sequence is almost surely feasible for all model types. (2) Within the MDM framework, it appears that models enforcing solid-body rotation match the young-cluster observations, but there is as yet nothing to show that differentially-rotating models are excluded. (3) The basic MDM assumes that all stars begin life in the weakly-coupled dynamo mode. But in very young clusters there is evidence that the MDM's assumptions place too many stars on the $C$-sequence. Thus, perhaps only a fraction (perhaps as few as half) of all stars initially occupy the weak-coupling mode. A statistical test of this conjecture may be feasible with the data that are presently in hand. (4) All model classes have difficulty fitting the shapes of $I$-sequences with age, especially for stars older than a few hundred MYr. Indeed, given this difficulty, the $\Omega^3$ torque law (hence the $t^{-1/2}$ period law) may be only an approximation. For recent evidence that this is so, based on stars with measured $P_{rot}$ and asteroseismic ages, see \citet{metcalfe2014}. Better modeling may require a function of both $\Omega$ and mass; making a useful guess about the form of such a function will be difficult, lacking a physical picture of the important processes. I am grateful to Sydney Barnes and to Marc Pinsonneault for conversations that inspired and informed this work, and to Travis Metcalfe, David Soderblom, Soeren Meibom, Lynne Hillenbrand, and to the anonymous referees for their useful comments on early versions of this paper. \clearpage | 14 | 3 | 1403.4525 |
1403 | 1403.1907_arXiv.txt | \baselineskip = 11pt \leftskip = 0.65in \rightskip = 0.65in \parindent=1pc {\small Observations from optical to centimeter wavelengths have demonstrated that multiple systems of two or more bodies is the norm at all stellar evolutionary stages. Multiple systems are widely agreed to result from the collapse and fragmentation of cloud cores, despite the inhibiting influence of magnetic fields. Surveys of Class 0 protostars with mm interferometers have revealed a very high multiplicity frequency of about 2/3, even though there are observational difficulties in resolving close protobinaries, thus supporting the possibility that all stars could be born in multiple systems. Near-infrared adaptive optics observations of Class I protostars show a lower binary frequency relative to the Class~0 phase, a declining trend that continues through the Class II/III stages to the field population. This loss of companions is a natural consequence of dynamical interplay in small multiple systems, leading to ejection of members. We discuss observational consequences of this dynamical evolution, and its influence on circumstellar disks, and we review the evolution of circumbinary disks and their role in defining binary mass ratios. Special attention is paid to eclipsing PMS binaries, which allow for observational tests of evolutionary models of early stellar evolution. Many stars are born in clusters and small groups, and we discuss how interactions in dense stellar environments can significantly alter the distribution of binary separations through dissolution of wider binaries. The binaries and multiples we find in the field are the survivors of these internal and external destructive processes, and we provide a detailed overview of the multiplicity statistics of the field, which form a boundary condition for all models of binary evolution. Finally we discuss various formation mechanisms for massive binaries, and the properties of massive trapezia. \\~\\~\\~}% | } \label{sec:introduction} Many reviews have been written on pre-main sequence binaries over the past 25 years, e.g., {\em Reipurth} (1988), {\em Zinnecker} (1989), {\em Mathieu} (1994), {\em Goodwin} (2010), and particular mention should be made of IAU Symposium No. 200 ({\em Zinnecker and Mathieu,} 2001), which is still today a useful reference. Most recently, {\em Duch\^ene and Kraus} (2013) review the binarity for stars of all masses and ages. Stimulated by the growing discoveries of multiple systems among young stars, there is increasing interest in the idea, first formulated by {\em Larson} (1972), that all stars may be born in small multiple systems, and that the mixture of single, binary, and higher-order multiples we observe at different ages and in different environments, may result from the dynamical evolution, driven either internally or externally, of a primordial population of multiple systems. While more work needs to be done to determine the multiplicity of newborn protostars, at least -- as has been widely accepted for some time -- binarity and multiplicity is clearly established as the principal channel of star formation. The inevitable implication is that dynamical evolution is an essential part of early stellar evolution. In the following we explore the processes and phenomena associated with the early evolution of multiple systems, with a particular emphasis on triple systems. | 14 | 3 | 1403.1907 |
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1403 | 1403.1817_arXiv.txt | Numerical simulations of minor mergers predict little enhancement in the global star formation activity. However, it is still unclear the impact they have on the chemical state of the whole galaxy and on the mass build-up in the galaxy bulge and disc. We present a two-dimensional analysis of NCG 3310, currently undergoing an intense starburst likely caused by a recent minor interaction, using data from the PPAK Integral Field Spectroscopy (IFS) Nearby Galaxies Survey (PINGS). With data from a large sample of about a hundred \hii regions identified throughout the disc and spiral arms we derive, using strong-line metallicity indicators and direct derivations, a rather flat gaseous abundance gradient. Thus, metal mixing processes occurred, as in observed galaxy interactions. Spectra from PINGS data and additional multiwavelength imaging were used to perform a spectral energy distribution fitting to the stellar emission and a photoionization modelling of the nebulae. The ionizing stellar population is characterized by single populations with a narrow age range \mbox{(2.5-5 Myr)} and a broad range of masses \mbox{(10$^4$--6$\times 10^{6}$ \msun\twospace)}. The effect of dust grains in the nebulae is important, indicating that 25--70\% of the ultraviolet photons can be absorbed by dust. The ionizing stellar population within the \hii regions represents typically a few percent of the total stellar mass. This ratio, a proxy to the specific star formation rate, presents a flat or negative radial gradient. Therefore, minor interactions may indeed play an important role in the mass build-up of the bulge. | The friction between gas and dust in a merger event can have an important impact on the evolution of the galaxies involved. Minor mergers are usually defined as the collision between two galaxies with a mass ratio smaller than 1:3-1:4. Enhanced star formation when compared with isolated objects has been observed in samples of interacting/merging galaxies (e.g.~\citealt{Kennicutt87,Barton03,Geller06,Woods07}). Numerical simulations of minor mergers indicate that they can trigger nuclear activity~\citep{Mihos94c,Hernquist95,Eliche-Moral11}, alter the morphologies of galaxies ~\citep{Robertson06} and activate bars~\citep{Laine99,Romano-Diaz08}. Contrary to major mergers, minor mergers are much less violent dynamical processes since they do not destroy the disc of the main progenitor. Nevertheless, they have been increasingly recognized as important players in galaxy evolution and, in particular, in the formation and assembly of bulges especially in lower mass systems (\citealt{Guo07},~\citealt{Hopkins10}, and references therein). Yet, whether they are also important for the total stellar mass build-up in galaxies in general is unclear and controversial~\citep{Bournaud07,Lopez-Sanjuan11,Newman12,Xu13}. The induced star formation associated with the gas motions created by an interaction or the presence of bars is also expected to have an impact in the chemical distribution of the galaxies. Inflows of metal poor gas from the outer parts of the galaxy can decrease the metallicity in inner regions and modify the radial abundance gradients across spiral discs~\citep{Rupke10}. In fact, some studies have found that interacting galaxies do not follow the well established correlation between luminosity and metallicity found in normal disc galaxies. Shallower or null metallicity gradients and relatively high metallicity \hii\onespace-like regions have been observed in the outer part of the galaxies in major merger events (~\citealt{Kewley06,Ellison08,Michel-Dansac08,Rupke08,Peeples09,Miralles-Caballero12,Sanchez14}). A similar effect can have the action of inward and outward radial flows of interstellar gas induced by the non-axisymmetrical potential of the bars (e.g.,~\citealt{Friedli94,Roy97} ). There is extensive literature on the impact of a major merger event on the evolution of the involved galaxies. However, only a handful recent works have been focused on minor mergers (e.g.~\citealt{Krabbe11,Alonso-Herrero12}). Therefore, more observational studies are needed to provide a deeper insight on the effect of less violent dynamical phenomena on galaxy evolution. NGC 3310 is a very distorted spiral galaxy classified as an SAB(r)bc by~\cite{deVaucouleurs91}, with strong star formation. The star formation activity, especially a vigorous circumnuclear star-forming ring, has been studied over a wide range of wavelengths from X-rays to radio (e.g.~\citealt{Balick81,Pastoriza93,Zezas98,Diaz00a,Elmegreen02,Hagele10b,Hagele13,Mineo12}). Several studies support that this galaxy collided with a poor metal dwarf galaxy, which caused a burst of star formation~\citep{Balick81,Schweizer88,Smith96}. It has also been suggested that NGC 3310 has actually experienced several interactions with small galaxies~\citep{Wehner06}. The starburst activity of this galaxy began some 100 Myr ago~\citep{Meurer00}, although some of the clusters are rather young, indicating that starburst galaxies may remain in the starburst mode for quite some time.~\cite{Pastoriza93} reported that the circumnuclear regions in NGC 3310 present low metal abundances (\mbox{0.2-0.4 Z$_\odot$}), in contrast to what is generally found in early-type spirals~\citep{Diaz07}. In order to provide a better insight on the effects of the past interaction in the disc of NGC 3310, we need to investigate the properties of the hot ionized gas and the stellar population distributed along the whole disc. Studies based on NGC 3310 have mainly been focused on the properties of the young massive population (i.e.~\mbox{$\tau < 10$ Myr} and stellar mass \mbox{m$_\star$ = 10$^5$-10$^6$ \msun\onespace}) in the circumnuclear region. These studies made use of photometric images and long-slit spectroscopy, which are limited to either spectral range and/or sampling biases (i.e. area coverage, only the most luminous clusters and \hii -like regions with a very limited range in ionization conditions or only a unique aperture in large sample of galaxies, etc.). With the advent of the Integral Field Spectroscopy (IFS) such limitations can be overcome or at least significantly diminished. Nowadays, the use of IFS to perform wide-field 2D analyses of galaxies is well established and continuously growing. Large fields of view (FoV) can now be observed with simultaneous spatial and spectral coverage. We thus devised the PPAK Integral-field-spectroscopy Nearby Galaxies Survey (PINGS;~\citealt{Rosales-Ortega10}) in order to solve the limitations just mentioned. This is a survey specially designed to obtain complete emission-line maps, stellar populations and extinction using an IFS mosaicking imaging for nearby (\mbox{$D_\mathrm{L} \leq $ 100 Mpc}) well-resolved spiral galaxies. It takes the advantage of one of the world's widest FoV integral field unit (IFU). This paper focuses thus on the characterization of the ionizing population in the stellar disc of NGC 3310 so as to study the impact of the minor merger on the star formation properties of the remnant. The specific goals of this study are: (i) to obtain gaseous abundance determinations of not a handful but a non-biased luminosity hundred or so \hii regions distributed all along the disc, which are necessary to better trace radial abundance gradients; (ii) to characterize the age, mass and other star formation properties of the ionizing stellar population and (iii) to investigate the extent at which the interaction could have affected the mass growth in the disc. The PINGS data, together with retrieved multiwavelength images covering from the near-$UV$ to the near-$IR$ spectral range, are well suited to deal with these issues with unprecedented statistics. In a companion paper we will focus on the study of the Wolf--Rayet (WR) population present in the circumnuclear regions and arms in NGC 3310. The presence of this population, which has been detected in the PINGS spectra, sets important constraints on the age and nature of the most massive ionizing stellar population (\mbox{i.e.~M $\geq$ 40 \msun\onespace}). The paper is organized as follows. We present the data set used in Sect.~\ref{sec:obs}. In Sect.~\ref{sec:analysis_results}, we describe the analysis techniques used (i.e. to identify the \hii regions, decouple the gaseous and the continuum stellar emission, to obtain the chemical abundances of the gas and to estimate the age and the mass of the ionizing stellar population) and present our abundance and stellar population property derivations for \hii regions identified in the disc of NGC 3310. We first discuss in Sect.~\ref{sec:discussion} the effects due to biases and systematics of the analysis techniques. We then proceed with the scientific discussion on the radial abundance gradient in the galaxy and on the star formation properties in the disc of NGC 3310 and how they might have been affected by the past minor interaction. We finally draw our conclusions in Sect.~\ref{sec:conclusions}. Throughout this paper, the luminosity distance to NGC 3310 is assumed to be 16.1 Mpc (taken from the NASA Extragalactic Database). With an adopted cosmology of \mbox{H$_0$ = 73 km s$^{-1}$ Mpc$^{-1}$} an angle of 1 arcsec corresponds to a linear size of 78 pc. \section[]{Observations and data acquisition} \label{sec:obs} \subsection{PINGS data} NGC 3310 observations were carried out with the 3.5m telescope of the Calar Alto Observatory using the Postdam Multi-Aperture Spectrograph (PMAS;~ \citealt{Roth05}) in the PMAS fibre package mode (PPAK;~\citealt{Verheijen04},~\citealt{Kelz06}). This was part of the PINGS (\citealt{Rosales-Ortega10}). In brief, the V300 grating was used to cover the 3700-7100 \AA{} spectral range with a spectral resolution of \mbox{10 \AA{}}, corresponding to \mbox{600 km s$^{-1}$}, at \mbox{$\lambda$ = 5000 \AA{}}. We took three pointings with a dithered pattern (three dithered exposures per pointing), using a mean acquisition time per PPAK field in dithering mode (including set-up + integration time) of \mbox{2$\times$600 s} per dithering position. This observing strategy allowed us to re-sample the PPAK 2.7 arcsec-diameter fibre to a final mosaic with a 1 arcsec spaxel sampling and a FoV of about \mbox{148 $\times$ 130 arcsec$^2$}. The data were reduced following~\cite{Sanchez06}, and can be summarized as follows: pre-reduction, identification of the location of the spectra on the detector, extraction of each individual spectrum, distortion correction of the extracted spectra, wavelength calibration, fibre-to-fibre transmission correction, flux calibration, allocation of the spectra to the sky position, dithered reconstruction and re-sampling. The prereduction processing was performed using standard \iraf\footnote{\iraf~is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.} packages while the main reduction was performed using the {\small R}3{\small D} software for fibre-fed and IFS data~\citep{Sanchez06}. A thorough description of all the reduction and flux calibration procedures is described in~\cite{Rosales-Ortega10} and~\cite{Sanchez11}. The reduced IFS data were stored in row-stacked-spectra (RSS) files. RSS format is a 2D FITS image where the $X-$ and $Y-$ axes contain the spectral and spatial information respectively, regardless of their position in the sky. This format requires an additional file that stores the position of the different spatial elements on the sky. After reducing each individual pointing with a first-order flux calibration we built a single RSS file for the mosaic following an iterative procedure: (1) a master pointing that has the best possible flux calibration and sky extinction correction and signal-to-noise ratio (S/N) is selected; (2) the mosaic is then constructed by adding consecutive pointings following the mosaic geometry; (3) overlapping spectra are replaced by the average between the previous pointing and the new rescaled spectra (obtained by using the average ratio of the brightest emission lines found in the overlapping spectra). (4) the resulting spectra are incorporated into the final RSS file, updating the corresponding position table. In order to obtain the most accurate absolute spectrophotometric calibration, an additional correction was performed by comparing the IFS data with available broad-band photometry in $B$, $g$ and $r$ band (see next section). The estimated spectrophotometric accuracy of the IFS mosaic is of the order of 10-15\%. \begin{figure} \centering \includegraphics[width=0.95\columnwidth]{figs/combined_im.eps} \caption{False colour image of NGC 3310, produced by the combination of the $u$ (in blue), $g$ (in green) and $r$ (in red) SDSS filters. Knots of star formation are clearly visible in the central region and extended outer regions. Overlaid apertures show the three pointings that were taken with PPAK, with a central position centred in the galaxy's nucleus and two offsets of (–35, 35) and (35, –35) arcsec in (RA, Dec.) in north-west and south-east directions respectively. } \label{fig:combined_im} \end{figure} A total of 8705 spectra were finally produced, spatially resolved in spaxels of \mbox{1 $\times$ 1 arcsec$^2$}. \subsection{Multi-wavelength data} We retrieved publicly available broad-band imaging of this galaxy in order to perform an absolute flux re-calibration. Specifically, we used the Sloan Digital Sky Survey (SDSS\footnote{http://www.sdss.org/}) broad-band $g-$ and $r-$ filter images (with a spatial resolution of about 1 arcsec) and an $HST$\footnote{http://www.stsci.edu/hst/} image taken with the Wide Field Planetary Camera 2 (WFPC2, with a spatial resolution of about 0.05 arcsec) using the $F439W$ filter (similar to $B$ Johnson). Although the latter does not cover the entire FoV of the galaxy, we could perform the calibration by obtaining the photometry using an aperture large enough to cover the central 30 arcsec. We present in Fig.~\ref{fig:combined_im} a false colour image of NGC 3310, produced using the $u$, $g$ and $r$ SDSS filters. From the figure, it can be clearly seen that NGC 3310 is a very distorted spiral galaxy with strong star formation, with a very bright central nucleus, surrounded by a ring of luminous HII regions. Given its morphology, a tailored mosaic pattern was constructed for this galaxy (overplotted hexagons in the figure). \begin{figure*} \includegraphics[trim = -1cm 7.3cm -1cm 0cm,clip=true,width=0.85\textwidth]{figs/n3310_emission_article.eps} \caption{Maps for the observed \ha flux, \ha EW, $A_V$ extinction and \oiii$\lambda$5007 to \hb ratio. Contours with the \ha emission are overplotted in each case. The centre of the galaxy, which is enclosed by an \ha peaked contour, is marked with a green plus sign. The physical scale of 1.5 kpc at the distance of the galaxy is represented by the straight line at the bottom-right corner of the first map. Axes scales are in arcsec and orientation is as usual: north up, east to the left.} \label{fig:emission_maps} \end{figure*} We also obtained UV images of the galaxy. In particular, taken with the $UVW2$ and $UVM2$ filters (with effective wavelenghts of 2087 and 2297 \AA{}, respectively), mounted on the OM camera onboard the \textit{XMM--Newton} Satellite\footnote{http://xmm.esac.esa.int/}. The observations, with ID 0556280201, were taken in 2008. NGC 3310 was observed for more than 38 and 8 ks with the $UVW2$ and $UVM2$ filters, respectively. We reduced the observation data files using {\small SAS} version 13.0.0. The {\small SAS}\footnote{http://xmm.esac.esa.int/sas/} script \textit{omichain} was used to produce calibrated images. The Sloan and OM ultraviolet images provide valuable information on the continuum emission of the young ionizing stellar population. \section[]{Analysis and results} \label{sec:analysis_results} We present here the results obtained from the analysis of the ionizing stellar population in NGC 3310 using optical IFS data together with available broad-band ancillary data. \subsection{2D general properties of the ionized gas} \label{sub:2D_gas} We study the spatially resolved distribution of the physical properties in the \hii regions of NGC 3310 by obtaining a complete 2D view of: (i) the main emission lines used in the optical range for typical abundance diagnostic methods; (ii) important spectral features useful for the analysis of the ionizing stellar populations. In order to extract any physical information from the data set, we first need to identify the detected emission lines of the ionized gas and to decouple them from the stellar continuum. A preliminary fast decoupling was performed using an improved version of the {\small FIT3D} package \citep{Sanchez06,Sanchez07}. This software includes several routines to model and subtract the underlying stellar population of a spectral energy distribution (SED) using synthetic stellar spectra, and subsequently to fit and deblend the nebular emission lines. We refer the reader to \cite{Sanchez07} for further details. \begin{figure*} \includegraphics[trim = -2cm 18.2cm 0cm 0cm,clip=true,width=0.85\textwidth]{figs/bpt_article.eps} \caption{\textbf{Left:} diagnostic diagram (see text) for all the spaxels with good quality measurements. The contours show the density distribution of spaxels. The Kewley et al. (\citeyear{Kewley01a}) red demarcation line, which is usually invoked to distinguish between star-forming regions (\hii\onespace) and other source of ionization (AGN, LINER or composite, C), is also plotted. The error-bars at the top-right indicate the typical mean errors for the considered line ratios. \textbf{Right:} colour-coded maps showing the 2D spatial distribution of the ionizing source of ionization: star-forming regions (in blue), LINER or composite (in yellow) and AGN (in red). } \label{fig:bpt} \end{figure*} As a result of the line fitting procedure on the stellar-subtracted (i.e. gas) spectra, a set of measured emission-line intensities was obtained for each observed spectrum of the final clean mosaic. From these sets of emission-line intensities, emission-line maps were created by interpolating the intensities derived for each individual line in each individual spectrum, based on the position tables of the clean mosaics, and correcting for the dithering overlapping effects when appropriate. The observed \ha\onespace /\hb line ratio was used to correct the line maps for extinction, on a spaxel-by-spaxel basis. See~\cite{Rosales-Ortega10} for a full description. We present a set of line emission maps and those with derived properties in Fig.~\ref{fig:emission_maps}. The top panel map on the left shows the 2D distribution of the \ha observed flux. The nuclear part of the galaxy is easily identified together with the two spiral arms extending to the north and south of the galaxy. Bright inner clumps are also clearly seen within the circumnuclear region and along the whole extent of the galaxy. The lowest level contours are likely to enclose diffuse-like emission. In practical, all regions with \ha emission peaks, the derived EWs \mbox{($ > 20$ \AA{})}, as shown on the top right map, are consistent with the presence of very young \mbox{(i.e. $\tau < 10$ Myr)} stellar populations. This is expected in \hii regions. In the nucleus, however, the relatively low values of the equivalent width (EW) distribution indicate the prevalence of the underlying old population. We used the reddening constants from the Balmer decrement between \ha and \hb as compared to the theoretical value for mean nebular conditions given by \cite{Osterbrock89} in order to estimate the reddening. We then used the law by \cite{Cardelli89}, assuming $R_V = 3.1$, in order to correct the emission-line fluxes. The distribution of dust extinction (lower left map) although somewhat clumpy, is typically low (\mbox{$A_V < 1$ mag)}. In fact, the average extinction derived from the map corresponds to \mbox{$\overline{A_V} = 0.35 \pm 0.31$ mag}. The extinction peaks up to about \mbox{$A_V > 2$ mag} only in the nucleus and along some diffuse-like emission areas. We also show the 2D distribution of the emission-line ratio log (\oiii $\lambda 5007$/\hb), a parameter sensitive to the excitation, which correlates with the effective temperature of the exciting stars~\citep{Hunter92}. The range sampled generally lies between 0 and about 0.6, which shows that the ionized gas excitation in this galaxy is not very high. As mentioned in the introduction, NGC 3310 is a very distorted spiral galaxy with strong and rather complex star formation, very likely undergoing a merger-driven global starburst~\citep{Smith96,Kregel01,Wehner06}. It is widely known that massive stellar populations as young as about less than 10 Myr (i.e. hot OB stars) can well be responsible for the ionization observed in galaxies. The identification of the main ionizing mechanism in an observed object can be relatively well accomplished by the use of the so-called diagnostic diagrams (\citealt{Baldwin81},~\citealt{Veilleux87}). They usually involve two or three strong emission lines (SEL) that depend on the ionization degree and, to a lesser extent, on electron temperature or abundance. Fig.~\ref{fig:bpt} (left) shows a common diagnostic diagram (log \oiii/\hb versus log \sii $\lambda \lambda$6717,6731/\ha\onespace) as derived for each spaxel. Colour-coded maps were also created (Fig.~\ref{fig:bpt}, right) so as to spatially identify the regions ionized by different physical processes. As shown in the figure, the vast contribution of the ionization in this galaxy comes from young massive stars (\hii\onespace-like ionization). There are only a few regions (mainly not associated with \ha peaks) associated with other ionization mechanisms, though with larger uncertainties in the determination of their emission-line ratios. This paper focuses on the ionizing stellar population. Thus, with these maps we can guarantee that our study on \hii regions in NGC 3310 is not perceptibly contaminated by other sources of ionization. \subsection{Identification of \hii regions and star--gas decoupling} The detection and segregation of \hii regions, and subsequent extraction of the spectra for each of them, was performed using the semi-automatic procedure \hiiexplorer (\citealt{Sanchez12b}). A segmentation map that identifies each detected \hii region is provided by the code, together with the corresponding extracted spectra. In our case, a total of 99 \hii regions were identified. Fig.~\ref{fig:hii_id} shows the segmentation map overplotted on the \ha map (left) and the identification of each ionizing region (right). The regions have typical radii of about 2--3 arcsec, similar to, or somewhat larger than the spatial resolution of the instrument. This translates into radii in the range of 150--250 pc, within the size range of extragalactic giant \hii regions (\citealt{Kennicutt84,Oey03,Hunt09,Lopez11}). Table~\ref{table:hii_catalogue} reports a catalogue with the main observed properties of the identified \hii regions in NGC 3310. \begin{figure*} \includegraphics[angle=90,trim = 2.7cm -1.5cm 3cm -2.0cm,clip=true,width=1.05\textwidth]{figs/n3310_segmentation_hii.eps} \caption{\textbf{Left:} \ha intensity map in arbitrary units with the apertures of the identified \hii regions from the \hiiexplorer routine. \textbf{Right:} \ha contour map showing the spatial 2D distribution of the identified \hii regions with their identification number (\mbox{HII ID} in tables).} \label{fig:hii_id} \end{figure*} As mentioned before, particular care has always been taken in subtracting the stellar continuum so as to correctly decouple the stellar continuum from the nebular line emission. When the analysis was carried out in a spaxel-by-spaxel basis, an optimized fast analysis aimed at obtaining the best polynomial fit to the data (not necessarily giving a meaningful physical solution) was done. For the \hii regions we made use of the spectral synthesis code \starlight (\citealt{Cid-Fernades04b,Cid-Fernandes05}). This code mixes computational techniques originally developed for empirical population synthesis with ingredients of evolutionary synthesis models. Briefly, an observed spectrum is fitted with a combination of \textit{N} simple stellar populations from a set of evolutionary synthesis models. Extinction by foreground dust is also modelled by the V-band extinction \av\twospace.~Line-of-sight (LOS) stellar motions are modelled as well, but given the rather low spectral resolution of the PINGS data ($\sim$ 600 km s$^{-1}$), off-set velocities and stellar velocity dispersions were set to a fixed default value which in any case does not affect our results since we do not intend to study the kinematics of this galaxy. Basically, four inputs are needed for \starlight\onespace: the observed spectrum, a configuration file, a mask-file to mask emission lines and a file that allocates the base spectra (i.e. the set of evolutionary synthesis models). In our analysis we made use of a compilation of a few hundreds of synthesis models covering metallicities from Z$_\odot / 200$ to $1.5 \times \mathrm{Z}_\odot$ and ages from 1 Myr to 17 Gyr. This set compiles models of \cite{Gonzalez-Delgado05} for \mbox{$\tau < $ 63 Myr} with the MILES library \cite[as updated by \citealt{Falcon-Barroso11}]{Vazdekis10} for larger ages. The models are based on the Salpeter initial mass function (IMF) and the evolutionary tracks by \cite{Girardi00}, except for the youngest ages (i.e. \mbox{$\tau =$ 1-3 Myr}), which are based on Geneva tracks (\citealt{Schaller92,Schaller93,Charbonnel93}). \begin{figure*} \centering \includegraphics[trim = 2cm 0cm 2cm -1cm,clip=true,angle=90,width=1.02\columnwidth]{figs/spe_starlight_hii_all_PyCasso_example_id4_neb_corr.eps} \includegraphics[trim = 2cm 0cm 2cm 0cm,clip=true,angle=90,width=1.02\columnwidth]{figs/spe_gas_starlight_hii_all_PyCasso_example_id4_neb_corr.eps} \includegraphics[trim = 2cm 0cm 2cm -1cm,clip=true,angle=90,width=1.02\columnwidth]{figs/spe_starlight_hii_all_PyCasso_example_id14_neb_corr.eps} \includegraphics[trim = 2cm 0cm 2cm 0cm,clip=true,angle=90,width=1.02\columnwidth]{figs/spe_gas_starlight_hii_all_PyCasso_example_id14_neb_corr.eps} \includegraphics[trim = 1cm 0cm 2cm -1cm,clip=true,angle=90,width=1.02\columnwidth]{figs/spe_starlight_hii_all_PyCasso_example_id60_neb_corr.eps} \includegraphics[trim = 1cm 0cm 2cm 0cm,clip=true,angle=90,width=1.02\columnwidth]{figs/spe_gas_starlight_hii_all_PyCasso_example_id60_neb_corr.eps} \caption{\textbf{Left-hand panel:} example of rest-frame observed spectra of three different \hii regions (left). Blue line shows the derived nebular continuum (subtracted before \starlight is run) and red line shows the continuum \starlight fit (C$_{\mathrm{fit}}$). Yellowish shaded areas correspond to masked spectral intervals where typical nebular and stellar (i.e. WR) features are not included in the model libraries (i.e. blue WR bump). Masked intervals are not used in the fit. \textbf{Right-hand panel:} corresponding residual gas spectrum (\mbox{= observed -- C$_{\mathrm{fit}}$ -- nebular spectrum}) for each \hii region. Typical emission lines and the WR bump are labelled on the plot at the top of the panel. Inset plot there shows a zoom of the \oiii$\lambda$4363 auroral line whereabouts in the spectrum.} \label{fig:SL_examples} \end{figure*} The observed spectrum was not used as an input for \starlight\twospace. Although the model templates used have enough spectral resolution to deal with our spectra, those corresponding to the ionizing population (i.e. $\tau \leq$ 10 Myr) lack the nebular emission component. The contribution of this component can be significant in massive \hii regions. We thus first subtracted a ``nebular continuum spectrum'' from each observed spectrum. This nebular spectrum was computed using the derived \ha luminosity for each region, assuming a metallicity of Z$_\odot$/3, following the procedure explained in~\cite{Molla09} and~\cite{Martin-Manjon10}. That particular metallicity was chosen because it is consistent with the gaseous abundances reported in~\cite{Pastoriza93}. It is also compatible with our derived metallicities (see Sect.~\ref{sec:radial_gradients}). Note that this continuum can be underestimated if the \ha luminosity is underestimated (i.e. if photon leakage or absorption by UV photons by dust grains is important). Fig.~\ref{fig:SL_examples} shows three examples of the fitted continuum spectrum (in red, left-hand panels) and the \textit{residual} gas spectrum (right-hand panels) for \hii regions with high and low S/N. As can be seen, the nebular continuum spectrum (in blue, left-hand panels) can contribute significantly to the measured emission (in region ID 14, this continuum represents about 25\% of the observed light at the reddest wavelengths). Although the residual spectrum has been identified as emission from ionized gas, sometimes a spectral feature centred around 4680 \AA{} can be observed. This stellar spectral feature, easily recognizable in the figure for the \hii region with ID 4, corresponds to the blue WR bump and indicates the presence of WR stars. Once \starlight is run, the contribution in light and in mass of the base spectrum that best fits the input spectrum is provided as a result. In general, less than 20-30 populations are needed to fit our spectra, where normally a handful of young populations dominates the luminosity and a handful of old populations dominates the mass (see examples in Fig.~\ref{fig:SL_pop_examples}). In order to assess the accuracy of the continuum subtraction, the code was run a hundred times for each \hii region spectrum. Once the analysis with \starlight is done, the continuum and gas spectra are decoupled, as in Sect.~\ref{sub:2D_gas}, though this time for the stacked spectra of the identified \hii regions, rather than for spectra of individual spaxels. Individual emission-line fluxes were then measured by considering spectral window regions of \mbox{$\sim$ 200 \AA{}}. We produced {\sc idl} routines to perform a simultaneous fitting of several emission lines within the spectral window with Gaussian functions. Only one spectral component is observed for each line (if different components exist, the difference in velocity must be below the spectral resolution of the data, $\sim$ 600 km s$^{-1}$). This was done for each of the 100 cleaned gas spectra for each \hii region. The statistical errors associated with the observed emission were computed taking into account: (1) the measuring method, given by the fitting and (2) the following expression: \begin{equation} \sigma_\mathrm{l} = \sigma_c N^{1/2} \left[1 + \frac{\mathrm{EW}}{\mathrm{N}\Delta} \right]^{1/2} \end{equation} where $\sigma_\mathrm{l}$ is the error in the observed line flux, $\sigma_c$ refers to the standard deviation in a box near the measured emission line, $N$ is the number of pixels used in the measurement of the line flux, EW is the line EW and $\Delta$ is the wavelength dispersion in \mbox{\AA{} pixel$^{-1}$}~\citep{Gonzalez-Delgado94}. The first term represents the error introduced in placing the continuum level and the second term scales the S/N of the continuum to the line. As a conservative approach, the maximum value between both error estimates was considered. For a given line, we took the median of the computed error and flux line of the 100 spectra as the adopted values for each \hii region, respectively. Adopted line intensities of the \hii regions are reported in Table~\ref{table:hii_catalogue}. We performed a sanity test to ensure that no overcorrection was done on the absorption stellar features. For instance, if the fitted old population is such that the \hb absorption is too strong, the obtained ratio \ha\onespace/\hb may well be (within errors) below its theoretical value in case of no dust extinction (i.e. \ha\onespace/\hb = 2.86, assuming case B recombination;~\citealt{Osterbrock89}). This test is described in Sect.~\ref{sec:tests_SL}. \begin{figure*} \centering \includegraphics[trim = -2cm 16cm 0cm 0.2cm,clip=true,width=0.9\textwidth]{figs/spe_starlight_hii_all_PyCasso_pop_example_id4_neb_corr.eps} \includegraphics[trim = -2cm 0cm 0cm 16.2cm,clip=true,width=0.9\textwidth]{figs/spe_starlight_hii_all_PyCasso_pop_example_id60_neb_corr.eps} \caption{Examples of light- (left) and mass- (right) weighted populations obtained with on run of the STARLIGHT fitting procedure for two identified \hii regions in NGC 3310. Different colours represent different stellar metallicities ($Z$). The derived total mass, in log and solar units (\mbox{log M$_\mathrm{T}$}), is also shown.} \label{fig:SL_pop_examples} \end{figure*} \begin{table*} \hspace{0.2cm} \begin{minipage}{0.6\textwidth} \renewcommand{\footnoterule}{\kern -0.65cm} % \begin{footnotesize} \caption{Identified circumnuclear \hii regions in NGC 3310 in previous studies.} \label{table:comparison_hagele} \begin{center} \begin{tabular}{@{\hspace{0.20cm}}l@{\hspace{0.20cm}}c@{\hspace{0.20cm}}@{\hspace{0.20cm}}c@{\hspace{0.15cm}}@{\hspace{0.15cm}}c@{\hspace{0.15cm}}@{\hspace{0.15cm}}c@{\hspace{0.15cm}}@{\hspace{0.15cm}}c@{\hspace{0.15cm}}@{\hspace{0.15cm}}c@{\hspace{0.15cm}}@{\hspace{0.15cm}}c@{\hspace{0.15cm}}@{\hspace{0.15cm}}c@{\hspace{0.15cm}}} \hline \hline \noalign{\smallskip} H{\tiny II} & ID & $L$ (H$\alpha$) & $L$ (H$\alpha$) & EW (H$\beta$) & EW (H$\beta$) & $c$ (H$\beta$) & $c$ (H$\beta$) \\ ID& H10 & & H10 & & H10 & & H10\\ \hline \noalign{\smallskip} 1+4 & J & 554 $\pm$ 55 & 573 & 55.6 $\pm$ 0.9 & 82.5 & 0.10 $\pm$ 0.05 & 0.23 \\ 3 & N & 161 $\pm$ 16 & 113 & 10.3 $\pm$ 0.2 & 11.0 & 0.14 $\pm$ 0.03 & 0.42 \\ 5 & R4 & 137 $\pm$ 13 & 144 & 26.1 $\pm$ 0.3 & 32.4 & 0.08 $\pm$ 0.03 & 0.23 \\ 7 & R5+R6+S6 & 130 $\pm$ 13 & 193 & 22.5 $\pm$ 0.2 & 16.7 & 0.09 $\pm$ 0.03 & 0.24 \\ 8 & R1+R2 & 219\footnote{Actually, our regions ID8+ID2 match those of R1+R2+R3+R16 in \cite{Diaz00a}, but cannot be individually separated with our observations. Adding up all fluxes we obtain $L$(H$\alpha$) = 535 for ID8+ID2 and about 415 for R1+R2+R3+R16.} $\pm$ 21 & 102 & 43.4 $\pm$ 0.3 & 28.6 & 0.28 $\pm$ 0.02 & 0.23 \\ 11 & R10+R11 & 108 $\pm$ 10 & 102 & 15.6 $\pm$ 0.2 & 9.7 & 0.05 $\pm$ 0.03 & 0.23 \\ 12 & R7 & 95\footnote{Large discrepancy due to aperture effects. The radius measured in ~\cite{Diaz00a} for this region corresponds to 1.5 arcsec, smaller than the 3 arcsec radius of the corresponding region detected with our automatic software.} $\pm$ 9 & 45 & 13.8 $\pm$ 0.2 & 19.4 & 0.00 $\pm$ 0.01 & 0.17 \\ \hline \noalign{\smallskip} \multicolumn{9}{@{} p{\columnwidth} @{}}{{\footnotesize \textbf{Notes.} \ha luminosities are in 10$^{38}$ erg s$^{-1}$ and EWs in \AA{}.}} \end{tabular} \end{center} \end{footnotesize} \end{minipage} \end{table*} \hii regions detected in previous studies (\citealt{Hagele10b}; hereafter, H10) have been identified and the \ha extinction-corrected luminosities, \hb EWs and extinction coefficients c(H$\beta$) are compared in Table~\ref{table:comparison_hagele}. Some discrepancies are found, very likely due to the different angular resolution and aperture among the different studies (e.g.,~\citealt{Pastoriza93,Diaz00a}; see footnotes in the table). \subsection{Chemical abundance properties of the \hii regions in NGC 3310} \label{sec:abundance_properties} With our sample of \hii regions we can investigate the radial distribution of the oxygen abundance in NGC 3310 with better statistics than works based on samples of a few number of \hii regions, basically due to the limitations on the use of slits. \subsubsection{Direct oxygen abundance determination} \label{sec:abundance_direct} In principle, recombination lines (i.e. \oiir~$\lambda$4649, $\lambda$4089) would provide the most accurate determination of the abundance, due to their weak dependence on nebular temperature. However, these lines are very faint and most of the observed emission in nebulae correspond to collisionally excited lines (CEL), whose intensities depend exponentially on the temperature. The electron temperature of the gas is useful as an abundance indicator since higher chemical abundances increase nebular cooling, leading to lower \hii region temperatures. This temperature can be determined from the ratios of auroral lines like \oiii $\lambda$4363 to lower excitation lines such as $\lambda\lambda$4959,5007, or \nii $\lambda$5755 to $\lambda\lambda$6548,6584. Methods that rely on the measurements of these lines in order to obtain the abundance are the so-called \textit{direct methods}. \begin{table*} \begin{minipage}{\textwidth} \renewcommand{\footnoterule}{} % \begin{small} \caption{Direct abundance estimates of \hii regions} \label{table:abundances} \begin{center} \begin{tabular}{@{\hspace{0.16cm}}l@{\hspace{0.16cm}}c@{\hspace{0.16cm}}@{\hspace{0.16cm}}c@{\hspace{0.16cm}}@{\hspace{0.16cm}}c@{\hspace{0.16cm}}@{\hspace{0.16cm}}c@{\hspace{0.16cm}}@{\hspace{0.16cm}}c@{\hspace{0.16cm}}@{\hspace{0.16cm}}c@{\hspace{0.16cm}}@{\hspace{0.16cm}}c@{\hspace{0.16cm}}@{\hspace{0.16cm}}c@{\hspace{0.16cm}}@{\hspace{0.16cm}}c@{\hspace{0.16cm}}@{\hspace{0.16cm}}c@{\hspace{0.16cm}}@{\hspace{0.16cm}}} \hline \hline \noalign{\smallskip} \hii& $I (\lambda$4636) & $t_{\mathrm{e}}$ \oiii $\lambda$4363 $\equiv t_3$ & $n_{\mathrm{e}}$ & $t_{2}~(t_{3}) $ & 12+ log (O/H) & $I (\lambda$5755) & t$_{\mathrm{e}}$ \nii $\lambda$5755 & O$^{+}$/H$^+$ & O$^{2+}$/H$^+$ & 12+ log (O/H) \\ ID & & ($\times$10$^4$) K & (cm$^{-3}$) & ($\times$10$^4$ K) & & & ($\times$10$^4$ K) & & & ($t_{3}$,$t_{\mathrm{e}}$ \nii $\lambda$5755) \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11) \\ \hline \noalign{\smallskip} 1& 1.37$\pm$ 0.30& 0.97$\pm$ 0.06& 108$\pm$ 8& 1.00$\pm$ 0.06& 8.30$\pm$ 0.10& 0.74$\pm$ 0.13& 1.04$\pm$ 0.08& 7.96& 7.96& 8.26$\pm$ 0.08\\ 4& 1.52$\pm$ 0.24& 1.03$\pm$ 0.05& 115$\pm$ 8& 1.03$\pm$ 0.06& 8.23$\pm$ 0.08& 0.64$\pm$ 0.12& 0.95$\pm$ 0.06& 8.19& 7.82& 8.34$\pm$ 0.09\\ 5& 1.93$\pm$ 0.29& 1.12$\pm$ 0.05& 123$\pm$ 17& 1.09$\pm$ 0.05& 8.09$\pm$ 0.07& \ldots & \ldots & \ldots & \ldots & \ldots \\ 7& 1.70$\pm$ 0.33& 1.13$\pm$ 0.07& 90$\pm$ 21& 1.13$\pm$ 0.06& 8.03$\pm$ 0.08& 0.89$\pm$ 0.18& 1.01$\pm$ 0.08& 8.02& 7.60& 8.16$\pm$ 0.12\\ 8& 1.84$\pm$ 0.42& 1.08$\pm$ 0.07& 112$\pm$ 18& 1.07$\pm$ 0.06& 8.17$\pm$ 0.10& 0.79$\pm$ 0.11& 1.00$\pm$ 0.05& 8.08& 7.76& 8.25$\pm$ 0.08\\ 13& 1.51$\pm$ 0.35& 1.07$\pm$ 0.07& 77$\pm$ 16& 1.10$\pm$ 0.06& 8.12$\pm$ 0.10& 1.19$\pm$ 0.11& 1.17$\pm$ 0.05& 7.81& 7.69& 8.06$\pm$ 0.06\\ 14& 1.64$\pm$ 0.36& 0.96$\pm$ 0.06& 37$\pm$ 6& 1.07$\pm$ 0.07& 8.30$\pm$ 0.10& \ldots & \ldots & \ldots & \ldots & \ldots \\ 15& 1.98$\pm$ 0.33& 1.14$\pm$ 0.06& 52$\pm$ 20& 1.19$\pm$ 0.05& 8.02$\pm$ 0.06& 0.89$\pm$ 0.14& 1.04$\pm$ 0.07& 8.03& 7.64& 8.18$\pm$ 0.09\\ 16& 2.03$\pm$ 0.34& 1.17$\pm$ 0.06& 108$\pm$ 24& 1.13$\pm$ 0.05& 8.07$\pm$ 0.07& 1.10$\pm$ 0.22& 1.19$\pm$ 0.12& 7.81& 7.59& 8.02$\pm$ 0.11\\ 19& 2.23$\pm$ 0.46& 1.35$\pm$ 0.11& 174$\pm$ 64& 1.16$\pm$ 0.05& 7.96$\pm$ 0.06& \ldots & \ldots & \ldots & \ldots & \ldots \\ 20& 2.61$\pm$ 0.45& 1.29$\pm$ 0.08& 109$\pm$ 48& 1.21$\pm$ 0.05& 7.95$\pm$ 0.05& \ldots & \ldots & \ldots & \ldots & \ldots \\ 21& 2.46$\pm$ 0.35& 1.27$\pm$ 0.07& 116$\pm$ 38& 1.19$\pm$ 0.05& 7.99$\pm$ 0.05& 1.26$\pm$ 0.25& 1.27$\pm$ 0.13& 7.74& 7.46& 7.93$\pm$ 0.12\\ 22& 2.18$\pm$ 0.48& 1.05$\pm$ 0.07& 34$\pm$ 15& 1.15$\pm$ 0.07& 8.16$\pm$ 0.09& \ldots & \ldots & \ldots & \ldots & \ldots \\ 26& 1.63$\pm$ 0.34& 1.06$\pm$ 0.06& 52$\pm$ 14& 1.12$\pm$ 0.06& 8.12$\pm$ 0.09& \ldots & \ldots & \ldots & \ldots & \ldots \\ 27& 3.68$\pm$ 0.47& 1.17$\pm$ 0.05& 92$\pm$ 25& 1.15$\pm$ 0.05& 8.12$\pm$ 0.05& \ldots & \ldots & \ldots & \ldots & \ldots \\ 32& 2.11$\pm$ 0.47& 1.05$\pm$ 0.07& 14: & 1.21$\pm$ 0.10& 8.12$\pm$ 0.09& \ldots & \ldots & \ldots & \ldots & \ldots \\ \hline \noalign{\smallskip} \multicolumn{11}{@{} p{\textwidth} @{}}{{\footnotesize \textbf{Notes.} Col (1): \hii region identification number. Col (2): reddening-corrected flux of the \oiii $\lambda$4363 auroral line with respect to \hb\onespace, normalized to \mbox{\hb = 100}.~Col(3): direct determination of the electron temperature of \oiii. Col (4): derived electron density. Col (5): derived electron temperature of \oii, assuming that \mbox{$t_\mathrm{e}$ (\oii) $\sim$ $t_\mathrm{e}$ (\nii)} and the theoretical relation between $t_\mathrm{e}$ (\oii) and $t_\mathrm{e}$ (\oiii) as prescribed in~\cite{Perez-Montero03} (Eq.~\ref{eq:t2_t3}). Col (6): derived oxygen abundance with a direct-temperature determination of \oiii. Col (7): reddening-corrected flux of the \nii $\lambda$5755 auroral line with respect to \hb, normalized to \mbox{\hb = 100}. Col (8): direct determination of the electron temperature for \nii. Col (9): O$^+$ ionic abundance, derived using both direct determinations of the electron temperature of \oiii~and \nii. Col (10): same as in col. (9), but for the O$^{2+}$ ion. Col. (11): derived oxygen abundance using both direct determinations of the electron temperature of \oiii~and \nii.}} \end{tabular} \end{center} \end{small} \end{minipage} \end{table*} We measured the auroral line \oiii $\lambda$4363 with a detection level of \mbox{S/N $>$ 4} from the ``residual'' gas spectra of 16 \hii regions. We refer the reader to Sect.~\ref{sec:t_obs_res}, where we argue about the systematics introduced when measuring this line on the observed spectrum. The determination of the electron temperature ($t_\mathrm{e}$\footnote{In what follows $t_\mathrm{e}$ denotes electron temperature in units of $10^4$ K.}) and other physical conditions of the gas such as the electron density ($n_\mathrm{e}$, in cm$^{-3}$), and the ionic abundances were obtained using the procedures outlined in~\cite{Perez-Montero07} and~\cite{Hagele08b}. We have assumed two distinct layers of ionization for each \hii region: a high ionization zone (\heii, \oiii, \neiii, etc.) and a low ionization zone (\oii, \nii, \sii, etc.), whose electron temperatures are given by $t_3$ and $t_2$, respectively. Different prescriptions can be found in the literature that relate the $t_3$ and the $t_2$ temperatures. In our case, the $t_2$ temperature was determined using photoionization models that take into account the dependence on the electron density~\citep{Perez-Montero03,Perez-Montero09}: \begin{equation} \label{eq:t2_t3} t_2 \equiv t_\mathrm{e}(\textrm{\oii}) = \frac{1.2 + 0.002n_\mathrm{e} + 4.2/n_\mathrm{e}}{t_3^{-1} + 0.08 +0.003n_\mathrm{e} + 2.5/n_\mathrm{e}}, \end{equation} where the electron density was determined from the \sii $\lambda\lambda$6717,6731 doublet. In a few cases the \nii$\lambda$5755 line was also detected and measured. In those cases, we could derive the temperature of \nii, the temperature of the low ionization zone. The ionic abundances were calculated based on the functional forms provided by~\cite{Hagele08b}, who published a set of equations for the determination of oxygen abundances in \hii regions based on a five-level atom model: \begin{flalign} & 12 + \textrm{log(O}^{2+}/\textrm{H}^+) & \mspace{-20.0mu}=~& \textrm{log}(\textrm{\oiii}\lambda\lambda4959,5007/\textrm{H}\beta) + 6.144~+ \\ & & &\mspace{-90.0mu} +1.251/t_3 - 0.55\textrm{log}t_3 \notag \\\notag\\ & 12 + \textrm{log(O}^+/\textrm{H}^+) & \mspace{-20.0mu}=~& \textrm{log}(\textrm{\oii}\lambda\lambda3727,3729/\textrm{H}\beta) + 5.992~+ \\ & & & \mspace{-90.0mu}+ 1.583/t_2 - 0.681\textrm{log}t_2 + \textrm{log}(1 + 0.00023n_\mathrm{e}) \notag \end{flalign} Finally, the total oxygen abundance was obtained assuming that \begin{equation} \frac{\textrm{O}}{\textrm{H}} = \frac{\textrm{O}^+}{\textrm{H}^+} + \frac{\textrm{O}^{2+}}{\textrm{H}^{+}} \end{equation} Auroral line measurements, electron density and temperatures, along with the derived oxygen abundances using the methodology described in this section are reported in Table~\ref{table:abundances}. With typical electron densities of the order of \mbox{100 cm$^{-3}$} and typical electron temperatures of the order of \mbox{10000 K}, the derived direct abundances are subsolar, in the range \mbox{8 $\lesssim$ 12 + log(O/H) $\lesssim$ 8.3}. \subsubsection{Strong-line methods} \label{sec:empirical_methods} The ratios used in direct methods involve the detection and measurement of at least one intrinsically weak line, which in objects of low excitation and/or low surface brightness, often result too faint to be observed. Given these limitations, \textit{strong-line methods} based on the use of strong, easily observable, optical lines have been developed throughout the years. Several abundance calibrators have been proposed involving different emission-line ratios and have been applied to determine oxygen abundances in objects as different as individual HII regions in spiral galaxies, dwarf irregular galaxies, nuclear starbursts and emission-line galaxies. By far, the most commonly strong-line calibrator used is the ratio (\oii $\lambda$3727 + \oii $\lambda\lambda$4959, 5007)/\hb, known as the $R_{23}$ method \citep{Pagel79}. However, it is known to present many problems basically because it is double valued with a wide transition/turn-over region (\mbox{12+log(O/H) $\sim$ 8.0--8.3}). Furthermore, a few observed circumnuclear \hii regions in NGC 3310 are known to have a moderately low metallicity (\mbox{12+log(O/H) $\sim$ 8--8.3};~\citealt{Pastoriza93}), just in the middle of the turn-over region of the calibrator. The spectral range covered by the PINGS data allows us, nevertheless, to employ more up-to-date strong-line calibrations that make use of more information via strong nitrogen and/or sulphur lines. This are as follows. \begin{itemize} \begin{figure*} \centering \includegraphics[trim = 0cm 1cm 0cm 0cm,clip=true,width=0.80\textwidth]{figs/HII_abundance_gradient1a.eps} \caption{\textbf{Top:} radial distribution of oxygen abundance in NGC 3310. $X-$ axis shows the deprojected radial distance. Different colours refer to different methods use to derive the oxygen abundance (see legend). Estimates from spectra obtained with data within the hexagonal PPAK FoV are plotted in solid symbols (either circles or triangles, the latter referring to $t_\mathrm{e}$-based estimates), whereas an open symbol means that the spectra were obtained from external fibres (see text). The horizontal line highlights the position of the solar abundance of \mbox{12 + log(O/H) = 8.69}~\citep{Asplund09} in the diagram. \textbf{Bottom:} data have been grouped in distance bins of 0.5$r$\reff and median values have been plotted. The error bars represent the dispersion within a given bin. The lines show a straight line fitted to the median values. We have not grouped the estimates derived from T$_\mathrm{e}$-based methods that use both the auroral \oiii~ and \nii~lines due to the lack of data.} \label{fig:metal_radial_gradients_a} \end{figure*} \item \textit{$O3N2$-parameter calibrations} -- The $O3N2$ parameter, first introduced by \cite{Alloin79}, depends on two SEL intensity ratios: \begin{equation} O3N2 = \textrm{log} \left ( \frac{\textrm{\oiii}\lambda5007}{\textrm{H}\beta} \times \frac{\textrm{H}\alpha}{\textrm{\nii}\lambda6584} \right ) \end{equation} This parameter is almost independent of either reddening correction or flux calibration. Several calibrations using this parameter have been defined (e.g.,~\citealt{Pettini04,Perez-Montero09}). Recently,~\cite{Marino13} have provided an improved calibration using the largest compilation so far of temperature-based abundance determinations, and has proved its validity for \mbox{12 + log(O/H) $> 8.1-8.2$} with a dispersion somewhat lower than 0.2 dex. \item \textit{ONS calibration} -- This calibration~\citep{Pilyugin10} is based on several strong-line-intensity ratios to \hb from several species, including oxygen, nitrogen and sulphur as \begin{flalign} \label{eq:indeces} &R_2 = \textrm{\oii}\lambda\lambda3727,3729/\textrm{H}\beta & \notag\\ &R_3 = \textrm{\oiii}\lambda\lambda4959,5007/\textrm{H}\beta & \\ &N_2 = \textrm{\nii}\lambda\lambda6548,6854/\textrm{H}\beta & \notag\\ &S_2 = \textrm{\sii}\lambda\lambda6717,6731/\textrm{H}\beta & \notag \end{flalign} It uses the excitation parameter, ($P = R_3/(R_3 + R_2)$), that takes into account the effect of the ionization parameter. This calibration was derived using a set of \hii regions with measured electron temperatures. \item \textit{C-method} -- The `counterpart' method, P12-C~\citep{Pilyugin12b}, is based on the standard assumption that \hii regions with similar intensities of SEL have similar physical properties and abundances. Given all the problems that different calibrations have (e.g., different branches, different applicability ranges, the no one-to-one correspondence between oxygen and nitrogen abundances) the authors propose a method that does not know a priori in which metallicity interval (or on which of the two branches) the \hii region is located. This calibration basically selects a number of reference (well-measured abundances) \hii regions and then the abundances in the target \hii region are estimated through extra-/interpolation. According to the authors, if the errors in the line measurements are within 10\%, then one can expect that the uncertainty in the \mbox{C-based} abundances is not in excess of 0.1 dex (although it can reach \mbox{0.15--0.2 dex} in the interval \mbox{7.8 $<$ 12 + log(O/H) $<$ 8.2}). \end{itemize} We made use of the calibrations outlined in order to search for any radial abundance gradient trend in \mbox{NGC 3310} within dispersions of \mbox{0.1-0.2 dex}, though larger systematic offsets can be expected from the results obtained from one calibration to another. \subsubsection{Radial abundance gradients} \label{sec:radial_gradients} We have only a limited sub-sample of \hii regions with reliable $t_\mathrm{e}$-based abundance determinations. We thus derived abundances for almost all identified \hii regions using the strong-line calibrations described in previous sections. Fig.~\ref{fig:metal_radial_gradients_a} shows the radial distribution of the oxygen abundance in NGC 3310 up to about four effective radii (\reff\onespace). At the assumed distance of this galaxy ($D_\mathrm{L}$ = 16.1 Mpc), this distance corresponds to about 11 kpc. We identify \reff as the half-light radius, which was determined using \galfit\footnote{http://users.obs.carnegiescience.edu/peng/work/galfit/galfit.html}, version 3.0~\citep{Peng10}, on the $g$-band SDSS image. Either assuming a typical S\'ersic (letting the index $n$ vary) + an exponential disc profiles or a rotating S\'ersic (simulating the spiral arms) + an exponential disc profiles, the resulting \reff is around 35 arcsec~(i.e.~\mbox{$\sim 2.5$ kpc}). For this part of the study, we have included in our catalogue spectra corresponding to the external fibres of the PPAK module (normally used to determine the local sky, grouped in bundles at $\sim$75 arcsec from the centre of the PPAK module) which show evident \hii\onespace-like emission with coincident redshift of that of NGC3310, i.e. fortuitous observations of \hii regions at very large galactocentric distances. Their 2D spatial distribution is shown in Fig.~\ref{fig:external_fibers}. In many cases, given the dithering used, the flux of 2 or 3 fibres could be integrated to obtain each spectrum of these `external' regions. Although the S/N of the continuum is generally very low, the emission lines are clearly detected. The extinction corrected line intensities are reported in Table~\ref{table:ext_fibers_catalogue}. These additional regions allow us to investigate if there is any abundance radial gradient in this galaxy up to more than 10 kpc. If this data set is not included we still can sample \hii regions within about 5 kpc or about 2.8\reff. Several interesting aspects can be inferred from the plot as follows. \begin{enumerate} \item All computed gaseous abundances are sub-solar, spanning the range \mbox{7.95 $<$ 12 + log(O/H) $<$ 8.45} (between a half and a fifth solar). \item All computed abundances using strong-line calibrations agree within 0.1--0.15 dex, covering a typical range \mbox{12 + log(O/H) = 8.2--8.4}. This is expected, since the accuracy of strong-line calibrations (\mbox{0.1--0.2 dex}), not included in the error bars, is of the order of this range. \item In practice, we have obtained $t_\mathrm{e}$-based estimates within one \reff. Their range span oxygen abundances between 8 and 8.3 with a larger dispersion than those computed with strong-line calibrations. In general, the $t_\mathrm{e}$-based estimates are also lower by about \mbox{0.2--0.3 dex}. With a sample of 16 \hii regions with direct abundance estimates and over 100 regions with strong-line estimates we can assure that the offset is not due to lack of statistics. In Sect.~\ref{sec:t_obs_res}, we discuss on this disagreement. \begin{figure} \centering \includegraphics[angle=90,trim = 0.5cm 1cm 2cm 3.5cm,clip=true,width=1.1\columnwidth]{figs/HII_ha_dens_map.eps} \caption{\ha contour map showing the spatial 2D distribution of the identified \hii regions and the external regions (with their identification number). While the size of the circles for the identified \hii regions represents approximately their actual size, that for the external regions corresponds to their average size. The circles are colour coded following the logarithm of the \ha intensity in units of \mbox{10$^{-16}$ erg s$^{-1}$ cm$^{-2}$}.} \label{fig:external_fibers} \end{figure} \item With a sample of over 100 \hii regions we do not see a clear abundance gradient in NGC 3310, further than 10 kpc away from the nucleus. A weak gradient might be present from the centre and up to 2\reff (5 kpc). We have computed the Spearman correlation coefficient for $r < 2$\reff and have obtained a possible correlation for abundances that were derived using the ONS and the \mbox{P-12C}~calibrations ($r = 0.63,0.72$, respectively). The derived slopes of the fit are 0.06 and 0.05 dex/\reff (\mbox{$\sim$ 0.02 dex/kpc}), respectively. Should an abundant gradient exist, it is significantly flatter than the observed gradients in galactic discs (i.e. \mbox{$\sim$ -0.08 dex/kpc};~\citealt{Vilchez88,Kennicutt96,Rosolowsky08,Costa10}) and the universal gradient proposed in \cite{Sanchez14} (i.e. \mbox{ $\sim$ -0.10 dex/\reff}). For abundances obtained using the $O3N2$ calibration and the direct method (using the \oiii $\lambda$4363 emission line), the data are not correlated, according to the Spearman's rank- order correlation test. Besides, the intrinsic dispersion of strong-line calibrations is typically \mbox{0.1--0.2} dex. All facts considered, we conclude that either the abundance gradient of the gas in the disc of NGC 3310 is flat or at least significantly flatter than gradients observed in spirals. \end{enumerate} \subsection{Characterization of the ionizing stellar population} With the spectral information provided with the IFU data and available public wide-band imaging we can perform a detailed study on the ionizing stellar populations in NGC 3310. In particular, the line flux ratios, the EW measurements and broad-band UV and optical images help us to tightly constrain the mass and the age of the ionizing stellar populations present in the \hii regions. \begin{figure*} \centering \includegraphics[trim = 8.5cm 0cm 0cm 0cm,clip=true,angle=90,width=0.9\textwidth]{figs/HII_ratio_plots1.eps} \caption{\oiii/\hb line intensity ratio versus several intensity ratios sensitive to the ionization structure of the nebulae for the identified \hii regions in NGC 3310. Seven interval classes have been defined as the shaded regions in the different plots. All ratios for a given \hii region lies on the same class or in-between two classes. A typical average point value for each class is drawn as a red cross.} \label{fig:ionization_ratios1} \end{figure*} The main advantage in subtracting the stellar continuum is that the end product of such procedure is the percentage of each contributing stellar population to the light and mass. That is, we can estimate the mass of each stellar population responsible for the continuum emission. We may note, however, that any analysis technique has its own advantages and limitations. In particular, given the limited spectral range fitted (i.e. part of the optical), \starlight gives a consistent description of the age of the `young' population within 0.15-0.20 dex independently of the stellar templates used for an average age of \mbox{$\tau \sim 100$ Myr}~\citep{Cid-Fernades13}. Constraining the age of the population at \mbox{$\tau \leq 10 $Myr} (expected for ionizing population) is highly uncertain using this technique alone. Therefore, including data from other spectral bands, especially at bluer wavelengths, helps to better constrain the properties of young ionizing populations. Since this population is ionizing the gas, the emission lines we observe in the gas spectra give us useful information on its properties. For that reason, in the following we first compare the measured emission-line fluxes with those computed in photoionization models. This comparison gives us a first rough estimate of the age of the ionizing population and of the presence of dust grains. Next, we perform a multiwavelength analysis, covering a wider spectral range using SDSS and \textit{XMM}-OM images. Finally, we combine both techniques to better constrain the age and the mass of the ionizing population. \begin{figure*} \centering \includegraphics[trim = -0.5cm 0cm 0cm -0.5cm,clip=true,angle=90,width=0.9\textwidth]{figs/HII_ratio_plots2.eps} \caption{Same as in Fig.~\ref{fig:ionization_ratios1}, but versus other sensitive intensity and intensity ratios. In this case no class has been defined since correlation are either weak (i.e. with \nii/\oii, proxy to the abundance ratio N/O) or non-existent. The derived \hb luminosity is given in units of \mbox{erg s$^{-1}$}. The EW has been corrected by the continuum of the non-ionizing population.} \label{fig:ionization_ratios2} \end{figure*} \subsubsection{Photoionization models} \label{sec:photo_models} First of all, we took advantage of the knowledge of the ionization conditions of the gas within an \hii region. The strength of different line flux ratios depends on the shape of the ionizing continuum (i.e. age and metallicity of the young stellar population) and on the conditions and geometry of the cloud (i.e. electron density, temperature, clumpiness, absorption by dust grains, etc.). Based on this conception, we show in Figs.~\ref{fig:ionization_ratios1} and~\ref{fig:ionization_ratios2} the dependence of the \oiii$\lambda$5007/\hb line intensity ratio (in log units) on other line ratios that provide information on the degree of ionization (e.g., the \oiii/\oii~ratio), the electron density of the cloud (ratios of the sulphur lines), the abundance, the electron temperature, the number of ionizing photons and the age of the burst (i.e. EW(\hb\onespace)). As Fig.~\ref{fig:ionization_ratios1} illustrates, there is a good correlation between the \oiii$\lambda$5007/\hb ratio and other line intensity ratios sensitive to the ionization structure of the cloud. We defined seven classes with different typical ratios (red dashed lines in the plot) and some width, which define the shaded areas, in such a way that in practically all cases the ratios for a given \hii region lies in the same class or in-between two classes. Class 1 would correspond to ratios on the bottom shaded area on the left with a typical log(\oiii/\hb\onespace) ratio of 0.05. Moving right and up in the plot, the other classes are defined by the area of the shaded rectangles up to class seven where the typical log(\oiii/\hb\onespace) ratio equals 0.6. On the other hand, as Fig.~\ref{fig:ionization_ratios2} shows, the ratio between the sulphur lines (sensitive to the electron density) and the \hb luminosities do not really depend on the \oiii/\oii~ratio. There is a mild dependence on the \nii/\ oii~ratio, sensitive to the abundance ratio N/O~\citep{Perez-Montero05,Perez-Montero09} and on the EW(\hb\onespace), which has been corrected for the contribution to the continuum by non-ionizing population as derived with \starlight (see next section). Finally, although for classes 1--4 the logarithm of the \hb luminosity spans the whole range sampled (i.e. 37.5--40), for classes 5--7 the range is more restricted, from somewhat lower than 38.5 to somewhat higher than 39.0. \begin{table*} \begin{minipage}{0.85\textwidth} \renewcommand{\footnoterule}{} % \begin{center} \caption{\cloudy simulations. Input line intensity ratio ranges, derived ages ($\tau$) and dust absorption factors ($f_{\mathrm{d}}$).} \label{table:cloudy_tramos} \begin{tabular}{cccccccc|cc} \hline \hline \multicolumn{1}{c}{Class} \vline & \multicolumn{7}{c}{Line ratio and EW ranges} \vline & \multicolumn{2}{c}{Result of the fit} \\ \multicolumn{1}{c}{} \vline & \multicolumn{1}{c}{\oii/\hb} & \multicolumn{1}{c}{\oiii/\hb} & \multicolumn{1}{c}{\nii/\hb} & \multicolumn{1}{c}{\sii$^{1}$/\hb} & \multicolumn{1}{c}{\sii$^{2}$/\hb} & \multicolumn{1}{c}{log L(\hb)} & \multicolumn{1}{c}{log EW (\hb)} \vline & \multicolumn{1}{c}{log ($\tau$)} & \multicolumn{1}{c}{$f_\mathrm{d}$} \\ \multicolumn{1}{c}{} \vline & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{(erg s$^{-1}$)} & \multicolumn{1}{c}{(\AA{})} \vline & \multicolumn{1}{c}{(Myr)} & \multicolumn{1}{c}{} \\\hline 1 & 3.16--5.00 & 1.00--1.26 & 0.63--1.26 & 0.63--1.26 & 0.53--0.84 & 37.5-38.5 & 1.35-1.65 & 6.71 $^{+0.02}_{-0.03}$ & 2.1 $^{+0.8}_{-0.4}$ \\ \noalign{\smallskip} & & & & & & 38.8-39.8 & & 6.71 $^{+0.01}_{-0.03}$ & 2.3 $^{+0.6}_{-0.4}$ \\ \noalign{\smallskip} 2 & 2.82--5.00 & 1.26--1.58 & 0.63--1.00 & 0.50--1.00 & 0.35--0.67 & 37.5-38.5 & 1.35-1.65 & 6.71 $^{+0.01}_{-0.03}$ & 2.4 $^{+0.9}_{-0.6}$ \\ \noalign{\smallskip} & & & & & & 38.8-39.8 & & 6.71 $^{+0.02}_{-0.03}$ & 1.9 $^{+0.6}_{-0.4}$ \\ \noalign{\smallskip} 3 & 2.50--4.47 & 1.58--2.00 & 0.50--0.80 & 0.47--0.79 & 0.28--0.56 & 37.5-38.5 & 1.6-2.1 & 6.65 $^{+0.02}_{-0.15}$ & 2.9 $\pm$ 1.2 \\ \noalign{\smallskip} & & & & & & 38.8-39.8 & & 6.65 $^{+0.02}_{-0.05}$ & 3.0 $^{+1.3}_{-0.9}$ \\ \noalign{\smallskip} 4 & 2.37--3.76 & 2.00--2.51 & 0.45--0.63 & 0.30--0.60 & 0.24--0.45 & 37.5-38.5 & 1.6-2.1 & 6.63 $^{+0.06}_{-0.04}$ & 1.3 $^{+0.4}_{-0.2}$ \\ \noalign{\smallskip} & & & & & & 38.8-39.8 & & 6.64 $^{+0.03}_{-0.06}$ & 1.6 $\pm$ 0.4 \\ \noalign{\smallskip} 5 & 2.24--3.76 & 2.51--3.16 & 0.32--0.56 & 0.28--0.47 & 0.21--0.38 & 38.5-39.5 & 1.6-2.1 & 6.63 $^{+0.04}_{-0.05}$ & 1.4 $^{+0.4}_{-0.3}$ \\ \noalign{\smallskip} 6 & 2.11--3.35 & 3.16--3.76 & 0.32--0.47 & 0.27--0.42 & 0.21--0.32 & 38.5-39.5 & 2.05-2.35 & 6.58 $^{+0.03}_{-0.06}$ & 1.2 $^{+0.5}_{-0.1}$ \\ \noalign{\smallskip} 7 & 1.99--2.82 & 3.76--4.22 & 0.22--0.35 & 0.22--0.35 & 0.13--0.24 & 38.5-39.5 & 2.05-2.35 & 6.55 $^{+0.06}_{-0.09}$ & 1.8 $^{+1.0}_{-0.6}$ \\ \hline \noalign{\smallskip} \multicolumn{10}{@{} p{\textwidth} @{}}{\textbf{Notes.} \oiii refers to \oiii$\lambda$5007 \AA{}, \nii to \nii$\lambda$6584 \AA{}, \sii$^{1}$ to \sii$\lambda$6717 \AA{} and \sii$^{2}$ to \sii$\lambda$6731 \AA{}.} \end{tabular} \end{center} \end{minipage} \end{table*} With this information, we have simulated the properties of the ionized gas and the stellar ionizing population for each class with the use of the photoionization code \cloudy (version 10.0;~\citealt{Ferland98}). We took as ionizing sources the SEDs of ionizing star clusters spanning ages from 1 to \mbox{10 Myr} using evolutionary synthesis techniques (\popstar\onespace;~\citealt{Molla09,Martin-Manjon10}). We used models with a Salpeter IMF, with masses between 0.15 and 100 \msun\onespace. We assumed in all the models a radiation-bounded spherical geometry, a constant density of 100 particles cm$^{-3}$ and a standard fraction of dust grains in the interstellar medium (ISM). The presence of solid grains within the ionized gas can have some consequences on the physical conditions of the nebulae that should not be neglected. The heating of the dust can affect the equilibrium between the cooling and heating of the gas and, thus, the electron temperature inside the nebulae. The command PGRAINS, included in the last version of \cloudy, implements the presence of dust grains as described in~\cite{VanHoof04}. In all the models, the calculation was stopped when the temperature was lower than 4000 K. We also assumed that the gas has the same metallicity as the ionizing stars, covering the values 0.2Z$_\odot$ (0.008) and 0.4Z$_\odot$ (0.004) since gaseous abundances of \hii regions in this galaxy range typically between these two values (see Sect.~\ref{sec:radial_gradients}). The other elemental abundances were set in solar proportions taking as a reference the phostosphere solar values given by~\cite{Asplund05}, except in the case of nitrogen, for which we considered three different values of log(N/O), according to the mild correlation observed in Fig.~\ref{fig:ionization_ratios2}: -1.05 (classes 6 and 7), -0.95 (classes 2--5) and -0.85 (class 1). We let the age of the ionizing population, the oxygen abundance, the number of ionizing photons, some geometrical parameters (inner radius and filling factor) and the content of dust grains vary in order to fit the line intensity ratios of oxygen, nitrogen and sulphur to \hb, together with the \hb luminosity and the continuum at \mbox{4885 \AA{}} (obtained with the EW(\hb\onespace)). Once a compatible solution was found, we fixed all the fitted parameters save the dust grain content, the age of the ionizing population and the number of ionizing photons and run a grid of models varying these parameters. They are much more sensitive to line ratio variations, especially to the oxygen-to-\hb ratio. A solution in the grid was considered positive if it lied between the limits set by the shaded areas in Fig.~\ref{fig:ionization_ratios1}. Note that any line ratio can be derived just by subtracting one value from the `y'-axis to that corresponding from the `x'-axis; for instance, \mbox{log (\oiii/\hb) -- log(\oiii/\nii) = log(\nii/\hb)}. A more constrained solution for each \hii region was obtained by comparing the observables derived with the model with the extinction corrected ratios, the \hb luminosity and the EW(\hb\onespace) of each region. Assumed intervals of the line intensity ratio for each class together with the solution for the ages are listed in Table~\ref{table:cloudy_tramos}. In general, the excitation can be explained in all cases by only one ionizing population of \mbox{3--5.5 Myr} and, unlike \starlight fitting, none around \mbox{1 Myr}. Another important output from the grid of models corresponds to the UV absorption factor due to the internal extinction within the cloud, denoted as $f_{\mathrm{d}}$, also provided in the table. That is, if \mbox{$f_{\mathrm{d}}$ = 1}, no relevant absorption by dust grains is expected and if it is larger than 1, then such a factor is missed from the observed Balmer emission light. As inferred from the table, in all cases some emission is lost due to this UV absorption. In some cases, the loss is compatible with being marginal (i.e. for classes 4--6). However, in general, about 33\% (\mbox{$f_{\mathrm{d}}$ = 1.5}) of the emitted UV photons or even more could be missed. Particularly, for class 3, the loss is expected to be quite high and up to more than a half of the emitted UV photons (\mbox{$f_{\mathrm{d}} > $ 2.0}) and even up to 75\% (\mbox{$f_{\mathrm{d}} \sim $ 4.0}). An individual model fit for each of the \hii region would be desirable. However, a few hundred iterations were needed in order to model only one class. This makes it a very long time consuming task. Nevertheless, we can complement the results obtained here with a spectrophotometric study by using a multiwavelength broad-band set of images and the spectral information provided by the Balmer emission lines. We develop this analysis in the following section. \subsubsection{Spectrophotometric analysis} \label{sec:spectrophot_analysis} \textit{XMM}-OM and SDSS imaging can provide useful information on young stellar populations. In particular, having the information of ultraviolet and \textit{u} broad-band emission makes a difference when trying to characterize ionizing stellar populations. The UV continuum is dominated by massive short-lived OB stars (\mbox{$\tau \leq$ 100 Myr}) and hence can be sensitive to star formation on time-scales of only 10 Myr or so. Likewise, as shown by~\cite{Anders04}, \textit{u}-band observations are essential for photometric investigations of young star clusters. Archive broad-band ultraviolet $UVW2$-$UVM2$ (OM) and \textit{u, i, z} (SDSS) images were retrieved. The main goal of our spectrophotometric study is to fit the SED of the young ionizing stellar population with models using the retrieved broad-band images and the spectral information provided by the IFU data. In particular, we gathered the data set as follows. \begin{enumerate} \item The five broad-band filter images just mentioned plus a set of three `simulated' broad-band images, produced with the convolution of the IFS cubes with three known $HST$ filter throughput curves: \mbox{$F439W \sim$ \textit{B} Johnson}, filter from the WFPC2 centred at \mbox{4300 \AA{}}; $F547M$, filter from the WFPC2 centred at \mbox{5479 \AA{}}; and $F621M$, filter from the WFC3 centred at \mbox{6219 \AA{}}. Fig.~\ref{fig:hst_filters} shows the integrated spectrum of the galaxy with the throughput filter curves overplotted. Note that, thanks to the star--gas decoupling analysis we avoid contamination by the nebular emission lines on the continuum broad-band images (i.e. H$\gamma$ Balmer line just in the middle of the $F439W$ filter). Altogether, with our compiled multiwavelength data, we cover homogeneously a rather large spectral range (from the near-UV to the near-IR \textit{z} band). \item The \ha and \hb line intensities and the respective EW, which set important constraints on the age of the ionizing stellar populations. The \ha\onespace/\hb ratio is also directly related to the LOS extinction. \end{enumerate} \begin{figure} \centering \includegraphics[trim = 0cm -1.0cm 0cm 1cm,angle=90,clip=true,width=0.45\textwidth]{figs/spectrum_fiters_hst.eps} \caption{Convolved $HST$ filters with the IFS cubes.} \label{fig:hst_filters} \end{figure} With the aid of single stellar population models we can try to explain the observed photometric and spectroscopic properties of each \hii region in NGC 3310. However, we first have to take into account the non-ionizing stellar population. The results obtained with the \starlight fitting are the key to decouple the light produced by ionizing and non-ionizing stellar populations. To that end we estimated, for each region and with the knowledge of the fitted stellar populations (i.e. \starlight result), which fraction of the light at the effective wavelength of each photometric filter comes from the former or the latter. We used a conservative cut of 15 Myr to separate ionizing from non-ionizing populations. We could directly estimate this ratio with the stellar libraries used in \starlight for the $HST$ filters, since the MILES library covers a wavelength range from 3525 to 7500 \AA{}. To derive the other ratios the synthetic \popstar templates were employed, since their spectral range covers all the filter data set used in this study and they include the nebular continuum contribution. We remind the reader that we performed 100 \starlight fits for each \hii region, which allowed us to estimate the uncertainties of these light ratios. In general, the light ratio for the bluest filters (i.e. \textit{UVW2,UVM2,u}) is quite low, \mbox{L$\mathrm{_{old}}$/L$\mathrm{_{young}} \leq$ 2-10\%} (i.e. practically all the light is related to ionizing population). Even if the relative uncertainties can be high (up to 60\%), they have little effect in the accuracy of the estimate of light related to young population. By contrast, the light ratio for red filters (i.e. \textit{i, z}) can be easily larger than \mbox{L$\mathrm{_{old}}$/L$\mathrm{_{young}} =~$50\%} and up to 70\%, with typical relative uncertainties of 20-30\%. In addition, by computing these ratios we are basically subtracting the contribution of the underlying old (in the sense of non-ionizing) stellar populations to the total emitted light. Therefore, we could correct the EWs of the \hii regions by subtracting this old population from the continuum. This corrected EW was used as an input parameter for the photoionization models in the previous section. \begin{figure*} \includegraphics[trim = -2cm 0cm -1cm -1cm,clip=true,width=0.9\textwidth]{figs/plot_sed_result_paper.eps} \caption{Synthetic best-fitting SED for four \hii regions. Photometric measurements corrected by non-ionizing population emission (not corrected) are overplotted in red (green). The correction is generally small (with some exception) for the ultraviolet data, while it is much more evident in redder filter photometric measurements. For the case where no solution is found, the value of $\chi^2_{\mathrm{min}}$ is labelled at the top right corner.} \label{fig:sed_fit} \end{figure*} The following step was to perform the photometry of the \hii regions in NGC 3310. With the `simulated' broad-band images with the $HST$ filters we directly added up all the flux contained in the spaxels that define the region. We want to use the same irregular aperture for all the images; hence, we preferred not to degrade all images to that with the worst one. Instead an IDL script was produced to add the flux of the same irregular aperture. Basically, all the images are re-sampled (preserving the flux) to have spaxels a factor of 10 smaller, so as to obtain a sub-spaxel photometry. The aperture is also re-sampled in such a way that the new aperture corresponds to the border of the previous one. Aperture coordinates are transformed to spaxel coordinates for each image and the flux within a given aperture is obtained adding up the flux of all the spaxels inside the aperture. Poisson noise is assumed, particularly important for the ultraviolet measurements, where only a few \mbox{counts s$^{-1}$} are detected in many regions. To account for differential spatial resolution the aperture is also shifted by 1 arcsec in four directions (north, south, east and west), and median values and dispersions are taken to compute the final flux and error for each \hii region. The response of the OM monitor at high count rates is not linear, an effect known as coincidence-loss ~\citep{Fordham00}. However, we have to corrected for this effect on our UV measurements because the count rates of the brightest \hii region on the individual exposures is of the order of \mbox{5 counts s$^{-1}$}, below the critical rate of \mbox{10 counts s$^{-1}$} where this effect becomes significant (10\%) according to the ``XMM-Newton Users Handbook'', Issue 2.11, 2013 (ESA: XMM-Newton SOC). The count rate for the rest of the \hii regions is well below \mbox{5 counts s$^{-1}$}, meaning that any systematic due to not correcting for this effect is well bellow 4\%, much smaller than the typical uncertainties of the photometric measurements (see Table~\ref{table:result_chi_square}). Once the photometry was performed, the correction due to the underlying old population was applied. Altogether, at this stage we have the flux of the light related to the ionizing population through seven broad-band filters, the corrected EWs and the observed \ha and \hb line fluxes. We have then compared observational and theoretical SEDs through a \mbox{$\chi^2$-fitting} procedure~\citep{Bik03} as \begin{equation} \chi^2(Z,\tau,A_V,m_\star) = \sum_{N} \frac{(f_{\mathrm{obs}} - f_{\mathrm{model}})^2}{\sigma^2_{\mathrm{obs}}} \end{equation} where $N$ denotes the number of filters and observables (photometric flux densities, fluxes and EWs of the emission lines; see Table~\ref{table:result_chi_square}) available for each \hii region; $f_{\mathrm{obs}}$ and $f_{\mathrm{model}}$ are the observed and model observables, respectively; and $\sigma_{\mathrm{obs}}$ is the weight for the fit (i.e. photometric, line flux measurements and underlying population correction uncertainties). The $\chi^2$ minimization procedure for fitting SEDs produces more satisfactory results for determining the ages, extinctions, and masses in galaxies (e.g.,~\citealt{Maoz01,Bastian05b,Diaz-Santos07}) than other widely used methods such as colour--colour diagrams. We first assumed that the stellar population responsible for the bulk of the ionization is a single stellar population for which four parameters were to be derived: metallicity ($Z$), age ($\tau$), extinction ($A_V$) and stellar mass ($m^{\mathrm{ion}}$). We used models with three different metallicities (\mbox{0.2,0.4 and 1.0 Z$_\odot$}). The expected (minimum) $\chi^2$ value of the best fit, $\chi^2_{\mathrm{min}}$, should be equal to the number of degrees of freedom ($\nu = N - 4$). Those solutions within $\chi^2_{\mathrm{min}} \pm \Delta\chi^2_{\mathrm{min}}$, with $\Delta\chi^2_{\mathrm{min}} = (2\nu)^{\frac{1}{2}}$, were taken to determine the range of acceptable solutions. This would be equivalent to taking the $\pm 1 \sigma$ solutions. Fig.~\ref{fig:sed_fit} illustrates the results of the SED minimization fitting technique for different \hii regions in our sample: with high (ID 1, 3) and low (ID 86, 96) S/N spectra. The change of the shape of the spectra is quite evident when the correction due to underlying non-ionizing population is applied. In Sect.~\ref{sec:photo_models} we explored the ionization structure of the seven classes, representative of the \hii regions. As a result we could estimate characteristic age and dust absorption factor ($f_\mathrm{d}$) intervals for each class. We have complemented those results with the SED fits presented here. In particular, we computed a grid of solutions of the $\chi^2$ minimization procedure by varying $f_\mathrm{d}$ from 1.0 to 4.5, that is, changing the modelled \ha and \hb flux and the EWs, which are divided by $f_\mathrm{d}$ (when trying to recover the observed values some flux, scaled to $f_\mathrm{d}$, is lost). For a given \hii region, we then took those sets of solutions of the $\chi^2$ minimization procedure that were at the same time compatible with the age and $f_\mathrm{d}$ intervals in the class to which the region belongs. Some disagreement was encountered between the age interval derived from the $\chi^2$ fit and from the \cloudy fit for a few \hii regions. However, the maximum difference is less than 1 Myr. For the vast majority of the regions the model that better reproduced the observables was that with \mbox{$Z$ = 0.4Z$_\odot$}, which is in agreement with the gaseous abundances derived in Sect.~\ref{sec:abundance_properties}. Given the young nature of the ionizing population, this is expected. The derived ages, stellar masses, internal extinctions and absorption factors are listed in Table~\ref{table:result_chi_square}. The fit was not successful for a few cases, demanding the presence of two ionizing stellar populations. A minimization analysis was performed in those cases, though large degeneracy is found on the properties of the derived populations. One of them usually ranges between 1 and 6 Myr, the other being 6--15 Myr old. Within these age ranges the mass is not generally well defined within factors of less than 5--10. We would like to mention that in a few cases no valid solutions were found for $f_\mathrm{d} = 1$, but for $f_\mathrm{d} > 1.0$. Thus, it may happen that the measured flux densities are related to a single stellar population but, since no solution is found, minimization techniques are immediately applied to a composite two-stellar-population model. As we have seen here, sometimes invoking a composite model is not necessary in order to reproduce the observed fluxes. As can be observed in the table, \hii regions are typically 2.5--5 Myr old. This is consistent with the presence of WR stars (see the spectral features in Fig.~\ref{fig:SL_examples}), given that this phase normally starts \mbox{2--3 Myr} after their birth~\citep{Meynet05}. The mass of the ionizing stars span, on the other hand, a large range, from about $10^{4}$ up to \mbox{6$\times 10^{6}$ \msun\onespace}. Note the asymmetry on the error estimates. It is also worth mentioning the typical significant absorption factors derived ($f_{\mathrm{d}}$ = 1.3--3.0). According to our combined photoionization and spectrophotometric modelling, we have seen that, in general, at least 25\% of the emitted UV photons from the OB stellar populations are absorbed by dust grains in the nebulae. \section[]{Discussion} \label{sec:discussion} \subsection{Reliability on the stellar subtraction} \label{sec:tests_SL} \begin{figure} \centering \includegraphics[trim = -0.5cm 2cm 0cm -2cm,angle=90,width=0.95\columnwidth]{figs/HII_sanity_check_balmer_b.eps} \caption{Balmer ratios with respect to \hb. The red asterisk marks the location on the plot of the theoretical ratio while the red box demarcates the ratio space where the values are within the expected systematics. To avoid confusion, typical error bars (median value) for \hii regions with ratios within the box are plotted on the left-hand side. The error is plotted for \hii regions with regions outside the plots.} \label{fig:sanity1} \end{figure} In our analysis, we have been able to subtract the underlying continuum of the spectra and hence to decouple the gaseous and stellar contributions to the measured emission. For some parts of our analysis, this subtraction is critical. This is the case for the measurement of the \oiii $\lambda$4363 \AA{} line, since it is very close to \hgamma\twospace, thus likely to be affected by a significant amount of underlying absorption. Here, we pay attention to the validity of such subtraction. We have hence checked the Balmer decrement ratios obtained once the extinction is corrected for each spectrum. Had we over-subtracted continuum absorption, negative extinction values and/or inconsistent Balmer ratios (i.e. \hb to \hgamma\onespace) would have been derived. We present in Fig.~\ref{fig:sanity1} the derived Balmer ratios (or differences in logarithm units) and compare them with the theoretical values according to \cite{Osterbrock89} and assuming a case B recombination with \mbox{$t_\mathrm{e}$ = 10,000 K} and \mbox{$n_\mathrm{e}$ = 100 cm$^{-3}$}. Under these conditions, \mbox{\ha\onespace/\hb = 2.86} and \mbox{\hgamma\onespace/\hb = 0.459}. Only four of them lie, within uncertainties, outside the systematic box. Although there are other 17 regions with ratios that lie outside the box, within uncertainties their ratios are consistent with the theoretical values. For those few cases where the ratio was not recovered because too much subtraction was performed, an extinction of $A_V = 0$ mag was assigned. \subsection{Biases on temperature and abundance derivations} \label{sec:t_obs_res} \subsubsection{Methodologies used} \label{sec:t_methods} \begin{figure*} \centering \includegraphics[angle=90,trim = -0.7cm 0cm 0cm 2cm,clip=true,width=0.95\columnwidth]{figs/helium_expample_spectrum_fit.eps} \includegraphics[angle=90,trim = 12cm 16.5cm 0.5cm -1cm,clip=true,width=1.0\columnwidth]{figs/HII_fit_lines_example.eps} \caption{\textbf{Left:} rest-frame spectrum for \hii region ID 19 and the fitted components. See label for the identification of colours. The derived continuum spectrum is also plotted. Several Balmer lines (\hb,\hgamma,\hdelta) and the \hei $\lambda$4771 \AA{} line are also identified and labelled. \textbf{Right:} zoomed view centred on the \hgamma spectral range. The red line shows the resulting fit of the two Gaussians (one for \hgamma and the other for \mbox{\oiii $\lambda$4363 \AA{}}) and the negative Gaussian (for the absorption).} \label{fig:fit_spectrum_id19} \end{figure*} In Sect.~\ref{sec:radial_gradients} (Fig.~\ref{fig:metal_radial_gradients_a}) we show the abundance gradient in the disc of NGC 3310. An intrinsic dispersion of about 0.15 dex is observed along the disc for the $t_\mathrm{e}$-based derived oxygen abundances. They also show an offset of about 0.3 dex with respect to the abundances derived using strong-line calibrations. In principle, it could be argued that abundances obtained through strong-line calibrations do suffer from typical systematics of \mbox{0.1--0.2 dex}. However, we also have to keep in mind that accurate electron temperature determinations depend on reliable auroral line measurements, such as \mbox{\sii $\lambda$6312 \AA{}}, \mbox{\nii $\lambda$5755 \AA{}} or \mbox{\oiii $\lambda$4363 \AA{}}. The latter is very close to the \hgamma line, which in young stellar populations can show a very wide profile (see~\citealt{Diaz88} for a detailed description of this complex spectral region). Given the spectral resolution of the PINGS data, the wings of both the oxygen auroral line and \hgamma blend. In fact, as shown in Fig.~\ref{fig:fit_spectrum_id19} (left), the auroral line sets over the absorption wing of \hgamma. A prominent stellar absorption can thus critically affect the measurement of the auroral line on the observed spectrum. Furthermore, the emission of this line is rather weak in regions with moderate abundance \mbox{(12 + log(O/H) $\sim$ 8.0)}, and undetectable in metal-rich environments. Altogether, a reliable detection and measurement on this line can be rather awkward. Very often, when fitting an emission line in a spectrum, a Gaussian function is assumed for the line and a straight line is used to fit the underlying continuum. For the specific case of \oiii $\lambda$4363 \AA{}, \hgamma is also included as another Gaussian function in the fit due to its proximity. We have compared our $t_\mathrm{e}$ (\oiii) ($\equiv t_3$) derivations with those that we would have obtained by fitting the auroral line directly on the `observed spectrum', without the subtraction of the continuum obtained with \starlight\onespace. Given that in most cases the stellar absorption is noticeable in the observed spectrum, instead of a straight line, the absorption was fitted with a broad Gaussian component with negative flux. An example of this is shown in Fig.~\ref{fig:fit_spectrum_id19} (right). Note that, as illustrated in the left-hand panel, part of the flux measured for the auroral line due to the fit actually corresponds to stellar continuum. The comparison of the electron temperature and the oxygen abundance using both methods is shown in Fig.~\ref{fig:metal_temp} (left and middle). The electron temperature is usually overestimated, which causes a general underestimation of the metallicity if the measurements are done on the observed (unsubtracted) spectra. The difference between the derived temperatures (i.e. metallicities) is correlated with the ratio between the predicted absorption of \hgamma with \starlight and the corrected \hgamma emission. It is hence directly related to the degree of absorption of the \hgamma emission-line (see Fig.~\ref{fig:metal_temp}, right). By subtracting such absorption and fitting the residual spectra we obtain higher abundance values, in better agreement with the literature. Therefore, we do not think that the methodology applied to the measurement of the \mbox{\oiii $\lambda$4363 \AA{}} line flux is behind the significant difference found between the direct and strong-line abundance estimates. \begin{figure*} \centering \includegraphics[trim = 5cm 0cm 5cm 0cm,angle=90,clip=true,width=0.92\textwidth]{figs/HII_abundance_temp.eps} \caption{\textbf{Left:} comparison between the derived temperature $t_3$ using the observed and the residual spectra. \textbf{Middle}: comparison between the derived oxygen abundance using the observed and the residual spectra. In both cases the line represents the 1:1 relation. \textbf{Right}: comparison between the difference in electron temperatures ($\Delta t_3 = t_\mathrm{e} \textrm{\oiii}_\textrm{obs} - t_\mathrm{e} \textrm{\oiii}_\textrm{res}$) and the flux ratio of \hgamma in absorption to corrected \hgamma in emission.} \label{fig:metal_temp} \end{figure*} \begin{figure*} \centering \includegraphics[trim = 4cm 0cm 4cm 0cm,angle=90,clip=true,width=0.92\textwidth]{figs/HII_abundance_temp2.eps} \caption{\textbf{Left:} comparison between the derived temperature $t_2$ using the $t_2$-$t_3$ relations provided by P\'erez-Montero \& D\'iaz (\citeyear{Perez-Montero03}; PM03) and Pilyugin et al. (\citeyear{Pilyugin10}; P10).~\textbf{Right}: relation between the derived oxygen abundance in each case. The line represents the 1:1 relation.} \label{fig:metal_temp2} \end{figure*} The use of different prescriptions used for the estimation of the $t_\mathrm{e} (\textrm{\oii})$ ($\equiv t_2$) may also contribute to the disagreement. As can be seen in Table~\ref{table:abundances}, the ion O$^+$ is generally more abundant than O$^{2+}$. That is, the abundance determination is dominated in most cases by the knowledge of $t_2$. In most cases, our direct abundance determinations rely on our derived $t_3$. Therefore, using one or other parametrizations between both electron temperatures may change our abundance estimate to a significant extent. There is not quite a consensus of how these temperatures are related. Several versions of the $t_2$-$t_3$ relation have been proposed, the most widely used by~\cite{Campbell86}, based on the \hii region models of~\cite{Stasinska82} is \begin{equation} t_2 = 0.7t_3 + 0.3 \end{equation} Several relations have been proposed during the last decades (e.g.,~\citealt{Pagel92,Izotov97,Oey00,Pilyugin06,Pilyugin07}). Here we focus on the relations proposed by~P\'erez-Montero \& D\'iaz (\citeyear{Perez-Montero03}; hereafter PM03) and Pilyugin et al. (\citeyear{Pilyugin10}; hereafter P10). In both cases, the physical conditions were derived using the five-level atom model for O$^+$, O$^{++}$ and N$^+$ ions, using the atomic data available. We compare these two works because the $ONS$ and $O3N2$ (O/N-corrected) calibrations were anchored to direct abundance determinations using a different $t_2$-$t_3$ relation. In particular,~PM03 claim that this relation is density dependent (Eq.~\ref{eq:t2_t3}). On the other hand,~P10 propose a relation quite similar to the commonly used ones (e.g.,~\citealt{Campbell86,Pagel92}): \begin{equation} t_2 = 0.672t_3 + 0.314 \end{equation} In Fig.~\ref{fig:metal_temp2}, we compare the derived electron temperature $t_2$ (left) and oxygen abundance (right) using both sets of equations. In general, if we make use of the relations proposed in P10, the derived temperatures and abundances are systematically somewhat lower and higher, respectively. Given the uncertainties, the systematics on the abundance estimate are not important or relevant for at least half of the cases, especially for abundances $\sim 8.0$ or lower. However, in a few cases, abundances can be up to 0.1--0.2 dex higher, closer to the expected abundance values obtained with the strong-line calibrations. Therefore, the use of one set of equations or another can introduce systematics in abundance determinations of typically 0.1 dex. \begin{figure*} \centering \includegraphics[trim = 4cm 0cm 4cm 0cm,angle=90,clip=true,width=0.92\textwidth]{figs/HII_abundance_temp3.eps} \caption{\textbf{Left:} comparison between the derived temperature $t_3$ using the conventional equilibrium methods (this study) and non-equilibrium methods (i.e. Kappa distribution).~\textbf{Right}: relation between the derived oxygen abundance in each case. The line represents the 1:1 relation.} \label{fig:metal_temp3} \end{figure*} Even taking into account this offset, the discrepancy between direct and strong-line abundance estimates are still significant. The compilations used in order to obtain the strong-line calibrations consist of several hundreds of \hii regions. With such a high parameter space of ionization conditions to explore (age and mass of the ionizing population, ionization parameter, metallicity, N/O, density, etc.), it would not be surprising that the direct and strong-line abundance estimates of \hii regions with different ionizing conditions as those in the compilations differed. Larger compilations or models covering as much as possible the parameter space of ionization conditions would be needed. \subsubsection{The abundance discrepancy problem} Discrepancies on abundance determinations have been observed for decades. Chemical abundances determined from the optical recombination lines are systematically higher than those determined from CEL. This problem, dating back to 70 yr (\citealt{Wyse42}), was first discussed in detail by \cite{Torres-Peimbert77}, and then regularly discussed in the literature (\citealt{Liu00,Stasinska04,Garcia-Rojas06,Garcia-Rojas07,Stasinska07,Mesa-Delgado08}). This is known as the `abundance discrepancy problem'. In addition, systematic differences between abundances determined using either direct measurements of ionic temperatures, or using SEL methods are reported in the literature (e.g.,~\citealt{Kennicutt03,Bresolin07,Bresolin09,Ercolano10,Pilyugin12a,Lopez-Sanchez12}). Unlike the systematics discussed in Sect.~\ref{sec:t_methods}, most of the works just mentioned focus on the nature of the calibration used to define the strong-line method applied. In fact, there remains a significant offset (see~\citealt{Perez-Montero10,Dors11}) between those SEL techniques based purely upon photoionization models~\citep{McGaugh91,Kewley02,Kobulnicky04} and those based upon an empirical alignment of the strong line intensities to abundances derived in objects for which the electron temperature has been directly estimated~\citep{Bresolin04,Pilyugin05,Pilyugin12b}. In some cases the abundance determinations via direct-temperature methods are favoured, (e.g.~\citealt{Bresolin09,Ercolano10}) and the discrepancies are explained by the presence of multiple ionization sources (not taken into account in one-dimensional ionization models). In other cases, techniques based on photoionization models are preferred (e.g.,~\citealt{Stasinska05,Lopez-Sanchez12}), since they produce electron temperature gradients inside \hii regions, and temperature fluctuations are assumed to be the main reason for the abundance discrepancy problem. Other physical scenarios have been proposed in order to explain this discrepancy, the most recent one exploring the fact that the electrons involved in collisional excitation and recombination processes may not be in thermal equilibrium (\citealt{Binette12,Nicholls12,Nicholls13}). Here, we can estimate how would our direct abundance estimates be affected under this assumption. However, we cannot know how our estimates using strong-line methods are affected. If we assume that the electrons involved in collisional excitation and recombination processes follow a non-equilibrium Kappa ($\kappa$) electron energy distribution rather than the widely assumed simple Maxwell--Boltzmann distribution, the `true' electron temperature in the ionization zone is lower than the derived value using standard methods, as shown in~\cite{Nicholls13}. They provide a means for estimating $\kappa$ with the knowledge of the ``apparent'' (i.e. derived using standard methods, like those used in this paper) \oiii~and \siii~electron temperatures (see their fig.~11). \cite{Hagele06} derived \oiii~and \siii~electron temperatures in a large compilation of \hii galaxies and giant extragalactic \hii regions. A relation between both temperatures was found as \begin{equation} \mathrm{T([S{\sc III}])} = (1.19 \pm 0.08) \times \mathrm{T([O{\sc III}])}) - (0.32 \pm 0.10) \end{equation} Using this relation, we have made a rough estimation of \mbox{$\kappa \sim 20$} within the range of temperatures in our study, in perfect agreement with the value obtained in~\cite{Dopita13}.~\cite{Nicholls13} also provide a method to correct the electron temperature derived using standard methods, once $\kappa$ is known (see their Eq.~36). Although we are not able to compute the \siii~electron temperature, we can estimate by how much a Kappa distribution with $\kappa \sim 20$ is affecting our temperature estimates, so as to speculate by up to how much our abundance determinations can be underestimated. As Fig.~\ref{fig:metal_temp3} shows, the electron temperatures might be overestimated by typically 2000 K, which translates into an underestimation (i.e. offset) of the oxygen abundance of typically 0.2 dex and up to 0.3 dex. This range agrees well with observed offsets (e.g.~\citealt{Lopez-Sanchez12}). Note, however, that three regions still keep low-metallicity values (\mbox{12 + log(O/H) $\sim$ 8.0}) even if this correction is applied (Fig.~\ref{fig:metal_temp3}, right). \subsection{Implications on the flat abundance gradient} The subject of abundance gradients in galaxies is currently a burning issue on galaxy evolution. The steepest abundance gradients were initially seen in late-type spiral galaxies (types \mbox{Sb--Scd}). Barred galaxies were thought to present shallower gradients ~\citep{Martin94,Zaritsky94}, though more recent studies, with larger samples, have opened the debate that this may not be the case~\citep{Sanchez12b}. Metallicity gradients can also be flattened or erased in interacting galaxies and remnants from mergers. We have shown in Sect.~\ref{sec:radial_gradients} that the radial abundance gradient in NGC 3310 is rather flat. This is consistent with the flat gradients obtained in~\cite{Sanchez14} for merging galaxies at different levels of the interaction process. In a recent work,~\cite{Werk11} derived abundances for a handful of even more external \hii regions (up to a projected distance of almost 17 kpc or 6.7\reff). Although their abundance estimates are systematically higher than our estimates by about 0.2--0.3 dex (they use the model-based calibration of $R_{23}$), even at these distances they remain high and a flat abundance gradient is also observed. However, only a handful of \hii regions at a given azimuthal direction were observed in that study. We have observed over 100 regions and at all azimuthal directions. Therefore, combining both our and their study, we can be certain that the abundance gradient in NGC 3310 is rather flat from the very central regions to the outermost parts of the galaxy, well beyond 4\reff. This galaxy has been classified as a barred spiral. The bar and the size of the ringed structure suggest that this starburst was triggered by a bar instability~\citep{Piner95}. The likely past merger event this galaxy had with a dwarf plausibly produced the bar instability which led to the starburst. During an interaction, large amounts of gas can flow towards the central regions, carrying less enriched gas from the outskirts of the galaxy into the central regions, which can erase any metallicity gradient and dilute the central metallicity. Our results suggest that we are witnessing the consequences of such metal mixing processes. \begin{figure} \hspace{-0.3cm} \includegraphics[angle=90,trim = 1cm 0cm 1cm 0cm,clip=true,width=1.03\columnwidth]{figs/HII_pop2a.eps} \caption{Comparison of the derived stellar ionizing mass using our spectrophotometric fitting (POP) with that derived using the extinction corrected \ha flux plus the corrected (from underlying non-ionizing population) \hb EW width using Diaz's~(\citeyear{Diaz98}) and our updated prescription (\ha D98 and \ha POP, respectively). Typical errors are plotted at the top right corner. Whenever the \ha flux and the EW(\hb) are used, they are corrected for the derived absorption by dust grains. The dotted line indicates a unity relation.} \label{fig:HII_pop2a} \end{figure} Werk and collaborators measured flat radial oxygen abundance gradients from the central optical bodies to the outermost regions of the galaxies in their sample. Given the different morphology of the galaxies, star-forming properties and level of disruption (13 systems, not all of them with signs of interaction) in their sample, they argued that metal transport processes in cold neutral gas rather than interactions may also play an important role in distributing the metals to the outermost parts of the galaxies (e.g., magnetorotational instabilities, thermal instability triggered self-gravitational angular momentum transport, etc.). However, given the large time-scales required (i.e. 1.5 Gyr) and that the metals generated by massive stars are generally returned to the ISM in just \mbox{$\sim$ 100 Myr}~\citep{Tenorio-Tagle96}, they concluded that the metal transport may be occurring predominantly in a hot gas component, a still unclear driver mechanism. In any case, these other mechanisms do not exclude that interactions (even weak interactions or minor mergers) effectively mix the chemical metal content in a galaxy. \subsection{Star formation in NGC 3310} \subsubsection{Different determinations of the mass of the ionizing population} In Sect.~\ref{sec:spectrophot_analysis}, we derive ages and masses for the ionized stellar population (i.e. with ages \mbox{$\tau < 10$ Myr}). We can compare the stellar mass of the ionizing population as derived there and the values of the same masses derived from the extinction-corrected \ha fluxes, using the expression from~\cite{Diaz98}: \begin{equation} \label{eq:diaz98} \mathrm{log}~m^{\mathrm{ion}} = \mathrm{log}~L(\mathrm{H}\alpha) - 0.86 \times \mathrm{log}~\mathrm{EW(H}\beta) - 32.61 \end{equation} This equation takes into account the evolutionary state of the ionizing stellar cluster, and the EW used corresponds to that that would be observed in the absence of an underlying population. As can be seen in Fig.~\ref{fig:HII_pop2a} masses derived with the SED fitting are not consistent with those obtained from the \ha flux. Actually, Eq.~\ref{eq:diaz98} is based basically on models by~\cite{Garcia-Vargas95a,Garcia-Vargas95b} and \cite{Stasinska96}, all of them assuming a Salpeter IMF. We have updated this relation using \popstar, the last version of these models. We have then explored the expected correlation between the number of ionizing photons per unit mass ($Q$(H)/M$_\odot$) and the EW of \hb, since both quantities decrease with the age of the cluster (see Fig.~\ref{fig:models_ha}). A linear regression fit gives \begin{figure} \centering \includegraphics[trim = 0cm -2cm 0cm 0.5cm,clip=true,angle=90,width=1.05\columnwidth]{figs/SFR_relations_POP_v1.eps} \caption{Relation between the number of ionizing photons per unit mass and the EW of \hb for different metallicities according to the \popstar Single Stellar Population models (Moll\'a et al.~\citeyear{Molla09},~Mart\'in-Manj\'on et al.~\citeyear{Martin-Manjon10}). Red solid line represents the best fit for the model with \mbox{$Z$ = 0.4Z$\odot$}.} \label{fig:models_ha} \end{figure} \begin{equation} \mathrm{log}~Q(\mathrm{H})/\mathrm{M}_\odot = (1.07 \pm 0.02) \times \mathrm{log}~\mathrm{EW}(\mathrm{H}\beta) + (43.76 \pm 0.03) \end{equation} for \mbox{$Z$ = 0.4Z$_\odot$}, and \begin{equation} \mathrm{log}~Q(\mathrm{H})/\mathrm{M}_\odot = (1.11 \pm 0.03) \times \mathrm{log}~\mathrm{EW}(\mathrm{H}\beta) + (43.70 \pm 0.05) \end{equation} for \mbox{$Z$ = Z$_\odot$} And the mass of the ionizing cluster, corrected by the evolutionary state is (for \mbox{Z = 0.4Z$_\odot$}): \begin{figure*} \includegraphics[angle=90,trim = -0.5cm 0cm 0cm -1cm,clip=true,width=0.95\textwidth]{figs/flux_cuts_paper.eps} \caption{\textbf{Top-left:} \ha intensity map, colour coded according to the intensity intervals defined on the right-hand (top-right) panel. \textbf{Top-right:} \ha intensity (in log in arbitrary units) versus the excitation-sensitive ratio \oiii/\oii~for each spaxel. Different intensity intervals, log I(\ha), are colour coded as: $<$ 0.48 (violet), 0.48--0.90 (blue), 0.9--1.48 (green), 1.48--2.00 (orange), $>$ 2.00 (red). The grey area highlights the absence of low-excited and at the same time very luminous spaxels. \textbf{Bottom-right:} same relation as above, but for the \hii regions and different intensity intervals, log I(\ha), colour-coded as: $<$ 2.0 (blue), 2.0--3.0 (green), $>$ 4.0 (red). \textbf{Bottom-left:} EW(\hb\onespace), only corrected by the presence of underlying non-ionizing population, versus excitation relation for the \hii regions, colour-coded according to the intensity intervals defined on the right-hand (bottom-left) panel. Superimposed tracks show the evolution of clusters of different initial mass with time along this relation, according to \popstar models. Tracks in solid lines correspond to \mbox{Z = 0.4Z$_\odot$}, in dashed line to \mbox{Z = 0.4Z$_\odot$} and in dotted line to \mbox{Z = 0.2Z$_\odot$}. The arrow at the upper-left corner illustrates by how much the tracks should be corrected if absorption by dust grains within the nebulae ($f_\mathrm{d}$) or escape ($f_\mathrm{L}$) of half of the ionizing photons occured.} \label{fig:flux_cuts} \end{figure*} \begin{equation} \label{eq:d98_updated} \mathrm{log}~m^{\mathrm{ion}} = \mathrm{log}~L(\mathrm{H}\alpha) - 1.07 \times \mathrm{log}~\mathrm{EW(H}\beta) - 31.90 \end{equation} If we use the new relation (for Z = 0.4Z$_\odot$, since the metallicity for the vast majority of \hii is around this value), then the derived mass is more similar to the adopted mass in this study (Fig.~\ref{fig:HII_pop2a}). Although within the uncertainties the mass are completely compatible, a small systematic offset of 0.1 dex is still present. Therefore, the mass obtained for the ionizing stellar population is little affected by the methodology used (SED $\chi^2$ minimization fitting or \ha and EW of \hb with the updated relation). It is interesting to mention that, if a fraction of photons escape or dust absorption of UV photons occur, both the \ha flux and the EW measurements are affected in a similar way. Let us take $f_\mathrm{Ld}$ as the factor of photons that escape from the nebulae (leaking photons; `L') and those are absorbed by dust grains (`d') within the nebulae. Since both the \ha flux and the EW are shortened by the same factor, it is easy to work out the resulting relation for the mass of the ionizing stellar population (for $Z$ = 0.4Z$_\odot$): \begin{flalign} & \mathrm{log}~m^{\mathrm{ion}} & \mspace{-20.0mu}=~& \mathrm{log}~L(\mathrm{H}\alpha_{\mathrm{obs}}) - 1.07 \times \mathrm{log}~\mathrm{EW(H}\beta_{\mathrm{obs}})~- \mspace{60.0mu}\\ & & & - 31.90 - 0.07\times\mathrm{log}~f_{Ld} \notag \end{flalign} If $f_\mathrm{Ld} = 2.0$, then the correction is just 0.02 dex. The typical range of $f_\mathrm{d}$ derived in this study (note that we have not estimated the fraction of leaking photons) is $f_\mathrm{d} = 1.3-3.5$. Actually, even if two thirds of the photons are missing (i.e. $f_\mathrm{d} = 3.0$), the correction would only amount 0.03 dex, which is lower than the typical uncertainty in the derivation of the mass. \subsubsection{Local evolutionary tracks} There is a clear correlation between the distance to the centre of the galaxy and the \ha luminosity measured in \mbox{NGC 3310}, the circumnuclear whereabouts being the most luminous (see emission-line maps in Fig.~\ref{fig:emission_maps}). In order to explore if there is an evolutionary effect behind this relation we have investigated the conditions of the ionization in several \ha luminosity intervals. As shown in Fig.~\ref{fig:flux_cuts} (top), the most luminous spaxels are generally also those with the hardest ionization. Even though there are a few spaxels with even higher degree of ionization, there is a clear envelope (lower part of grey area in the figure) at which no spaxel is very luminous and with low ionization. This cannot be a selection effect, because a spaxel with such conditions (being more luminous than average) should be observed. This effect, though less evident, is also observed when considering the \hii regions (Fig.~\ref{fig:flux_cuts}, bottom-right). The EW of \hb\onespace, once corrected by the continuum of non-ionizing populations, is a good indicator of the age of an ionizing cluster, i.e. of its evolutionary state~\citep{Dottori81}. A relation between the EW(\hb\onespace) and the degree of ionization has been observed in \hii galaxies~\citep{Hoyos06}. With our data we can reproduce a similar relation for the \hii regions of NGC 3310 (Fig.~\ref{fig:flux_cuts}, bottom-left). Thus, this effect seems to be a local one, at least at the scale of one or a few hundred pc. According to the evolutionary tracks, the higher the initial mass of the ionizing population the harder the degree of ionization in the cloud for a fixed age. Note that these tracks are also metallicity dependent. At high metallicities, for a given age and mass of the ionizing population, the degree of ionization of the gas (i.e. \oiii/\oii ratio) is lower and the EW just slightly smaller than at low metallicities. If, in general, the most luminous were more massive than the less luminous population, then the envelope we observe in the figure would be perfectly understandable. However, there is a general mismatch between observational data and models, quite evident in the figure. Given that the continuum from the underlying population has been subtracted, two reasons can be responsible for this disagreement, mainly: (i) absorption of UV photons by dust grains within the nebulae, which we have been able to roughly quantify in our analysis; (ii) escape of ionizing photons, which has been assumed to be negligible in this study. The arrow in Fig.~\ref{fig:flux_cuts} (bottom-left) exemplify by how much the tracks should be corrected by one or another. Additionally, the tracks shown in the figure only span a range up to \mbox{2$\times 10^5$ \msun}. Since the number of ionizing photons scales with the mass of the cluster, we would expect that by allowing a larger range in mass to the models the tracks would move towards harder ionizing regimes. With the aid of the model tracks, we can speculate on the evolutionary state of the observed \hii regions. For instance, if the mass of the ionizing population is of the order of \mbox{$10^6$ \msun} (the typical mass obtained for the most luminous ones, as reported in Table~\ref{table:result_chi_square}) and assuming that the tracks move towards harder ionizing regimes at higher masses, then two possibilities can explain the observations: (i) the most luminous population is typically older than the less luminous ionizing population; (ii) the effect of dust absorption of UV photons and/or photon leakage can be important, which would explain at the same time why no \hii regions with high luminosity and low excitation are observed (i.e. \mbox{log\oiii/\oii $>$ 0.4}). \subsubsection{Star Formation Rates} Although by definition, the star formation rate (SFR) of a starburst is zero when we see it several Myr later, with the knowledge of the mass and the age of the ionizing stellar population we can estimate an average SFR for each \hii region. The integrated value can give us a picture of the most recent star formation history of the galaxy (i.e. the rhythm at which the galaxy has been forming clusters during the last few Myr). We have made estimates of the SFR of the \hii regions just by computing the ratio of the mass and the age. Additionally, we have obtained another estimate by using the most widely used SFR rate calibrator in the optical, provided by Kennicutt (\citeyear{Kennicutt98}; K98). This calibrator relates the recent SFR with the \ha luminosity as \begin{equation} \label{eq:sfr} \mathrm{SFR} (\mathrm{M}_\odot \mathrm{yr}^{-1}) = 7.49 \times 10^{-42}~L\mathrm{(H}\alpha)~(\mathrm{erg s}^{-1}) \end{equation} The estimated SFRs using Kennicutt's calibration are systematically lower than expected, even if we correct for absorption of dust grains (see Fig.~\ref{fig:HII_pop2b}). As cautioned in~\cite{Kennicutt07}, the SFR derived using Eq.~\ref{eq:sfr} for an individual \hii region, using a continuous star formation conversion relevant to entire galaxies, has limited physical meaning because the stars are younger and the region under examination is experiencing an instantaneous event when considered on any galactic evolutionary or dynamical time-scale. \begin{figure} \hspace{-0.3cm} \includegraphics[angle=90,trim = 1cm 0cm 1cm 0cm,clip=true,width=1.03\columnwidth]{figs/HII_pop2b.eps} \caption{Comparison of the derived SFR using different methods our spectrophotometric fitting (POP) and the prescription by Kennicutt (\citeyear{Kennicutt98}; K98). Whenever the \ha flux and the EW(\hb) are used, they are corrected for the derived absorption by dust grains. The dotted line indicates a unity relation.} \label{fig:HII_pop2b} \end{figure} The integrated SFR using each method is 4.4 (Eq.~\ref{eq:sfr}) and 13.8 (spectrophotometric SED fitting), in units of \mbox{\msun yr$^{-1}$}. These two estimates are in agreement with SFRs for starburst galaxies with moderate star formation~\citep{Kennicutt98,Leitherer00}. Given our estimated age range (\mbox{$\tau = $ 2.5 -- 5 Myr}) for the ionizing population, lower values using Kennicutt's calibration are expected. Reported total SFR estimates are of the order of \mbox{3--8.6 \msun yr$^{-1}$}~\citep{Smith96,Werk11,Mineo12}. They are within the range of (or somewhat below than) our estimates. \subsection{Mass growth in the disc of NGC 3310} In Sect.~\ref{sec:spectrophot_analysis} we have shown that the ages of the ionizing population within the \hii regions span a very narrow range (\mbox{i.e.~$\tau = 2.5-5.0$ Myr};~see Table~\ref{table:result_chi_square}). With such a narrow age range and a large \hb luminosity range (i.e. log \hb$ \sim 1-3.5$;~see Fig.~\ref{fig:ionization_ratios2}), we can easily infer that there is not a correlation between the luminosity of an \hii region and the age of the ionizing population; that is, the most luminous \hii regions do not tend to be the youngest. Thus, we can assume that the luminosity of the \hii regions is roughly proportional to their masses, being their age a second-order effect. \begin{table*} \begin{minipage}{0.65\textwidth} \renewcommand{\footnoterule}{} % \begin{small} \caption{Comparison of mass derivations and ratios with those in H10.} \label{table:comparison_hagele2} \begin{center} \begin{tabular}{lccccccc} \hline \hline \noalign{\smallskip} H{\tiny II} & ID & m$^{\mathrm{ion}}$ & m$^{\mathrm{ion}}$ & m$^{\mathrm{LOS}}_\star$ & m$^{dyn}_\star$ & m$^{\mathrm{ion}}$/m$_\star$ & m$^{\mathrm{ion}}$/m$_\star$ \\ ID & H10 & & H10 & & H10 & (\%) & (\%) H10 \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) \\ \hline \noalign{\smallskip} 1+4 & J & 6.5$^{+1.6}_{-1.5}$ & 1.29--3.14 & 220 $\pm$ 40 & \ldots & 3.0$^{+1.0}_{-0.8}$ & \ldots \\ \noalign{\smallskip} 3 & N & 6.7$^{+1.1}_{-0.9}$ & 3.49 & 531$^{+161}_{-82}$ & 74 $\pm$ 9 & 1.3 $\pm$ 0.3 & 4.7 \\ \noalign{\smallskip} 5 & R4 & 3.9$^{+1.7}_{-1.1}$ & 1.76 & 177$^{+106}_{-35}$ & 89 $\pm$ 3 & 2.1$^{+1.0}_{-0.7}$ & 2.0 \\ \noalign{\smallskip} 7 & R5+R6+S6 & 3.2$^{+1.4}_{-0.9}$ & 3.36 & 143$^{+27}_{-14}$ & 103 $\pm$ 12 & 2.1$^{+0.9}_{-0.6}$ & 3.3 \\ \noalign{\smallskip} 8 & R1+R2 & 1.9 $\pm$ 0.6 & 1.39 & 90$^{+42}_{-21}$ & 91: & 2.0$^{+0.8}_{-0.6}$ & 1.5 \\ \noalign{\smallskip} 11 & R10+R11\footnote{Only masses for R10 are given in H10.} & 4.4 $\pm$ 0.7 & 1.57 & 144$^{+36}_{-6}$ & 59 $\pm$ 3 & 2.9 $\pm$ 0.5 & 2.7 \\ \noalign{\smallskip} 12 & R7 & 4.7$^{+1.3}_{-1.1}$ & 0.87 & 157$^{+31}_{-11}$ & 141 $\pm$ 6 & 2.8 $\pm$ 0.7 & 0.6 \\ \hline \noalign{\smallskip} \multicolumn{8}{@{} p{\columnwidth} @{}}{{\footnotesize \textbf{Notes.} Col (1): \hii identification ID used in this study. Col (2): \hii identification ID of the individual or group of regions identified in H10, that correspond those identified in this study. Col (3): mass of the ionizing population derived in this study. Col (4): mass of the ionizing population derived in H10. Col (5): total stellar mass along the LOS derived in this study. Col (6): dynamical mass derived in H10. Col (7): ratio of the ionizing to the total stellar mass obtained in this study. Col (8): ratio of the ionizing to the total stellar mass (i.e. dynamical mass) obtained in H10. All masses are given in 10$^6$ \msun.}} \end{tabular} \end{center} \end{small} \end{minipage} \end{table*} The contribution of the ionizing population to the total stellar population for each \hii region (i.e. the young to total stellar mass ratio, m$^{\mathrm{ion}}$/m$_\star$) can be roughly estimated by taking the derived mass of the \starlight fitting as the total mass of the \hii region. Note that the total stellar mass actually represents the stellar mass along the LOS. Therefore, our estimation really represents a lower limit to the percentage. We would like to point out that the uncertainties on the derived total stellar masses (via the 100 realizations of the \starlight fitting for each region) are generally strongly asymmetric. We thus took the $1\sigma$ uncertainties as the last values included within the 68\% on the left ($\sigma^{-}$) and on the right ($\sigma^{-}$) of the mass distribution, centred on the median value. To better estimate the uncertainties on the m$^{\mathrm{ion}}/$m$_\star$ ratio we have used the techniques developed in~\cite{Barlow03,Barlow04}. In short, when an experimental result is represented as $x^{+\sigma^+}_{-\sigma^{-}}$, being $\sigma^+$ and $\sigma^-$ different, a non-symmetric distribution can represent $x$. Among the functions proposed in those papers, we modelled each variable (i.e. mass) using a ``Variable Gaussian'' parametrization. With an asymmetric distribution representing each variable we made a few tens of thousands of Monte Carlo runs for each \hii region using the {\sc idl} routine `genrand', which allows us to obtain random numbers following a given distribution (not necessarily normal) so as to obtain a reliable estimate of the mass ratio with its $\sigma^+$ and $\sigma^-$ uncertainty. The derived m$^{\mathrm{ion}}$/m$_\star$ ratios range from 0.2 to about 7 per cent. A comparison for the circumnuclear regions in NGC 3310 identified in previous studies is shown in Table~\ref{table:comparison_hagele2}. Despite the fact that, with some exceptions, the ratios are similar, the disagreement between ionizing population and total stellar masses separately is evident, up to factors of more than 2 for the nucleus. Masses from the ionizing population reported in H10 were computed using Eq.~\ref{eq:diaz98}. Apart from the systematic introduced by the use of the updated version presented in this study, aperture effects can contribute significantly to the differences in the reported \ha luminosities and EW(\hb\onespace), as Table~\ref{table:comparison_hagele} illustrates. In general, we have obtained higher mass values. In addition, we have generally computed higher total stellar masses because: (i) we have derived the LOS stellar mass; and (ii) H10 derived the total stellar mass of each cluster within an \hii region and then added up all the individual estimates for each region. In our calculations, the intracluster mass (probably from the disc) is included. Still, the ratios reported here and those obtained in H10 span a similar range, being always lower than 10\%. All these values are also similar to those reported in \hii regions and \hii galaxies observed in other studies~\citep{Alonso-Herrero01,Hagele09,Perez-Montero10}. \begin{figure} \centering \includegraphics[angle=90,trim = -1cm -2cm 1cm -1cm,clip=true,width=0.5\textwidth]{figs/HII_pop1.eps} \caption{Radial distribution of the ratio between the stellar mass of the ionizing population and the total stellar mass along the LOS. The values are colour coded according to the \ha surface density flux in \mbox{10$^{-16}$ erg s$^{-1}$ cm$^{-2}$ \AA{}$^{-1}$ arcsec$^{-2}$}. Only data for which an estimate of the ionizing mass via the SED fitting technique is plotted.} \label{fig:HII_pop1} \end{figure} We show in Fig.~\ref{fig:HII_pop1} the radial distribution of this ratio (in terms of percentage) and its relation with the \ha flux surface density. In general, those regions with higher \ha flux surface density are located at smaller radii (with a few exceptions). The radial distribution of the young-to-total-stellar ratio is much more scattered. From the centre and up to about 1.5\reff~(where we cover the complete radial FoV), a 4.5$\sigma$ mild correlation is found, according to the Spearman's rank-order correlation test. However, if we consider the whole radial range, such correlation cease to exist in statistical terms. Given the narrow age range of the ionizing population we can roughly assume that any variation of the ratio between the ionizing population and the total stellar mass relates to a variation in the specific SFR (sSFR). In fact, if we compute the sSFR (just by subtracting the total mass from our estimates of the SFR) and plot it against the radial distance, we obtain a similar plot to that shown in Fig.~\ref{fig:HII_pop1}. Therefore, just by examining this figure we can have some insight on the mass growth in the galaxy disc. In the framework of the inside-out scenario, the SFR should be a strongly varying function of the galactocentric distance.~\cite{Munyoz-Mateos07} studied the radial profiles of sSFR for a sample of 161 nearby spiral galaxies. They found a large dispersion in the slope of these profiles with a slightly positive mean value, which they interpreted as proof of a moderate inside-out disc formation. Although they did not find any clear dependence of the sSFR gradient on the environment, they argued that transitory episodes of enhanced star formation in the inner parts of the disc can lead to a currently smaller SFR scalelength (gradual growth of the size of the disc with time) than in the past. That is, the gradient can hence be weakened or be even negative. It is well known that mergers in general can induce radial mixing processes, such as inflows of external gas on to the central regions and trigger starbursts (e.g.,~\citealt{Barnes96,Rupke10}). As mentioned before, the global starburst in NGC 3310 is likely to have a minor merger origin~\citep{Smith96,Kregel01,Wehner06}. The mild negative gradient of the sSFR in NGC 3310 can well be another signature of a past merger event. This suggests that the minor merger event may be playing an important role in the mass build-up on the bulge, in agreement with recent models~\citep{Hopkins10}. \section[]{Conclusions} \label{sec:conclusions} We have performed an IFS analysis in the distorted spiral galaxy NGC 3310, covering up to about 3 effective radii. This represents an unprecedented simultaneous spatial and spectroscopic coverage for this galaxy, which underwent a minor merger interaction some hundred Myr ago. While major mergers are known to cause dramatic changes in the progenitor galaxies, the impact of a minor merger is still not well understood. We have thus investigated on the evolution of the stellar and chemical properties of the galaxy on account of this past event. The paper relies on the analysis of the optical spectra of about a hundred \hii regions identified along the disc and spiral arms. Chemical abundances of the gas have been obtained by analysing the continuum-subtracted emission-line spectra, different techniques have been employed, and their radial distribution has been studied. We first fitted the SED of the galaxies using the program \starlight in order to quantify the contribution of the underlying stellar population and perform such continuum subtraction. With the knowledge of the ionizing conditions of the \hii regions and the aid of ultraviolet and optical/NIR imaging we have characterized the properties (i.e. age, mass, SFR) of the ionizing population. The most important results of this study are summarized as follows. \begin{enumerate} \item All derived gaseous oxygen abundances using strong-line diagnostics, consistent with a sub-solar value \mbox{(12 + log(O/H) $\sim$ 8.2--8.4)}, are similar to those reported for circumnuclear \hii regions present in this galaxy. With a sample of over 100 \hii regions we observe a rather flat abundance gradient in the disc of NGC 3310 out to about 10 kpc away from the nucleus. We can thus confirm the evidence that the minor merger event had a substantial impact on metal mixing in the remnant. \item A direct ($t_\mathrm{e}$-based) oxygen abundance determination was possible in 16 \hii regions, located in the central regions of the galaxy. The derived values are somewhat lower and present more dispersion than those obtained using strong-line calibrations. With a statistically significant sample of \hii regions, we report on an offset of 0.2--0.3 dex between direct and strong-line abundance estimates. We argue several reasons behind the discrepancy: systematic uncertainties in the calibrations due to different ionization condition properties of the gas and different prescriptions used to relate electron temperatures between the ionic species. We further investigate the effect of the oversimplified assumption that the electrons in the nebulae are in thermal equilibrium on the determination of the direct abundances. Under the assumption of a non-equilibrium Kappa electron energy distribution, the adopted abundances would be increased by up to 0.2--0.3 dex. \item With the use of single stellar population and photoionization models, we have been able to constrain the main properties of the ionizing stellar population within the \hii regions. In general, the presence of a single population is sufficient to explain the measured broad-band (from ultraviolet to $z$ band) and ionizing line-flux. The age of the ionizing population spans a narrow range of 2.5--5 Myr, whereas the mass range is quite large, from about 10$^4$ to \mbox{6$\times 10^6$ \msun\onespace}. Given the ionized gas line ratios, dust grains must be present in most of the \hii regions, causing the absorption from a few percent and up to more than two-thirds (typical absorption factors of \mbox{$f_\mathrm{d} = $1.3-3.5}) of the UV photons. \item We have updated prescriptions to derive the stellar mass of the ionizing population, correcting by its evolutionary state, with the knowledge of the \ha flux and the EW of \hb\onespace. The ionizing mass has little dependence on photon losses by either UV photon leakage or absorption of UV photons by dust grains within the nebulae. The typical uncertainties of the derived masses, generally within a factor of 1.5--2, are in fact much higher than any correction that should be applied were these losses even of the order of 66\%. \item The derived average global SFR over time-scales \mbox{$>$ 6 Myr}, 4.4 \mbox{\msun yr$^{-1}$}, is consistent with other studies made at other wavelengths. However, the average global SFR for the last few Myr (i.e. \mbox{$\lesssim$ 5 Myr}) is about a factor of 3 higher. \item The mass of the ionizing population represents generally less than 5\% of the estimated population along the LOS, down to about 0.2\%. Taking into account that the contribution of the old mass of the disc is not subtracted, this result is consistent with other studies that support that in circumnuclear regions the ratio of the ionizing to total stellar mass is typically of the order of a few percent, less than 10\%. The radial distribution of the specific SFR (proportional to this ratio) in the disc of NGC 3310 suggests that minor interactions indeed can play an important role in the formation and assembly of the bulge. \end{enumerate} \section*{Acknowledgements} \begin{small} We would like to thank the anonymous referee for useful comments that have helped improve the quality and clarify the content of the paper. This work has been partially supported by projects AYA2010-21887-C04-03 and AYA2010-21887-C04-01 of the Spanish National Plan for Astronomy and Astrophysics, and by the project AstroMadrid, funded by the Comunidad de Madrid government under grant CAM S2009/ESP-1496, partially using funds from the EU FEDER programme. FFRO acknowledges the Mexican National Council for Science and Technology (CONACYT) for financial support under the programme Estancias Posdoctorales y Sab{\'a}ticas al Extranjero para la Consolidaci{\'o}n de Grupos de Investigaci{\'o}n, 2010-2012. This research has made use of the NASA/IPAC Extragalactic Database which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We have made use of observations obtained with \mbox{$XMM-Newton$}, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. \end{small} \renewcommand{\item}{\itemold} \bibliographystyle{mn2e}% \bibliography{my_bib.bib}{} \newpage \begin{onecolumn} \appendix \begin{footnotesize} \begin{landscape} | \subsection{Reliability on the stellar subtraction} \label{sec:tests_SL} \begin{figure} \centering \includegraphics[trim = -0.5cm 2cm 0cm -2cm,angle=90,width=0.95\columnwidth]{figs/HII_sanity_check_balmer_b.eps} \caption{Balmer ratios with respect to \hb. The red asterisk marks the location on the plot of the theoretical ratio while the red box demarcates the ratio space where the values are within the expected systematics. To avoid confusion, typical error bars (median value) for \hii regions with ratios within the box are plotted on the left-hand side. The error is plotted for \hii regions with regions outside the plots.} \label{fig:sanity1} \end{figure} In our analysis, we have been able to subtract the underlying continuum of the spectra and hence to decouple the gaseous and stellar contributions to the measured emission. For some parts of our analysis, this subtraction is critical. This is the case for the measurement of the \oiii $\lambda$4363 \AA{} line, since it is very close to \hgamma\twospace, thus likely to be affected by a significant amount of underlying absorption. Here, we pay attention to the validity of such subtraction. We have hence checked the Balmer decrement ratios obtained once the extinction is corrected for each spectrum. Had we over-subtracted continuum absorption, negative extinction values and/or inconsistent Balmer ratios (i.e. \hb to \hgamma\onespace) would have been derived. We present in Fig.~\ref{fig:sanity1} the derived Balmer ratios (or differences in logarithm units) and compare them with the theoretical values according to \cite{Osterbrock89} and assuming a case B recombination with \mbox{$t_\mathrm{e}$ = 10,000 K} and \mbox{$n_\mathrm{e}$ = 100 cm$^{-3}$}. Under these conditions, \mbox{\ha\onespace/\hb = 2.86} and \mbox{\hgamma\onespace/\hb = 0.459}. Only four of them lie, within uncertainties, outside the systematic box. Although there are other 17 regions with ratios that lie outside the box, within uncertainties their ratios are consistent with the theoretical values. For those few cases where the ratio was not recovered because too much subtraction was performed, an extinction of $A_V = 0$ mag was assigned. \subsection{Biases on temperature and abundance derivations} \label{sec:t_obs_res} \subsubsection{Methodologies used} \label{sec:t_methods} \begin{figure*} \centering \includegraphics[angle=90,trim = -0.7cm 0cm 0cm 2cm,clip=true,width=0.95\columnwidth]{figs/helium_expample_spectrum_fit.eps} \includegraphics[angle=90,trim = 12cm 16.5cm 0.5cm -1cm,clip=true,width=1.0\columnwidth]{figs/HII_fit_lines_example.eps} \caption{\textbf{Left:} rest-frame spectrum for \hii region ID 19 and the fitted components. See label for the identification of colours. The derived continuum spectrum is also plotted. Several Balmer lines (\hb,\hgamma,\hdelta) and the \hei $\lambda$4771 \AA{} line are also identified and labelled. \textbf{Right:} zoomed view centred on the \hgamma spectral range. The red line shows the resulting fit of the two Gaussians (one for \hgamma and the other for \mbox{\oiii $\lambda$4363 \AA{}}) and the negative Gaussian (for the absorption).} \label{fig:fit_spectrum_id19} \end{figure*} In Sect.~\ref{sec:radial_gradients} (Fig.~\ref{fig:metal_radial_gradients_a}) we show the abundance gradient in the disc of NGC 3310. An intrinsic dispersion of about 0.15 dex is observed along the disc for the $t_\mathrm{e}$-based derived oxygen abundances. They also show an offset of about 0.3 dex with respect to the abundances derived using strong-line calibrations. In principle, it could be argued that abundances obtained through strong-line calibrations do suffer from typical systematics of \mbox{0.1--0.2 dex}. However, we also have to keep in mind that accurate electron temperature determinations depend on reliable auroral line measurements, such as \mbox{\sii $\lambda$6312 \AA{}}, \mbox{\nii $\lambda$5755 \AA{}} or \mbox{\oiii $\lambda$4363 \AA{}}. The latter is very close to the \hgamma line, which in young stellar populations can show a very wide profile (see~\citealt{Diaz88} for a detailed description of this complex spectral region). Given the spectral resolution of the PINGS data, the wings of both the oxygen auroral line and \hgamma blend. In fact, as shown in Fig.~\ref{fig:fit_spectrum_id19} (left), the auroral line sets over the absorption wing of \hgamma. A prominent stellar absorption can thus critically affect the measurement of the auroral line on the observed spectrum. Furthermore, the emission of this line is rather weak in regions with moderate abundance \mbox{(12 + log(O/H) $\sim$ 8.0)}, and undetectable in metal-rich environments. Altogether, a reliable detection and measurement on this line can be rather awkward. Very often, when fitting an emission line in a spectrum, a Gaussian function is assumed for the line and a straight line is used to fit the underlying continuum. For the specific case of \oiii $\lambda$4363 \AA{}, \hgamma is also included as another Gaussian function in the fit due to its proximity. We have compared our $t_\mathrm{e}$ (\oiii) ($\equiv t_3$) derivations with those that we would have obtained by fitting the auroral line directly on the `observed spectrum', without the subtraction of the continuum obtained with \starlight\onespace. Given that in most cases the stellar absorption is noticeable in the observed spectrum, instead of a straight line, the absorption was fitted with a broad Gaussian component with negative flux. An example of this is shown in Fig.~\ref{fig:fit_spectrum_id19} (right). Note that, as illustrated in the left-hand panel, part of the flux measured for the auroral line due to the fit actually corresponds to stellar continuum. The comparison of the electron temperature and the oxygen abundance using both methods is shown in Fig.~\ref{fig:metal_temp} (left and middle). The electron temperature is usually overestimated, which causes a general underestimation of the metallicity if the measurements are done on the observed (unsubtracted) spectra. The difference between the derived temperatures (i.e. metallicities) is correlated with the ratio between the predicted absorption of \hgamma with \starlight and the corrected \hgamma emission. It is hence directly related to the degree of absorption of the \hgamma emission-line (see Fig.~\ref{fig:metal_temp}, right). By subtracting such absorption and fitting the residual spectra we obtain higher abundance values, in better agreement with the literature. Therefore, we do not think that the methodology applied to the measurement of the \mbox{\oiii $\lambda$4363 \AA{}} line flux is behind the significant difference found between the direct and strong-line abundance estimates. \begin{figure*} \centering \includegraphics[trim = 5cm 0cm 5cm 0cm,angle=90,clip=true,width=0.92\textwidth]{figs/HII_abundance_temp.eps} \caption{\textbf{Left:} comparison between the derived temperature $t_3$ using the observed and the residual spectra. \textbf{Middle}: comparison between the derived oxygen abundance using the observed and the residual spectra. In both cases the line represents the 1:1 relation. \textbf{Right}: comparison between the difference in electron temperatures ($\Delta t_3 = t_\mathrm{e} \textrm{\oiii}_\textrm{obs} - t_\mathrm{e} \textrm{\oiii}_\textrm{res}$) and the flux ratio of \hgamma in absorption to corrected \hgamma in emission.} \label{fig:metal_temp} \end{figure*} \begin{figure*} \centering \includegraphics[trim = 4cm 0cm 4cm 0cm,angle=90,clip=true,width=0.92\textwidth]{figs/HII_abundance_temp2.eps} \caption{\textbf{Left:} comparison between the derived temperature $t_2$ using the $t_2$-$t_3$ relations provided by P\'erez-Montero \& D\'iaz (\citeyear{Perez-Montero03}; PM03) and Pilyugin et al. (\citeyear{Pilyugin10}; P10).~\textbf{Right}: relation between the derived oxygen abundance in each case. The line represents the 1:1 relation.} \label{fig:metal_temp2} \end{figure*} The use of different prescriptions used for the estimation of the $t_\mathrm{e} (\textrm{\oii})$ ($\equiv t_2$) may also contribute to the disagreement. As can be seen in Table~\ref{table:abundances}, the ion O$^+$ is generally more abundant than O$^{2+}$. That is, the abundance determination is dominated in most cases by the knowledge of $t_2$. In most cases, our direct abundance determinations rely on our derived $t_3$. Therefore, using one or other parametrizations between both electron temperatures may change our abundance estimate to a significant extent. There is not quite a consensus of how these temperatures are related. Several versions of the $t_2$-$t_3$ relation have been proposed, the most widely used by~\cite{Campbell86}, based on the \hii region models of~\cite{Stasinska82} is \begin{equation} t_2 = 0.7t_3 + 0.3 \end{equation} Several relations have been proposed during the last decades (e.g.,~\citealt{Pagel92,Izotov97,Oey00,Pilyugin06,Pilyugin07}). Here we focus on the relations proposed by~P\'erez-Montero \& D\'iaz (\citeyear{Perez-Montero03}; hereafter PM03) and Pilyugin et al. (\citeyear{Pilyugin10}; hereafter P10). In both cases, the physical conditions were derived using the five-level atom model for O$^+$, O$^{++}$ and N$^+$ ions, using the atomic data available. We compare these two works because the $ONS$ and $O3N2$ (O/N-corrected) calibrations were anchored to direct abundance determinations using a different $t_2$-$t_3$ relation. In particular,~PM03 claim that this relation is density dependent (Eq.~\ref{eq:t2_t3}). On the other hand,~P10 propose a relation quite similar to the commonly used ones (e.g.,~\citealt{Campbell86,Pagel92}): \begin{equation} t_2 = 0.672t_3 + 0.314 \end{equation} In Fig.~\ref{fig:metal_temp2}, we compare the derived electron temperature $t_2$ (left) and oxygen abundance (right) using both sets of equations. In general, if we make use of the relations proposed in P10, the derived temperatures and abundances are systematically somewhat lower and higher, respectively. Given the uncertainties, the systematics on the abundance estimate are not important or relevant for at least half of the cases, especially for abundances $\sim 8.0$ or lower. However, in a few cases, abundances can be up to 0.1--0.2 dex higher, closer to the expected abundance values obtained with the strong-line calibrations. Therefore, the use of one set of equations or another can introduce systematics in abundance determinations of typically 0.1 dex. \begin{figure*} \centering \includegraphics[trim = 4cm 0cm 4cm 0cm,angle=90,clip=true,width=0.92\textwidth]{figs/HII_abundance_temp3.eps} \caption{\textbf{Left:} comparison between the derived temperature $t_3$ using the conventional equilibrium methods (this study) and non-equilibrium methods (i.e. Kappa distribution).~\textbf{Right}: relation between the derived oxygen abundance in each case. The line represents the 1:1 relation.} \label{fig:metal_temp3} \end{figure*} Even taking into account this offset, the discrepancy between direct and strong-line abundance estimates are still significant. The compilations used in order to obtain the strong-line calibrations consist of several hundreds of \hii regions. With such a high parameter space of ionization conditions to explore (age and mass of the ionizing population, ionization parameter, metallicity, N/O, density, etc.), it would not be surprising that the direct and strong-line abundance estimates of \hii regions with different ionizing conditions as those in the compilations differed. Larger compilations or models covering as much as possible the parameter space of ionization conditions would be needed. \subsubsection{The abundance discrepancy problem} Discrepancies on abundance determinations have been observed for decades. Chemical abundances determined from the optical recombination lines are systematically higher than those determined from CEL. This problem, dating back to 70 yr (\citealt{Wyse42}), was first discussed in detail by \cite{Torres-Peimbert77}, and then regularly discussed in the literature (\citealt{Liu00,Stasinska04,Garcia-Rojas06,Garcia-Rojas07,Stasinska07,Mesa-Delgado08}). This is known as the `abundance discrepancy problem'. In addition, systematic differences between abundances determined using either direct measurements of ionic temperatures, or using SEL methods are reported in the literature (e.g.,~\citealt{Kennicutt03,Bresolin07,Bresolin09,Ercolano10,Pilyugin12a,Lopez-Sanchez12}). Unlike the systematics discussed in Sect.~\ref{sec:t_methods}, most of the works just mentioned focus on the nature of the calibration used to define the strong-line method applied. In fact, there remains a significant offset (see~\citealt{Perez-Montero10,Dors11}) between those SEL techniques based purely upon photoionization models~\citep{McGaugh91,Kewley02,Kobulnicky04} and those based upon an empirical alignment of the strong line intensities to abundances derived in objects for which the electron temperature has been directly estimated~\citep{Bresolin04,Pilyugin05,Pilyugin12b}. In some cases the abundance determinations via direct-temperature methods are favoured, (e.g.~\citealt{Bresolin09,Ercolano10}) and the discrepancies are explained by the presence of multiple ionization sources (not taken into account in one-dimensional ionization models). In other cases, techniques based on photoionization models are preferred (e.g.,~\citealt{Stasinska05,Lopez-Sanchez12}), since they produce electron temperature gradients inside \hii regions, and temperature fluctuations are assumed to be the main reason for the abundance discrepancy problem. Other physical scenarios have been proposed in order to explain this discrepancy, the most recent one exploring the fact that the electrons involved in collisional excitation and recombination processes may not be in thermal equilibrium (\citealt{Binette12,Nicholls12,Nicholls13}). Here, we can estimate how would our direct abundance estimates be affected under this assumption. However, we cannot know how our estimates using strong-line methods are affected. If we assume that the electrons involved in collisional excitation and recombination processes follow a non-equilibrium Kappa ($\kappa$) electron energy distribution rather than the widely assumed simple Maxwell--Boltzmann distribution, the `true' electron temperature in the ionization zone is lower than the derived value using standard methods, as shown in~\cite{Nicholls13}. They provide a means for estimating $\kappa$ with the knowledge of the ``apparent'' (i.e. derived using standard methods, like those used in this paper) \oiii~and \siii~electron temperatures (see their fig.~11). \cite{Hagele06} derived \oiii~and \siii~electron temperatures in a large compilation of \hii galaxies and giant extragalactic \hii regions. A relation between both temperatures was found as \begin{equation} \mathrm{T([S{\sc III}])} = (1.19 \pm 0.08) \times \mathrm{T([O{\sc III}])}) - (0.32 \pm 0.10) \end{equation} Using this relation, we have made a rough estimation of \mbox{$\kappa \sim 20$} within the range of temperatures in our study, in perfect agreement with the value obtained in~\cite{Dopita13}.~\cite{Nicholls13} also provide a method to correct the electron temperature derived using standard methods, once $\kappa$ is known (see their Eq.~36). Although we are not able to compute the \siii~electron temperature, we can estimate by how much a Kappa distribution with $\kappa \sim 20$ is affecting our temperature estimates, so as to speculate by up to how much our abundance determinations can be underestimated. As Fig.~\ref{fig:metal_temp3} shows, the electron temperatures might be overestimated by typically 2000 K, which translates into an underestimation (i.e. offset) of the oxygen abundance of typically 0.2 dex and up to 0.3 dex. This range agrees well with observed offsets (e.g.~\citealt{Lopez-Sanchez12}). Note, however, that three regions still keep low-metallicity values (\mbox{12 + log(O/H) $\sim$ 8.0}) even if this correction is applied (Fig.~\ref{fig:metal_temp3}, right). \subsection{Implications on the flat abundance gradient} The subject of abundance gradients in galaxies is currently a burning issue on galaxy evolution. The steepest abundance gradients were initially seen in late-type spiral galaxies (types \mbox{Sb--Scd}). Barred galaxies were thought to present shallower gradients ~\citep{Martin94,Zaritsky94}, though more recent studies, with larger samples, have opened the debate that this may not be the case~\citep{Sanchez12b}. Metallicity gradients can also be flattened or erased in interacting galaxies and remnants from mergers. We have shown in Sect.~\ref{sec:radial_gradients} that the radial abundance gradient in NGC 3310 is rather flat. This is consistent with the flat gradients obtained in~\cite{Sanchez14} for merging galaxies at different levels of the interaction process. In a recent work,~\cite{Werk11} derived abundances for a handful of even more external \hii regions (up to a projected distance of almost 17 kpc or 6.7\reff). Although their abundance estimates are systematically higher than our estimates by about 0.2--0.3 dex (they use the model-based calibration of $R_{23}$), even at these distances they remain high and a flat abundance gradient is also observed. However, only a handful of \hii regions at a given azimuthal direction were observed in that study. We have observed over 100 regions and at all azimuthal directions. Therefore, combining both our and their study, we can be certain that the abundance gradient in NGC 3310 is rather flat from the very central regions to the outermost parts of the galaxy, well beyond 4\reff. This galaxy has been classified as a barred spiral. The bar and the size of the ringed structure suggest that this starburst was triggered by a bar instability~\citep{Piner95}. The likely past merger event this galaxy had with a dwarf plausibly produced the bar instability which led to the starburst. During an interaction, large amounts of gas can flow towards the central regions, carrying less enriched gas from the outskirts of the galaxy into the central regions, which can erase any metallicity gradient and dilute the central metallicity. Our results suggest that we are witnessing the consequences of such metal mixing processes. \begin{figure} \hspace{-0.3cm} \includegraphics[angle=90,trim = 1cm 0cm 1cm 0cm,clip=true,width=1.03\columnwidth]{figs/HII_pop2a.eps} \caption{Comparison of the derived stellar ionizing mass using our spectrophotometric fitting (POP) with that derived using the extinction corrected \ha flux plus the corrected (from underlying non-ionizing population) \hb EW width using Diaz's~(\citeyear{Diaz98}) and our updated prescription (\ha D98 and \ha POP, respectively). Typical errors are plotted at the top right corner. Whenever the \ha flux and the EW(\hb) are used, they are corrected for the derived absorption by dust grains. The dotted line indicates a unity relation.} \label{fig:HII_pop2a} \end{figure} Werk and collaborators measured flat radial oxygen abundance gradients from the central optical bodies to the outermost regions of the galaxies in their sample. Given the different morphology of the galaxies, star-forming properties and level of disruption (13 systems, not all of them with signs of interaction) in their sample, they argued that metal transport processes in cold neutral gas rather than interactions may also play an important role in distributing the metals to the outermost parts of the galaxies (e.g., magnetorotational instabilities, thermal instability triggered self-gravitational angular momentum transport, etc.). However, given the large time-scales required (i.e. 1.5 Gyr) and that the metals generated by massive stars are generally returned to the ISM in just \mbox{$\sim$ 100 Myr}~\citep{Tenorio-Tagle96}, they concluded that the metal transport may be occurring predominantly in a hot gas component, a still unclear driver mechanism. In any case, these other mechanisms do not exclude that interactions (even weak interactions or minor mergers) effectively mix the chemical metal content in a galaxy. \subsection{Star formation in NGC 3310} \subsubsection{Different determinations of the mass of the ionizing population} In Sect.~\ref{sec:spectrophot_analysis}, we derive ages and masses for the ionized stellar population (i.e. with ages \mbox{$\tau < 10$ Myr}). We can compare the stellar mass of the ionizing population as derived there and the values of the same masses derived from the extinction-corrected \ha fluxes, using the expression from~\cite{Diaz98}: \begin{equation} \label{eq:diaz98} \mathrm{log}~m^{\mathrm{ion}} = \mathrm{log}~L(\mathrm{H}\alpha) - 0.86 \times \mathrm{log}~\mathrm{EW(H}\beta) - 32.61 \end{equation} This equation takes into account the evolutionary state of the ionizing stellar cluster, and the EW used corresponds to that that would be observed in the absence of an underlying population. As can be seen in Fig.~\ref{fig:HII_pop2a} masses derived with the SED fitting are not consistent with those obtained from the \ha flux. Actually, Eq.~\ref{eq:diaz98} is based basically on models by~\cite{Garcia-Vargas95a,Garcia-Vargas95b} and \cite{Stasinska96}, all of them assuming a Salpeter IMF. We have updated this relation using \popstar, the last version of these models. We have then explored the expected correlation between the number of ionizing photons per unit mass ($Q$(H)/M$_\odot$) and the EW of \hb, since both quantities decrease with the age of the cluster (see Fig.~\ref{fig:models_ha}). A linear regression fit gives \begin{figure} \centering \includegraphics[trim = 0cm -2cm 0cm 0.5cm,clip=true,angle=90,width=1.05\columnwidth]{figs/SFR_relations_POP_v1.eps} \caption{Relation between the number of ionizing photons per unit mass and the EW of \hb for different metallicities according to the \popstar Single Stellar Population models (Moll\'a et al.~\citeyear{Molla09},~Mart\'in-Manj\'on et al.~\citeyear{Martin-Manjon10}). Red solid line represents the best fit for the model with \mbox{$Z$ = 0.4Z$\odot$}.} \label{fig:models_ha} \end{figure} \begin{equation} \mathrm{log}~Q(\mathrm{H})/\mathrm{M}_\odot = (1.07 \pm 0.02) \times \mathrm{log}~\mathrm{EW}(\mathrm{H}\beta) + (43.76 \pm 0.03) \end{equation} for \mbox{$Z$ = 0.4Z$_\odot$}, and \begin{equation} \mathrm{log}~Q(\mathrm{H})/\mathrm{M}_\odot = (1.11 \pm 0.03) \times \mathrm{log}~\mathrm{EW}(\mathrm{H}\beta) + (43.70 \pm 0.05) \end{equation} for \mbox{$Z$ = Z$_\odot$} And the mass of the ionizing cluster, corrected by the evolutionary state is (for \mbox{Z = 0.4Z$_\odot$}): \begin{figure*} \includegraphics[angle=90,trim = -0.5cm 0cm 0cm -1cm,clip=true,width=0.95\textwidth]{figs/flux_cuts_paper.eps} \caption{\textbf{Top-left:} \ha intensity map, colour coded according to the intensity intervals defined on the right-hand (top-right) panel. \textbf{Top-right:} \ha intensity (in log in arbitrary units) versus the excitation-sensitive ratio \oiii/\oii~for each spaxel. Different intensity intervals, log I(\ha), are colour coded as: $<$ 0.48 (violet), 0.48--0.90 (blue), 0.9--1.48 (green), 1.48--2.00 (orange), $>$ 2.00 (red). The grey area highlights the absence of low-excited and at the same time very luminous spaxels. \textbf{Bottom-right:} same relation as above, but for the \hii regions and different intensity intervals, log I(\ha), colour-coded as: $<$ 2.0 (blue), 2.0--3.0 (green), $>$ 4.0 (red). \textbf{Bottom-left:} EW(\hb\onespace), only corrected by the presence of underlying non-ionizing population, versus excitation relation for the \hii regions, colour-coded according to the intensity intervals defined on the right-hand (bottom-left) panel. Superimposed tracks show the evolution of clusters of different initial mass with time along this relation, according to \popstar models. Tracks in solid lines correspond to \mbox{Z = 0.4Z$_\odot$}, in dashed line to \mbox{Z = 0.4Z$_\odot$} and in dotted line to \mbox{Z = 0.2Z$_\odot$}. The arrow at the upper-left corner illustrates by how much the tracks should be corrected if absorption by dust grains within the nebulae ($f_\mathrm{d}$) or escape ($f_\mathrm{L}$) of half of the ionizing photons occured.} \label{fig:flux_cuts} \end{figure*} \begin{equation} \label{eq:d98_updated} \mathrm{log}~m^{\mathrm{ion}} = \mathrm{log}~L(\mathrm{H}\alpha) - 1.07 \times \mathrm{log}~\mathrm{EW(H}\beta) - 31.90 \end{equation} If we use the new relation (for Z = 0.4Z$_\odot$, since the metallicity for the vast majority of \hii is around this value), then the derived mass is more similar to the adopted mass in this study (Fig.~\ref{fig:HII_pop2a}). Although within the uncertainties the mass are completely compatible, a small systematic offset of 0.1 dex is still present. Therefore, the mass obtained for the ionizing stellar population is little affected by the methodology used (SED $\chi^2$ minimization fitting or \ha and EW of \hb with the updated relation). It is interesting to mention that, if a fraction of photons escape or dust absorption of UV photons occur, both the \ha flux and the EW measurements are affected in a similar way. Let us take $f_\mathrm{Ld}$ as the factor of photons that escape from the nebulae (leaking photons; `L') and those are absorbed by dust grains (`d') within the nebulae. Since both the \ha flux and the EW are shortened by the same factor, it is easy to work out the resulting relation for the mass of the ionizing stellar population (for $Z$ = 0.4Z$_\odot$): \begin{flalign} & \mathrm{log}~m^{\mathrm{ion}} & \mspace{-20.0mu}=~& \mathrm{log}~L(\mathrm{H}\alpha_{\mathrm{obs}}) - 1.07 \times \mathrm{log}~\mathrm{EW(H}\beta_{\mathrm{obs}})~- \mspace{60.0mu}\\ & & & - 31.90 - 0.07\times\mathrm{log}~f_{Ld} \notag \end{flalign} If $f_\mathrm{Ld} = 2.0$, then the correction is just 0.02 dex. The typical range of $f_\mathrm{d}$ derived in this study (note that we have not estimated the fraction of leaking photons) is $f_\mathrm{d} = 1.3-3.5$. Actually, even if two thirds of the photons are missing (i.e. $f_\mathrm{d} = 3.0$), the correction would only amount 0.03 dex, which is lower than the typical uncertainty in the derivation of the mass. \subsubsection{Local evolutionary tracks} There is a clear correlation between the distance to the centre of the galaxy and the \ha luminosity measured in \mbox{NGC 3310}, the circumnuclear whereabouts being the most luminous (see emission-line maps in Fig.~\ref{fig:emission_maps}). In order to explore if there is an evolutionary effect behind this relation we have investigated the conditions of the ionization in several \ha luminosity intervals. As shown in Fig.~\ref{fig:flux_cuts} (top), the most luminous spaxels are generally also those with the hardest ionization. Even though there are a few spaxels with even higher degree of ionization, there is a clear envelope (lower part of grey area in the figure) at which no spaxel is very luminous and with low ionization. This cannot be a selection effect, because a spaxel with such conditions (being more luminous than average) should be observed. This effect, though less evident, is also observed when considering the \hii regions (Fig.~\ref{fig:flux_cuts}, bottom-right). The EW of \hb\onespace, once corrected by the continuum of non-ionizing populations, is a good indicator of the age of an ionizing cluster, i.e. of its evolutionary state~\citep{Dottori81}. A relation between the EW(\hb\onespace) and the degree of ionization has been observed in \hii galaxies~\citep{Hoyos06}. With our data we can reproduce a similar relation for the \hii regions of NGC 3310 (Fig.~\ref{fig:flux_cuts}, bottom-left). Thus, this effect seems to be a local one, at least at the scale of one or a few hundred pc. According to the evolutionary tracks, the higher the initial mass of the ionizing population the harder the degree of ionization in the cloud for a fixed age. Note that these tracks are also metallicity dependent. At high metallicities, for a given age and mass of the ionizing population, the degree of ionization of the gas (i.e. \oiii/\oii ratio) is lower and the EW just slightly smaller than at low metallicities. If, in general, the most luminous were more massive than the less luminous population, then the envelope we observe in the figure would be perfectly understandable. However, there is a general mismatch between observational data and models, quite evident in the figure. Given that the continuum from the underlying population has been subtracted, two reasons can be responsible for this disagreement, mainly: (i) absorption of UV photons by dust grains within the nebulae, which we have been able to roughly quantify in our analysis; (ii) escape of ionizing photons, which has been assumed to be negligible in this study. The arrow in Fig.~\ref{fig:flux_cuts} (bottom-left) exemplify by how much the tracks should be corrected by one or another. Additionally, the tracks shown in the figure only span a range up to \mbox{2$\times 10^5$ \msun}. Since the number of ionizing photons scales with the mass of the cluster, we would expect that by allowing a larger range in mass to the models the tracks would move towards harder ionizing regimes. With the aid of the model tracks, we can speculate on the evolutionary state of the observed \hii regions. For instance, if the mass of the ionizing population is of the order of \mbox{$10^6$ \msun} (the typical mass obtained for the most luminous ones, as reported in Table~\ref{table:result_chi_square}) and assuming that the tracks move towards harder ionizing regimes at higher masses, then two possibilities can explain the observations: (i) the most luminous population is typically older than the less luminous ionizing population; (ii) the effect of dust absorption of UV photons and/or photon leakage can be important, which would explain at the same time why no \hii regions with high luminosity and low excitation are observed (i.e. \mbox{log\oiii/\oii $>$ 0.4}). \subsubsection{Star Formation Rates} Although by definition, the star formation rate (SFR) of a starburst is zero when we see it several Myr later, with the knowledge of the mass and the age of the ionizing stellar population we can estimate an average SFR for each \hii region. The integrated value can give us a picture of the most recent star formation history of the galaxy (i.e. the rhythm at which the galaxy has been forming clusters during the last few Myr). We have made estimates of the SFR of the \hii regions just by computing the ratio of the mass and the age. Additionally, we have obtained another estimate by using the most widely used SFR rate calibrator in the optical, provided by Kennicutt (\citeyear{Kennicutt98}; K98). This calibrator relates the recent SFR with the \ha luminosity as \begin{equation} \label{eq:sfr} \mathrm{SFR} (\mathrm{M}_\odot \mathrm{yr}^{-1}) = 7.49 \times 10^{-42}~L\mathrm{(H}\alpha)~(\mathrm{erg s}^{-1}) \end{equation} The estimated SFRs using Kennicutt's calibration are systematically lower than expected, even if we correct for absorption of dust grains (see Fig.~\ref{fig:HII_pop2b}). As cautioned in~\cite{Kennicutt07}, the SFR derived using Eq.~\ref{eq:sfr} for an individual \hii region, using a continuous star formation conversion relevant to entire galaxies, has limited physical meaning because the stars are younger and the region under examination is experiencing an instantaneous event when considered on any galactic evolutionary or dynamical time-scale. \begin{figure} \hspace{-0.3cm} \includegraphics[angle=90,trim = 1cm 0cm 1cm 0cm,clip=true,width=1.03\columnwidth]{figs/HII_pop2b.eps} \caption{Comparison of the derived SFR using different methods our spectrophotometric fitting (POP) and the prescription by Kennicutt (\citeyear{Kennicutt98}; K98). Whenever the \ha flux and the EW(\hb) are used, they are corrected for the derived absorption by dust grains. The dotted line indicates a unity relation.} \label{fig:HII_pop2b} \end{figure} The integrated SFR using each method is 4.4 (Eq.~\ref{eq:sfr}) and 13.8 (spectrophotometric SED fitting), in units of \mbox{\msun yr$^{-1}$}. These two estimates are in agreement with SFRs for starburst galaxies with moderate star formation~\citep{Kennicutt98,Leitherer00}. Given our estimated age range (\mbox{$\tau = $ 2.5 -- 5 Myr}) for the ionizing population, lower values using Kennicutt's calibration are expected. Reported total SFR estimates are of the order of \mbox{3--8.6 \msun yr$^{-1}$}~\citep{Smith96,Werk11,Mineo12}. They are within the range of (or somewhat below than) our estimates. \subsection{Mass growth in the disc of NGC 3310} In Sect.~\ref{sec:spectrophot_analysis} we have shown that the ages of the ionizing population within the \hii regions span a very narrow range (\mbox{i.e.~$\tau = 2.5-5.0$ Myr};~see Table~\ref{table:result_chi_square}). With such a narrow age range and a large \hb luminosity range (i.e. log \hb$ \sim 1-3.5$;~see Fig.~\ref{fig:ionization_ratios2}), we can easily infer that there is not a correlation between the luminosity of an \hii region and the age of the ionizing population; that is, the most luminous \hii regions do not tend to be the youngest. Thus, we can assume that the luminosity of the \hii regions is roughly proportional to their masses, being their age a second-order effect. \begin{table*} \begin{minipage}{0.65\textwidth} \renewcommand{\footnoterule}{} % \begin{small} \caption{Comparison of mass derivations and ratios with those in H10.} \label{table:comparison_hagele2} \begin{center} \begin{tabular}{lccccccc} \hline \hline \noalign{\smallskip} H{\tiny II} & ID & m$^{\mathrm{ion}}$ & m$^{\mathrm{ion}}$ & m$^{\mathrm{LOS}}_\star$ & m$^{dyn}_\star$ & m$^{\mathrm{ion}}$/m$_\star$ & m$^{\mathrm{ion}}$/m$_\star$ \\ ID & H10 & & H10 & & H10 & (\%) & (\%) H10 \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) \\ \hline \noalign{\smallskip} 1+4 & J & 6.5$^{+1.6}_{-1.5}$ & 1.29--3.14 & 220 $\pm$ 40 & \ldots & 3.0$^{+1.0}_{-0.8}$ & \ldots \\ \noalign{\smallskip} 3 & N & 6.7$^{+1.1}_{-0.9}$ & 3.49 & 531$^{+161}_{-82}$ & 74 $\pm$ 9 & 1.3 $\pm$ 0.3 & 4.7 \\ \noalign{\smallskip} 5 & R4 & 3.9$^{+1.7}_{-1.1}$ & 1.76 & 177$^{+106}_{-35}$ & 89 $\pm$ 3 & 2.1$^{+1.0}_{-0.7}$ & 2.0 \\ \noalign{\smallskip} 7 & R5+R6+S6 & 3.2$^{+1.4}_{-0.9}$ & 3.36 & 143$^{+27}_{-14}$ & 103 $\pm$ 12 & 2.1$^{+0.9}_{-0.6}$ & 3.3 \\ \noalign{\smallskip} 8 & R1+R2 & 1.9 $\pm$ 0.6 & 1.39 & 90$^{+42}_{-21}$ & 91: & 2.0$^{+0.8}_{-0.6}$ & 1.5 \\ \noalign{\smallskip} 11 & R10+R11\footnote{Only masses for R10 are given in H10.} & 4.4 $\pm$ 0.7 & 1.57 & 144$^{+36}_{-6}$ & 59 $\pm$ 3 & 2.9 $\pm$ 0.5 & 2.7 \\ \noalign{\smallskip} 12 & R7 & 4.7$^{+1.3}_{-1.1}$ & 0.87 & 157$^{+31}_{-11}$ & 141 $\pm$ 6 & 2.8 $\pm$ 0.7 & 0.6 \\ \hline \noalign{\smallskip} \multicolumn{8}{@{} p{\columnwidth} @{}}{{\footnotesize \textbf{Notes.} Col (1): \hii identification ID used in this study. Col (2): \hii identification ID of the individual or group of regions identified in H10, that correspond those identified in this study. Col (3): mass of the ionizing population derived in this study. Col (4): mass of the ionizing population derived in H10. Col (5): total stellar mass along the LOS derived in this study. Col (6): dynamical mass derived in H10. Col (7): ratio of the ionizing to the total stellar mass obtained in this study. Col (8): ratio of the ionizing to the total stellar mass (i.e. dynamical mass) obtained in H10. All masses are given in 10$^6$ \msun.}} \end{tabular} \end{center} \end{small} \end{minipage} \end{table*} The contribution of the ionizing population to the total stellar population for each \hii region (i.e. the young to total stellar mass ratio, m$^{\mathrm{ion}}$/m$_\star$) can be roughly estimated by taking the derived mass of the \starlight fitting as the total mass of the \hii region. Note that the total stellar mass actually represents the stellar mass along the LOS. Therefore, our estimation really represents a lower limit to the percentage. We would like to point out that the uncertainties on the derived total stellar masses (via the 100 realizations of the \starlight fitting for each region) are generally strongly asymmetric. We thus took the $1\sigma$ uncertainties as the last values included within the 68\% on the left ($\sigma^{-}$) and on the right ($\sigma^{-}$) of the mass distribution, centred on the median value. To better estimate the uncertainties on the m$^{\mathrm{ion}}/$m$_\star$ ratio we have used the techniques developed in~\cite{Barlow03,Barlow04}. In short, when an experimental result is represented as $x^{+\sigma^+}_{-\sigma^{-}}$, being $\sigma^+$ and $\sigma^-$ different, a non-symmetric distribution can represent $x$. Among the functions proposed in those papers, we modelled each variable (i.e. mass) using a ``Variable Gaussian'' parametrization. With an asymmetric distribution representing each variable we made a few tens of thousands of Monte Carlo runs for each \hii region using the {\sc idl} routine `genrand', which allows us to obtain random numbers following a given distribution (not necessarily normal) so as to obtain a reliable estimate of the mass ratio with its $\sigma^+$ and $\sigma^-$ uncertainty. The derived m$^{\mathrm{ion}}$/m$_\star$ ratios range from 0.2 to about 7 per cent. A comparison for the circumnuclear regions in NGC 3310 identified in previous studies is shown in Table~\ref{table:comparison_hagele2}. Despite the fact that, with some exceptions, the ratios are similar, the disagreement between ionizing population and total stellar masses separately is evident, up to factors of more than 2 for the nucleus. Masses from the ionizing population reported in H10 were computed using Eq.~\ref{eq:diaz98}. Apart from the systematic introduced by the use of the updated version presented in this study, aperture effects can contribute significantly to the differences in the reported \ha luminosities and EW(\hb\onespace), as Table~\ref{table:comparison_hagele} illustrates. In general, we have obtained higher mass values. In addition, we have generally computed higher total stellar masses because: (i) we have derived the LOS stellar mass; and (ii) H10 derived the total stellar mass of each cluster within an \hii region and then added up all the individual estimates for each region. In our calculations, the intracluster mass (probably from the disc) is included. Still, the ratios reported here and those obtained in H10 span a similar range, being always lower than 10\%. All these values are also similar to those reported in \hii regions and \hii galaxies observed in other studies~\citep{Alonso-Herrero01,Hagele09,Perez-Montero10}. \begin{figure} \centering \includegraphics[angle=90,trim = -1cm -2cm 1cm -1cm,clip=true,width=0.5\textwidth]{figs/HII_pop1.eps} \caption{Radial distribution of the ratio between the stellar mass of the ionizing population and the total stellar mass along the LOS. The values are colour coded according to the \ha surface density flux in \mbox{10$^{-16}$ erg s$^{-1}$ cm$^{-2}$ \AA{}$^{-1}$ arcsec$^{-2}$}. Only data for which an estimate of the ionizing mass via the SED fitting technique is plotted.} \label{fig:HII_pop1} \end{figure} We show in Fig.~\ref{fig:HII_pop1} the radial distribution of this ratio (in terms of percentage) and its relation with the \ha flux surface density. In general, those regions with higher \ha flux surface density are located at smaller radii (with a few exceptions). The radial distribution of the young-to-total-stellar ratio is much more scattered. From the centre and up to about 1.5\reff~(where we cover the complete radial FoV), a 4.5$\sigma$ mild correlation is found, according to the Spearman's rank-order correlation test. However, if we consider the whole radial range, such correlation cease to exist in statistical terms. Given the narrow age range of the ionizing population we can roughly assume that any variation of the ratio between the ionizing population and the total stellar mass relates to a variation in the specific SFR (sSFR). In fact, if we compute the sSFR (just by subtracting the total mass from our estimates of the SFR) and plot it against the radial distance, we obtain a similar plot to that shown in Fig.~\ref{fig:HII_pop1}. Therefore, just by examining this figure we can have some insight on the mass growth in the galaxy disc. In the framework of the inside-out scenario, the SFR should be a strongly varying function of the galactocentric distance.~\cite{Munyoz-Mateos07} studied the radial profiles of sSFR for a sample of 161 nearby spiral galaxies. They found a large dispersion in the slope of these profiles with a slightly positive mean value, which they interpreted as proof of a moderate inside-out disc formation. Although they did not find any clear dependence of the sSFR gradient on the environment, they argued that transitory episodes of enhanced star formation in the inner parts of the disc can lead to a currently smaller SFR scalelength (gradual growth of the size of the disc with time) than in the past. That is, the gradient can hence be weakened or be even negative. It is well known that mergers in general can induce radial mixing processes, such as inflows of external gas on to the central regions and trigger starbursts (e.g.,~\citealt{Barnes96,Rupke10}). As mentioned before, the global starburst in NGC 3310 is likely to have a minor merger origin~\citep{Smith96,Kregel01,Wehner06}. The mild negative gradient of the sSFR in NGC 3310 can well be another signature of a past merger event. This suggests that the minor merger event may be playing an important role in the mass build-up on the bulge, in agreement with recent models~\citep{Hopkins10}. | 14 | 3 | 1403.1817 |
1403 | 1403.3812_arXiv.txt | We investigate the possible occurrence of a Bose-Einstein condensed phase of matter within neutron stars due to the formation of Cooper pairs among the superfluid neutrons. To this end we study the condensation of bosonic particles under the influence of both a short-range contact and a long-range gravitational interaction in the framework of a Hartree-Fock theory. We consider a finite-temperature scenario, generalizing existing approaches, and derive macroscopic and astrophysically relevant quantities like a mass limit for neutron stars. | \label{sec:BECintro} In this work we present a model for a quantum phenomenon with impact on macroscopically large scales by considering the possible occurrence of a Bose-Einstein condensate (BEC) in compact astrophysical objects. Laboratory experiments on cold gases have first confirmed \cite{1995Corn,1995Kett} the existence of a particular state of matter for bosonic particles when cooled down to ultracold temperatures in low-density environments. Originating from Bose's re-derivation of Planck's law of black body radiation \cite{1924Bose}, Einstein predicted this phenomenon employing a new statistics for the distributions of massive bosons in an ensemble, thereby describing a synchronization of the wave functions of all particles in the system \cite{1925Eins}. Velocity-distribution data from experiments show a macroscopic occupation of the ground state, thus demonstrating the existence of a quantum phenomenon with impacts on large scales. \\ Even though the effect is known from laboratory physics, it can be considered in completely different circumstances as well, as for example in compact objects in astrophysics. Generally a BEC is created when the temperature in a system falls below the critical temperature \begin{equation} \label{eq:Tcrit} T_{\mathrm{crit}} = \left[ \frac{n}{\zeta(3/2)} \right]^{2/3} \frac{2\pi \hbar^2}{mk_B} \,, \end{equation} corresponding to the point where the thermal de Broglie wavelength equals the average interparticle distance, so the wave functions of individual particles overlap and synchronize. Rather surprisingly, considering the typical temperatures and densities in astrophysical scenarios extracted from observations, condition~\eqref{eq:Tcrit} seems to be met in some cases of compact objects. A possible example for BECs in compact objects in astrophysics are boson stars - either as an abstract concept of a bosonic field in a spherically symmetric metric \cite{2012Klei}, or as the concrete case of a star consisting of bosonic particles. Helium white dwarfs have been considered as candidates before \cite{2011Benv,2000NagC}, even though due to the ongoing fusion processes inside the star the abundance of objects solely made up of helium is presumably small. Another problem is posed by the ionization of Helium at temperatures higher than about $10^5\, \mathrm{K}$, which makes the theory of a BEC of neutral bosons effectively inapplicable in that case. More realistically, white dwarfs can be described by an approach considering a background lattice of positive ions immersed in a sea of electrons. \\ Alternatively, the existence of BECs in neutron stars has been suggested \cite{2011Cha2}. Neutron stars have been considered firstly by Tolman \cite{1939Tolm} as well as Oppenheimer and Volkoff \cite{1939Oppe}. They investigated a fluid of self-gravitating neutrons, for which the equation of state is determined by Fermi statistics, in the context of general relativity embedded in a spherically symmetric metric, and searched for stable equilibrium configurations of the system. In the scenario assumed by Tolman, Oppenheimer and Volkoff (TOV), the gravitational collapse of a cloud of neutrons is counterbalanced by the degeneracy pressure of the neutrons as a consequence of the Pauli exclusion principle. The maximum stable mass of such a system, the TOV limit, was found to be about $0.7 \,M_{\odot}$ \cite{1939Tolm,1939Oppe}. In contradiction to this original prediction, observations \cite{2010Demo} have found neutron stars with masses up to a value of $2\,M_{\odot}$. Hence, there has been an abundance of proposals and models to explain the observed masses of neutron stars \cite{2007Haen}. The existence of all kinds of states or types of matter in the core of the objects was suggested, reaching from strange baryons over heavy mesons like kaons or pions to quark matter, while the crust of neutron stars is usually assumed to consist of neutrons and electrons \cite{2012Belv}. \\ BECs in neutron stars are feasible despite the fact that neutrons are fermions. A general consensus exists over the fact that neutrons in a neutron star should be in a superfluid phase \cite{2011Page}, i.e. the particles are bound in Cooper pairs and can be treated as composite bosons with an effective mass of $m=2m_n$, which can form a BEC. A microscopically exact way of treating such a system is provided by the theory of a BCS-BEC-crossover \cite{1993Sade,1997Enge}, i.e. a transition from the quantum state of superfluidity (BCS phase) to a Bose-Einstein condensate. The theory describes the pairing mechanism between neutrons, allowing for a coexistence of single neutrons and neutron pairs in a mixed state of Fermi and Bose fluids. The phenomenon has been observed in the laboratory on weakly bound molecules formed by two fermionic atoms \cite{2003Grei}, and has more recently also been applied to the case of nuclear or neutron matter. Calculations in Refs. \cite{2005Astr,2006Mats,2007Marg,2013Sala} show that nuclear forces between nucleons, in particular neutrons, lead to the formation of nucleon pairs, which can be treated as effective bosons in a BEC under appropriate conditions. The phenomenon of nucleon pairing was firstly proposed in 1935 by a phenomenological formula by Weizs\"acker \cite{1935Weiz} in the context of atomic nuclei. Later on, the superfluidity of fermionic particles was formulated microscopically exactly in terms of a BCS-type theory, which was then applied to the case of nucleons inside an atomic core, and by now the treatment of superfluidity in nuclear matter is well established \cite{2010Brin}. Superfluidity in the context of neutron stars can be described in the same way as in atomic nuclei - physically, neutron stars are nothing but a gigantic atomic nucleus, consisting of neutrons and protons which are subject to the same pairing effect as in atomic nuclei. \\ In the present work, we use several assumptions and simplifications which differ from the picture of an atomic nucleus. Firstly, we assume the system to be purely made up by neutrons, and neglect the presence of other particles as protons and electrons. Further, we approach the system in a purely phenomenological way and treat the paired neutrons as effective bosons which form the BEC. There is no fermionic component in our system, i.e. we assume the pairing of the neutrons as strong enough to be able to consider them as perfectly bosonic. Typical densities in the center of neutron stars lie around $10^{14} \,\mathrm{g}/\mathrm{cm}^3$, whereas in the outer regimes densities decrease to about $10^{6} \,\mathrm{g}/\mathrm{cm}^3$. Assuming an effective boson mass of $m=2m_n$, according to~\eqeqref{eq:Tcrit} this corresponds to critical temperatures of $10^{10}\, \mathrm{K}$ to $10^{5}\, \mathrm{K}$, respectively. Thus it is potentially possible during the initial stages of the evolution of a neutron star to fulfill condition~\eqref{eq:Tcrit} and consider the presence of a neutron-pair BEC. \\ Given that the known scattering length of neutrons in nuclear matter is quite large, the interior of neutron stars is actually better described by the unitary regime, i.e. the transition phase between the BCS and the BEC limits. It is clear that for a realistic description it is necessary to consider also the single neutrons in the star and set up the exact theory of the BCS-BEC crossover. The cases of a pure BCS phase and a pure BEC phase then have to result as limits of this general crossover theory. In the literature, neutron stars are usually described in one of the limiting states, i.e. the BCS fluid. In this work we will investigate the opposite limit of a BEC fluid as a first step towards the unifying crossover theory. \\ ~\\ Systems of self-gravitating bosonic (and fermionic) particles have already been considered some time ago in Ref. \cite{1969Ruff}. For the case of Newtonian gravity, the investigations have resulted in unstable configurations for bosons, which could only be stabilized by the inclusion of general relativistic effects. However, in contrast to our model the particles in Ref. \cite{1969Ruff} are assumed to be free, only subject to gravitational interactions. In our model, contact interaction, i.e. hard shell scattering between bosons, will be employed to stabilize the system against gravitational collapse. Thus, even for zero temperature with vanishing thermal pressure and in the case of Newtonian gravity, contact interaction provides the necessary pressure to counterbalance gravity. \\ A system of bosons in a Bose-Einstein condensed phase with contact and gravitational interactions, such as the system we are considering, for the case of zero temperatures has recently been treated in Ref. \cite{2011Cha2} and applied to the example of superfluid neutron stars. A generalization to a BEC at finite temperatures was recently worked out in Ref. \cite{2012Hark}, but then applied to the example of a dark matter BEC in a Friedmann-Robertson-Walker universe. The theory of Bose-Einstein condensation for the case of bosonic dark matter was also considered by other authors, see Refs. \cite{2011Cha1,2011Hark,2012Liet}. Due to the widely unknown nature and properties of dark matter, it is, however, a rather speculative field, and the effects of the presence of a Bose-Einstein condensate of dark matter particles in contrast to thermal phase dark matter are difficult to detect, most likely only by the gravitational lensing behaviour of dark matter halos. The environmental conditions in dark matter halos are supposedly suitable for the existence of a BEC of dark matter particles though, assuming that dark matter is bosonic \cite{2011Mato}. \\ The scenario of a BEC at finite temperatures has never been extended to the example of compact objects, so the present work represents the first contribution in this direction. In~\secref{sec:T0} we first review the zero-temperature case as presented in Ref. \cite{2011Cha2}, before outlining the contents of the main body of the paper which contains our own work in~\secref{sec:presentwork}, including a motivation for the specific choice of treatment. \subsection{Zero-temperature case} \label{sec:T0} A BEC subject to contact and gravitational interaction has been formulated in Ref. \cite{2011Cha2} via a Heisenberg equation for the bosonic field operator $\hat{\Psi}(\mb{x},t)$ representing bosons with mass $m$. The corresponding second-quantized Hamiltonian operator for this system reads \begin{eqnarray} \label{eq:Ham} \hat{\mathcal{H}} &=& \int d^3x \,\hat{\Psi}^{\dag}(\mb{x},t) \bigg[ -\frac{\hbar^2}{2m} \Delta - \mu \\ &~& ~~~~~~~~+ \frac{1}{2} \int d^3x' \, \hat{\Psi}^{\dag}(\mb{x}',t) U(\mb{x},\mb{x}') \hat{\Psi}(\mb{x}',t) \bigg] \hat{\Psi}(\mb{x},t) \,, \nonumber \end{eqnarray} where $\mu$ denotes the chemical potential in the grand-canonical treatment, and the interaction term $U(\mb{x},\mb{x}')$ in the presence of contact and gravitational interaction reads \begin{equation} \label{eq:interactions} U(\mb{x}-\mb{x}') = g\, \delta(\mb{x}-\mb{x}') - \frac{G m}{|\mb{x}-\mb{x}'|}\,. \end{equation} Here $g = 4\pi \hbar^2 a/m$ denotes the strength of the repulsive contact interaction, with $a$ being the s-wave scattering length of the bosons in the system, while $G$ is Newton's gravitational constant. The resulting Heisenberg equation of motion defined from the Hamiltonian~\eqref{eq:Ham} reads \begin{eqnarray} \label{eq:Heisenberg} && i\hbar \frac{\partial}{\partial t} \hat{\Psi}(\mb{x},t) = \bigg[ -\frac{\hbar^2}{2m} \Delta \\ &&~~~~~+ g \big|\hat{\Psi}(\mb{x},t)\big|^2 -\int d^3x' \frac{G m^2}{|\mb{x}-\mb{x}'|} \, \big|\hat{\Psi}(\mb{x},t)\big|^2 \bigg] \hat{\Psi}(\mb{x},t) \,. \nonumber \end{eqnarray} To implement the presence of a condensate as well as of thermal and quantum fluctuations, the field operator can be split into a mean field condensate and fluctuations. For the zero-temperature case, where no thermal fluctuations are present, and weak enough interparticle interactions such that quantum fluctuations can be neglected as well, a mean field condensate is assumed, represented by the wave function \begin{equation} \Psi(\mb{x},t) = \langle \hat{\Psi}(\mb{x},t) \rangle \,. \end{equation} The Heisenberg equation~\eqref{eq:Heisenberg} then reduces to the Gross-Pitaevskii (GP) equation, \begin{equation} \label{eq:GP} i\hbar \frac{\partial}{\partial t} \Psi(\mb{x},t) = \bigg[ -\frac{\hbar}{2m} \Delta + g \left|\Psi(\mb{x},t)\right|^2 + \Phi(\mb{x},t) \bigg] \Psi(\mb{x},t) \,, \end{equation} where we have defined the Newtonian gravitational potential as \begin{equation} \Phi(\mb{x},t) = -\int d^3x' \frac{G m^2}{|\mb{x}-\mb{x}'|} \, \big| \Psi(\mb{x}',t)\big|^2 \,. \end{equation} Assuming a Madelung representation of the condensate wave function, i.e. using an ansatz featuring an amplitude and a phase, \begin{equation} \label{eq:ansatz} \Psi(\mb{x},t) = \sqrt{n_{\mb{0}}(\mb{x},t)} ~ e^{iS(\mb{x},t)} \,, \end{equation} we can identify the density of the condensate as \begin{equation} n_{\mb{0}}(\mb{x},t) = \left|\Psi(\mb{x},t)\right|^2 \,. \end{equation} With~\eqref{eq:ansatz}, the Gross-Pitaevskii equation~\eqref{eq:GP} decomposes into two equations by setting its real and imaginary part to zero separately. This results in two coupled hydrodynamic equations, i.e. the continuity equation and the Euler equation for the density $n_{\mb{0}}$ and for the velocity field $\mb{v}=\hbar \,\nabla S/m$, \begin{subequations} \begin{align} \frac{\partial n_{\mb{0}}}{\partial t} + \nabla\cdot (n_{\mb{0}} \,\mb{v}) &= 0 \,,\\ m\,n_{\mb{0}} \left[\frac{d\mb{v}}{dt} + (\mb{v}\cdot \nabla) \,\mb{v} \right] &= - \frac{g}{2} \nabla n_{\mb{0}}^2 - m\,n_{\mb{0}} \,\nabla \Phi - \nabla\cdot \sigma^Q_{ij}\,. \label{eq:Euler} \end{align} \end{subequations} The last term in the Euler equation contains the so-called quantum stress tensor \begin{equation} \sigma^Q_{ij} = \frac{\hbar^2}{4 m}\, n_{\mb{0}} \,\nabla_i \nabla_j \ln n_{\mb{0}} \,, \end{equation} which represents a quantum contribution originating from the Laplacian term in the Gross-Pitaevskii equation. Commonly the Thomas-Fermi (TF) approximation is adapted, in which the kinetic term is neglected, and the quantum stress tensor is dropped. Also all other time dependences are neglected from here on since we restrict ourselves to static configurations only. \\ By comparison of~\eqeqref{eq:Euler} with the general form of the Euler equation of a fluid, we can identify the pressure of the condensate from the first term on the RHS as \begin{equation} p = \frac{g}{2} \,n_{\mb{0}}^2\,. \end{equation} It is non-zero even for zero temperature, which is a direct consequence of the presence of the contact interaction. For zero contact interaction, the pressure vanishes as well, as should be the case for a free Bose gas \cite{1980Land}. Defining the mass density of the system as \begin{equation} \rho = m\, n_{\mb{0}} \, \end{equation} leads to the equation of state \begin{equation} \label{eq:EoSwithrho} p = \frac{g}{2m^2} \,\rho^2\,. \end{equation} This is a polytropic equation of state, in general written as \begin{equation} \label{eq:EoS} p = \kappa \, \rho^{\gamma} \,, \end{equation} where $\gamma = 1 + 1/n$ defines the polytropic index $n$, and $\kappa$ represents a suitable constant of proportionality. In the present case of a BEC we have $n=1$ and $\kappa = 2\pi \hbar^2 a / m^3$. \\ Neglecting all time dependent terms in~\eqeqref{eq:Euler} and employing the TF approximation leads to \begin{equation} \label{eq:Euler2} \nabla p = -\rho\, \nabla \Phi\,. \end{equation} Combining \eqsref{eq:EoSwithrho},~\eqref{eq:Euler2} and the Poisson equation for the gravitational potential, \begin{equation} \label{eq:Poisson} \nabla^2 \Phi = -4 \pi G \, \rho \,, \end{equation} results in the so-called Lane-Emden equation, a second-order differential equation for the mass density of the condensate $\rho$ as a function of the radial coordinate $r$. With the substitutions $\chi = \left( \rho / \rho_c \right)^{1/n}$, where $\rho_c$ is the central condensate density, as well as the dimensionless length scale $\xi = r\, \sqrt{4\pi G / \left[ \kappa (n+1) \rho_c^{-1+1/n} \right]}$, the Lane-Emden equation reads \begin{equation} \frac{1}{\xi^2} \frac{d}{d\xi}\left( \xi^2 \,\frac{d\chi}{d\xi} \right) = -\chi^n \,. \end{equation} For $n=1$ the system can be solved analytically, yielding the corresponding mass limit straightforwardly. The exact solution in this case is found as \begin{equation} \label{eq:LaneEmden} \chi \left(\xi\right) = \frac{\sin \xi}{\xi} \,, \end{equation} which gives the radius $R_0$ of the star by the condition $\chi \left(\xi_0 \right) =0$, i.e. $\xi_0 = \pi$, yielding the condensate radius \begin{equation} \label{eq:R0ChavHark} R_0 = \pi \, \sqrt{\frac{\hbar^2 a}{G m^3}} \,. \end{equation} The mass of the object can then be obtained by integrating the density profile up to that point, \begin{equation} \label{eq:ChavHarkMass} M = 4 \pi^2 \, \left( \frac{\hbar^2 a}{G m^3} \right)^{3/2} \rho_c \,, \end{equation} and depends on the condensate density at the center of the star $\rho_c$. These results were already obtained in Ref. \cite{2011Cha2} and applied to the example of neutron stars. Some physical criterion has to be invoked in order to determine a limit on the maximum mass of the configuration. A limit on the central density can follow from demanding that the adiabatic speed of sound in the fluid at the center of the star be bound by the speed of light. Alternatively a limiting mass can be calculated from the criterion of gravitational collapse, derived from the Schwarzschild radius of the configuration. In Ref. \cite{2011Cha2}, the Schwarzschild limit resulted in a maximum mass of about $2.3\, M_{\odot}$. \\ We would like to note that the results for the equation of state can also be used in more general versions of the theory, i.e. when extending the treatment to general relativistic settings. Considering the Einstein equations with an ansatz for a spherically symmetric metric leads to the Tolman-Oppenheimer-Volkoff equation \cite{1939Tolm,1939Oppe}, \begin{equation} \label{eq:TOV} \frac{dP(r)}{dr}= -\frac{G\left[ \rho(r) + \frac{P(r)}{c^2} \right] \left[ \frac{4\pi P(r) r^3}{c^2} + M(r) \right]}{r^2 \, \left[1-\frac{2G M(r)}{rc^2}\right]}\,. \end{equation} This equation, together with an equation of state $p=p(\rho)$ as e.g. given by~\eqref{eq:EoSwithrho}, and the mass conservation equation \begin{equation} \label{eq:mass} \frac{dM(r)}{dr} = 4\pi \rho(r) \,r^2 \end{equation} completely determines the system in question. In this way, the equation of state extracted from the above procedure can be used in the context of general relativity as well. This was worked out for the zero-temperature condensate in Ref. \cite{2011Cha2} in addition to the Newtonian case. Alternatively, the equation of state might serve as an input parameter in astrophysical simulations for compact objects which do not consider the physics inside the star from first principles but approach the issue on a more phenomenological level \cite{2001Latti}. \subsection{Finite-temperature case applied to neutron stars} \label{sec:presentwork} In the work presented in this paper, we carry out a generalization of the above treatment, aiming at deriving a theory of a Bose-Einstein condensate subject to repulsive contact interaction and attractive gravitational interaction for the case of finite temperatures. A first step in this direction in the framework of the Heisenberg equation~\eqref{eq:Heisenberg} was performed in Ref. \cite{2012Hark}, where the field operator is split into a mean field contribution and a fluctuating term, i.e. $\hat{\Psi}(\mb{x},t) = \langle \hat{\Psi}(\mb{x},t) \rangle + \hat{\psi}(\mb{x},t)$. However, the authors solely calculated the equation of state of condensate and thermal density, and applied them to the example of dark matter, deriving the resulting expansion behaviour of the universe in a cosmological scenario. In our case however, we investigate the behaviour of a self-gravitating Bose-Einstein condensate in compact objects, compute the density profiles of a BEC star at finite temperatures and derive relevant macroscopic quantities, which can then be compared to astrophysical observations. \\ To do so, we first need to determine the appropriate treatment for the scenario in question. One aspect to be reflected upon is the gravitational framework of the theory, i.e. the choice between Newtonian gravity and general relativity. Estimating the typical size scales of the system and comparing them to their corresponding Schwarzschild radii, \begin{equation} r_S = \frac{2G M}{c^2} \,, \end{equation} shows whether the general relativistic regime is reached or Newtonian gravity suffices for the description of the gravitational interactions. Furthermore, we need to consider the typical velocities of particles in the system in order to be able to distinguish between non-relativistic and relativistic dispersion relations. From the typical temperatures in compact objects we can estimate the particle velocities from \begin{equation} v = \sqrt{\frac{2k_B T}{m}} \,, \end{equation} and a comparison with the speed of light $c$ will determine the appropriate treatment. For $v \ll c$, we can resort to a non-relativistic quantum-mechanical treatment with a Schr\"o\-din\-ger-type equation as outlined above, whereas for $v \sim c$, it would be necessary to formulate the theory in terms of a relativistic description with the Klein-Gordon equation. \\ The case of a neutron star can at least partly be treated with a non-relativistic dispersion relation, since typical temperatures range from $10^{11} - 10^{12} \, \mathrm{K}$ at the initial stages, and decrease down to $10^6 \,\mathrm{K}$ after several years, corresponding to thermal velocities of $0.09 \, c$ and $0.3\cdot 10^{-3}\, c$, respectively. As for the gravitational theory, the typical size of a neutron star is estimated to be about $12\, \mathrm{km}$, and at the observed masses between $1 - 2 \,M_{\odot}$, typical radii are only about $2 - 4$ times larger than the respective Schwarzschild radii, which means that a general relativistic description should be necessary. \\ Despite these numbers, for the sake of simplicity here we develop a theory which is non-relativistic in both regards, i.e. a model for a non-relativistic BEC in Newtonian gravity, and evaluate later to what extent the theory is applicable to neutron stars. We treat the system in the framework of a Hartree-Fock theory, and set up self-consistency equations for the densities of the BEC and the thermal cloud of excited atoms. To this end we start from a general Hamiltonian and derive the governing Hartree-Fock equations for the wave functions of the particles in the ground state and in the thermally excited states. The detailed derivations of this part are shown in the appendix, as the Hartree-Fock theory for bosons has been worked out in the literature before, see e.g. Ref. \cite{1997Oehb}. Still for the general case of a Hamiltonian with unspecified interactions $U(\mb{x},\mb{x}')$ we then consider the semi-classical limit of the theory and derive the equations for the macroscopic densities of condensate and thermal excitations. In~\secref{sec:CG}, we start from the respective equations of motion in the semi-classical approximation for the case of contact and gravitational interaction. We show the numerical solution of the system of equations in~\secref{sec:Num}, and then derive astrophysical consequences and quantities in~\secref{sec:astro}, like the size scales and maximum mass of the system and the equation of state of matter inside the star. We investigate the physical viability of the system and obtain a limit for the maximally possible masses in analogy to the TOV-limit. In~\secref{sec:Concl} ultimately, we comment on the significance of our work in the astrophysical context and conclude the part with an outlook to further investigations. \\ ~\\ ~\\ | \label{sec:Concl} The work presented in this paper investigated the occurrence of a BEC phase in compact astrophysical objects such as neutron stars. A careful consideration of the typical environments showed that the neutrons inside neutron stars are likely to form pairs due to the strong nuclear forces between them, similarly to an atomic nucleus, i.e. are present in a superfluid state. These neutron pairs are considered as the effective bosonic elementary particle in the BEC. The model presented in this article starts from this simplified picture of very strongly bound neutron pairs as perfect bosons, and does not take into account the presence of single neutrons or other particle species. Our work represents a first step towards an alternative description of neutron stars based on the phenomenon of BCS-BEC-crossover in nuclear or neutron matter, and increasing efforts by theoreticians to consider these scenarios validate our efforts to compute observable quantities that can be compared to observations. \\ We would like to emphasize though that a physically more exact treatment would require the investigation of the BCS-BEC crossover itself along the lines of Refs. \cite{2005Astr,2006Mats,2007Marg,2013Sala}, not just the BEC limit. The full crossover would unify the different physical behaviour of the BCS and BEC regimes into one theory, and would apply to both fermion and boson stars simultaneously in the respective limits of the theory. The treatment we have set up must result from the complete crossover theory as the BEC limit, and should thus only be regarded as an approximate solution to the issue. \\ In the BEC limit, the system was treated within the framework of a Hartree-Fock theory, starting from a Hamiltonian including contact and gravitational interactions between the particles. Self-consistency equations determining the wave functions of condensate and thermal fluctuations were obtained from the variation of the free energy of the system. In analogy to these derivations, the semi-classical limit of both the free energy and the Hartree-Fock equations was formulated, describing the system in terms of the densities of condensate and thermal fluctuations. The resulting equations were processed further up to a certain point, before the solutions for both the profiles of condensate and thermal density as a function of the radial distance from the center of the star were obtained by numerical procedures. Integrating out the obtained densities leads to the total mass of the system, along with other quantities of astrophysical consequences. From our model, we have obtained objects with radii of about $6\, \mathrm{km}$, masses of about $2.3\, M_{\odot}$ and central densities around $\rho_c \simeq 10^{16} \mathrm{g}/ \mathrm{cm}^3$, which approximately coincide with the typical values to be expected for neutron stars. Since from the zero-temperature limit and the subsequent analysis for finite temperatures, the radial extension of the system was found to be around $6\, \mathrm{km}$, decreasing with a temperature dependence proportional to $T^{3/2}$, we were able to employ the Schwarzschild criterion of gravitational collapse in order to derive a mass limit on the neutron stars, which lead to a maximum mass of about $2.3\, M_{\odot}$, decreasing proportional to $T^{3/2}$ as well. The order of magnitude of these results seems plausible considering observational evidence. \\ As already stated at the outset, the theory contains several simplifications, introduced in order to make the system more treatable. Some of them were mathematically motivated, whereas others have been general physical assumptions within our model from the beginning. We considered a phenomenon mainly known from ultracold quantum gases in laboratory scenarios and applied an established mathematical treatment to a rather unusual field of application, namely the large scales of astrophysics. It is therefore to be expected that simplifications and idealizations are necessary in order to obtain results. \\ On the mathematical side, we have carried out a Hartree-approximation for the gravitational part of the interactions, which eliminated the bilocal Fock terms in the expressions. The inclusion of these terms could perhaps be treated in form of an appropriate local density approximation. \\ The theory is limited to low temperatures, where by definition the particles in the thermal phase are few and the condensate dominates. However, the necessity to develop a more complete theory featuring a smoother description of the high-temperature transition region between condensate and thermal state of the system, incorporating the breakdown of the condensate as a phase transition, is obvious. \\ A further assumption of the theory is a spatially constant temperature throughout the star, which is unlikely to hold in realistic physical situations. This is closely connected to the breakdown of the condensate towards the outer layers of the star, where the density and thus the critical temperature decrease, and at a certain point the condition $T < T_{\mathrm{crit}}$ for the formation of a condensate cannot be met anymore. The inclusion of spatial variation of temperature in the self-consistency equations would thus allow for a much more detailed and realistic model. \\ Finally, we would like to comment on the possibility of rotation. It is presumed that most of the compact objects in the universe rotate, since an evolution of a completely static system is highly unlikely in an initially hot and violent universe. Rotation of BECs in laboratory environments have been shown to exhibit new phenomena like the formation of vortices of normal phase matter inside the BEC \cite{2009Fett}, growing with increasing temperature until the breakdown of condensate at the transition to the thermal phase. The existence of a vortex in a Bose star, or, more realistically, a grid of vortices, should be assumed, which grow in width and finally cause a transition to a normal phase Bose star with increasing temperature. The inclusion of rotation is expected to lead to a destabilization of the system due to the presence of tidal forces, and thus should lead to a higher maximum mass counterbalancing the increased outwards forces. Further, rotation could potentially help to explain dynamical phenomena observed in neutron stars, like e.g. glitches in the rotation frequency, and would provide further means to compare our results to observations. \\ Thus there is a large number of possibilities to generalize and extend the present work. | 14 | 3 | 1403.3812 |
1403 | 1403.1356_arXiv.txt | Optimised population synthesis provides an empirical method to extract the relative mix of stellar evolutionary stages and the distribution of atmospheric parameters within unresolved stellar systems, yet a robust validation of this method is still lacking. We here provide a calibration of population synthesis via non-linear bound-constrained optimisation of stellar populations based upon optical spectra of mock stellar systems and observed Galactic Globular Clusters (GGCs). The MILES stellar library is used as a basis for mock spectra as well as templates for the synthesis of deep GGC spectra from \citet{S05}. Optimised population synthesis applied to mock spectra recovers mean light-weighted stellar atmospheric parameters to within a mean uncertainty of 240 K, 0.04 dex, and 0.03 dex for \Teff, \logg, and [Fe/H], respectively. We use additional information from HST/ACS deep colour-magnitude diagrams (CMDs) from \citet{Ata} and literature metallicities to validate our optimisation results on GGCs. Decompositions of both mock and GGC spectra confirm the method's ability to recover the expected mean light-weighted metallicity in dust-free conditions ($E(B-V) \lsim 0.15$) with uncertainties comparable to evolutionary population synthesis methods. Dustier conditions require either appropriate dust-modelling when fitting to the full spectrum, or fitting only to select spectral features. We derive light-weighted fractions of stellar evolutionary stages from our population synthesis fits to GGCs, yielding on average a combined $25\pm6$ per cent from main sequence and turnoff dwarfs, $64\pm7 $ per cent from subgiant, red giant and asymptotic giant branch stars, and $15\pm7 $ per cent from horizontal branch stars and blue stragglers. Excellent agreement is found between these fractions and those estimated from deep HST/ACS CMDs. Overall, optimised population synthesis remains a powerful tool for understanding the stellar populations within the integrated light of galaxies and globular clusters. | \label{sec:Intro} Fundamental information on the physical processes which dominate the formation and evolution of galaxies can be gleaned from the study of their stellar populations. Early studies of galaxies' stellar content relied on the technique of \textit{population synthesis}, wherein the integrated spectrum of a galaxy is decomposed into a sum of suitably-weighted spectra of individal stars with known basic properties such as temperature, surface gravity, and metallicity \citep{spinrad, faber, oconnell, pickles}. In order to obtain information such as age or star formation history, stellar evolutionary models should then be applied subsequent to the decomposition. Advances in our knowledge of stellar evolution have however enabled a new technique for stellar population analyses, so-called \textit{evolutionary population synthesis} \citep{Renzini81,Buzzoni89, Brucha93,Maraston98}. By combining individual stellar spectra with isochrones and an initial mass function, integrated spectra of entire galaxies (or stellar clusters) can then be constructed over a wide range of ages and metallicities. Thus, evolutionary population synthesis folds in evolutionary models as part of the spectral decomposition. The power of the latter technique to reduce the degrees of freedom in stellar population analyses resulted in the demise of the former. However, various uncertainties affecting current stellar evolution models \citep[e.g. thermally-pulsating asymptotic giant branch, horizontal branch, and blue straggler stars;][]{Maraston07,ConroyGunn09}, especially pertaining to the brightest phases of stellar evolution, are cause for concern in any application of evolutionary population synthesis. For instance, the presence of blue horizontal branch stars in elliptical galaxies, coupled to the lack of a predictive theory for their origins, can be misinterpreted as their having recently experienced a burst of star formation \citep{Maraston&Thomas00}. Population synthesis, on the other hand, should in principle be free from the outshining effect that uncertain phases of stellar evolution have on stellar population analyses. We therefore expect this technique to be able to unravel at once the contributions of all stars to the integrated light of a stellar system. In light of these issues and the availability of exceptional computing power, we wish to re-examine and validate the population synthesis optimisation method as a means to provide estimates of the stellar content of unresolved systems independent of any assumed stellar evolution model. And while the latter is true, it should still be noted that the coverage in age, metallicity, and surface gravity of the adopted stellar basis may have a significant impact on the final spectral decompositions \citep{Koleva2008}. Before applying the population synthesis technique to galaxy spectra, it must be rigorously tested on data samples for which the underlying stellar contents are known. In this paper, we use both mock and observational data to test the technique under realistic (imperfect) observing conditions. Owing to the existence of deep integrated spectra \citep[hereafter S05]{S05} and colour-magnitude diagrams \citep[hereafter CMDs;][]{Ata} as well as high-resolution star-by-star spectroscopic abundances (\citealt{Harris}; \citealt{Roediger2014}, and references therein) for them, Galactic globular clusters (GGCs) provide the best astrophysical test bed for population synthesis. Specifically, we test the ability of the technique to recover the luminosity-weighted distributions of stellar atmospheric parameters (effective temperature, surface gravity, metalliticy, and colour), as well as the contributions of various evolutionary phases to the integrated light of GGCs which can be directly validated with corresponding estimates based on CMDs. In doing so, we identify regions of parameter space (both observational and physical) where the technique may fail to reproduce known stellar system data. It should be noted that, without the inclusion of a stellar evolutionary model, population synthesis cannot derive evolutionary properties of stellar systems such as age and star formation histories; properties that we do not attempt to measure in this paper. To our knowledge, no study of this kind has addressed the reliability of population synthesis methods using both mock and real data as constraints. \citet{Koleva2008} performed a similar study to our own using {\it evolutionary} population synthesis on the same S05 GGC spectra used here. We will show below that our population synthesis method is just as reliable in the determination of GGC metallicity despite the lack of stellar evolution modelling. The computational engine central to our numerical decompositions is a non-linear bound-constrained optimisation. Similar spectral decompositions of stellar systems via constrained optimisation have been applied before \citep[e.g.][]{Macarthur09, CidFernandes05, Walcher06}. Other inversion methods used to fit stellar spectra or SSP models to integrated spectra have also been reported recently by, e.g. \citet{Vergely2002}, \citet{Moultaka05}, \citet{Ocvirk06}, \citet{tojeiro07}, \citet{Koleva2008}, and \citet{koleva2009}. The organization of the paper is as follows. In \se{libs}, we present our libraries of GGC and stellar spectra. In \se{Optimisation}, we describe the optimisation algorithm used for decomposing mock and observed integrated spectra into sums of individual stellar spectra, as well as establish the typical level of random and systematic errors inherent to any given decomposition. We then apply our algorithm in \se{popsynth} to the GGC integrated spectra of S05 to determine the fractional contributions (by light) of stellar parameters (effective temperature, surface gravity and metallicity) for each cluster. These fractions in turn yield estimates of each cluster's light-weighted metallicity and stellar evolutionary budget. \se{met} and \se{CMD} present a comparison against independent constraints. Our discussion and conclusions are presented in \se{conc}, followed by two appendices. \ap{AppendixA} includes our reconstruction of each GGC spectrum analyzed in this paper. Finally, deep CMDs for the 24 S05 GGCs in common with the HST/ACS database of \citet{Ata}, along with their breakdown into the various stellar evolutionary zones, are presented and compared with CMDs derived from population synthesis in \ap{AppendixC}. | \label{sec:conc} We have tested the method of non-linear optimisation (population synthesis) to decompose the integrated spectra of stellar systems into distributions of fundamental stellar parameters. To this end, we have used the spectral MILES library \citep{MILES} to construct a suitable basis for the optimisation. Our decomposition method was tested on mock spectra constructed from the spectral library basis, yielding relative uncertainties of 20 per cent in the light fractions and absolute total light noise levels of 5 per cent or less, for a given star. The stellar atmospheric parameters \Teff, \logg, and [Fe/H] of mock spectra constructed from stars outside our stellar basis were also extracted with great accuracy by our optimisation technique. The mean errors between mock and fitted atmospheric parameters are 240 K, 0.04 dex, and 0.03 dex for \Teff, \logg, and [Fe/H], respectively. Having established the reliability of our spectral decomposition method, we applied our code to the individual integrated spectra of 41 Galactic globular clusters from the collection of \citet{S05}. These spectra were decomposed into relative fractions (by light) of a suitably chosen basis of stellar spectra from the MILES library. The light-weighted GGC metallicities obtained from population synthesis agree well with those of \citet{Harris} and our own literature compilation \citep{S05} when an appropriate reddening model is included in the decomposition. In the absence of such a model, good agreement for highly reddened clusters is only found when the continuum is removed (i.e. only prominent absorption features enter the fit). The decompositions based on our optimised population synthesis were compared with CMD data of the 24 S05 GGCs which overlap with those from \citet{Ata}. Our CMD analysis yielded light-weighted luminosity fractions for various stellar evolutionary stages as well as their $V-I$ colour distributions. We found superb agreement between these quantities and the luminosity fractions derived from our population synthesis optimisations. The extracted spectroscopic luminosity fractions are reported in the abstract and in \Table{lumFracTableComp} are compared against similar values from CMDs. Overall, we find the technique of numerical optimisation to be a reliable tool for extracting the mean metallicity and light fractions of stellar populations in unresolved stellar systems. Some caveats pertaining to the depth of the spectroscopic data and the line of sight reddening must be taken into consideration. | 14 | 3 | 1403.1356 |
1403 | 1403.3679_arXiv.txt | In this work the results from the quantum process of matter creation have been used in order to constrain the mass of the dark matter particles in an accelerated Cold Dark Matter model (Creation Cold Dark Matter, CCDM). In order to take into account a back reaction effect due to the particle creation phenomenon, it has been assumed a small deviation $\varepsilon$ for the scale factor in the matter dominated era of the form $t^{\frac{2}{3}+\varepsilon}$. Based on recent $H(z)$ data, the best fit values for the mass of dark matter created particles and the $\varepsilon$ parameter have been found as $m=1.6\times10^3$ GeV, restricted to a 68.3\% c.l. interval of ($1.5<m<6.3\times10^7$) GeV and $\varepsilon = -0.250^{+0.15}_{-0.096}$ at 68.3\% c.l. For these best fit values the model correctly recovers a transition from decelerated to accelerated expansion and admits a positive creation rate near the present era. Contrary to recent works in CCDM models where the creation rate was phenomenologically derived, here we have used a quantum mechanical result for the creation rate of real massive scalar particles, given a self consistent justification for the physical process. This method also indicates a possible solution to the so called ``dark degeneracy'', where one can not distinguish if it is the quantum vacuum contribution or quantum particle creation which accelerates the Universe expansion. | The idea of an accelerating universe is indicated by type Ia Supernovae observations \cite{SN,ast05}, and from a theoretical point of view, a hypothetical exotic component with large negative pressure may drive the evolution in an accelerating manner. This exotic component is usually termed quintessence or dark energy and represents about 70\% of the material content of the universe (see \cite{reviewDE} for a review). The simplest example of dark energy is a cosmological constant $\Lambda$ \cite{weinberg,padmana,martin}, and recently the 7 year WMAP \cite{wmap7} have indicated no deviation from the standard $\Lambda$-Cold Dark Matter ($\Lambda$CDM) model. Nevertheless, recently a new kind of accelerating cosmology with no dark energy has been investigated in the framework of general relativity, called Creation Cold Dark Matter (CCDM) \cite{lima01,limafernando,debnath,RoanyPacheco10,LJONote,JesusEtAl11}. In this scenario the present accelerating stage of the universe is powered by the negative pressure describing the gravitational particle creation of cold dark matter particles, with no need of a dark energy fluid. Such phenomenological models are constructed by giving a specific form to the creation rate but with no further physical grounds. Here we present a creation rate derived from a quantum mechanical particle creation process for real massive scalar fields and we constrain the mass of the field in order to satisfy the observational data. This way, our model has the advantage to be self consistent from first principles. As far as we know it is the first time that a real quantum process of matter creation is analysed in the context of CCDM model. Our analysis can be seen as a first approximation of the full quantum creation process, as it takes into account the effect of creation into the evolution of the scale factor as a second order effect, which can be understood as a kind of back reaction effect in the expansion. The nature and origin of the dark matter (DM) is still a mystery (see \cite{DMrev,bookDM} for a review and \cite{tenpoint} for a ten-point test that a new particle has to pass in order to be considered a viable dark matter candidate), thus such accelerating cold dark matter models have the advantage of explaining the present stage of acceleration of the Universe and the origin of the dark matter, two of the main challenges of the present cosmology. From a quantitative point of view, the search for candidates to particles of DM has increased in the context of new theories beyond the standard model of particle physics\footnote{For a good reference, see chapters 7 to 12 of \cite{bookDM}. According to the theory of Big Bang Nucleosynthesis (BBN), the simplest and most plausible form of non-baryonic cold dark matter particle are the WIMPs (Weakly Interacting Massive Particles). The determination of the relic density for the WIMPs depends on the evolution of the universe before BBN, and if its mass is $m>100$ MeV it could freeze out before BBN and would be the earliest remnants of cold dark matter in the universe. A specific kind of WIMP particle is the WIMPZILLA, a very massive relic from Big Bang, that might be produced at the end of inflation by the gravitational creation of matter during the accelerated expansion. If its mass is about $10^{13}$ GeV it might be the dark matter in the universe. Supersymmetric particles are also candidates to dark matter in models beyond the Standard Model, since that cold dark matter are predicted in a very natural way in models of supersymmetry. The Lightest Supersymmetric Particles (LSP) as neutralino and gravitino are some kinds of particles expected from these models. For LSP particles a typical mass range is 50-1000 GeV. Theories based on Kaluza-Klein (KK) parity in Universal Extra Dimension (UED) model leads to masses of about 500-1500 GeV. For theories based on warped extra dimensions, the Lightest $Z_3$ Particle (LZP) model predicts a mass of about 20 GeV - 1 TeV. There are also non-WIMP dark matter candidates, as the axions and sterile neutrinos. Axions have a double motivation in astroparticle models since they solve the strong CP problem and are also candidate to dark matter. Although being a good candidate, several constraints imposed by different experiments and models ties the axion mass to about 1 eV or $10^{-3}$ eV, a very tiny mass. The sterile neutrino is also very light, with mass of about 1-100 keV. From these models we see that the mass of dark matter particles can be accommodated in a large spectrum of values for different theories.} The first self-consistent macroscopic formulation of the matter creation process was presented in \cite{Prigogine} and formulated in a covariant form in \cite{CLW}. In comparison to the standard equilibrium equations, the process of creation at the expense of the gravitational field is described by two new ingredients: a balance equation for the particle number density and a negative pressure term in the stress tensor. Such quantities are related to each other in a very definite way by the second law of thermodynamics. In particular, the creation pressure depends on the creation rate and may operate, at level of Einstein's equations, to prevent either a space-time singularity \cite{Prigogine,AGL} or to generate an early inflationary phase \cite{LGA}. The quantum process of particle creation has been studied by several authors \cite{davies,fulling,grib,mukh2,partcreation,staro,pavlov01,pavlov02,gribmama02,fabris01} in the last five decades, and the results are well known. Recently the gravitational fermion production in inflationary cosmology was revisited for both the large and the small mass regimes \cite{chung}. In this article we analyse results for the rate of creation of real massive scalar particles needed to accelerate the universe as currently observed, assuming that the particles created are dark matter particles. Based on recent observational data, we constrain the value of the mass of the dark matter particles. The paper is organised as follows. In Section II it is presented the macroscopic effects of particle creation in CCDM model. In Section III it is presented only the results for real massive scalar particle creation in Friedmann models based on \cite{staro}. The general theory of particle creation is briefly presented in the Appendix for sake of generality. The main results are in Section IV where it is constrained the dark matter mass using the results of the previous section into the CCDM model equations of Section II. In Section V it is compared the quantum CCDM model with some phenomenological models and $\Lambda$CDM. The conclusions are presented in Section VI. | In this paper we have analysed a model where a quantum process of particle creation can be responsible for the present acceleration of the universe, the so called CCDM model. Contrary to recent works where the creation rate was only phenomenologically proposed, here we have used a quantum mechanical result for the creation rate of real massive scalar particles in FRW expanding universes in order to constrain the mass of the Dark Matter particle. As far as we know, it is the first time that the results from the quantum mechanical creation process is applied to study the effects on the accelerated expansion of the universe. The quantum creation process admits self corrections to the Hubble expansion rate so that we can interpret this like a kind of back-reaction effect. Such effects could give rise to a small correction $\varepsilon$ of the scale factor on the present matter dominated era. The best fit values found using observational results are $\varepsilon = -0.25$ and $m=1.6\times10^3$ GeV. With such values the model correctly presents a transition from decelerated to accelerated phase, and the particle creation rate is positive near the present epoch. It is important to notice that the lower mass limit obtained by this method ($\sim1 - 10$ GeV), is exactly of the same order of the values expected by experiments of dark matter detectors as DAMA ($\sim15 - 120$ GeV) \cite{dama2008}. The best fit value for the mass can also be compared to different theories of dark matter in the modern cosmological models. According to theories presented in the Introduction, our model correctly predicts the mass as the same order of the mass of LSP, UED and LZP particles, besides satisfying the constraints imposed by the WIMPs model, namely $m>100$ MeV. Different manners to take into account the self interaction of the field on the expansion rate are possible, leading to different back-reactions effects. Such studies are under investigation. | 14 | 3 | 1403.3679 |
1403 | 1403.4573_arXiv.txt | {The Einstein radius of a gravitational lens is a key characteristic. It encodes information about decisive quantities such as halo mass, concentration, triaxiality, and orientation with respect to the observer. Therefore, the largest Einstein radii can potentially be utilised to test the predictions of the $\Lambda$CDM model.} {Hitherto, studies have focussed on the single largest observed Einstein radius. We extend those studies by employing order statistics to formulate exclusion criteria based on the $n$ largest Einstein radii and apply these criteria to the strong lensing analysis of 12 MACS clusters at $z>0.5$.} {We obtain the order statistics of Einstein radii by a Monte Carlo approach, based on the semi-analytic modelling of the halo population on the past lightcone. After sampling the order statistics, we fit a general extreme value distribution to the first-order distribution, which allows us to derive analytic relations for the order statistics of the Einstein radii.} {We find that the Einstein radii of the 12 MACS clusters are not in conflict with the $\Lambda$CDM expectations. Our exclusion criteria indicate that, in order to exhibit tension with the concordance model, one would need to observe approximately twenty Einstein radii with $\theta_{\rm eff}\gtrsim 30\arcsec$, ten with $\theta_{\rm eff}\gtrsim 35\arcsec$, five with $\theta_{\rm eff}\gtrsim 42\arcsec$, or one with $\theta_{\rm eff}\gtrsim 74\arcsec$ in the redshift range $0.5\le z\le 1.0$ on the full sky (assuming a source redshift of $z_{\rm s}=2$). Furthermore, we find that, with increasing order, the haloes with the largest Einstein radii are on average less aligned along the line-of-sight and less triaxial. In general, the cumulative distribution functions steepen for higher orders, giving them better constraining power.} {A framework that allows the individual and joint order distributions of the $n$-largest Einstein radii to be derived is presented. From a statistical point of view, we do not see any evidence of an \textit{Einstein ring problem} even for the largest Einstein radii of the studied MACS sample. This conclusion is consolidated by the large uncertainties that enter the lens modelling and to which the largest Einstein radii are particularly sensitive.} | \label{sec:intro} The Einstein radius \citep{Einstein1936}, suitably generalised to non-circular lenses, is a key characteristic of every strong lensing system \citep[see e.g.][for recent reviews of gravitational lensing]{Bartelmann2010, Kneib2011, Meneghetti2013}. As a measure of the size of the tangential critical curve, it is very sensitive to a number of basic halo properties, such as the density profile, concentration, triaxiality, and the alignment of the halo with respect to the observer, but also to the lensing geometry, which is fixed by the redshifts of the lens and the sources \citep[see e.g.][]{Oguri2003, Oguri2009}. Moreover, the distribution of the sample of Einstein radii as a whole is strongly influenced by the underlying cosmological model. Here, not only cosmological parameters like the matter density, $\Omega_{\rm m}$, and the amplitude of the mass fluctuations, $\sigma_8$, but also the choice of the mass function, as well as the merger rate, have a strong impact. Recent studies gave rise to the so-called \textit{Einstein ring problem}, the claim that the largest observed Einstein radii \citep[see e.g.][]{Halkola2008, Umetsu&Broadhurst2008, Zitrin2011a, Zitrin2012} exceed the expectations of the standard $\Lambda$CDM cosmology \citep{Broadhurst&Barkana2008, Oguri2009, Meneghetti2011}. The comparison of theory and observations was performed by either comparing the largest observed Einstein radii with semi-analytic estimates of the occurrence probabilities of the strongest observed lens systems or with those found in numerical simulations. The most realistic treatment is certainly based on numerical simulations, which naturally include the impact of gas physics and mergers. However, for the statistical assessment of the strongest gravitational lenses, the number of simulation boxes and their sizes themselves are usually too small to sufficiently sample the extreme tail of the Einstein ring distribution. A sufficient sampling of the extreme value distribution of the largest Einstein radius roughly requires the simulation of $\sim 1000$ mock universes and a subsequent strong lensing analysis for each cluster sized halo \citep{Waizmann2012c}. In this series of papers on the strongest gravitational lenses, we studied several aspects of the Einstein radius distribution. We utilised a semi-analytic approach that allows a sufficient sampling of the extreme tail of the Einstein radius distribution at the cost of a simplified lens modelling. In the first paper \citep[][herafter Paper I]{Redlich2012}, we introduced our method for the semi-analytic modelling of the Einstein radius distribution. We then studied the impact of cluster mergers on the optical depth for giant gravitational arcs of selected cluster samples and on the distribution of the largest Einstein radii. The second work \citep[][herafter Paper II]{Waizmann2012c} focussed on the extreme value distribution of the Einstein radii and the effects that strongly affect it, such as triaxiality, alignment, halo concentration, and the mass function. We could also show that the largest known observed Einstein radius at redshifts of $z>0.5$ of MACS J0717.5+3745 \citep{Zitrin2009, Zitrin2011a, Medezinski2013} is consistent with the $\Lambda$CDM expectations. Now, in the third paper of this series, we extend the previous works by applying order statistics to the distribution of Einstein radii. Inference based on a single observation is difficult for it is a priori unknown whether the maximum is really drawn from the supposedly underlying distribution, or whether it is an event caused by a very peculiar situation that was statistically not accounted for. This is particularly important for strong lensing systems, which are heavily influenced by a number of different physical effects. It is therefore desirable to formulate $\Lambda$CDM exclusion criteria that are based on a number of observations instead of a single event. This goal can be accomplished by means of order statistics. We obtain the order statistic by Monte Carlo (MC) sampling of the hierarchy of the largest Einstein radii, using the semi-analytic method from Paper I, which is based on the work of \cite{Jing2002, Oguri2003}, and \cite{Oguri2009}. By fitting the generalised extreme value distribution to the first-order distribution, we derive analytic expressions for all order distributions and use them to formulate $\Lambda$CDM exclusion criteria. In the last part, we finally compare the theoretical distributions with the results of the strong lensing analysis of 12 clusters of the massive cluster survey \citep[MACS,][]{Ebeling2001, Ebeling2007} at redshifts of $z>0.5$ by \cite{Zitrin2011a}. This paper is structured as follows. In \autoref{sec:order}, we introduce the mathematical prerequisites of order statistics, followed by a brief summary of the method for semi-analytically modelling the distribution of Einstein radii in \autoref{sec:samER}. Then, in \autoref{sec:prepConsid}, we present first results of the MC sampling of the order statistics. Afterwards, in \autoref{sec:dist_order}, we study the order statistical distributions and derive exclusion criteria based on the $n$ largest Einstein radii. This is followed by a comparison with the MACS sample in \autoref{sec:MACSsample} and an introduction of the joint two-order distributions in \autoref{sec:joint_distributions}. In \autoref{sec:conclusions}, we briefly summarize our main results and finally conclude. For consistency with our previous studies, we adopt the \textit{Wilkinson Microwave Anisotropy Probe 7--year} (WMAP7) parameters $(\Omega_{\Lambda 0}, \Omega_{{\rm m}0}, \Omega_{{\rm b}0}, h, \sigma_8) = (0.727, 0.273, 0.0455, 0.704, 0.811)$ \citep{Komatsu2011} throughout this work. | \label{sec:conclusions} In this work, a study of the order statistics of the largest effective Einstein radii has been presented. Using the semi-analytic method that we introduced in Paper I of this series, we sampled the distributions of the twelve largest Einstein radii in the redshift range of $0.5\le z\le 1.0$, assuming full coverage sky, the Tinker mass function, and a source redshift of $z_{\rm s}=2$. Thus, we generalise the statistical analysis of the single largest effective Einstein ring of Paper II to the one of the $n$-largest Einstein rings. Our main results can be summarised as follows. \begin{itemize} \item The order statistics of the Einstein radii allows formulating $\Lambda$CDM exclusion criteria for the $n$-largest observed Einstein radii. We find that, in order to exhibit tension with the concordance model, one would need to observe roughly twenty Einstein radii with $\theta_{\rm eff}\gtrsim 30\arcsec$, ten with $\theta_{\rm eff}\gtrsim 35\arcsec$, five with $\theta_{\rm eff}\gtrsim 42\arcsec$, or one with $\theta_{\rm eff}\gtrsim 74\arcsec$ in the redshift range $0.5\le z\le 1.0$, assuming full sky coverage and a fixed source redshift of $z_{\rm s}=2$. \item In the sample of semi-analytically simulated Einstein radii, the twelve largest radii stem from a wide range in mass. The sample mean in mass only slightly decreases with increasing order, while a large relative scatter of $\sim 40$ per cent is maintained. Additionally, we find that the haloes giving rise to the largest Einstein radii are on average well aligned along the line-of-sight and, with increasing rank, less triaxial. This finding supports the notion that, for the sample of the largest Einstein radii, triaxiality and halo alignment along the line-of-sight matter more than mass. \item For the sampled cdfs of the first twelve order statistics, we find a steepening of the cdfs with increasing order. This indicates that the higher orders are, in principle, more constraining. Using a GEV-based fit to the distribution of the maxima, we could show that the semi-analytic sample is self-consistent with the statistical expectation of the order statistics. \item A comparison of the theoretically expected distributions with the MACS sample shows that the twelve reported Einstein radii of \cite{Zitrin2009} are consistent with the expectations of the concordance model. This conclusion would be consolidated further by (a) the inclusion of mergers and (b) the recent PLANCK cosmological parameters that indicate higher values of $\Omega_{{\rm m}0}$ and $\sigma_8$ in comparison to the WMAP7 parameters used in this analysis. Because we expect a large number of haloes to be potentially able to produce very large Einstein rings, the consistency of the studied MACS clusters with the $\Lambda$CDM expectations does not come as a surprise in view of the incompleteness of the sample. \item The method presented in this work allows calculation of joint distributions of an arbitrary combination of orders. As an example, we study the joint pdf of the two-order statistics and show that it is most likely that the largest and second largest Einstein rings are found to be realised with values very close to each other. For larger differences in the two orders, the gap between the observed values is expected to increase. \end{itemize} We presented a framework that allows the individual and joint order distributions of the $n$-largest Einstein radii to be derived. The presented method of formulating $\Lambda$CDM exclusion criteria by sampling the order statistical distribution is so general that it can easily be adapted to different survey areas and redshift ranges or can be included in an improved lens modelling. Such improvements will most certainly comprise the inclusion of mergers and realistic source distributions. From a statistical point of view, we do not see any evidence of an \textit{Einstein ring problem} for the studied MACS sample. This conclusion is consolidated by the large uncertainties that enter the modelling of the lens distribution, which the largest Einstein radii are particularly sensitive to. \begin{figure*} \centering \includegraphics[width=0.99\linewidth]{fig6.eps} \caption{Pdfs of the joint two-order statistics of the effective Einstein radius for different combinations of the first with higher orders as indicated in the upper right of each panel. The distributions are calculated for the redshift range of $0.5\le z\le 1.0 $ on the full sky. The color bar is set to range from $0$ to the maximum of the individual joint pdf in each panel. The red error bars denote the observed effective Einstein radii as listed in \autoref{tab:MACS_clusters}} \label{fig:joint_distributions} \end{figure*} | 14 | 3 | 1403.4573 |
1403 | 1403.2163_arXiv.txt | {We present a detailed study of the circumstellar gas distribution and kinematics of the semi-regular variable star RS Cnc on spatial scales ranging from $\sim 1''$ ($\sim$150~AU) to $\sim 6'$ ($\sim$0.25 pc). Our study utilizes new CO1-0 data from the Plateau-de-Bure Interferometer and new \HI 21-cm line observations from the Jansky Very Large Array (JVLA), in combination with previous observations. New modeling of CO1-0 and CO2-1 imaging observations leads to a revised characterization of RS Cnc's previously identified axisymmetric molecular outflow. Rather than a simple disk-outflow picture, we find that a gradient in velocity as a function of latitude is needed to fit the spatially resolved spectra, and in our preferred model, the density and the velocity vary smoothly from the equatorial plane to the polar axis. In terms of density, the source appears quasi-spherical, whereas in terms of velocity the source is axi-symmetric with a low expansion velocity in the equatorial plane and faster outflows in the polar directions. The flux of matter is also larger in the polar directions than in the equatorial plane. An implication of our model is that the stellar wind is still accelerated at radii larger than a few hundred AU, well beyond the radius where the terminal velocity is thought to be reached in an asymptotic giant branch star. The JVLA \HI data show the previously detected head-tail morphology, but also supply additional detail about the atomic gas distribution and kinematics. We confirm that the `head' seen in \HI is elongated in a direction consistent with the polar axis of the molecular outflow, suggesting that we are tracing an extension of the molecular outflow well beyond the molecular dissociation radius (up to $\sim$0.05 pc). The $6'$-long \HI `tail' is oriented at a PA of 305$^{\circ}$, consistent with the space motion of the star. The tail is resolved into several clumps that may result from hydrodynamic effects linked to the interaction with the local interstellar medium. We measure a total mass of atomic hydrogen $M_{\rm HI}\approx 0.0055 M_{\odot}$ and estimate a lower limit to the timescale for the formation of the tail to be $\sim6.4\times10^4$ years.} | Asymptotic Giant Branch (AGB) stars are undergoing mass loss at a high rate. One of the best tracers of AGB outflows are the rotational lines of carbon monoxide (CO). From the modeling of the line profiles it has been possible to derive reliable expansion velocities and mass loss rates (Ramstedt et al. 2008). In addition imaging at high spatial resolution allows us to describe the geometry and the kinematics of these outflows in the inner circumstellar regions where the winds emerge and where their main characteristics get established (Neri et al. 1998). High quality observations of CO line emissions at high spectral resolution have shown that some profiles are composite, with a narrow component superimposed on a broader one, revealing the presence of two winds with different expansion velocities (Knapp et al. 1998, Winters et al. 2003). Using high spatial resolution data obtained in the CO1-0 and 2-1 lines, Libert et al. (2010) have suggested that the composite line-profiles of the semi-regular AGB star \rscnc ~probably originate from an axi-symmetrical geometry with a slowly expanding equatorial disk and a faster perpendicular bipolar outflow. Other cases of AGB stars with axi-symmetrical expanding shells have been identified in a CO mapping survey of AGB stars by Castro-Carrizo et al. (2010). It shows that the axi-symmetry which is often observed in post-AGB stars (e.g. Sahai et al. 2007) may develop earlier when the stars are still on the AGB. Although extremely useful, CO as a tracer is limited to the inner parts of the circumstellar shells because, at a distance of typically $\sim$ 10$^{17}$\,cm, it is photo-dissociated by the interstellar radiation field (ISRF). At larger distances, it is necessary to use other tracers, such as dust or atomic species. The \HI line at 21\,cm has proved to be an excellent spatio-kinematic tracer of the external regions of circumstellar shells (e.g. G\'erard \& Le~Bertre 2006, Matthews \& Reid 2007). In particular, the \HI map of \rscnc ~presented by Matthews \& Reid shows a 6$'$-long tail, in a direction opposite to the space motion of the central star, and clearly different from that of the bipolar flow observed in CO at shorter distances (2--10$''$) by Libert et al. (2010). In such a case the shaping mechanism is thought to be due to the motion of the star relative to the local interstellar medium (Libert et al. 2008, Matthews et al. 2013). Thus \rscnc ~is an ideal target to study, in the same source, the two main effects that are expected to shape circumstellar environments, and to evaluate their respective roles. In this paper, we revisit \rscnc ~with new high spatial resolution data obtained in CO at 2.6 mm and in \HI at 21 cm. Our goal is to combine observations in these two complementary tracers, in order to describe the spatio-kinematic structure of the circumstellar shell from its center to the interstellar medium (ISM). The stellar properties of \rscnc ~are summarized in Table~\ref{basicdata}. Until recently, a distance of 122 pc was adopted from the parallax measured using Hipparcos (Perryman et al. 1997). However, new analyses of the Hipparcos data led to somewhat larger estimates of the distance, 129$_{-16}^{+16}$ pc (Famaey et al. 2005) and 143$_{-10}^{+12}$ \,pc (van Leeuwen 2007). In the present work, we adopt the improved values of the parallax and proper motions by van Leeuwen, and scale the published results with the new estimate of the distance. We also adopt the peculiar solar motion from Sch\"onrich et al. (2010). RS\,Cnc is an S-type star (CSS\,589, in Stephenson's (1984) catalogue) in the Thermally-Pulsing AGB phase of evolution: Lebzelter \& Hron (1999) reported the presence of Tc lines in its spectrum. \begin{table} \caption{Properties of \rscnc.} \begin{tabular}{lll} \hline parameter & value & ref.\\ \hline distance & 143 pc & 1 \\ MK Spectral type & M6eIb-II(S) & 2 \\ variability type & SRc: & 2 \\ pulsation periods & 122 and 248 days & 3 \\ effective temperature & 3226 K & 4 \\ radius & 225 \Rsol & 4 \\ luminosity & 4945 \Lsol & 4 \\ LSR radial velocity (\Vstar) & 6.75 \kms & 5 \\ expansion velocity & 2.4/8.0 \kms & 5 \\ mass loss rate & 1.7 10$^{-7}$ \Msold & 6 \\ 3D space velocity; PA & 15 \kms; 155$^\circ$ & this work \\ \hline \end{tabular}\\ {\bf References in the table:\\} (1) Hipparcos (van Leeuwen 2007)\\ (2) GCVS (General Catalogue of Variable Stars)\\ (3) Adelman \& Dennis (2005)\\ (4) Dumm \& Schild (1998)\\ (5) Libert et al. (2010)\\ (6) Knapp et al. (1998)\\ \label{basicdata} \end{table} \section[]{CO observations} \label{COdata} \subsection{summary of previous data} \label{olddata} RS Cnc was imaged in the CO1-0 and 2-1 lines by Libert et al. (2010). An on-the-fly (OTF) map covering a region of 100$''\times$100$''$ with steps of 4$''$ in RA and 5$''$ in Dec was obtained at the IRAM 30-m telescope. Interferometric data were obtained with the Plateau-de-Bure Interferometer (PdBI) in three configurations, B, C and D, i.e. with baselines ranging from 24-m to 330-m. All sets of observations were obtained with a spectral resolution corresponding to 0.1 \kms. The data from the 30-m telescope and the PdBI were merged and images in 1-0, with a field of view (fov) of 44$''$ and a spatial resolution of $\sim$2.3$''$, and in 2-1, with a fov of 22$''$ and a spatial resolution of $\sim$1.2$''$, were produced. Libert et al. presented the corresponding channel maps with a spectral resolution of 0.4 \kms. These maps show clearly that the broad and narrow spectral components reported by Knapp et al. (1998) originate from two different regions that Libert et al. (2010) described as a slowly expanding ($\sim$ 2\,\kms) equatorial disk/waist and a faster ($\sim$\,8\,\kms) bipolar outflow. Libert et al. estimated that the polar axis lies at an inclination of $\sim45^{\circ}$ with respect to the plane of the sky and is projected almost north-south, along a position angle (PA) of $\sim10^{\circ}$. \subsection{new data} \label{newdata} In January and February 2011, we obtained new data in the \COone ~line with the PdBI array in configurations A and B, increasing the baseline coverage up to 760\,m. The new data were obtained in dual polarizations and covered a bandwidth of 3.6\,GHz centered at 115.271\,GHz, the nominal frequency of the CO1-0 line. Two units of the narrow band correlator were set up to cover the CO line with a spectral resolution of 39\,kHz over a bandwidth of 20\,MHz, and the adjacent continuum was observed by the wideband correlator WideX (Wideband Express) with a channel spacing of 1.95\,MHz. These observations resulted in 12\,h of on-source integration time with the 6 element array and reach a 1$\sigma$ thermal noise level of 12\,mJy/beam in 0.2\,km\,s$^{-1}$ channels. The synthesized beam is 0.92$''\times$ 0.78$''$ at a position angle PA$ = 62^{\circ}$. \subsection{continuum} \label{continuum} We used the new WideX data to produce a continuum image of RS Cnc at 115 GHz. The data were integrated over a 2 GHz band, excluding the high frequency portion of the band that is affected by atmospheric absorption. A single point source is clearly detected. The source is unresolved, and there is no evidence of a companion. It has a flux density of 5.4$\pm$0.3 mJy, which is consistent with the flux density reported by Libert et al. (2010). It is slightly offset south-west with respect to the center of phase because we used the coordinates at epoch 2000.0 from Hipparcos. The offset (--0.15$''$ in RA and --0.37$''$ in Dec) is consistent with the proper motion reported by Hipparcos ($-$11.12\,mas\,yr$ ^{-1}$ in RA and --33.42 mas yr$ ^{-1}$ in Dec, van Leeuwen 2007). \begin{figure} \centering \epsfig{figure=fig1.pdf,angle=0,width=8.0cm} \caption{Continuum map at 115 GHz of RS Cnc (A+B configuration data obtained in 2011). The cross corresponds to the 2000.0 position of the star (RA 09:10:38.800, Dec 30:57:47.30). The contour levels are separated by steps of 0.90mJy/beam ($\equiv$\,20$\sigma$). The beam is 0.92$''\times0.78''$ (PA = 62$^{\circ}$).} \label{continuummap10} \end{figure} \subsection{channel maps in CO1-0} \label{channelmaps} The channel maps obtained in 2011 across the CO1-0 line are dominated by a compact central source. However, at 6.6\,\kms ~(Fig.~\ref{6p6kmpersec-channelmap10}), we observe a companion source at $\sim$1$''$ west-north-west (PA$\sim$300$^\circ$). This source is detected from 5.8 to 6.8\,\kms, but not outside this range. In the channel map at 6.6\,\kms, in which it is best separated, it has an integrated flux of 93$\pm$6 mJy, as compared to 300$\pm$20 mJy for the central source. This secondary source is clearly not at the origin of the bipolar outflow, which is aligned on the central source. Within errors, the central source coincides with the continuum source discussed in the previous section. \begin{figure} \centering \epsfig{figure=fig2.pdf,angle=0,width=8.8cm} \caption{Continuum subtracted CO1-0 channel map at 6.6 \kms ~(A+B configuration data obtained in 2011). The contour levels are separated by steps of 24 mJy/beam ($\equiv\,2\sigma$). The negative contours are in dotted lines.} \label{6p6kmpersec-channelmap10} \end{figure} \subsection{merging (CO1-0)} \label{merging} Finally, the new data (observed in the extended A and B configurations) were merged with the old ones already presented by Libert et al. (2010). These were obtained in the previous B, C, and D configurations and combined with short spacing observations obtained on the IRAM 30\,m telescope. The final combined data set now covers a spectral bandwidth of 580\,MHz, resampled to a spectral resolution of 0.2\,km\,s$^{-1}$. The 1 $\sigma$ thermal noise in the combined data cube is 8.7\,mJy/beam (for a channel width of 0.2 \kms) and the synthesized beam is 1.15$''\,\times$0.96$''$ at PA\,=\,67$^\circ$, similar to the resolution already obtained on CO2-1 (Libert et al. 2010). In Fig.~\ref{spectralmapCO10}, we present the resulting spectral map that we have derived by using a circular restoring beam with a gaussian profile of FWHM\,=\,1.2$''$. The line profiles are composed of three components whose relative intensities depend on the position in the map. One notes also that the two extreme components, at $\sim$\,2\,\kms ~and $\sim$12 \kms, tend to deviate more from the central component as the distance to the central source increases. In Fig.~\ref{triple-CO10}, three spectra obtained in the south of the central position are overlaid. One notes a shift in velocity of the red peaks, which correspond to the southern polar outflow at $\sim$12-14 \kms) relative to the central peaks at $\sim$5-8 \kms, which correspond to the emission close to the equatorial plane, with distance to the central source. \begin{figure*} \centering \epsfig{figure=fig3.pdf,angle=0,width=18.cm} \caption{CO1-0 spectral map of RS Cnc obtained with a restoring beam of 1.2$''$. The offsets with respect to the center of phase are given in the upper left corner of each panel (step=1.4$''$). North is up, and east is to the left.} \label{spectralmapCO10} \end{figure*} \begin{figure} \centering \epsfig{figure=fig4.pdf,angle=0,width=8.0cm} \caption{Spectra obtained at different positions (centre, 1.4$''$ south, 2.8$''$ south) in a beam of 1.2$''$ (cf. Fig.~\ref{spectralmapCO10}). } \label{triple-CO10} \end{figure} \section[]{CO model} \label{COmodel} \subsection{description} \label{description} In order to constrain the spatio-kinematic structure of \rscnc, we have constructed a model of CO emission adapted to any geometry and based on a code already developed by Gardan et al. (2006). A ray-tracing approach, taking into account the velocity-dependent emission and absorption of each element along a line of sight, allows us to reconstruct the flux obtained, within an arbitrary beam, from a source which has an arbitrary geometry. The density, the excitation temperature and the velocity are defined at each point of the circumstellar shell. The code can then produce synthetic spectral maps that can be compared to the observed ones. The populations of the rotational levels of the CO molecules are calculated assuming local thermodynamic equilibrium. The temperature profile is assumed to vary as r$^{-0.7}$, where r is the distance from the center of the star, and is scaled to models kindly provided by Sch\"oier \& Olofsson (2010, private communication; Fig.~\ref{tempRSCnc}). The latter profiles were obtained using the radiative transfer code developed in spherical geometry by Sch\"oier \& Olofsson (2001). The same temperatures are adopted to calculate for each element the thermal Doppler broadening, assuming a Maxwellian distribution of the velocities. \begin{figure} \centering \epsfig{figure=fig5.pdf,angle=0,width=8.0cm} \caption{Temperature profiles for different mass loss rates from Sch{\"o}ier \& Olofsson (2010, private communication). The thin line represents the temperature profile adopted in this work.} \label{tempRSCnc} \end{figure} \subsection{application to RS Cnc} \label{application} Following Libert et al. (2010) the source is defined by an equatorial plane and a polar axis. It is thus axi-symmetric and we need only two angles, which for instance define the orientation of the polar axis. Hereby, for simplicity we will use the angle of inclination of this axis over the plane of the sky (AI), and the position angle of the projection on the plane of the sky of this axis of symmetry (PA). We assume that the velocities are radial and that the outflows are stationary. Thus, the product v$\times$n$\times$r$^2$ (where v is the velocity, n the density, and r the distance to the centre) is kept constant along every radial direction. In order to account for the velocity gradient observed in the line profiles (Fig.\,\ref{triple-CO10}), we adopt a dependence of the velocity in r$^{\alpha}$, $\alpha$ being the logarithmic velocity gradient (Nguyen-Q-Rieu et al. 1979). We adopt a stellar CO/H abundance ratio of 4.0\,10$^{-4}$ (all carbon in CO, Smith \& Lambert 1986). Then we take a dependence of the CO abundance ratio with r from the photo-dissociation model of Mamon et al. (1988) for a mass loss rate of 1.0$\times10^{-7}$ \Msold ~(see below). The external limit is set at 20$''$ ($\sim$\,4.3\,10$^{16}$\,cm). In addition, we assume an He/H abundance ratio of 1/9. The star is offset from the center of the map by the amount measured on the continuum map (Fig.~\ref{continuummap10}). Finally, we adopt a stellar radial velocity \Vlsr\,=\,6.75\,\kms ~(cf. Table\,\ref{basicdata}). In our preferred model of RS\,Cnc, the density and the velocity are varying smoothly from the equatorial plane to the polar axis. The profiles of the density and the velocity are shown in Figs.~\ref{profd} and \ref{profv}, respectively. The latitude ($\theta$, $\mu$=sin$\theta$) dependence was obtained by a combination of exponential functions of $\mu$. In order to adjust the parameters of the model we used the {\mbox {\sc minuit}} package from the CERN program library (James \& Roos 1975), which minimizes the sum of the square of the deviations (i.e. modeled minus observed intensities). The minimization is obtained on the CO1-0 spectral map, which has the best quality, and the same parameters are applied for the \COtwo ~map. The flux of matter varies from 0.53$\times10^{-8}$\,\Msold\,sr$^{-1}$ in the equatorial plane to 1.59$\times10^{-8}$ \Msold\,sr$^{-1}$ in the polar directions (Fig.\,\ref{profmdot}). The total mass loss rate is 1.24$\times10^{-7}$ \Msold. The mass loss rate integrated within the two polar cones ($|\mu|>$0.5) is 0.83$\times10^{-7}$ \Msold. The exponent in the velocity profile varies from $\alpha$\,=\,0.13 in the equatorial plane, to $\alpha$\,=\,0.16 in the polar directions (Fig.\,\ref{velgradient}). \begin{figure} \centering \epsfig{figure=fig6.pdf,angle=0,width=8.0cm} \caption{The density profiles (in hydrogen atom number) in our preferred model as a function of $\mu$ ($\equiv$\,sin\,$\theta$, $\theta$ being the angle with respect to the equator) and for various distances from the central star. The profile for r=1 arcsec (r= 0.1 arcsec) is scaled by a factor 1/100 (1/10000, respectively).} \label{profd} \end{figure} \begin{figure} \centering \epsfig{figure=fig7.pdf,angle=0,width=8.0cm} \caption{Same as in Fig.~\ref{profd}, but for the velocity.} \label{profv} \end{figure} \begin{figure} \centering \epsfig{figure=fig8.pdf,angle=0,width=8.0cm} \caption{The flux of matter as a function of $\mu$.} \label{profmdot} \end{figure} \begin{figure} \centering \epsfig{figure=fig9.pdf,angle=0,width=8.0cm} \caption{Velocity profiles in the equatorial plane ($\mu$ = 0) and along the polar axis ($\mu = \pm$ 1).} \label{velgradient} \end{figure} In Figs.~\ref{FitdataCO10} and \ref{FitdataCO21}, we present a comparison of the spectra obtained in CO1-0 and CO2-1 together with the results of the model. We obtain a good compromise between the 2-1 and 1-0 data and the model, although with a slight excess of the model in 2-1 in particular in the central part of the map. The orientation of the source obtained with the minimization algorithm is defined by AI\,=\,52$^{\circ}$ (angle of inclination of the polar axis over the plane of the sky), and PA\,=\,10$^{\circ}$ (position angle of the projection of this axis over the plane of the sky). \begin{figure*} \centering \epsfig{figure=fig10.pdf,angle=0,width=9.4cm} \caption{Central part of the CO1-0 spectral map of RS Cnc together with the fits (dotted lines, in red in the electronic version) obtained in Sect.~\ref{application}.} \label{FitdataCO10} \end{figure*} \begin{figure*} \centering \epsfig{figure=fig11.pdf,angle=0,width=9.4cm} \caption{Same as in Fig.~\ref{FitdataCO10}, but for CO2-1. The original Libert et al. (2010) data have been resampled to 0.2 \kms.} \label{FitdataCO21} \end{figure*} \section[]{VLA and JVLA Observations} \label{HIdata} \HI imaging observations of RS~Cnc obtained with the Very Large Array (VLA) \footnote{The VLA of the National Radio Astronomy Observatory (NRAO) is operated by Associated Universities, Inc. under cooperative agreement with the National Science Foundation.} in its D configuration (0.035-1.03~km baselines) were previously presented by Matthews \& Reid (2007; see also Libert et al. 2010). Those data were acquired using dual circular polarizations and a 0.77~MHz bandpass. On-line Hanning smoothing was applied in the VLA correlator, yielding a data set with 127 spectral channels and a channel spacing of 6.1~kHz ($\sim$1.29~\kms). Further details can be found in Matthews \& Reid. For the present analysis, the VLA D configuration data were combined with new \HI 21-cm line observations of RS~Cnc obtained using the Jansky Very Large Array (JVLA; Perley et al. 2011) in its C configuration (0.035-3.4~km baselines). The motivation for the new observations was to obtain information on the structure and kinematics of the \HI emission on finer spatial scales than afforded by the D configuration data alone, thereby enabling a more detailed comparison between the \HI and CO emission (see Sect.~\ref{COdata}). The JVLA C configuration observations of RS~Cnc were obtained during observing sessions on 2012 March~2 and 2012 April~19. A total of 4.8~hours was spent on-source. Observations of RS~Cnc were interspersed with observations of the phase calibrator J0854+2006 approximately every 20 minutes. 3C286 (1331+305) was observed as a bandpass and absolute flux calibrator. The JVLA WIDAR correlator was configured with 8 subbands across each of two independent basebands, both of which measured dual circular polarizations. Only data from the first baseband pair (A0/C0) were used for the present analysis. Each subband had a bandwidth of 0.25~MHz with 128 spectral channels, providing a channel spacing of 1.95~kHz ($\sim$0.41~\kms). The 8 subbands were tuned to contiguously cover a total bandwidth of 2~MHz. The bulk of the JVLA data were taken with the central baseband frequency slightly offset from the LSR velocity of the star. However, additional observations of the phase and bandpass calibrators were made with the frequency center shifted by $-1.5$~MHz and $+$1.5~MHz, respectively, to eliminate contamination from Galactic \HI emission in the band and thus permit a robust bandpass calibration and more accurate bootstrapping of the flux density scale. Data processing was performed using the Astronomical Image Processing System (AIPS; Greisen 2003). Data were loaded into AIPS directly from archival science data model (ASDM) format files using the {\sc BDFI}n program available in the Obit software package (Cotton 2008). This permitted the creation of tables containing on-line flags and system power measurements. After updating the antenna positions and flagging corrupted data, an initial calibration of the visibility data was performed using the AIPS task {\sc TYAPL}, which makes use of the system power measurements to provide optimized data weights (Perley 2010). Calibration of the bandpass and the frequency-independent portion of the complex gains was subsequently performed using standard techniques, taking into account the special considerations for JVLA data detailed in Appendix~E of the AIPS Cookbook.\footnote{http://www.aips.nrao.edu/cook.html} The gain solutions for the fifth subband were interpolated from the adjacent subbands because of line contamination. Following these steps, time-dependent frequency shifts were applied to the data to compensate for the Earth's motion. \begin{figure*} \centering \epsfig{figure=fig12.pdf,angle=0,width=17.0cm} \caption{\HI channel images of RS~Cnc obtained from combined (J)VLA C and D configuration data. Contour levels are ($-$6[absent],$-$4.2,$-$3,3,4.2,6,8.5)$\times$1.4~mJy beam$^{-1}$. A $u$-$v$ tapering of 4k$\lambda$ (see Sect.~\ref{HIimaging}) was used to produce these images. The lowest contour is $\sim 3\sigma$. The synthesized beam size is \as{57}{9}$\times$\as{54}{2}. The star symbol marks the stellar position of RS\,Cnc from Hipparcos.\protect\label{fig:HIcmaps}} \end{figure*} \subsection{Imaging the Continuum} An image of the 21-cm continuum emission within a $\sim50'$ region centered on the position of RS~Cnc was produced using only the C configuration data. After excluding the first and last two channels of each subband and the portion of the band containing line emission, the effective bandwidth was $\sim$1.7~MHz in two polarizations. Robust +1 weighting (as implemented in AIPS) was used to create the continuum image, producing a synthesized beam of \as{17}{4}$\times$\as{14}{3}. The RMS noise in the resulting image was $\sim$\,0.11\,mJy\,beam$^{-1}$. The brightest continuum source within the $\sim30'$ JVLA primary beam was located $\sim$\am{12}{6} northwest of RS~Cnc, with a flux density of 110$\pm$1~mJy. No continuum emission was detected from RS~Cnc itself, and we place a 3$\sigma$ upper limit on the 21~cm continuum emission at the position of the star within a single synthesized beam to be $<$0.33~mJy. Using Gaussian fits, we compared the measured flux densities of the six brightest sources in the primary beam with those measured from NRAO VLA Sky Survey (Condon et al. 1998), and found the respective flux densities to be consistent to within formal measurement uncertainties. \subsection{Imaging the \HI Line Emission\protect\label{HIimaging}} Because the C and D configuration observations of RS~Cnc were obtained with different spectral resolutions, prior to combining them the C configuration data were boxcar smoothed and then resampled to match the channel spacing of VLA D configuration data. Subsequently, the C and D configuration data sets were combined using weights that reflected their respective gridding weight sums as reported by the AIPS task {\sc IMAGR}. The combined data set contained 127 spectral channels with a channel spacing of 6.1~kHz and spanned the LSR velocity range from $+81.2$~\kms\ to $-$81.2~\kms. Before imaging the line emission, the continuum was subtracted from the combined data set using a first order fit to the real and imaginary parts of the visibilities in the line-free portions of the band (taken to be spectral channels 10-50 and 77-188). Three different \HI spectral line image cubes were produced for the present analysis. The first used natural weighting of the visibilities, resulting in a synthesized beam size of \as{36}{2}$\times$\as{31}{6} at a position angle (PA) of $87^{\circ}$ and an RMS noise of $\sim$1.1~mJy beam$^{-1}$ per channel. For the second image cube, the visibility data were tapered using a Gaussian function with a width at the 30\% level of 4~k$\lambda$ in the $u$ and $v$ directions. This resulted in a synthesized beam of \as{57}{9}$\times$\as{54}{1} at PA=$-88^{\circ}$ and an RMS noise level of $\sim$1.4~mJy beam$^{-1}$ per channel. The third data cube used Gaussian tapering of 6~k$\lambda$, resulting in a synthesized beam of \as{49}{5}$\times$\as{44}{8} at PA=89$^{\circ}$ and RMS noise of $\sim$1.3~mJy beam$^{-1}$ per channel. | 14 | 3 | 1403.2163 |
|
1403 | 1403.2355_arXiv.txt | {Ethylene oxide (c-C$_{2}$H$_{4}$O), and its isomer acetaldehyde (CH$_{3}$CHO), are important complex organic molecules because of their potential role in the formation of amino acids. The discovery of ethylene oxide in hot cores suggests the presence of ring-shaped molecules with more than 3 carbon atoms such as furan (c-C$_{4}$H$_{4}$O), to which ribose, the sugar found in DNA, is closely related.} {Despite the fact that acetaldehyde is ubiquitous in the interstellar medium, ethylene oxide has not yet been detected in cold sources. We aim to understand the chemistry of the formation and loss of ethylene oxide in hot and cold interstellar objects (i) by including in a revised gas-grain network some recent experimental results on grain surfaces and (ii) by comparison with the chemical behaviour of its isomer, acetaldehyde.} {We introduce a complete chemical network for ethylene oxide using a revised gas-grain chemical model. We test the code for the case of a hot core. The model allows us to predict the gaseous and solid ethylene oxide abundances during a cooling-down phase prior to star formation and during the subsequent warm-up phase. We can therefore predict at what temperatures ethylene oxide forms on grain surfaces and at what temperature it starts to desorb into the gas phase.} {The model reproduces the observed gaseous abundances of ethylene oxide and acetaldehyde towards high-mass star-forming regions. In addition, our results show that ethylene oxide may be present in outer and cooler regions of hot cores where its isomer has already been detected. Our new results are compared with previous results, which focused on the formation of ethylene oxide only.} {Despite their different chemical structures, the chemistry of ethylene oxide is coupled to that of acetaldehyde, suggesting that acetaldehyde may be used as a tracer for ethylene oxide towards cold cores.} | Heterocycles are complex organic molecules containing heavier elements, in addition to carbon, in their ring structures. Among this class of compounds, O-bearing species are particularly important in the study of the interstellar medium (ISM) because of their links to the presence of life. Ribose, in particular, is one of the molecules associated with the molecular structure of DNA. Considering simpler heterocyclic molecules than ribose, we arrive at ethylene oxide, also called oxirane (c-C$_{2}$H$_{4}$O). Ethylene oxide is the smallest cyclic species containing oxygen, where it is bonded to two carbon atoms. Acetaldehyde (CH$_{3}$CHO), a non-cyclic isomer of ethylene oxide, has an important role as an evolutionary tracer of different astronomical objects \citep{Herbst09}. c-C$_{2}$H$_{4}$O was first detected in the ISM by \citet{Gottlieb73} and has been subsequently observed towards different astrochemical objects; particularly important is its discovery in regions of star formation by \citet{Johansson84} and by \citet{Turner91}. The formation of ethylene oxide in high-mass star-forming regions has been extensively investigated. It was first detected by \citet{Dickens97} in the galactic centre source Sgr B2(N) and its column densities were found to be in the 10$^{13}$--10$^{14}$ cm$^{-2}$ range \citep{Ikeda01}. Unlike ethylene oxide, acetaldehyde has been detected in the cold gas of the dark cloud TMC-1 \citep{Matthews85}, in quiescent regions \citep{Minh00}, and towards hot cores \citep{Nummelin98}. In all regions, acetaldehyde seems to be spatially correlated to CH$_{3}$OH. Their abundances vary within three orders of magnitude in the Galactic Center \citep{Requena08}; in particular, the ratio of CH$_{3}$OH-to-CH$_{3}$CHO ranges from $\sim$ 10 in cold dark clouds up to 100 in hot cores. However, deviations from these values are possible \citep{Bisschop07, Bisschop08}; in particular, \citet{Oberg11} found a ratio much greater than 100 towards the protostar SMM1 within the Serpens core. The ratio between the fractional abundance of acetaldehyde and ethylene oxide lies in the range 1--9 towards several high-mass star-forming regions \citep{Nummelin98, Ikeda01}. There are no observations of vinyl alcohol (CH$_{2}$CHOH), the second structural isomer of ethylene oxide, in star-forming regions with the exception of its detection towards the Galactic Centre by \citet{Turner01}. Even in star-forming regions, ethylene oxide and acetaldehyde both have low rotational temperatures between 20 and 40 K \citep{Nummelin98}. In these regions, the emission from acetaldehyde originates mainly in cool envelopes, where the rotational temperature may not be that much below the kinetic temperature, which may also be the case for ethylene oxide. However, recent observations by \citet{Belloche13} towards the Galactic Center found a rotational temperature of 100 K associated with both ethylene oxide and acetaldehyde. Laboratory experiments have been performed with the aim of determining the potential mechanisms of production for ethylene oxide and acetaldehyde under interstellar conditions. Using electron irradiation of mixtures of CO and CH$_{4}$ as well as CO$_{2}$ with C$_{2}$H$_{4}$ ices, \citet{Bennett05} looked at the formation of acetaldehyde, ethylene oxide and vinyl alcohol in the solid state. They found that acetaldehyde forms with both mixtures, while ethylene oxide and vinyl alcohol can only be produced from irradiation of carbon dioxide and ethylene as reactants. In addition, \citet{Ward11} recently studied the solid state formation of ethylene oxide in a single reaction involving atomic oxygen and ethylene, which were accreted onto a solid substrate. These recent laboratory data suggest potential routes for the formation of ethylene oxide on grain surfaces started by an association reaction between atomic oxygen and ethylene. In the gas phase ethylene reacts with O atoms by readily breaking its C--C double bond \citep{Occhiogrosso13} in order to produce CO, instead of involving addition reactions in which O is attached across the double C--C bond to form the cyclic species. The feasibility of a new solid state route for ethylene oxide production under hot core conditions has recently been studied by \citet{Occhiogrosso12}. In particular, the authors were able to match the observed abundances of gaseous ethylene oxide in regions of star-formation where temperatures were high enough for the desorption of water ices to occur, and for ethylene oxide to sublime via co-desorption with water at temperatures at and above 100 K. Note that in light of the low rotational excitation temperature of ethylene oxide \citep{Nummelin98} the radiation may be emitted in the outer envelope, which would imply that ethylene oxide, like acetaldehyde, desorbs at lower temperatures in the collapse and heat up towards the protostellar core, below the 100 K assumed by \citet{Occhiogrosso12}. In this paper, we extend our study of ethylene oxide formation by including a more complex chemistry for this molecule. We also insert a complete reaction network for the formation and destruction of one of its isomers, acetaldehyde. Given the lack of observational data on vinyl alcohol in star-forming regions, we do not include this isomer in our calculations. For the purpose of the present study, we employ an alternative code labelled MONACO \citep{Vasyunin13} to our standard UCL\_CHEM code and use a different approach for the treatment of the experimental data for the formation of c-C$_{2}$H$_{4}$O from atomic oxygen and ethylene \citep{Ward11}. We do not attempt to include the high-energy mechanisms of \citet{Bennett05} since neither code is equipped to model these processes effectively. In Section 2, we describe the details of the MONACO chemical model and we dedicate a subsection (2.1) to the computational treatment of the laboratory data. In Section 3, we present the results from the MONACO network and code, and we report a comparison with previous theoretical and observational work in subsection 3.1. Our conclusions are given in Section 4. \begin{table*}[ht] \begin{center} \caption{Non-zero initial abundances of species with respect to {\it n$_{H}$} used in the MONACO chemical model, based on \citet{Wakelam08}.} \begin{tabular}{ccccccc} \hline H & H$_{2}$ & He & N & O & C$^{+}$ & S$^{+}$ \\ \hline 1.0$\times$10$^{-03}$ & 4.9$\times$10$^{-01}$ & 9.0$\times$10$^{-02}$ & 7.6$\times$10$^{-05}$ & 2.6$\times$10$^{-04}$ & 1.2$\times$10$^{-04}$ & 8.0$\times$10$^{-08}$ \\ \hline Si$^{+}$ & Fe$^{+}$ & Na$^{+}$ & Mg$^{+}$ & Cl$^{+}$ & P$^{+}$ & F$^{+}$\\ \hline 8.0$\times$10$^{-09}$ & 3.0$\times$10$^{-09}$ & 2.0$\times$10$^{-09}$ & 7.0$\times$10$^{-09}$ & 1.0$\times$10$^{-09}$ & 2.0$\times$10$^{-10}$ & 6.7$\times$10$^{-09}$ \\ \hline \end{tabular} \end{center} \end{table*} | We used the MONACO code, as implemented by \citet{Vasyunin13}, to model the formation and destruction of ethylene oxide and acetylene for a typical hot core. In particular, we extended the MONACO model to include recent experimental results \citep{Ward11} on ethylene oxide formation on icy mantle analogues by the association of oxygen atoms and ethylene. For comparison, we considered a previous study by \citet{Occhiogrosso12} focused on the formation of solid ethylene oxide and we inserted into UCL\_CHEM code, a reaction network for the formation and the loss pathways of acetaldehyde. We then ran a model with the same physical parameters as in the simulation performed using the MONACO model. Our main conclusions from this computational analysis are: \begin{enumerate} \item By employing the two different codes, ethylene oxide and acetaldehyde show an increase in their gaseous abundances at low temperatures during the warm-up phase of the star formation process. In particular, both codes for ethylene oxide display a plateau after they reach their peak abundances, while, in both cases, the amount of acetaldehyde slightly decreases (after its peak value) due to the reaction with H$_{3}$O$^{+}$ to form C$_{2}$H$_{5}$O$^{+}$ and H$_{2}$O (see reaction 11). \item The theoretical evidence of early desorption at relatively low temperatures suggests that ethylene oxide might exist at an observable level in the outer and cooler regions of hot cores, where its isomer has already been detected. \item Both models show an efficient formation of ethylene oxide and acetaldehyde on grains already at early stages during the collapse phase. After $\sim$ 10$^{6}$ years the importance of the surface reaction for ethylene oxide formation becomes comparable to its production in the gas phase thanks to the loop reactions in which acetaldehyde is destroyed to form C$_{2}$H$_{5}$O$^{+}$ (which is in turn one of the reactants to produce gaseous ethylene oxide, as shown in reaction 8). \item The theoretical ratios between the fractional abundances of the two isomers evaluated with the UCL\_CHEM and MONACO models fit well within the range of values reported in the literature for the case of a hot core source \citep{Nummelin98, Ikeda01}. This factor may be important to quantify the amount of ethylene oxide towards cold regions based on the acetaldehyde abundance in these astronomical environments. Moreover, the calculated column densities of both isomers (at 200 K and 1.2$\times$10$^{6}$ yrs) perfectly match those from recent observations towards SgrB2 sources \citep{Belloche13}. \item A final important consideration regards the theoretical treatment of the experimental results. Despite the fact that the same laboratory data \citep{Ward11} have been used in the present study as well as in \citet{Occhiogrosso12}, different assumptions were made in the two cases in converting experimental data for use in the interstellar environment. The consistency between the two codes in reproducing the ISM chemistry of ethylene oxide and acetaldehyde may be a confirmation of the reliability of the scientific justification asserted in both studies. \end{enumerate} | 14 | 3 | 1403.2355 |
1403 | 1403.5269_arXiv.txt | We investigate the origin of galaxy bimodality by quantifying the relative role of intrinsic and environmental drivers to the cessation (or `quenching') of star formation in over half a million local Sloan Digital Sky Survey (SDSS) galaxies. Our sample contains a wide variety of galaxies at $z$=0.02-0.2, with stellar masses of 8$< \rm{log(M_{*}/M_{\odot}})<$12, spanning the entire morphological range from pure disks to spheroids, and over four orders of magnitude in local galaxy density and halo mass. We utilise published star formation rates and add to this recent GIM2D photometric and stellar mass bulge + disk decompositions from our group. We find that the passive fraction of galaxies increases steeply with stellar mass, halo mass, and bulge mass, with a less steep dependence on local galaxy density and bulge-to-total stellar mass ratio (B/T). At fixed internal properties, we find that central and satellite galaxies have different passive fraction relationships. For centrals, we conclude that there is less variation in the passive fraction at a fixed bulge mass, than for any other variable, including total stellar mass, halo mass, and B/T. This implies that the quenching mechanism must be most tightly coupled to the bulge. We argue that radio-mode AGN feedback offers the most plausible explanation of the observed trends. | \begin{figure*} \includegraphics[width=0.49\textwidth,height=0.49\textwidth]{galaxies_face_on.pdf} \includegraphics[width=0.49\textwidth,height=0.49\textwidth]{galaxies_edge_on.pdf} \caption{A collage of face-on (inclination $<$ 30 degrees, {\it left panel}) and edge-on (inclination $>$ 60 degrees, {\it right panel}) galaxy images from our SDSS sample in ugriz wavebands, with z $<$ 0.1. In both panels, from {\it bottom to top} galaxies increase in stellar mass with log($M_{*}/M_{\odot}$) = 8 -- 9, 9 -- 10, 10 -- 11, 11 -- 12 in each row. From {\it left to right} galaxies increase in bulge-to-total stellar mass ratio, with B/T = 0 -- 0.2, 0.2 -- 0.4, 0.4 -- 0.6, 0.6 -- 0.8, 0.8 -- 1 in each column. Postage stamps are 40$''$ $\times$ 40$''$, which corresponds to $\sim$ 15 -- 70 kpc on each side across the redshift range of these images. Not all types of galaxy represented here are equally likely, e.g. high B/T high $M_{*}$ galaxies are much more common than low B/T high $M_{*}$ galaxies, conversely, high B/T low $M_{*}$ galaxies are much rarer than low B/T low $M_{*}$ galaxies (see Fig. 2 for the distributions). Note how galaxies appear redder in colour as we increase stellar mass at a fixed B/T ratio (moving up a column), and as we increase B/T ratio at a fixed stellar mass (moving along a row).} \end{figure*} One of the most important unresolved questions in modern cosmology is how galaxies form and evolve over cosmic time (see e.g. Conselice 2013 for a review). The existence of two principal types of galaxies may be inferred from the bimodality of several fundamental galaxy properties, most notably for colour - magnitude (or stellar mass), colour - concentration, and colour - morphology (Strateva et al. 2001, Kauffmann et al. 2003, Brinchmann et al. 2004, Baldry et al. 2004, Baldry et al. 2006, Driver et al. 2006, Bamford et al. 2009). The galaxy population is divided into an actively star forming `blue cloud' where galaxies exhibit a tight correlation between stellar mass and star formation rate, SFR, known as the star forming main sequence (e.g. Brinchmann et al. 2004), and a principally passive `red sequence' where there is no positive SFR - stellar mass correlation. For the red sequence there is a relationship between colour and stellar mass (or luminosity), such that more massive (or luminous) galaxies become progressively redder (e.g. Strateva et al. 2001). Relatively few galaxies lie midway between the two peaks, and those that do are given the designation of `green valley', or transition, galaxies. Understanding the fundamental reason behind the galaxy bimodality, and particularly the transition between the blue cloud and red sequence, is the goal of much active research in contemporary extragalactic astrophysics. A common attempt to explain the origin of galaxy bimodality appeals to the dual component nature of galaxies, i.e. that galaxies are in effect structurally bulge + disk systems (to first order). In general disks are found to be bluer in colour than bulges (e.g. Peletier \& Balcells 1996) which has led, for example, Driver et al. (2006) to argue for the necessity of routine bulge + disk decompositions of galaxy structural components when investigating the evolution of galaxy properties through star formation. The primary use of colour in the bimodal distributions is best understood as a proxy for global star formation rate per unit stellar mass, or sSFR, which indicates the relative importance of ongoing star formation to established stellar populations in the overall integrated light distribution of a galaxy. Thus, galaxies separate out in terms of whether or not they are experiencing substantial ongoing formation or not. In most cases, lower stellar mass and lower S\'{e}rsic index galaxies tend to be bluer (and hence have higher sSFRs) than higher stellar mass and higher S\'{e}rsic index systems (Baldry et al. 2004, Driver et al. 2006, Baldry et al. 2006, Bamford et al. 2009). Similar relationships are found for luminosity and stellar light concentration (e.g. Strateva et al. 2001, Driver et al. 2006). These relationships are complicated by the impact of local environment on the process of star formation, where there is a pronounced effect for star formation to be suppressed preferentially in higher density environments (e.g. Butcher \& Oemler 1984, Balogh et al. 2004, Cooper et al. 2006, van den Bosch et al. 2008, Peng et al. 2010, Peng et al. 2012). Additionally there is a tendency for galaxies at higher densities to be more bulge dominated and hence have higher S\'{e}rsic index and concentration parameters (Dressler 1984, Moran et al. 2007, Tasca et al. 2009). Disentangling the various effects on current formation efficiency is essential in coming to understand how and why galaxies become the way they are today. Many proposed mechanisms for inducing the observed cessation in star formation and subsequent build up of the red sequence have been suggested. In particular, Peng et al. (2010, 2012) argue for the separate influence of galaxy stellar mass and local environment on the formation of passive galaxies. This implies that there must be at least two distinct routes by which galaxies can reduce their SFRs and become passive, one coupled to the local environment and one to internal properties. Further, Peng et al. (2010, 2012) construct a phenomenological model, which fits the observed data extremely well; however, this does not necessarily reveal the base physical process(es) which cause the transition of galaxies from the blue cloud (of actively star forming main sequence galaxies) to the red sequence (of passive galaxies). Theoretically, a number of physical mechanisms for quenching \footnote{The term `quenching' is commonly used in the literature to express the fact or process of star formation coming to an end in a galaxy (e.g. Peng et al. 2010, 2012, Mendel et al. 2013, Woo et al. 2013). In this sense it is interchangeable with `cessation'. However, it is not a universally accepted as a useful or desirable term. This is largely due to the implicit assumption that some mechanism is needed to {\it cause} the cessation in star formation, i.e. that galaxies would otherwise be actively forming stars. In this paper we shall use the term `quenching' from time to time to refer to those proposed mechanisms which do cause the shutting down of star formation, and try to avoid its usage in the more general sense.} have been suggested. These can be, loosely, divided into environmental and intrinsic (mass-correlating) processes. Environmentally, effects such as ram pressure stripping, galaxy tidal interaction and harassment, stifling of the gas supply routes to galaxies from hot gas in massive halos, and preprocessing of gas into stars from extensive merging in groups prior to cluster formation can all lead to the shutting down of star formation in galaxies (Balogh et al. 2004, Boselli et al. 2006, Cooper et al. 2006, Cortese et al. 2006, Moran et al. 2007, Font et al. 2008, van den Bosch et al. 2008, Berrier et al. 2009, Tasca et al. 2009, Peng et al. 2010, 2012, Hirschmann et al. 2013, Wetzel et al. 2013). Proposed intrinsic drivers of quenching in models include quasar-mode AGN feedback (Hopkins et al. 2006a,b, Hopkins et al. 2008), and radio-mode AGN feedback (Croton et al. 2006, Bower et al. 2008, Guo et al. 2011). Quasar-mode AGN feedback may be thought of as the blowing out of cold gas from the centre of galaxies in cataclysmic events such as during enhanced periods of nuclear activity throughout the major merging of gas rich galaxies (see Nulsen et al. 2005, Dunn et al. 2010, Feruglio et al. 2010, Fabian 2012, and Cicone et al. 2014 for observational evidence). Alternatively, radio-mode AGN feedback involves the gentle heating of gas in the halos of massive galaxies from jets over long timescales (up to several Gyrs) resulting in disruption of supply routes for replenishment of cold gas needed as fuel for star formation (e.g. McNamara et al. 2000, McNamara et al. 2007, Fabian et al. 2012). Other intrinsic mechanisms for quenching may arise from the virial shock heating of infalling accreted cold gas onto galaxies in halos above some critical dynamical mass (often cited as around $M_{\rm crit} \sim 10^{12-13} M_{\odot}$) leading to the shutting off of star formation in those galaxies (Dekel \& Birnboim 2006 and Dekel et al. 2009). Furthermore, the potential of the bulge structural component to stabilise giant molecular cloud collapse (which are the sites of star formation) through tidal torques has been argued for in Martig et al. (2009). Finally, major and minor galaxy mergers and interactions can give rise to enhanced star formation rates, and hence elevated gas depletion (e.g. Ellison et al. 2008, Darg et al. 2010, Patton et al. 2013, Hung et al. 2013), as well as increased supernova and stellar feedback which may also accelerate the transition of galaxies from the blue cloud to the red sequence. Galaxy mergers and interactions are also found to enhance nuclear activity (e.g. Ellison et al. 2011, Silverman et al. 2011, Ellison et al. 2013) and thus couple to increased AGN feedback as well. There is currently some debate as to whether residing in a galaxy pair will increase (as argued for in Robotham et al. 2013) or decrease (as argued for in Wild et al. 2009) the star formation of galaxies. Most probably the effect is varied depending on the timescale and stage of the interaction. Widely separated (non-interacting) pairs will merely trace local environment (e.g. Patton et al. 2013) so one might expect that since being in a pair is more probable at higher local densities (up to a point), residing in a pair might lead to lower star formation rates due to environmental effects. Closer (interacting) pairs are found to provoke enhanced star formation (Ellison et al. 2008,2010, Scudder et al. 2012, Patton et al. 2013), and the final coalescence of galaxies at the end of the merger sequence leads initially to the highest enhancements in star formation (e.g. Ellison et al. 2013). Thereafter, most probably, depletion in gas supplies will result in reduced star formation later in the post-merger phase (as in Wild et al. 2009). However, in this scenario, in order for a galaxy to remain passive some additional process(es) will be required to prevent cold gas accretion re-invigorating the galaxy, such as AGN feedback (e.g. Bower et al. 2006, 2008) or halo-mass-quenching (e.g. Dekel \& Birnboim 2006). Most of the intrinsically-driven routes for galaxies to become passive are expected to couple to the bulge component primarily. For example, AGN and the central black holes have well documented scaling relations with the bulge properties (mass, velocity dispersion, luminosity), e.g. Magorrian et al. (1998), Ferrarese \& Merritt (2000), Gebhardt et al. (2000), Haring \& Rix (2004). At a fixed stellar mass, galaxies with higher bulge-to-total stellar mass ratios (B/T) tend to reside in higher mass halos, and hence will be affected more by shock heating of accreted gas from cold streams into their halos (Dekel et al. 2009, Woo et al. 2013). Also, bulge mass and B/T will couple with the capacity of a bulge to stabilize the collapse of giant molecular clouds in surrounding disks, leading to a relation between the bulge and the passive fraction (Martig et al. 2009). Finally, galaxy merging tends to result in growing the bulge component (e.g. Toomre \& Toomre 1972) and thus gas depletion may also correlate with the extent of the bulge structure. Since most of the theoretically favoured mechanisms to achieve the cessation of star formation are predicted to correlate more strongly with the bulge structure than that of the whole galaxy, it is desirable to look for these predicted relationships explicitly in observations. Indirect observational evidence of the importance of the bulge has been noted for several years now. Kauffmann et al. (2003) and Brinchmann et al. (2004) both find indirect evidence for the importance of the bulge in star formation cessation, noting strong correlations between SFR and stellar mass density and concentration of light, which are effectively proxies for `bulgeness' of galaxy. Drory \& Fisher (2007) demonstrate that the type of bulge (as well as the bulge-to-total light ratio) is important in forming galaxy bimodality in colour, with classical pressure supported bulges being required to make a galaxy red, and pseudo-bulges being insufficient. Bell et al. (2008) find that high S\'{e}rsic index bulges are always present in truly passive systems, further implicating the role of the classical bulge in star formation cessation. Two recent papers, Cheung et al. (2012) and Fang et al. (2013), also look for the effect of indirect indicators of the bulge (central stellar mass surface density within 1 kpc) coupling to the star forming properties of the whole galaxy. They find that at a fixed stellar mass there is a differential impact on the red (passive) fraction due to central stellar mass surface density, which suggests that mass-quenching (as in Peng et al. 2010, 2012) is a process perhaps more directly linked with the bulge. Woo et al. (2013), however, have argued for stellar-mass-quenching being better understood as halo-mass-quenching for central galaxies, with virialised shock heating of infalling gas in massive halos being the root cause of star formation cessation (e.g. Dekel \& Birnboim 2006). In this paper we investigate the role of the bulge in constraining star formation directly, utilising the largest photometric and stellar mass bulge + disk decomposition catalogue in existence (Simard et al. 2011, Mendel et al. 2014). In Fig. 1 we show an illustration of SDSS galaxies separated into bins of stellar mass and bulge-to-total stellar mass ratio (B/T) from our decomposition, for both face-on and edge-on systems. We examine the role of bulge-to-total stellar mass ratio (B/T), bulge mass, and disk mass in addition to halo mass, total stellar mass, and local density which have previously been studied (e.g. Peng et al. 2010,2012, Woo et al. 2013). We find that bulge mass correlates most tightly with the passive fraction for central galaxies. This paper is structured as follows. Section 2 outlines the sources of our data, including details on the derivation of star formation rates, stellar masses, halo masses, and bulge + disk decompositions. Section 3 presents our methods and techniques, particularly in reference to our metric for defining passive, $\Delta$SFR. In section 4 we present our results, including the dominant role of the bulge in constraining the passive fraction. Section 5 provides a discussion of our results in terms of the context of the substantial body of literature on this subject, and we go on to present a feasibility argument for the explanation of our observed trends through radio-mode AGN feedback. We conclude in Section 6. An appendix is also included where we discuss the various tests and checks we have performed on the data to assess the reliability of our bulge + disk decompositions. Throughout this paper we assume a (concordance) $\Lambda$CDM Cosmology with: H$_{0}$ = 70 km s$^{-1}$ Mpc$^{-1}$, $\Omega_{m}$ = 0.3, $\Omega_{\Lambda}$ = 0.7, and adopt AB magnitude units. | In this paper we have studied the star forming properties of over half a million SDSS galaxies at z = 0.02 - 0.2, with stellar masses in the range 8 $< {\rm log(M_{*}/M_{\odot}}) <$ 12. Our sample contains a large variety of morphological types from pure spheroids to disks, via a sequence in bulge-to-total stellar mass ratios, and encompasses a range in halo mass and local galaxy density of over four orders of magnitude. We use the SDSS DR7 (Abazajian et al. 2009) with spectroscopically determined SFRs from Brinchmann et al. (2004). We construct a definition of passive from the distance to the star forming main sequence, $\Delta$SFR, that each galaxy resides at. Specifically, we define a galaxy to be passive if it is forming stars at a rate a factor of ten lower than similar stellar mass and redshift galaxies which are actively star forming. This metric clearly distinguishes star forming from passive galaxies (see Fig. 6). We construct the passive fraction, which is the fraction of passive galaxies to total galaxies in a given sub-sample, weighted by the inverse of the volume over which galaxies of given magnitudes and colours would be visible in the SDSS, thus removing observer bias. In particular, we use bulge + disk decompositions in ugriz photometry (from Simard et al. 2011) and in stellar mass (from Mendel et al. 2014), and group membership and halo masses from Yang et al. (2007, 2009). We investigate the effects on the passive fraction of varying total stellar mass, halo mass, bulge mass, bulge-to-total stellar mass ratio (B/T), disk mass, local galaxy over-density, and central - satellite divisions. We summarise our key results here. \noindent {\bf For the whole sample:} \noindent $\bullet$ We find that the SFR - $M_{*}$ relation is not dependent on B/T structure or local galaxy density for star forming galaxies (Fig. 5), and, thus, that stellar mass and redshift are the only drivers of this relation. \noindent $\bullet$ The $\Delta$SFR parameter cleanly divides galaxies into two populations, a star forming and passive peak. The star forming peak is dominated by lower stellar and halo masses, lower B/T ratios, and lower local over-densities, whereas the passive peak is dominated by higher stellar and halo masses, higher B/T ratios, and higher local over-densities (see Figs. 6 \& 7). \noindent $\bullet$ We find positive correlations between the passive fraction and total halo mass, stellar mass, and B/T structure for both central and satellite galaxies (Fig. 8). \noindent $\bullet$ We also find that satellite galaxies have higher passive fractions for their stellar masses and B/T structures than central galaxies. This effect is more pronounced at low stellar masses, suggesting that the environmental processes which cause cessation in star formation are more effective in lower mass galaxies. \noindent $\bullet$ At a fixed halo mass we find that centrals are more passive than satellites, most probably due to their relatively higher stellar masses. This suggests that intrinsic drivers to the passive fraction dominate over environmental effects. For the remainder of our analyses in this paper we select only central galaxies where additional environmental effects to halo mass are found to be negligible. \noindent {\bf For central galaxies:} \noindent $\bullet$ We find a correlation between B/T structure and the passive fraction, but note that there is large variation at a fixed B/T with both stellar and halo mass (Figs. 10 \& 11). \noindent $\bullet$ We also find a strong correlation between the passive fraction and total stellar and halo mass, but we discover that this correlation varies substantially with B/T structure (Fig. 12), such that more spheroidal (higher B/T) galaxies are more frequently passive for their stellar or halo mass than more disk-like (lower B/T) galaxies. \noindent $\bullet$ The passive fraction - bulge mass relation exhibits the least variation in terms of the other variables considered, suggesting that bulge mass is the primary driver of the passive fraction. In fact we find far more variation at a fixed stellar or halo mass with varying bulge mass range than at a fixed bulge mass with varying stellar or halo mass range (see Fig. 13 and compare to Figs. 10 \& 11). \noindent $\bullet$ We quantify the maximum difference in passive fraction ($\delta f_{p}^{\rm max}$) between the highest and lowest binnings of each variable in turn at fixed other galaxy properties (see Tab. 1). We also compute the area enclosed ($A(\delta f_{p})$) between the highest and lowest binnings of each variable at fixed other galaxy properties (see Tab. 2). \noindent $\bullet$ From the $\delta f_{p}^{\rm max}$ and $A(\delta f_{p})$ statistics we find that there is significantly less variation at a fixed bulge mass than for any other variable, including halo mass, stellar mass, and B/T structure. \noindent $\bullet$ At a fixed bulge mass, there is greater variation in the passive fraction with disk mass than for any other variable. This implies that the disk mass is the next most important variable to know after bulge mass, ahead of, e.g, halo mass and local galaxy density. We construct a plausibility argument for the explanation of our observed trends through radio-mode AGN feedback in \S 5.2. In particular, we demonstrate that the total energy available to feedback on galaxies from the AGN is proportional to the black hole mass, and hence also tightly correlated with the bulge mass (e.g. Haring \& Rix 2004). Thus, bulge mass is expected to correlate better with the passive fraction than current instantaneous AGN luminosity or accretion rate. We go on to consider whether our results are consistent with various other proposed quenching mechanisms in \S 5.3. We conclude that the tighter correlation between passive fraction and bulge mass, than with halo mass or B/T structure, rule our halo mass quenching (e.g. Dekel \& Birnboim 2006) and morphological quenching (e.g. Martig et al. 2009) as dominant routes for star formation cessation. We also argue that the presence of substantial passive disk components in our sample rules out major merging and AGN quasar-mode feedback as the dominant quenching mechanism, preferring the gentler radio-mode process. In summary, we explore the origin of galaxy bimodality through a detailed analysis of the star forming properties of over half a million local SDSS galaxies, for which we have bulge + disk decompositions. We evaluate how the passive fraction varies as a function of both intrinsic galaxy structural properties, and of environment. Our most important result is that the passive fraction for central galaxies is more tightly coupled to bulge mass, than any other intrinsic property, including total stellar mass, halo mass, and B/T structure. This requires that the physical mechanism(s) for inducing the cessation of star formation must be strongly coupled to the bulge. Finally, we argue that radio-mode AGN feedback offers the most plausible theoretical framework for an explanation of this observational result. | 14 | 3 | 1403.5269 |
1403 | 1403.4215_arXiv.txt | The intrinsic alignment of galaxy shapes with the large-scale density field is a contaminant to weak lensing measurements, as well as being an interesting signature of galaxy formation and evolution (albeit one that is difficult to predict theoretically). Here we investigate the shapes and relative orientations of the stars and dark matter of halos and subhalos (central and satellite) extracted from the MassiveBlack-II simulation, a state-of-the-art high resolution hydrodynamical cosmological simulation which includes stellar and AGN feedback in a volume of $(100$\hmpc$)^3$. We consider redshift evolution from $z=1$ to $0.06$ and mass evolution within the range of subhalo masses, $10^{10} -6.0 \times 10^{14.0}$\hMsun. The shapes of the dark matter distributions are generally more round than the shapes defined by stellar matter. The projected root-mean-square (RMS) ellipticity per component for stellar matter is measured to be $e_\text{rms} = 0.28$ at $z=0.3$ for $\msubhalo> 10^{12.0}$\hMsun, which compares favourably with observational measurements. We find that the shapes of stellar and dark matter are more round for less massive subhalos and at lower redshifts. By directly measuring the relative orientation of the stellar matter and dark matter of subgroups, we find that, on average, the misalignment between the two components is larger for less massive subhalos. The mean misalignment angle varies from $\sim 30^{\circ}-10^{\circ}$ for $M \sim 10^{10} - 10^{14} \hMsun$ and shows a weak dependence on redshift. We also compare the misalignment angles in central and satellite subhalos at fixed subhalo mass, and find that centrals are more misaligned than satellites. We present fitting formulae for the shapes of dark and stellar matter in subhalos and also the probability distributions of misalignment angles. | \label{S:intro} Weak gravitational lensing is a useful probe to constrain cosmological parameters since it is sensitive to both luminous and dark matter \citep{{2002PhRvD..65b3003H},{2004PhRvD..70l3515B},{2004PhRvD..69h3514I},{2004ApJ...601L...1T},{2004ApJ...600...17B},{2010GReGr..42.2177H}}. In particular, weak lensing surveys can be used to probe theories of modified gravity and provide constraints on the properties of dark matter and dark energy \citep{{2006astro.ph..9591A},{2013PhR...530...87W}}. Many upcoming surveys like Large Synoptic Survey Telescope(LSST)\footnote{http://www.lsst.org/lsst/} and Euclid\footnote{http://sci.esa.int/euclid/} aim to determine the constant and dynamical parameters of the dark energy equation of state to a very high precision using weak lensing. However, constraining cosmological parameters with sub-percent errors in future cosmological survey requires the systematic errors to be well below those in typical weak lensing measurements with current datasets. The intrinsic shapes and orientations of galaxies are not random but correlated with each other and the underlying density field. This is known as intrinsic galaxy alignments. The intrinsic alignment (IA) of galaxy shapes with the underlying density field is an important theoretical uncertainty that contaminates weak lensing measurements \citep{{2000MNRAS.319..649H},{2000ApJ...545..561C},{2002MNRAS.335L..89J},{2004PhRvD..70f3526H}}. Accurate theoretical predictions of IA through analytical models and $N$-body simulations \citep{2004PhRvD..70f3526H,2006MNRAS.371..750H,2010MNRAS.402.2127S,2013MNRAS.436..819J} in the $\Lambda$CDM paradigm is complicated by the absence of baryonic physics, which we expect to be important given that the alignment of interest is that of the observed, baryonic component of galaxies. So, we either need simulations that include the physics of galaxy formation or $N$-body simulations with rules for galaxy shapes and alignments. Proposed analysis methods to remove IA from weak lensing measurements either involve removing considerable amount of cosmological information (which requires very accurate redshift information; nulling methods: \citealt{2008A&A...488..829J, 2009A&A...507..105J}), or involve marginalizing over parametrized models of how the intrinsic alignments affect observations as a function of scale, redshift and galaxy type \citep[e.g., ][]{2007NJPh....9..444B,2010A&A...523A...1J,2012JCAP...05..041B}. The simultaneous fitting method, with a relatively simple intrinsic alignments model, was used for a tomographic cosmic shear analysis of CFHTLenS data \citep{2013MNRAS.432.2433H}. The latter methods, while preserving more cosmological information than nulling methods, can only work correctly if there is a well-motivated intrinsic alignments model as a function of galaxy properties. Existing candidates for the intrinsic alignment model to be used in such an approach include the linear alignment model \citep{2004PhRvD..70f3526H} or simple modifications of it (e.g., using the nonlinear power spectrum: \citealt{2007NJPh....9..444B}), $N$-body simulations populated with galaxies and stochastically misaligned with halos in a way that depends on galaxy type \citep{2006MNRAS.371..750H}, and the halo model \citep{2010MNRAS.402.2127S}, which includes rules for how central and satellite galaxies are intrinsically aligned. In this study, we use the large volume, high-resolution hydrodynamic simulation, MassiveBlack-II \citep{2014arXiv1402.0888K}, which includes a range of baryonic processes to directly study the shapes and alignments of galaxies. In particular, we measure directly the shapes of the dark and stellar matter components of halos and subhalos (modeled as ellipsoids in three dimensional space). We examine how shapes evolve with time and as a function of halo/subhalo mass. Previous work used $N$-body simulations and analytical modeling to study triaxial shape distributions of dark matter halos as a function of mass and their evolution with redshift \citep{{2005ApJ...618....1H},{2006MNRAS.367.1781A},{2005ApJ...632..706L},{2012JCAP...05..030S}}. More recently, hydrodynamic cosmological simulations have also been used to study the effects of baryonic physics on the shapes of dark matter halos \citep{{2005ApJ...627L..17B},{2006EAS....20...65K},{2010MNRAS.405.1119K},{2013MNRAS.429.3316B}}. Here, using a high-resolution hydrodynamic simulation in a large cosmological volume that incorporates the physics of star formation and associated feedback as well as black hole accretion and AGN feedback, we focus on measuring directly the shapes of the stellar components of galaxies and examine the misalignments between stars and dark matter in galaxies (central and satellite). We also measure the projected (2D) shapes for comparison with observations. This study is important because the measured intrinsic alignments of galaxies are related to the projected shape correlations of the stellar component of subgroups (galaxies) by the density-ellipticity and ellipticity-ellipticity correlations \citep{2006MNRAS.371..750H}. By measuring the projected ellipticities of the stellar and dark matter component of simulated galaxies, we can attempt to understand the differences between these two. In addition, we can do a basic comparison of the stellar components with observational results, and validate the realism of the simulated galaxy population. Another aspect of the problem that we consider in this paper is the relative orientation of the stellar component of the halo with its dark matter component. Many dark matter-only simulations have illustrated that dark matter halos exhibit large-scale intrinsic alignments \citep[e.g., ][]{2002A&A...395....1F,2005ApJ...618....1H,2006MNRAS.370.1422A,2006MNRAS.371..750H}, but the prediction of galaxy intrinsic alignments from halo intrinsic alignments requires a statistical understanding of the relationship between galaxy and halo shapes. To date, there has been no direct measurement of galaxy versus halo misalignment with a large statistical sample of galaxies through hydrodynamic simulations. Recently, \cite{2014arXiv1402.1165D} studied the alignment between the spin of galaxies and their host filament direction using a hydrodynamical cosmological simulation of box size $100\hmpc$. Studies of misalignment based on SPH simulations of smaller volumes detected misalignments between the baryonic and dark matter component of halos \citep{{2003MNRAS.346..177V},{2005ApJ...628...21S},{2010MNRAS.405..274H},{2011MNRAS.415.2607D}}. These studies considered the correlation of spin and angular momentum of the baryonic component with dark matter. The spin correlations are arguably more relevant for the intrinsic alignments of spiral galaxies \citep{2004PhRvD..70f3526H}, whereas the observed intrinsic alignments in real galaxy samples are dominated by red, pressure-supported, elliptical galaxies \citep{2011MNRAS.410..844M,2011A&A...527A..26J}; hence a study of the correlation of projected shapes is more relevant for the issue of weak lensing contamination. However, to make precise predictions based on the halo or subhalo mass at different redshifts, we need a hydrodynamic simulation of very large volume and high resolution. The MassiveBlack-II SPH simulation meets those requirements, making it a good choice for this kind of study. Others arrived at constraints on misalignments using $N$-body simulations and calibrating the misalignments by adopting a simple parametric form to agree with observationally detected shape correlation functions \citep{{2009RAA.....9...41F},{2009ApJ...694..214O}}. There are also studies of the alignment of a central galaxy with its host halo where it is assumed that the satellites trace the dark matter distribution \citep[e.g., ][]{2008MNRAS.385.1511W}. By using hydrodynamic simulations, we can directly calculate the misalignment distributions for all galaxies as a function of halo mass and cosmic time. Resolution of the galaxies into centrals and satellites also helps to understand the effect of local environment. This paper is organized as follows. In Section~\ref{S:methods}, we describe the SPH simulations used for this work and the methods used to obtain the shapes and orientations of groups and subgroups. In Section~\ref{S:shapes}, we give the axis ratio distributions of dark matter and stellar matter of subgroups. In Section~\ref{S:misalignments}, we show our results for misalignments of the stellar component of subgroups with their host dark matter subgroups. In Section~\ref{S:censat} we compare the shape distributions and misalignment angle between centrals and satellites. Finally, we summarize our conclusions in Section~\ref{S:conclusions}. The functional forms for our results are provided in the Appendix. | \label{S:conclusions} In this study, we used the MBII cosmological hydrodynamic simulation to study halo and galaxy shapes and alignments, which are relevant for determining the intrinsic alignments of galaxies, an important contaminant for weak lensing measurements with upcoming large sky surveys. While $N$-body simulations have been used in the past to study intrinsic alignments, it is also important to study the effects due to inclusion of the physics of galaxy formation; this includes effects both on the overall shapes (ellipticities) of the galaxies and halos, but also on any misalignment between them. In order to study this particular issue, we measured the shapes of dark matter and stellar component of groups and subgroups. Previous studies have used $N$-body simulations to study the mass dependence and redshift evolution of the shapes of dark matter halos and subhalos \citep{{2005ApJ...632..706L},{2006MNRAS.367.1781A},{2007ApJ...671.1135K},{2008MNRAS.385.1511W},{2008MNRAS.388L..34K},{2012JCAP...05..030S}}. Our results are qualitatively consistent with several trends identified in previous work. The first such trend that we confirm using SPH simulations is that subhalos are more round than halos \citep{{2006EAS....20...65K},{2007ApJ...671.1135K}}. The second trend that we confirm is that the shapes of less massive subhalos are more round than more massive subhalos \citep{{2008MNRAS.388L..34K},{2008MNRAS.385.1511W}} and as we go to lower redshifts, the subhalos also tend to become rounder \citep{{2005ApJ...618....1H},{2006MNRAS.367.1781A},{2012JCAP...05..030S}}. The effect of including baryonic physics on the shapes of dark matter halos was studied previously using hydrodynamic simulations in a box of smaller size and resolution compared to ours \citep{{2006EAS....20...65K},{2010MNRAS.405.1119K},{2013MNRAS.429.3316B}}. \cite{2006EAS....20...65K} found that the axis ratios of dark matter halos increase due to the inclusion of gas cooling, star formation, metal enrichment, thermal supernovae feedback and UV heating. \cite{2013MNRAS.429.3316B} found that there is no major effect on shapes under strong feedback, but they observed a significant change in the inner halo shape distributions. \cite{2010MNRAS.405.1119K} found that there is no effect on the shapes of dark matter subhaloes, where they included gas dynamics, cooling, star formation and supernovae feedback. Here, we took advantage of the extremely high resolution of MBII to directly study the mass dependence and redshift evolution of the shapes of the stellar component of subhalos in addition to dark matter. However, we did not study the effect of baryonic physics on dark matter shapes by comparison with a reference dark matter only simulation in this work. We found that the shapes of the dark matter component of subhalos are more round than the stellar component. Similar to dark matter subhalo shapes, the shapes of the stellar component also become more round as we go to lower masses of subhalos and lower redshifts. We are also able to calculate the projected rms ellipticity per single component for stellar matter of subhalos, which can be directly compared with observational results in \cite{2012MNRAS.425.2610R}. While the observed result is 0.36 at the given mass range, from our simulation, we measured a value of 0.28 at $z = 0.3$ for $M > 10^{12}$\hMsun, which is close, particularly given the uncertainties that result from observational selection effects that are not present in the simulations and that drive the RMS ellipticity to larger values, and given the different radial weighting in the two measurements. By modelling subhalos as ellipsoids in 3D, we are able to calculate the misalignment angle between the orientation of dark matter and stellar component. Previous studies of misalignments in simulations used either low-resolution hydrodynamic simulations, or $N$-body simulations with a scheme to populate halos with galaxies and assign a stochastic misalignment angle and other assumptions \citep{{2005ApJ...628...21S},{2006MNRAS.371..750H},{2009RAA.....9...41F},{2009ApJ...694..214O},{2010MNRAS.405..274H},{2011MNRAS.415.2607D}}. By direct calculation from our high-resolution simulation data, we found that in massive subhalos, the stellar component is more aligned with that of dark matter, qualitatively similar to results that have been inferred previously through other means. For instance, at $z = 0.06$, the mean misalignment angles in mass bins from $10^{10.0} - 10^{11.5}$\hMsun, $10^{11.5} - 10^{13.0}$\hMsun, and $10^{13.0} - 10^{15.0}$\hMsun\ are $34.10^{\circ}$, $27.73^{\circ}$, $13.87^{\circ}$, respectively. The amplitude of misalignment increases as we go to lower redshifts. The total mean misalignment angle of $30.05^{\circ}$, $30.86^{\circ}$, $32.71^{\circ}$ at $z = 1.0$, $0.3$, $0.06$ respectively shows an increasing trend, though the trend is far weaker than trends with mass at fixed redshift. We also found that the misalignments are larger for 3D shapes when compared to projected shapes. It is to be noted here that we have not split our sample of subhalos according to the type of galaxy. The dependence of our results on galaxy type or color will be investigated in a future study. It is fairly well established that the alignment mechanism for discs and elliptical galaxies is different, so this is a necessary next step to obtain measurements which can be directly compared against observations and used as input for modeling. Finally, we considered the axis ratios and misalignments in central and satellite subgroups according to their parent halo mass and individual mass of subgroups. We concluded that the shape of stellar component of satellites is more round than that of centrals. We also conclude that the satellite subgroups are more aligned when compared to centrals in similar mass range. Observationally, it is not possible to directly measure the misalignments in centrals and satellites. Misalignment studies for central galaxies were done earlier by \cite{{2008MNRAS.385.1511W},{2009ApJ...694..214O}}. Using data and Monte Carlo simulations, \cite{2008MNRAS.385.1511W} predict a Gaussian distribution of misalignment angle with zero mean and a standard deviation of $23^{\circ}$ for their sample of red and blue centrals. \cite{2009ApJ...694..214O} used $N$-body simulations and an HOD model for assigning galaxies to halos. The alignment of central LRG's with host halos is assumed to follow a Gaussian distribution with zero mean. Okumura et al. arrived at a standard deviation of $35^{\circ}$ to match the observed ellipticity correlation. Our predictions of misalignments for central and satellite subgroups are direct measurements that could be done through hydrodynamic simulations which include the physics of star formation. In conclusion, we found that the axis ratios of the shapes of stellar component of subhalos are smaller when compared to that of dark matter. The shapes of both dark matter and stellar component tend to become more round at low masses and low redshifts. We measured the misalignment between the shapes of dark matter and stellar component and found that the misalignment angles are larger at lower masses and increase slightly towards lower redshifts. We found that the dependence is more on the mass of subhalo than redshift. Finally, we split our subhalos sample into centrals and satellites and found that in similar mass range, the satellites have smaller misalignment angles. We initiated this study with the goal of predicting intrinsic alignments and constraining their impact on weak gravitational lensing measurements. In this paper, we presented our results on the axis ratios and orientations of both the dark matter and stellar matter of subhalos. Future work will include the dependence of these results on the radial weighting function used to measure the inertia tensor (as in \citealt{2012JCAP...05..030S}), galaxy type and the difference between the shape of the stellar mass versus of the luminosity distribution. We will also present our results on the intrinsic alignment two-point correlation functions in a future paper. Finally, future work should include investigation of the impact of changes in the prescription for including baryonic physics in the simulations. % | 14 | 3 | 1403.4215 |
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