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1609 | 1609.00022_arXiv.txt | We identify a pre-explosion counterpart to the nearby Type~IIP supernova ASASSN-16fq (SN~2016cok) in archival Hubble Space Telescope (HST) data. The source appears to be a blend of several stars that prevents obtaining accurate photometry. However, with reasonable assumptions about the stellar temperature and extinction, the progenitor almost certainly had an initial mass $M_* \ltorder 17 M_\odot$ and was most likely in the mass range $M_*=8$-$12M_\odot$. Observations once ASASSN-16fq has faded will have no difficulty accurately determining the properties of the progenitor. In 8 years of Large Binocular Telescope (LBT) data, no significant progenitor variability is detected to RMS limits of roughly 0.03~mag. Of the six nearby SN with constraints on low level variability, SN~1987A, SN~1993J, SN~2008cn, SN~2011dh, SN~2013ej and ASASSN-16fq, only the slowly fading progenitor of SN~2011dh showed clear evidence of variability. Excluding SN~1987A, the 90\% confidence limit implied by these sources on the number of outbursts over the last decade before the SN that last longer than 0.1~years (FWHM) and are brighter than $M_R<-8$ mag is approximately $N_{out} \ltorder 3$. Our continuing LBT monitoring program will steadily improve constraints on pre-SN progenitor variability at amplitudes far lower than achievable by SN surveys. | \label{sec:introduction} At the end of their lives, all massive ($\gtorder 8M_\odot$) stars must undergo core collapse once their iron cores become too massive to be stable. In most cases, this leads to a supernova (SN) explosion probably driven by some combination of neutrino heating and the effects of turbulence and convection (see the recent review by \cite{Muller2016} and, e.g., recent results by \citealt{Couch2015}, \citealt{Dolence2015}, \citealt{Wongwathanarat2015}). The visible properties of the successful SNe then depend on the degree of mass loss, ranging from Type~IIP SN which have retained most of their hydrogen envelopes, to Type~Ic SN which appear to have been stripped even of helium (e.g., \citealt{Filippenko1997}). The mass loss is controlled by some combination of intrinsic effects such as winds and extrinsic effects such as binary mass transfer (see the review by \citealt{Smith2014b}). There is no strong requirement that more than roughly 50\% of core collapses lead to successful SN (e.g., neutrino backgrounds, \citealt{Lien2010}; star formation rates, \citealt{Horiuchi2011}; nucleosynthesis, \citealt{Brown2013}, \citealt{Clausen2015}) and a 10-30\% fraction of failed SN producing black holes without a dramatic external explosion is both expected in many modern analyses of the ``explodability'' of stars (e.g., \citealt{Ugliano2012}, \citealt{OConnor2013}, \citealt{Pejcha2015}, \citealt{Ertl2016}, \citealt{Sukhbold2016}) and would provide a natural explanation of the compact remnant mass function (\citealt{Kochanek2014}, \citealt{Kochanek2015}, \citealt{Clausen2015}). Indeed, scenarios for the recent gravitational wave detection of a merging black hole binary (\citealt{Abbott2016}) all invoke at least one failed SN (e.g., \citealt{Belczynski2016}, \citealt{Woosley2016}). A powerful means of probing these issues is to work out the mapping between successful SNe and their progenitor stars. This is a challenging observational program (see the reviews by \citealt{Smartt2009} and \citealt{Smartt2015}) which has slowly been carried out over the last 20 years (e.g., \citealt{VanDyk2003}, \citealt{Smartt2004}, \citealt{Li2006}, \citealt{Smartt2009b}, \citealt{EliasRosa2009}, \citealt{EliasRosa2011}, \citealt{Maund2011}, \citealt{VanDyk2011}, \citealt{Fraser2012}, \citealt{Fraser2014}). With one possible exception (\citealt{Cao2013}, \citealt{Folatelli2016}, see \cite{Eldridge2013} for a discussion of limits), all the identified progenitors are of Type~II (IIP, IIL, IIb, or IIn). As first pointed out by \cite{Kochanek2008} and then better quantified by \cite{Smartt2009b}, there appears to be a deficit of higher mass SN progenitors. In particular, \cite{Smartt2009b} only identified Type~IIP progenitors with masses of $\ltorder 17M_\odot$ even though stars up to $25$-$30M_\odot$ are expected to explode as red supergiants with most of their hydrogen envelopes. While attempts have been made to explain this using extinction by winds (\citealt{Walmswell2012}, but see \citealt{Kochanek2012}) or by modifying stellar evolution (e.g. \citealt{Groh2013}), the same problem of missing, higher mass progenitors is seen in examinations of the stellar populations near local group SN remnants (\citealt{Jennings2014}). \cite{Jerkstrand2014} also argue that no Type~IIP SN have shown nucleosynthetic evidence for a higher mass ($M_*>20M_\odot$) progenitor. Following the proposal of \cite{Kochanek2008}, \cite{Gerke2015} have been carrying out a search for failed SN with the Large Binocular Telescope (LBT), identifying one promising candidate (see also \citealt{Reynolds2015}). The progenitor of this candidate for a failed SN appears to be a red supergiant in exactly the mass range missing from searches for the progenitors of successful SN (Adams et al. 2016, in preparation). \begin{figure*} \centering \includegraphics[width=\textwidth]{fig1.ps} \caption{Final nuclear burning stages as a function of progenitor mass based on the standard, non-rotating, $12$-$100M_\odot$, solar metallicity models of \protect\cite{Sukhbold2014} and \protect\cite{Woosley2007}. The gray bands show, from top to bottom, the periods of core carbon, oxygen and silicon burning, separated by periods of shell burning. The points associated with SN~2009ip indicate the timing of its outbursts relative to its presumed explosion along with its estimated mass range. The sub-panel to the right shows 16 thin vertical lines for the (control) time periods sampled by PTF for 16 Type~IIn SN, with heavy black points and lines for the time periods associated with outbursts (\protect\citealt{Ofek2014}). The masses of the progenitors of these stars are unknown but they are generally assumed to be large. For comparison, the sub-panel also indicates the present day lower limits for the 1840 and 1655 outbursts of $\eta$~Car and P~Cyg. The boxes at lower masses show the progenitor mass ranges and the time periods that can be surveyed for progenitor variability for SN~1987A, SN~1993J, SN~2008cn, SN~2011dh, SN~2013ej, and ASASSN-16fq. For a Salpeter IMF with SN occurring in the mass range from $8$ to $100M_\odot$, 50\% of SN arise from the mass range from $8$ to $13.1M_\odot$. } \label{fig:bigpicture} \end{figure*} A second recent puzzle about SN progenitors is that some appear to have outbursts (\citealt{Pastorello2007}, \citealt{Fraser2013}, \citealt{Mauerhan2013}, \citealt{Ofek2014}, \citealt{Ofek2016}) and/or eject significant amounts of mass (see \citealt{Galyam2012}, \citealt{Smith2014b}) shortly before they explode. The most extreme mass-loss events ($\dot{M} \sim M_\odot$/year) likely explain the rare, superluminous Type~IIn SNe (\citealt{Smith2007}), but the inferred mass loss rates are frequently $\dot{M} \gtorder 10^{-3}M_\odot$/year even for normal Type IIn SNe (see, e.g., \citealt{Kiewe2012}). The local systems known to reach such extreme mass loss rates are the Luminous Blue Variables (LBVs), with $\eta$~Carinae as the most spectacular example (see \citealt{Humphreys1994}). The rate of $\eta$~Carinae-like events is roughly 10\% of the SN rate (\citealt{Kochanek2011}, \citealt{Khan2015a}, \citealt{Khan2015b}), which is sufficient to explain the occurrence of the extreme Type~IIn superluminous SN. Any association of LBV eruptions with the very late phases of stellar evolution would roughly require the typical $M_* \gtorder 50 M_\odot$ star to have at least one eruption in the $\sim 10^3$~year period after carbon ignition (\citealt{Kochanek2011}). On the other hand, theoretical models to explain pre-SN outbursts and Type~IIn SNe have favored mechanisms associated with the last few years, corresponding to the neon/oxygen burning phases or later (\citealt{Quataert2012}, \citealt{Shiode2014}, \citealt{Smith2014}, \citealt{Woosley2015}). In this picture, massive stars must have two separate mechanisms for triggering outbursts, one to explain the LBVs and a second to explain the pre-SN outbursts. The existence of any transients associated with the last $\ltorder 10^3$~years (or less) of stellar life requires a causal mechanism associated with these final phases (see the discussion in \citealt{Kochanek2011}). Figure~\ref{fig:bigpicture} shows the dependence of the final nuclear burning stages on progenitor mass for the standard, non-rotating, $12$-$100M_\odot$, solar metallicity models of \cite{Sukhbold2014} and \protect\cite{Woosley2007}. We show the periods of core and shell carbon, oxygen and silicon burning -- the neon burning phase is not as energetically important. The large scale structure in Figure~\ref{fig:bigpicture}, with the shortest time scales for intermediate masses, is driven by the rapid increase in mass loss for the higher mass stars. The smaller scale variations in the mass-dependence of the post-carbon burning phases are due to the complex interplay of the burning phases and their consequences for structure of the stellar core (see \cite{Sukhbold2014} for a detailed discussion). We illustrate the outbursts associated with Type~IIn SN in Figure~\ref{fig:bigpicture} by SN~2009ip and the Palomar Transient Factory (PTF) sample of Type~IIn SN considered by \cite{Ofek2014}. SN~2009ip has an estimated progenitor mass of $50$-$80M_\odot$ (\citealt{Smith2010}) and showed a series of outbursts before the apparent explosion (see, e.g., \citealt{Smith2010}, \citealt{Foley2011}, \citealt{Mauerhan2013}, \citealt{Pastorello2013}, \citealt{Margutti2014}). For the PTF sample, the progenitor masses are unknown. PTF data are available for the last few years before the SN, as shown by the lines spanning the survey times for each SN. \cite{Ofek2014} detect 5 outbursts and argue that it is highly probable that all Type~IIn SN experience outbursts and that many are simply missed due to the survey depth and cadence. The outbursts shown in Figure~\ref{fig:bigpicture} are associated with the very last phases of carbon shell burning through the early phases of oxygen shell burning. It seems probable, particularly in the case of SN~2009ip, that outbursts cannot be restricted to the time period after the initiation of core oxygen burning. As a contrast, if the eruption mechanism of LBVs had any correlation with these last phases, it would have to be associated with the carbon burning phase, as illustrated in Figure~\ref{fig:bigpicture} by the 1840 and 1655 outbursts of $\eta$ Car and P Cygni (see \citealt{Humphreys1994}). Broadly speaking, there are two possible scenarios associated with these pre-SN transients. The first option is that only the high amplitude events seen in the SN surveys or implied by the Type~IIn SNe exist and they are associated with a very narrow range of progenitor parameter space (e.g. mass, metallicity, rotation). The second option is that the outburst mechanism is relatively generic, and the existing events simply represent the high amplitude tail of a much broader distribution. Unfortunately, the existing systematic searches for outbursts (e.g. \citealt{Ofek2014}, \citealt{Bilinski2015}, \citealt{Strotjohann2015}) are all part of searches for supernovae and essentially cannot detect significantly lower amplitude transients. Like building the mapping between SN and progenitors, building the mapping between pre-SN outbursts and progenitors requires surveys of much greater sensitivity than searches for SN. Unfortunately, where data deep enough to observe progenitors are already rare, having multiple epochs of such data to study progenitor variability is rarer still. At present, such data only exists for the progenitors of SN~1987A (see \cite{Plotkin2004} and references therein), SN~1993J (\citealt{Cohen1995}), SN~2008cn (\citealt{EliasRosa2009}, \citealt{Maund2015}), SN~2011dh (\citealt{Szczygiel2012}), and SN~2013ej (\citealt{Fraser2014}). These sources all have progenitor detections and mass estimates, placing them below $20 M_\odot$. Figure~\ref{fig:bigpicture} shows the region of progenitor mass and remaining life time the data can probe. The variability constraints for SN~1987A and SN~1993J are relatively poor and only SN~2011dh shows clear evidence for low levels of variability. All these systems are also in the $\ltorder 20M_\odot$ mass range suggested by \cite{Shiode2014} for wave-driven mass loss at solar metallicity and some are likely near the $\sim 10M_\odot$ mass range associated with the explosive silicon burning mechanism of \cite{Woosley2015}. \begin{figure*} \begin{center} \includegraphics[width=0.45\textwidth]{fig2a.ps} \includegraphics[width=0.45\textwidth]{fig2b.ps}\llap{\raisebox{0.0cm}{\includegraphics[width=2.5cm,height=2.5cm]{fig2c.ps}}} \end{center} \caption{Identification of a progenitor candidate for ASASSN-16fq. The left panel shows an image of the SN taken with LBT, aligned to the pre-explosion HST ACS/WFC F814W image shown in the right panel. The position of the SN is indicated in both panels. The inset in the right, pre-explosion panel shows a 3\farcs0$\times$3\farcs0 region centered on the progenitor candidate, with the derived SN position indicated.} \label{fig:progenitor} \end{figure*} Here we report on the properties of the progenitor of ASASSN-16fq (SN~2016cok). ASASSN-16fq was discovered (\citealt{Bock2016}) in NGC~3627 (M~66) by the All-Sky Automated Survey for Supernovae (ASAS-SN, \citealt{Shappee2014}) on 28 May 2016 and was spectroscopically classified as a Type~IIP SN (\citealt{Zhang2016}). There are multiple epochs of HST data because of the debated transient SN~1997bs (\citealt{VanDyk2000}, \citealt{Smith2011}, \citealt{Kochanek2012b}, \citealt{Adams2015}) and the Type~IIL SN~2009hd (\citealt{EliasRosa2011}, \citealt{Tinyanont2016}). It is also one of the galaxies monitored as part of the search for failed supernovae with the LBT (\citealt{Kochanek2008}, \citealt{Gerke2015}), allowing a deep search for progenitor variability over its last 8 years (see Figure~\ref{fig:bigpicture}). In \S2 we identify and describe the progenitor primarily based on archival HST data to make a rough estimate of its luminosity and initial mass. In \S3, we search for variability from the progenitor using the data from the LBT. We discuss the results in \S4, focusing on an extended discussion of supernova progenitor variability. Following \cite{Gerke2015}, we adopt a distance of $10.62$~Mpc from \cite{Kanbur2003} and a Galactic extinction of of $E(B-V)=0.03$~mag from \cite{Schlafly2011}. | We have clearly identified a counterpart to ASASSN-16fq in archival HST data. Unfortunately, our constraints on the properties of the progenitor are far from satisfactory, presumably due to the blending of multiple stars with the progenitor even at the resolution of HST. However, for a broad range of reasonable assumptions about its temperature and the amount of extinction, its properties are consistent with a lower-mass ($8$-$12M_\odot$) red supergiant. The data almost certainly require an upper mass limit of $M_* \ltorder 17 M_\odot$ that matches the mass limit associated with the red supergiant problem (\citealt{Smartt2009b}) or the more general problem of missing higher mass SN progenitors originally identified by \cite{Kochanek2008}. The only real escape from this conclusion is to give the progenitor a far higher than expected temperature, but this option quickly drives the progenitor luminosity to be extraordinarily high. While we view this possibility as unlikely, it would make the progenitor of ASASSN-16fq far more remarkable than simply making it a garden variety red supergiant of modest mass. Observations either with the LBT or HST once the SN has faded will have no difficulty making accurate photometric measurements of the progenitor. Table~\ref{tab:progvary} summarizes the available information on the variability of SN progenitors beyond the large outbursts probed by \cite{Ofek2014}, \cite{Bilinski2015} and \cite{Strotjohann2015}. Information is available for the Type~IIpec SN~1987A (photographic, \citealt{Plotkin2004}), the Type~IIb SN~1993J (V-band, \citealt{Cohen1995}), the Type~IIP SN~2008cn (V-band, \citealt{EliasRosa2009}, \citealt{Maund2015}), the Type~IIb SN~2011dh (R-band, \citealt{Szczygiel2012}) and the Type~IIP SN~2013ej (I-band, \citealt{Fraser2014}) in addition to ASASSN-16fq. Based on the review of \cite{Smartt2009}, we adopt progenitor masses of $14$-$20M_\odot$ for SN~1987A and $15 M_\odot$ for SN~1993J. We use an upper limit of $<16 M_\odot$ for SN~2008cn following \cite{Maund2015}, $(13\pm 3)M_\odot$ for SN~2011dh following \cite{Maund2011}, and $8$-$15.5M_\odot$ for SN~2013ej (\citealt{Fraser2014}). We use our estimate of $8$-$12 M_\odot$ from \S2 for ASASSN-16fq. We also report the time period spanned by the variability data and (roughly) the corresponding nuclear burning phases based on Figure~\ref{fig:bigpicture}. The data for SN~1987A, SN~1993J, SN~2008cn and SN~2013ej probably only sample the carbon shell burning phase. The LBT data for SN~2011dh, like that for ASASSN-16fq, probably samples the last phases of carbon shell burning through the early phases of oxygen shell burning. We can characterize the ``random,'' ``steady'', and ``outburst'' variability of these SN progenitors. Limits on the random variability are illustrated by the ``Var'' estimates of the intrinsic variability as a function of the progenitor mass in Figure~\ref{fig:vary2}. The variance ``Var'' is estimated by subtracting the mean of the reported photometric uncertainties ($\langle\hbox{Err}\rangle$) from the root mean square (RMS) of the light curve, ($\hbox{Var}=(\hbox{RMS}^2-\langle\hbox{Err}\rangle^2)^{1/2}$). The intrinsic variability is defined to be zero if the mean errors exceed the RMS, as is the case for SN~2013ej and the \cite{Maund2015} results for SN~2008cn. These quantities are reported in Table~\ref{tab:progvary}. Limits on the steady variability are illustrated in Figure~\ref{fig:vary3} by the estimates of the linear luminosity slopes as a function of progenitor mass. The upper limits used for all but SN~2011dh are drawn at the absolute value of the slope plus the error estimate. The slope estimates and the goodness of fit are included in Table~\ref{tab:progvary}. Of these SN, only SN~2011dh is clearly variable, but with the small number of epochs available to \cite{Szczygiel2012} it is also possible to interpret it as ellipsoidal variability given the binary models for the progenitor system by \cite{Benvenuto2013}. For comparison, typical slopes estimated from the end points of stellar evolution models are $10^{-3}$ to $10^{-4}$~mag/year (e.g., \citealt{Schaller1992}, \citealt{Heger2000}). The limit on the slope for SN~1987A is by far the tightest due to the long time span of the data. Obviously, these systems are heterogeneously selected and sample different final burning phases (see Figure~\ref{fig:bigpicture}), but they also appear to be the only published progenitors with adequate data to test for these lower levels of variability. We can characterize outbursts by adding Gaussian bursts in luminosity (quadratic in magnitude) defined by a peak luminosity $L_{peak}$ and a burst FWHM $t_{peak}$ to the light curves of all the sources in Table~\ref{tab:progvary} except SN~1987A. We allow the outbursts during an eruption time corresponding to the last $t_{out}$ before the SN. We normalize the available light curves to have a $\chi^2$ per degree of freedom, $N_{dof}$, of at most unity (i.e. ignoring the variability of SN~2011dh) when fit as having a constant flux. We then add model outbursts at random times and conservatively define detection to be when the $\chi^2$ for fitting the ``fake'' data containing an outburst as having a constant flux exceeds the larger of $2N_{dof}$ and $N_{dof}+4$. Figure~\ref{fig:outburst} shows the results, quantified as the detection probability per SN, $P_d$, for peak outburst luminosities of $M_R=-6$, $-8$, $-10$ and $-12$~mag, corresponding to $\lambda L_\lambda \simeq 10^{4.0}$, $10^{4.8}$ $10^{5.6}$ and $10^{6.4}L_\odot$. The detection probabilities can then be converted to 90\% confidence limits on the number of outbursts per SN as \begin{equation} N_{out} < { 2.30 \over N_{SN} P_d } = 0.46 P_d^{-1} \end{equation} where $N_{SN}=5$ since we have excluded SN~1987A from the analysis. The rate of eruptions during the eruption period is then $r_{out} = N_{out}/t_{out}$. The general pattern of the detection probabilities $P_d$ in Figure~\ref{fig:outburst} is relatively easy to understand. Short outbursts become increasingly difficult to detect because of the finite temporal sampling of the data. Long outbursts ultimately become difficult to detect because they show no time variability over the finite temporal extent of the data (although for sufficiently bright transients the luminosity would be incompatible with any progenitor). The results for long outbursts eventually correspond to the slope limits of Figure~\ref{fig:vary3}. The sensitivity is highest for eruption periods extending to roughly $10$~years because SN~1993J, SN~2008cn and SN~2013ej only contribute on these time scales. For the shortest eruption periods ($t_{out}$), only SN~2011dh contributes, and for long eruption periods, there is no information outside the last roughly $10$~years before the SN. Figure~\ref{fig:outburst2} shows outburst limits computed in the same manner for the sample of $27$ Type~IIb SN considered by \cite{Strotjohann2015} for comparison. \cite{Ofek2014} and \cite{Strotjohann2015} provide $5\sigma$ R-band luminosity limits, $L_{PTF}$, for 15~day bins of the data, each containing a variable number, $N_{PTF}$, of epochs. For simplicity, we simply spread the reported number of epochs uniformly over their 15 day bin (with temporal spacings of $1/2:1:1 \cdots 1:1:1/2$ over the bin), each with a ($1\sigma$) uncertainty per epoch of $L_{PTF}N_{PTF}^{1/2}/5$. We can then apply our formalism with only minor ambiguities for very short time scale ($t_{peak} \ltorder 15$~day) outbursts. Figure~\ref{fig:outburst2} shows the results for the \cite{Strotjohann2015} sample at $M_R=-12$ and $-10$~mag. The Type~IIn sample considered by \cite{Ofek2014} has even less sensitivity to low luminosity outbursts because the typical SN is more distant and there are fewer SN in the sample. As we can see from comparing Figures~\ref{fig:outburst} and \ref{fig:outburst2}, the PTF sample is more sensitive to very luminous outbursts and far less sensitive to outbursts closer to the progenitor luminosity. This is simply because, relative to the sample in Table~\ref{tab:progvary}, the PTF data has more continuous, but very shallow, coverage of a larger number of SN. The rate limits of the two samples cross near peak luminosities of $M_R=-12$~mag ($\lambda L_\lambda \simeq 10^{6.4}L_\odot$), where the relative sensitivity depends on the burst duration. By $M_R=-10$~mag ($\lambda L_\lambda \simeq 10^{5.6}L_\odot$), the deeper data we use here is more sensitive independent of the outburst duration. The PTF data has negligible sensitivity to the fainter $M_R=-8$ and $-6$~mag outbursts. In essence, the two approaches are complimentary. SN surveys like PTF will better constrain the rates of high luminosity, shorter transients -- they will generally have larger numbers of SN observed with higher cadence. However, even with the co-addition of data, SN surveys simply lack the sensitivity to probe variability significantly below $\sim 10$ times the luminosity of the progenitor stars. Deep monitoring data, like that from our LBT survey, are sensitive to very low levels of variability (down to $\sim 1\%$ of the progenitor luminosity, Figure~\ref{fig:vary1}), but are limited by the SN rate in nearby galaxies ($\sim 1$~year) and the lower cadence of any monitoring project on large telescopes. SN surveys like PTF are also largely limited to studying the relationships between outburst and SN properties, as done by \cite{Ofek2014}, because most of the SN will be too distant for measurements of the progenitor properties. Any survey which can measure variability on the scale of the progenitor luminosity or fainter can, by definition, also determine the properties of the progenitor. As a result, studies like the LBT survey (\citealt{Kochanek2008}, \citealt{Gerke2015}) are better suited to studying the relationship between outbursts and progenitors. An obvious next step is to systematically analyze the variability of all the SN progenitors in the LBT survey data, which will provide a relatively homogeneous, volume-limited sample, rather than the heterogeneous sample represented by Table~\ref{tab:progvary}. | 16 | 9 | 1609.00022 |
1609 | 1609.00487_arXiv.txt | We have selected a set of 17 visual binaries that demonstrate great inconsistency between the systemic mass obtained through Kepler's Third Law as compared to that calculated through standard mass-luminosity and mass-spectrum relationships. A careful inspection of orbital data and parallaxes showed that the current orbits of nine binaries (WDS 00155$-$1608, WDS 00174+0853, WDS 05017+2050, WDS 06410+0954, WDS 16212$-$2536, WDS 17336$-$3706, WDS 19217$-$1557, WDS 20312+1116, and WDS 21118+5959) do not need to be improved, instead we recommend different parallax (distance) value for them. On the other hand, we considered that eight orbits (WDS 02366+1227, WDS 02434-6643, WDS 03244-1539, WDS 08507+1800, WDS 09128$-$6055, WDS 11532-1540, WDS 17375+2419, and WDS 22408$-$0333) had to be improved. Due to various reasons mentioned in this paper, their distances should most likely be corrected unless better orbital solutions and/or more precise parallaxes are reported. To obtain consistent mass values, the use of the dynamical parallax is still recommended for 5 out of the 8 improved orbits. For WDS 02434$-$6643, WDS 09128$-$6055, and WDS 11532$-$1540, the improvement itself yields reasonable mass sums while maintaining $\pi_{Hip}$ within a 1-2 $\sigma$ margin. New distance estimates for 16 stars (mainly based on the obtained dynamical parallaxes) and individual comments for all objects are presented and discussed. | Visual binaries are a fundamental source of data on stellar masses as well as a key observational interface for theoretical stellar evolution models. The determination of accurate orbits in binary systems with well established parallaxes represents a direct and reliable method for obtaining the dynamical mass of stars through Kepler's Third Law, thus providing a useful constraint on binary star formation and evolution mechanisms (Torres 2010, Mathieu 1994). The direct application of Kepler's Third Law sometimes leads to an anomalous dynamical mass for various reasons such as poorly determined parallaxes and/or orbital elements, the existence of unknown companion(s), etc. The differential photometry of pairs whose combined brightness is usually well known allows us to estimate the luminosity and mass of individual components through empirical mass--luminosity (M$-$L) and mass--spectrum relationships (Gray 2005, Schmidt-Kaler 1982). Similarly, the accuracy of these relations is affected by various factors such as luminosity effects, magnitude difference, variability, etc. (See Table 1). In the paper of Malkov et al. (2012), dynamical masses were reported for a selected sample of 652 visual binaries with essentially good quality orbital solutions, along with estimated masses of their individual components. For a pair with reasonably well-determined orbital elements, any large difference between these two sums could possibly (but not only) indicate either an imprecise or even erroneous parallax. On the other hand, such inconsistent data represent a good starting point for a more detailed overview and further improvement of the actual orbital elements. Obviously, certain criteria should be applied in order to characterize the level of inconsistency and to select the final set of objects as well. In Section 2, we describe the requirements for the binaries to be selected for further analysis. We also explain the effect of the trigonometric parallax on the observed inconsistency between dynamical and photometric masses. Comments on particular systems along with brief presentations of their improved orbits and masses are given in Section 3. The obtained results are summarized in Section 4. | \label{sec:conclusions} Of 652 visual binaries with essentially good quality orbits, a set of 17 pairs with largely inconsistent (with standard mass-luminosity and mass-spectrum calibrations) dynamical masses was selected. The main results of this study can be summarized as follows:\\ $\bullet$ On the basis of a careful overview of orbital and astrophysical data, new distance estimates (differing from those of {\em Hipparcos}) that restore the observed dynamical mass consistency for 16 stars are suggested.\\ $\bullet$ We found no significant difference between original and reprocessed {\em Hipparcos} data applications when detecting dynamical mass inconsistency.\\ $\bullet$ Recent orbital solutions for 8 binaries are briefly discussed. Three of them led us to reasonable dynamical masses while remaining within the 1-2 $\sigma$ margin of the {\em Hipparcos} parallax.\\ $\bullet$ Inconsistency of different mass estimates should be considered as an indicator for imprecise parallax and/or orbital elements of the binary system.\\ $\bullet$ $M_{ph}$ is generally underestimated, especially for systems with large parallax error. | 16 | 9 | 1609.00487 |
1609 | 1609.01162_arXiv.txt | We report on a search for new low-surface-brightness galaxies (LSBGs) using Sloan Digital Sky Survey (SDSS) data within the GAMA equatorial fields. The search method consisted of masking objects detected with SDSS \photo, combining {\it gri} images weighted to maximise the expected signal-to-noise ratio (SNR), and smoothing the images. The processed images were then run through a detection algorithm that finds all pixels above a set threshold and groups them based on their proximity to one another. The list of detections was cleaned of contaminants such as diffraction spikes and the faint wings of masked objects. From these, selecting potentially the brightest in terms of total flux, a list of 343 LSBGs was produced having been confirmed using VISTA Kilo-degree Infrared Galaxy Survey (VIKING) imaging. The photometry of this sample was refined using the deeper VIKING $Z$ band as the aperture-defining band. Measuring their $g-i$ and $J-K$ colours shows that most are consistent with being at redshifts less than 0.2. The photometry is carried out using an \textsc{auto} aperture for each detection giving surface brightnesses of $\mu_{r} \ga 25$\,mag arcsec$^{-2}$ and magnitudes of $r > 19.8$\,mag. None of these galaxies are bright enough to be within the GAMA main survey limit but could be part of future deeper surveys to measure the low-mass end of the galaxy stellar mass function. | \label{sec:intro} Most galaxy surveys to date have been limited by a combination of apparent magnitude and surface-brightness (SB) constraints. This has led to an over-representation of luminous high-SB galaxies compared to a complete volume-limited sample \citep{Cross+02}. Generally, flux-limited samples have been used to construct our picture of galaxy types, e.g., the Hubble Tuning Fork \citep{Hubble+1926}. However, the majority of galaxies are, in fact, low-luminosity or low-mass `dwarfs' \citep{Binggeli+88,Karachentsev+04,Driver+05,Baldry+2012}. Whilst many are late-type spirals, they often do not fit neatly into the `tuning fork'. Dwarf galaxies have, for example, been classified as: irregulars \citep{Hubble+1926, DeVauc+1959}, dwarf ellipticals \citep{Shapley+38}, dwarf spheroidals \citep{DeVauc+1968}, blue compact dwarfs \citep{Zwicky+71}, little blue spheroids \citep{Kelvin+14}, blue diffuse dwarfs \citep{James+15}, and ultra diffuse galaxies \citep{vanDokkum+15}.\footnote{Note we do not include ultra-compact dwarfs \citep[UCDs;][]{Phillipps+01} in this classification list. They typically have half-light radii closer to the values of globular clusters \citep{Gilmore+07}, and are most likely the central star-cluster remnants of larger galaxies \citep{Jennings+15, Janz+16}. As \cite{Kissler+04} argued, they are ``neither dwarf galaxies nor ultra compact''.} $\Lambda$ Cold Dark Matter ($\Lambda$CDM) simulations have been used to make predictions for the number density of low-mass galaxies. When compared to observations these simulations show a discrepancy, known as the substructure problem \citep{Moore+99}, which can be characterised in two distinct ways. The first is the so-called missing satellite problem: the deficiency of the number of observed satellites, around the Milky Way in particular, compared to the number of sub-halos predicted by models \citep{Klypin+99, Moore+99}. The second deals with the discrepancy between the predicted number of halos and observed galaxies on a cosmological scale \citep[e.g.,][]{Peebles+01}. There has been progress towards reducing the discrepancy between simulations and observations in the Local Group with the discovery of many faint dwarf galaxies around the Milky Way \citep{Gilmore+07,Irwin+07,Walsh+07,Belokurov+10} and M31 \citep{Ibata+07,Martin+09,Richardson+11,Martin+132}. Furthermore, the number of galaxies in simulations can be reduced by, for example, changing cold dark matter to warm dark matter \citep{Xi+13,Lapi+15}, or by suppression of dwarf galaxy formation from a photo-ionizing background \citep{Benson+02_2,Somerville02}. Unlike their satellite counterparts, which have a more complex and turbulent formation history, field dwarf galaxies form and evolve in isolation. Despite processes such as supernova feedback \citep{Ferrara+2000} and heating from the cosmic ionising background radiation \citep{Hoeft+06}, they generally have a larger cool gas fraction and higher star formation rate than those dwarfs that are gravitationally bound to a larger system. Instead of being stripped away, most of their gas can cool back into the system \citep{Rosenbaum+09}. Thus, the simulations and observations of low-mass field galaxies test a different regime to satellite galaxies. There is currently a significant difference in the number density of low-mass systems ($10^{6.5}\msun < \mstar < 10^{7} \msun$) between observations and simulations. For instance \cite{Guo+11}, through the use of simulations, predicted a number density of 0.1 Mpc$^{-3}$ dex$^{-1}$. Currently the best observations put that number density at $\sim$ 0.02 Mpc$^{-3}$ dex$^{-1}$ within this mass range, from \cite{Baldry+2012} using the Galaxy And Mass Assembly \citep[GAMA;][]{Driver+09b} survey. Therefore, observations must push to deeper magnitudes, and lower masses, in order to test whether observational SB limits are the reason, or part of the reason, for the discrepancy. The detection of faint low-mass galaxies is challenging, dwarf systems have an intrinsically lower surface brightness than their higher-mass counterparts and so are more difficult to detect against the sky \citep{Disney+76,Disney+83,Kormendy+85,Baldry+08}. A typical definition in the literature for low-surface-brightness galaxies (LSBGs) is to have a central surface brightness of $\mu_{B} \ga 23$ mag arcsec$^{-2}$ \citep{McGaugh+96,Impey+1997}. This surface brightness makes them difficult to detect against the sky and leads to detection biases \citep{Disney+76}. Finding LSBGs is thus key to accounting for, and characterising, the dwarf galaxy populations of both satellites and isolated galaxies. A full accounting is needed to comprehensively test models of galaxy formation that include low-mass galaxies. \subsection{Searches for field dwarf galaxies} There are different environments to consider when searching for LSBGs and these environments can be broadly defined as: (i) nearby satellite galaxies within the Local Group (e.g.\ \citealt{Koposov+08,Walsh+09}); (ii) satellites in external groups and clusters (e.g.\ \citealt{Davies+16,vanDokkum+15}); and (iii) field galaxies away from luminous galaxies and clusters, or within a random cosmological volume. Compared to the Local Group, where stars can be resolved, and around luminous galaxies and in clusters, where deep imaging is more easily done and membership is more easily assigned, finding LSBGs in the field is more problematic. A large area of the sky needs to be covered in order to obtain a cosmologically representative sample. This means that a lower depth is obtained in the imaging compared with targeted cluster surveys given the same amount of observing time. In addition, redshifts need to be obtained for galaxies in order to assign distances \citep{BlantonLowLum+05,Geller+12}. To improve detection of these systems, specialised algorithms can be used to find LSBGs in images from wide surveys such as the Sloan Digital Sky Survey \citep[SDSS,][]{York+2000}. \cite{Kniazev+04} used SDSS data to search for galaxies of large angular size recovering most of the LSBGs from the \citet{Impey+96} catalogue. Fainter features can be found by coadding images paying careful attention to sky subtraction \citep{Fliri+16}; and/or known galaxies can be masked out, meaning specialised algorithms can be applied to the images to search for fainter light from LSBGs that were not initially detected \citep{Scaramella+09}. Similar techniques, including smoothing of masked images, can be used to search for low-SB tidal features \citep{Miskolczi+11}. \cite{James+15} used a search of the SDSS data to search for galaxies with similar morphology to Leo~P \citep{Giovanelli+13}, which has embedded H\two\ regions within a blue diffuse galaxy, and were able to detect $\sim 100$ of these sources. Star-forming dwarf galaxies dominate the field dwarf population \citep{Geha+12}. Therefore they can be detected using radio H\one\ surveys, such as the Arecibo Legacy Fast ALFA survey \citep[ALFALFA,][]{Giovanelli+05}, because they typically have high H\one\ to stellar mass ratios \citep{Baldry+08,Huang+12}. The searching of optical images is then eased considerably, by knowing where to look, for example: \cite{Trachternach+06} and \cite{Du+15} have confirmed many hundreds of new LSBGs based on their H\one\ detections, mostly in the field; \cite{Sand+15} confirmed five new blue diffuse dwarf galaxies within 10 Mpc, associated with `high-velocity clouds' found in ALFALFA data; and \cite{Tollerud+15}, using a blind H\one\ survey \citep[GALFA-H\one, ][]{Peek+11}, were able to detect two more faint diffuse galaxies, again within 10 Mpc. \subsection{Aims of this analysis} \label{sec:aims} The galaxy stellar mass function (GSMF) is a fundamental tool used in studying the demographics of galaxies \citep{Bell+03,Baldry+08,Muzzin+13}. It describes the number density of galaxies as a function of their mass within a volume of the Universe. The GAMA survey team has accurately described the GSMF down to $\mstar = 10^8 \msun$. The current incarnation, however, is likely incomplete at masses below this due to SB limits \citep{Baldry+2012}. As such, in order to push below this limit it is important to carry out a search of the SDSS DR7 data within the GAMA fields. SDSS data have been chosen for this work as this survey has already demonstrated its suitability for finding low-SB systems \citep{Kniazev+04}. The GAMA survey has made significant progress towards uncovering and classifying the dwarf population. For instance, \cite{Baldry+2012} showed that the most common type of galaxy in the Universe is likely star-forming dwarf galaxies rather than passive. \cite{Kelvin+14,Kelvin+14b} measured the contribution of `little blue spheroids', Sd spirals and irregulars to the low-mass and low-luminosity number densities. \cite{Mahajan+15} showed that star-forming dwarf galaxies formed a unimodal population using various photometric and derived properties. However, progress still needs to be made into the search for, and detection of, LSBGs within this survey to work towards completing the census of galaxies. This search is complicated, and the method employed depends on the type of data that is provided and the nature of the objects being searched for. The distance range desired for the detection of LSBGs in this paper is around 10 to 100\,Mpc, which places them beyond the range of the local group and volume \citep{McConnachie+12}. The volume out to 100\,Mpc over the GAMA equatorial fields is 18\,000\,Mpc$^3$. This is more cosmologically representative than studies in the local volume ($<10$\,Mpc) because of the larger volume and longer sight lines that cut through filaments and void-like regions. A specialised detection algorithm was developed to detect LSBGs, which are difficult to detect because of sky noise and artefacts. This paper deals with the method for the creation and implementation of such a search algorithm to find these LSBGs within SDSS imaging, with comparisons to VISTA Kilo-degree Infrared Galaxy Survey \citep[VIKING,][]{Edge+13} imaging. This is being used to confirm or deny a detection as the VIKING $Z$ band is $\sim 1$ magnitude deeper than SDSS $r$ band when compared to an average SED for a low-redshift galaxy \citep{Driver+12}. In future, we plan to focus on finding similar objects in VIKING and, eventually, Kilo-Degree Survey (KiDS; \citealt{kuijken+11}) images which have deeper limits in surface brightness than SDSS. Initially this can be done using a standard method (e.g.\ Source Extractor), before using this information to create masks to then apply the methods described and tested in this paper. The outline of the paper is as follows. In \S\,\ref{sec:surveys}, the different survey data are described; \S\,\ref{sec:ImRed} deals with the development and implementation of the image processing code; \S\,\ref{sec:DetAl} describes the algorithm used to search the images to find the LSBGs hidden within; and \S\,\ref{sec:Results} presents the results and catalogue. Summary and conclusions are presented in \S\,\ref{sec:sum+con}. | \label{sec:sum+con} This work attempts to answer a simple question: are there any LSBGs hidden within the GAMA equatorial regions that could contribute to the low-mass end of the GAMA GSMF? Using images from the SDSS, and a specially developed algorithm to process the images and detect the objects it was discovered that whilst there are LSBGs, they do not meet the required magnitude cut of $r < 19.8\,$mag. Therefore they do not affect the GAMA GSMF at low masses as presented in \cite{Baldry+2012}. If they are low-mass galaxies, they could be significant for any attempt to measure further down the GSMF using a deeper sample such as from the Wide Area VISTA Extragalactic Survey (WAVES; \citealt{DriverWave+16}). The algorithm created consisted of several parts: the weighting and coadding of the images, masking, and smoothing to bring out any hidden objects within the images. A cut of $5\sigma$ was then applied to the images to identify any pixels with a high enough SNR to be considered a detection. After clumping the detected pixels into candidate objects, a set of constraints were applied to the these objects. This removed most of them as erroneous detections such as from extended wings of bright stars and galaxies that were not masked out, and from stray light from bright stars in neighbouring fields. After a final comparison to VIKING $Z$ band, 343 new galaxy detections were confirmed. The magnitudes and surface brightnesses of the final sample were determined primarily using an \textsc{auto} aperture. The majority of objects were consistent with being at low redshift, $z<0.2$, when comparing a $J-K$ vs $g-i$ plot of all candidates to the GAMA main survey (Fig.~\ref{fig:color}). This plot is a good proxy for photometric redshift and can give a visual indication of whether the objects are at low or high redshift. Only a minority are likely to be in our cosmological neighbourhood within 100\,Mpc, however, it should be noted that the uncertainties in the colours are probably underestimated because of the difficulty in measuring accurate photometry of LSBGs. Fig.~\ref{fig:sbmags} shows how the newly discovered sample compare to the main GAMA survey in terms of surface brightness and magnitude. It is clear that the systems discovered in this work are too faint to be included in any calculations of the GSMF using the GAMA main survey limit. However, the LSBG catalogue can be used in future studies as a test sample for deeper imaging in the same regions. Source detection software run on deeper imaging such as KiDS and VIKING should readily detect these galaxies, however, this is by no means a given as errors in sky subtraction and/or flat fielding can cause problems in identifying and characterising low-SB features and galaxies. In future, we plan to use a source extraction run on the VIKING-$Z$ band mosaics matched to the GAMA redshifts to improve on estimates of the low-mass end of GSMF. | 16 | 9 | 1609.01162 |
1609 | 1609.03956_arXiv.txt | Dark matter simulations can serve as a basis for creating galaxy histories via the galaxy-dark matter connection. Here, one such model by \citet{Bec15} is implemented with several variations on three different dark matter simulations. Stellar mass and star formation rates are assigned to all simulation subhalos at all times, using subhalo mass gain to determine stellar mass gain. The observational properties of the resulting galaxy distributions are compared to each other and observations for a range of redshifts from 0-2. Although many of the galaxy distributions seem reasonable, there are noticeable differences as simulations, subhalo mass gain definitions, or subhalo mass definitions are altered, suggesting that the model should change as these properties are varied. Agreement with observations may improve by including redshift dependence in the added-by-hand random contribution to star formation rate. There appears to be an excess of faint quiescent galaxies as well (perhaps due in part to differing definitions of quiescence). The ensemble of galaxy formation histories for these models tend to have more scatter around their average histories (for a fixed final stellar mass) than the two more predictive and elaborate semi-analytic models of \citet{Guo13,Hen15}, and require more basis fluctuations (using PCA) to capture 90\% of the scatter around their average histories. The codes to plot model predictions (in some cases alongside observational data) are publicly available to test other mock catalogues at https://github.com/jdcphysics/validation/ . Information on how to use these codes is in the appendix. | Galaxies are expected to form within the deep potential wells of dark matter halos (\citet{WhiRee78,Blu84}, for a general introduction see \citet{MovdBWhi10}). This galaxy-dark matter connection suggests that simulations of the histories and spatial distributions of dark matter halos can be used as scaffolding for models of galaxy histories and distributions. Simulating galaxy properties based upon dark matter simulations ranges from from detailed semi-analytic models (see, for example, reviews by \citet{Bau06,Ben10}) of several galaxy properties at all times, which model and predict many different processes, to models such as the halo model which assign galaxies of a certain kind to dark matter halos at a fixed time by requiring that they match observed clustering and number counts (\citet{Sel00,PeaSmi00,CooShe02}, also see more recent incarnations such as \citet{Hea16}) or variants such as conditional luminosity functions \citep{YanMovdB03}) or abundance matching in luminosity and (proxy for) halo mass (e.g. \citet{ValOst06,ConWec09}). The resulting galaxy distributions can then be compared to observations, testing the physical assumptions used in their construction. These methods are also used to construct mock galaxy catalogues (synthetic skies) to aid in designing and analyzing galaxy surveys. More time intensive hydrodynamical simulations, which include and thus fix the baryonic physics and subgrid models for each cosmological run are also being developed, see e.g. \citet{BorKra12,Nei12} for some comparisons of trade-offs. All of these approaches are currently being developed and extended. Here, a simple model defined by \citet{Bec15}\footnote{\citet{Bec15} more generally gives a probabilistic framework for combining simulations and observations to get simulated galaxy properties consistent with the chosen observations.} is explored. It creates statistical samples of galaxy formation histories based upon the growth of dark matter subhalos, producing stellar masses and star formation rates for every subhalo in the simulation. (In what follows the terms subhalo and halo will be used interchangeably unless specifically noted.) Much of the physics is encapsulated in an average relation between stellar mass and halo growth found by \citet{BWCz8,BWCshort}. \citet{BWCz8} matched observations of stellar mass functions and star formation rates to average dark matter halo histories at a series of redshifts, and found that \begin{equation} \frac{d M^*}{dt} \sim f(M_h,z(t)) \frac{dM_h}{dt} \; . \label{eq:dmsdmh} \end{equation} Each subhalo has stellar mass $M^*$ and subhalo mass $M_h$ (virial mass, in their approach). The star formation efficiency $f(M_h, z(t))$ is a weakly time dependent function of subhalo mass $M_h$ and is publicly available at www.peterbehroozi.com/data.html. The simple \citet{Bec15} model uses this relation for average stellar mass gain to assign stellar mass and star formation rates to individual subhalos throughout their histories in a dark matter simulation, once a rule for inheriting stellar mass from progenitor galaxies is added. \citet{Bec15} suggested one such rule for inheriting stellar mass, as well as the addition of a random component to star formation. (Stellar mass is also lost due to aging.) Galaxy distributions produced by the \citet{Bec15} model, with his simulation, have a $z=0$ galaxy stellar mass function close to observations. The $z=0$ star formation rates are also bimodal, although not agreeing as closely with observations in detail \citep{Bec15}. A wealth of galaxy properties follow from having a stellar mass and star formation rate attached to each galaxy throughout its history, in addition to the stellar masses and star formation rates themselves. Colors can be found by integrating a stellar population synthesis model over the star formation rate history. Galaxy positions, velocities and environments are immediate, inherited from the host dark matter simulation. In particular, colors are linked to environment inasmuch as environment affects halo growth. It is thus interesting to examine further properties of this model beyond redshift zero, and how it depends upon different simulations and other properties. The inheritance of stellar mass, the definitions of halo mass and halo mass gain, and the underlying dark matter simulation are all varied here, and compared to observations at redshifts 0 to 2. In addition, properties of the ensemble of resulting galaxy formation histories are compared to those of three other methods, two full blown semi-analytic models and one straw man model. Several other simple models have also been proposed, predicting an assortment of galaxy properties for redshifts zero and above, for example those by \citet{Wan07,Bou10,Cat11,MutCroPoo13,Lil13,TacTreCar13,Bir14,Lu14,Lu15}. The approach in the \citet{Bec15} model seems closest to that of \citet{MutCroPoo13}, as the stellar masses are tied to subhalo properties directly (with the gas physics implicit). The underlying simulations and the construction of the galaxy histories are described in \S \ref{sec:background}. In \S \ref{sec:simmeas}, comparisons are made with several observations at different redshifts. The ensemble of galaxy histories of this simple model are compared via PCA (as in \citet{CohVdV15}) to some other more predictive models based upon dark matter simulations, in \S \ref{sec:histories}. Discussion and conclusions are in \S\ref{sec:conc}. The appendix \S\ref{sec:appmsmh} gives the formulae in detail for the two stellar mass to halo mass prescriptions which are compared to the models in \S \ref{sec:simmeas}. Appendix \S\ref{sec:howto} describes how to make the plots used in \S\ref{sec:simmeas} for a single mock galaxy catalogue, using codes at https://www.github.com/jdcphysics/validation/ (the code valid\_suite.py in the code subdirectory vsuite). To use this code, a list of galaxy stellar masses, star formation rates and subhalo masses are needed as input, which can lie in either a light cone, a fixed time periodic box, or just have some fixed redshift and a random position (if generated analytically). Most of the observational data for these tests are in the redshift range 0 to 1, i.e. overlapping with redshifts at the centers of the currently running dark energy survey (DES, www.darkenergysurvey.org) and the upcoming LSST (www.lsst.org). | \label{sec:conc} The \citet{Bec15} model assigns stellar masses and star formation rates to subhalos in a dark matter simulation, primarily using halo mass gain to determine stellar mass gain. Galaxy distributions and histories were calculated for three different dark matter simulations, with differing cosmologies, mass definitions, mass history constructions and time step separations, to find out how much these simulation and other differences affect observable properties in this model, and how well the different variations match current observations at several redshifts. Bimodality in the star formation rate occurred for all implementations, with the scatter in the star forming branch roughly due to changes in accretion history, and the center and scatter for the quiescent branch put in by hand (which would otherwise be at zero star formation rate). The division between quiescent and star forming galaxies as a function of stellar mass and star formation rate differs from that found in \citet{Mou13}, but some difference may be due to differences stellar mass definitions. Another difference between these observations and the models is that the split between the model star forming and quiescent galaxies does not evolve as strongly as redshift increases (to higher star formation rates). This is in part because the center of quiescent branch, put in by hand, is currently fixed at all redshifts, while observationally the quiescent branch increases in star formation rate with redshift. (The model star forming branch does rise, although not fast enough for its peak to remain within the star forming branch of \citet{Mou13} at high redshift.) For stellar mass functions, no variant matched observations perfectly for all redshifts, although the best fit to stellar mass functions at low redshift was based on a simulation with cosmology and mass definition similar to that used to construct the model's star formation efficiencies. Using a simulation based upon the current best fit cosmology gives stellar mass functions which are too high at low redshift, consistent with the halo mass function being larger in the current best fit cosmology. At low redshift, using the instantaneous mass as dark matter halo mass rather than the smoothed and constrained $SAM\_M_{\rm vir}$ produced a slight increase in the stellar mass functions at the lower stellar masses, and using both instantaneous mass and only subtracting the mass of the most massive progenitor (rather than a weighted sum of all progenitor masses) gives a further increase. At high redshift, the stellar mass functions seem less sensitive to choices of halo mass and methods of inheriting stellar mass from progenitors. Some dependence upon cosmology remains. All tend to be high relative to the central value for the observed stellar mass functions, especially near the bend in the stellar mass function, although the models based upon the cosmology used to calculate the star formation efficiencies might be argued to be closer. Dividing the quiescent and star forming galaxies according to the bimodality seen in star formation rate, the quiescent galaxy stellar mass function tended to be too high for all models at low stellar mass. For the tree model, where satellite subhalos are assigned their infall mass aside from mergers, satellites are almost all quiescent (about 1 percent have enough random star formation to be classified as star forming using the 'by eye' separation from the $M^*-SFR$ diagrams). The excess of faint quiescent galaxies also appears in the other models, however, which can have 1/3 or more satellites which are forming stars. The models had two variations for inheriting stellar mass, from either 1 or 2 progenitors. These two cases tend to bracket the observed stellar mass function at low redshift and high stellar mass. At higher redshift, they get closer to each other but also increase relative to the observed stellar mass function, with both eventually lying mostly above at $z\sim 2$. The models all seem to be above the central stellar mass to halo mass relations calculated from observations, although close enough to be within errors for most cases. Aside from the tree model, the stellar mass to halo mass relation changed significantly between the 1 and 2 progenitor variants at high stellar mass, with the latter rising far above observations. These results suggest some ways to improve the model. \begin{itemize} \item Presumably the star formation efficiencies would work better for the current cosmology simulations if the efficiencies were calculated assuming the best current fit cosmology. This should help with the overshoot in estimated stellar mass for many redshifts, perhaps including the tendency to fall high at high redshift for all the models. In addition, more data is now available on stellar mass functions and star formation rates at these redshifts. \item Tying the star formation rate of satellites to subhalo mass gain for satellites is difficult in some halo finders, for instance those which fix the satellite subhalo mass to infall mass aside from mergers. % Perhaps some other way of having the satellite star formation rate evolve would also work (for instance the decaying star formation rate in \citet{Lu14}, or the delayed quenching of \citet{ajcf13}\footnote{I thank P. Behroozi for mentioning this latter variant is being explored by other groups.}). \item The quiescent branch, put in by hand, likely should increase in star formation rate as the redshift increases. \item It seems a combination of inheriting from 1 and 2 progenitors (or maybe more) might succeed. This could perhaps depend upon the stellar mass and/or mass ratios of progenitors\footnote{I thank M. van Daalen for these suggestions.}. For instance, \citet{MosNaaWhi13} note that for higher halo mass, more stellar mass comes in from mergers, so perhaps some sort of final halo mass dependence would also be appropriate. The stellar mass to halo mass relation often shows a strong sensitivity to 1 or 2 progenitors contributing stellar mass. \item The high values of $M^*(M_h)$ relative to observations, if not improved by changing the cosmology to the current best fit (the current best fit cosmology has more high mass halos than that used in the star formation efficiencies \citep{BolPla16}), may be improved by making more stellar mass go into the ICL, even from a single progenitor. \end{itemize} It would be also interesting if certain properties (e.g. the excess of faint quiescent galaxies at high redshift) could not be improved by only changing the small number of physical assumptions currently in the model. The underlying assumption is that galaxies self-regulate (e.g. as in \citet{OWLS,HopQuaMur11}) their growth, so that the influx of halo mass (and thus presumably baryons) combined with the mass dependence of star formation is enough to capture many of the properties of evolution. Looking at the ensemble of galaxy histories, with fixed final stellar mass, all 6 \citet{Bec15} based models considered had average histories differing from the semi-analytical models. For low final stellar mass galaxies, all 6 had very similar average histories, as final stellar mass increase, these became distinct. For the highest final stellar mass studied, $M^* = 10^{11} M_\odot$, the average histories of the 2 progenitor bol and bolp models, where the inherited stellar mass of a galaxy is the sum of that of its two largest progenitors, follows the average history of galaxies for which $M^*=M^*(M_h)$ at every time step. Compared to the two semi-analytic models, there is often more scatter around the average histories for the models constructed here (except for the highest final stellar mass), and they require the same or more basis fluctuations to capture at least 90\% of the variance. It would be interesting to see how other similar simple models, e.g., \citet{Wan07,Bou10,Cat11,MutCroPoo13,Lil13,TacTreCar13,Bir14,Lu14,Lu15}, compare in these ensemble properties as well. Given the simplicity of this model, it seems interesting to pursue it further, as it appears that many of its predictions work reasonably well at redshifts above zero. It would be interesting to look in further detail at the simulated galaxy populations, for instance to see if starbursting galaxies appear automatically within the population and if so, if their number agrees with observations. The dark matter simulations also include galaxy positions and velocities, and the full cosmological cosmic web. When more high redshift observations with large volume become available, it would be interesting to compare the model with additional observations such as clustering a function of stellar mass, star formation rate (once that is better understood in the model) and environmental properties. For instance, if conformity of central galaxies in halos is indeed tied to halo growth \citet{HeaBehvdB16}, see also \citet{HahPorDek09}, this effect is built into this model, as are other properties tying stellar mass and star formation rate to halo growth. It would also be interesting to push the model to higher redshifts. | 16 | 9 | 1609.03956 |
1609 | 1609.01738_arXiv.txt | {In this work we investigate the semi-classical backreaction for a quantised conformal scalar field and classical vacuum energy. In contrast to the usual approximation of a closed system, our analysis includes an environmental sector such that a quantum-to-classical transition can take place. We show that when the system decoheres into a mixed state with particle number as the classical observable de Sitter space is destabilized, which is observable as a gradually decreasing Hubble rate. In particular we show that at late times this mechanism can drive the curvature of the Universe to zero and has an interpretation as the decay of the vacuum energy demonstrating that quantum effects can be relevant for the fate of the Universe.} \emailAdd{[email protected]} \begin{document} | Devising a quantum theory of gravity has turned out to be an extremely difficult problem, which to this day remains without a complete solution. As originally suggested in \cite{mol,ros}, a useful approximation for the study of the backreaction of the quantum matter onto the spacetime geometry is obtained by treating space-time classically and using the expectation value of the quantised energy-momentum tensor as the source term in the Einstein equation \ee{G_{\mu\nu}= \f{8\pi G}{c^4}\langle\hat{T}_{\mu\nu}\rangle\,.\label{eq:semiE}} This semi-classical approach has many applications \cite{Birrell:1982ix}, most notably it may be used to predict black hole evaporation \cite{Hawking:1974sw}. In conditions where quantum gravity is unimportant this framework is expected to give reliable results, although it is not without issues \cite{Kuo:1993if,Kibble:1980ia,eppley}. Usually to a good approximation systems of macroscopic size can be described in terms of classical physics, despite the fact that the classical configurations that are frequently encountered in Nature are only a small subset of all possible quantum states: quantum interference, or more descriptively, "cat states" named after Schr\"{o}dinger's famous thought experiment are generally absent. In the decoherence program the emergence of a classical reality from the quantum realm i.e. the quantum-to-classical transition is explained by using no other mechanisms than what are provided by quantum theory \cite{Zeh:1970zz,Zurek:1982ii,Zurek:1981xq,Joos:1984uk}, see \cite{Schlosshauer:2003zy,Zurek:2003zz,Zeh:1995jg,Kiefer:1997hv,Zurek:1991:vv} for a historical account and a more complete list of references. The key element is the realization that a macroscopic quantum system is never completely isolated or closed and inevitably its wave function will be influenced by environmental degrees of freedom, which themselves are not directly observable. This results in a change of the systems characteristics, where the quantum phases decohere leading to a suppression of the interference terms while the eigenstates of the classical observables remain intact. In a way decoherence sifts through the Hilbert space of all states filtering out the ones that are the most stable under environmental monitoring \cite{Kuebler:1973mm,Zurek:1992mv,Zurek:1993:pu,Zurek:1998ji}. Hence, decoherence provides an explanation why classicalization occurs and which particular observables are the robust classical ones. In the inflationary paradigm, decoherence is vital for the predictions for the large scale structure of the Universe in that it provides a mechanism by which initially quantum fluctuations transform into classical perturbations \cite{Polarski:1995jg,Kiefer:1998qe,Kiefer:2006je,Campo:2008ju,Campo:2008ij, Kiefer:2008ku,Burgess:2006jn,Burgess:2014eoa,Martineau:2006ki,Nelson:2016kjm}. This highlights a more general crucial feature of quantum theory: in order to obtain predictions that are in accord with the classical world around us, one must often consider an open quantum system, see for example \cite{Calzetta:2008iqa,Giulini:1996nw} for more discussion. As one of the main points of this work we argue that an unobservable environmental sector and in particular decoherence can also qualitatively change the predictions of semi-classical gravity, as advocated also in \cite{Tegmark:2011pi}. Some of the issues of closed quantum systems can be understood by considering the evolution of pure states: unitarity forces a pure state to always remain pure and hence to contain no entropy. For the many examples of cosmological particle creation \cite{Bernard:1977pq,Parker,Audretsch:1978qu, Parker:1968mv,Parker:1968mv1,Parker:1968mv3} this implies that the system contains correlations not present in a thermal distribution, despite a thermal average particle number \cite{Kandrup:1988sg,Kandrup:1988zv, Hu:1986jd,Parker:2009uva,Hu:1986jj}. For example, in the Unruh effect \cite{Unruh:1976db} where an accelerated observer sees the Minkowski space vacuum -- a pure state -- as thermally occupied, a truly thermal state is obtained only after a coarse graining over the unobservable environment is performed \cite{Crispino:2007eb,Unruh:1983ms}. A similar step is also required for obtaining a thermal density matrix for black holes \cite{Hawking:1976ra}. An increase in entropy can be seen as loss of information \cite{Shannon:1948zz,Jaynes:1957zza} and is a generic result of coarse graining because an open system can disperse information from the system into the environment. Open quantum systems in particle creation and semi-classical backreaction are investigated in \cite{Calzetta:1993qe,Hu:2008rga,Calzetta:1990zu, Calzetta:1999zr,Paz:1991nd,Anderson:2005hi, Calzetta:1995ys, Kiefer:2001wn} and coarse graining in the cosmological context is studied in \cite{Kandrup:1988zv,Hu:1986jd,Hu:1986jj,Brandenberger:1992jh,Prokopec:1992ia, Gasperini:1993yf,KeskiVakkuri:1993vk,Lin:2010pfa}. Due to the highly symmetric nature of de Sitter space, its stability in the quantised theory has been the subject of considerable interest \cite{Tsamis:1996qq2,Padmanabhan:2002ha,Tsamis:1996qq3,Geshnizjani:2002wp,Unruh:1998ic,Geshnizjani:2003cn,Tsamis:1996qq, Tsamis:1996qq0,Tsamis:1996qq1,Brandenberger:1999su,ford,Bousso:2001mw,Torrieri:2015kla,Polyakov:2007mm,Polyakov:2007mm1, Polyakov:2007mm2,akh,Marolf:2010zp,Marolf:2010nz,Marozzi:2006ky,Marozzi:2012tp,Finelli:2011cw,Marozzi:2014xma,ArkaniHamed:2007ky,Greene:2005wk, Rigopoulos:2016oko,Firouzjaee:2015bqa,clif,Antoniadis:1985pj,Markkanen:2016vrp,Mottola:1984ar,Mottola:1985qt, Anderson:2013ila,Anderson:2013ila1,Kachru:2003aw,Goheer:2002vf,Sekiwa:2006qj,Padmanabhan:2003gd,Koivisto:2010pj, Albrecht:2014hxa,Rajaraman:2016nvv}. In the semi-classical approach the global de Sitter manifold that includes a contracting phase has been argued to be unstable in \cite{Mottola:1984ar,Anderson:2013ila,Anderson:2013ila1}. However, in the current cosmological framework the primary interest is in the exponentially expanding patch of de Sitter space as given by the flat Friedmann--Lema\^{i}tre--Robertson--Walker (FLRW) % coordinates. In the expanding patch it has been shown that at least in the semi-classical approach for a closed system with a non-interacting scalar field and a non-tachyonic effective mass the system equilibrates to a de Sitter invariant state, the Bunch-Davies vacuum, and no instabilities arise \cite{Anderson:2000wx,markrajan,Habib:1999cs,Albrecht:2014hxa}. But in a scenario where the Bunch-Davies state is allowed to decohere it is not obvious that de Sitter symmetry can be respected. In fact, a violation of de Sitter symmetry from decoherence has been noted to arise when the inflationary perturbations classicalise \cite{Kiefer:2008ku}. Via the semi-classical approach we will study the effects from decoherence in a model consisting of a conformal quantum scalar field and classical vacuum energy, with a focus on the implications for the fate of a Universe dominated by dark energy. When the system is closed this scenario leads to eternal exponential expansion, but we argue that decoherence can change this conclusion. We will work in the units $\hbar\equiv c\equiv k_B\equiv1$ and with the conventions (+,+,+) of \cite{Misner:1974qy}. | The decoherence program has provided a compelling explanation as to why out of all the states allowed by quantum theory only the ones we may characterize as classical are frequently encountered in Nature. The key realization is that macroscopic systems are never closed but continuously influenced by their environment. This leads to the suppression of quantum interference. As this continuous environmental monitoring alters the state of the system also the gravitational backreaction changes. In this work we have studied backreaction via the semi-classical Einstein equation for a model consisting of a conformally coupled scalar field and classical vacuum energy in the presence of a decoherence inducing environment. Our approach was to postulate that % interference between particle number eigenstates is negligible producing a classical statistical ensemble of states with definite particle number. This was motivated by the fact that at least for the current Universe with weak curvature, to a good approximation particles are robust classical observables. Choosing the pointer basis to be something different than the number basis is likely to lead to different results. For example, the classicalization of the primordial pertubations from inflation is believed to take place in the field amplitude basis \cite{Polarski:1995jg,Kiefer:2006je,Kiefer:2008ku,Burgess:2006jn}, although with a similar violation of de Sitter invariance \cite{Kiefer:2008ku}. Precisely determining a pointer basis for a conformal scalar field in the late time Universe presumably would require a first principle analysis with a specific chosen form for the environmental interaction. For a closed system with a conformal scalar field on a de Sitter background the Bunch-Davies vacuum acts as an equilibrium state and is a stable solution under semi-classical backreaction \cite{markrajan}. But it is also a state with no entropy and in the presence of an environment that decoheres the system leading to particles as classical observables any entropy generation results in particle creation and a violation of de Sitter invariance. Because of the competing nature of the two effects, the equilibration of the quantum field into a pure state due to the expansion of space and the transforming of pure states into mixed ones via decoherence, the particle creation is expected to be continuous. This provides a mechanism by which over long periods of time the Hubble rate can be significantly reduced, which is the main conclusion of this work. By using the semi-classical approach we found a self-consistent solution for the Hubble rate in the presence of constant particle creation that after time scales $\sim10^{100}$-times the age of the Universe modified the dynamics of a spacetime intialized to de Sitter to eventually behave as $H\sim(M_{\rm pl}^2/t)^{1/3}$. We argued via consistency that this has an interpretation as the decay of the vacuum energy and has important implications for the fate of a Universe dominated by dark energy. Decoherence can be seen to arise from irreversible delocalization of information from the system into the unobservable environment. In this work we left the environment unspecified, but in order for this process to be possible some type of environmental degrees of freedom must exist. For a local observer it seems natural to assume observational access to only a subset of all possible degrees of freedom. For example, spacelike separations of events and, in particular for de Sitter space, particle horizons obviously impose loss of correlations. % Macroscopic observers probing the particle content of the Universe such as ourselves may as well play a role, in particular for inducing classicalization in the particle number basis. Although our discussion was kept free of a reference to a thermodynamic equilibrium, due to the deep connection between horizons and thermodynamics \cite{Gibbons:1977mu,Padmanabhan:2002sha,Padmanabhan:2003gd,Padmanabhan:2009vy} it is possible that also here a thermal interpretation is applicable. The "hot tin can" description valid for de Sitter space in static coordinates \cite{kof,Kaloper:2002cs,Susskind:2003kw} when implemented in an expanding space has already been shown to lead to very similar conclusions as presented here \cite{clif}. On general grounds a thermodynamic instability of de Sitter space was argued to exist in \cite{Antoniadis:2006wq,Mottola:1985qt,Sekiwa:2006qj}. % | 16 | 9 | 1609.01738 |
1609 | 1609.00328_arXiv.txt | \noindent Tram et al. 2016 recently pointed out in \cite{Tram:2016rcw} that power-law inflation in presence of a dark radiation component may relieve the $3.3\,\sigma$ tension which exists within standard \LCDM between the determination of the local value of the Hubble constant by Riess et al. (2016) \cite{R16} and the value derived from CMB anisotropy data \cite{planck2015} by the \Planck collaboration. In this comment, we simply point out that this interesting proposal does not help in solving the $\sigma_8$ tension between the \Planck data and, e.g., the weak lensing measurements. Moreover, when the latest constraints on the reionization optical depth obtained from \Planck HFI data \cite{newtau} are included in the analysis, the $H_0$ tension reappears and this scenario looses appeal. | \label{sec:introduction} The tension in the Hubble constant between the constraints coming from the \Planck satellite \cite{planck2013} and \cite{planck2015} and the local measurements of Riess at al. \cite{R11} and \cite{R16} has recently gained statistical significance ($3.3\,\sigma$) within the \LCDM framework, especially when considering the new constraints on the reionization optical depth obtained with \Planck HFI data \cite{newtau}. Many proposals have been suggested to solve this tension (see for example \cite{planck2013,planck2015,darkradiation,interacting,voids,Ben-Dayan:2014swa,variance,DiValentino:2016hlg,Bernal:2016gxb,Ko:2016uft}). Two possible extensions to the $\Lambda$CDM scenario have attracted significant attention. One is the possibility of a dark radiation component with $N_{\rm eff}>3.046$, which does not seem workable any more in light of the new \Planck HFI constraint on the optical depth \cite{newtau} for which $N_{\rm eff}=2.91_{-0.37}^{+0.39}$ at $95\%$ c.l. from Planck TTTEEE+SIMlow. The other extension is a dark energy equation of state different from $w = -1$ (see \cite{DiValentino:2016hlg}). However, recently, the authors of \cite{Tram:2016rcw} pointed out that, by considering a power-law inflation (hereafter PLI), introduced the first time by \cite{Lucchin:1984yf}, in presence of a dark radiation component, the local value of the Hubble constant by Riess et al. 2016 \cite{R16} and the most recent CMB anisotropy data by the \Planck collaboration \cite{planck2015} are in perfect agreement, provided $\Delta N_{\rm eff}=0.62\pm0.17$ at $68\%$ c.l.. Given the well-known correlations between parameters within \LCDM, we consider in this comment the implication of this scenario (PLI with a free dark radiation) for the $z=0$ linear power normalisation, $\sigma_8$ or clustering parameter. Indeed, within \Planck-normalised \LCDM, there is already a 2\,$\sigma$ tension with the weak lensing measurements of $\sigma_8$ from the CFHTLenS survey \cite{Heymans:2012gg, Erben:2012zw} and KiDS-450 \cite{Hildebrandt:2016iqg}. We also assess the effect of adding the CMB polarization $B$ modes constraint provided by the common analysis of \Planck, BICEP2 and Keck Array \cite{BKP}, or the new determination on the reionization optical depth obtained with \Planck HFI data \cite{newtau} (which was not considered by \cite{Tram:2016rcw}). | \label{sec:conclusions} Recently, the authors of \cite{Tram:2016rcw} pointed out that by considering a power law inflation model and a free dark radiation component, the local measurements of the Hubble constant provided by Riess et al. 2016 \cite{R16}, i.e., $H_0=73.00\pm1.75$ km/s/Mpc at $68\%$ cl, is in perfect agreement with the value that follows when analysing the \Planck CMB anisotropy data \cite{planck2015}, inducing a $\Delta N_{\rm eff}=0.62\pm0.17$ at $68\%$ cl. In this comment, we confront that scenario (PLI+dark radiation) with more data than initially considered. As noted in the previous section, the Hubble constant and the clustering parameter are positively correlated, therefore a higher $H_0$ value corresponds to an increased value of $\sigma_8$. When the $H_0$ tension subsides, this degeneracy produces a shift of the mean value of the clustering parameter which exacerbates the tension with the weak lensing measurements from the CFHTLenS survey \cite{Heymans:2012gg, Erben:2012zw} and KiDS-450 \cite{Hildebrandt:2016iqg} We then considered the implication of adding the CMB polarization $B$ modes dataset provided by the common analysis of \Planck, BICEP2 and Keck Array \cite{BKP}. In this case, interestingly, a value of $r$ different from zero at more than 2\,$\sigma$ is preferred, $r=0.074_{-0.033}^{+0.027}$ at $68\%$ cl for Planck TTTEEE + lowTEB + BKP (in the power-law inflation case), while the agreement between $H_0$ from Riess et al. 2016 \cite{R16} and the \Planck data is maintained. However, when considering the new constraints on the reionization optical depth from Planck HFI data \cite{newtau}, the lower value preferred by that data on the neutrino effective number $N_{\rm eff}$ restores the tension on $H_0$ between the datasets and the standard value for $N_{\rm eff}$ is recovered. The most recent data (given the $\Delta \chi ^2$) therefore does not really lend support to the power-law inflation model with dark radiation. | 16 | 9 | 1609.00328 |
1609 | 1609.02607_arXiv.txt | We present new HST/WFC3-IR narrowband [Fe~{\sc ii}] images of protostellar jets in the Carina Nebula. Combined with 5 previously published sources, we have a sample of 18 jets and 2 HH objects. All of the jets we targeted with WFC3 show bright infrared [Fe~{\sc ii}] emission, and a few H$\alpha$ candidate jets are confirmed as collimated outflows based on the morphology of their [Fe~{\sc ii}] emission. Continuum-subtracted images clearly separate jet emission from the adjacent ionization front, providing a better tracer of the collimated jet than H$\alpha$ and allowing us to connect these jets with their embedded driving sources. The [Fe~{\sc ii}] 1.64 $\mu$m/H$\alpha$ flux ratio measured in the jets is $\gtrsim 5$ times larger than in the adjacent ionization fronts. The low-ionization jet core requires high densities to shield Fe$^+$ against further ionization by the FUV radiation from O-type stars in the H~{\sc ii} region. High jet densities imply high mass-loss rates, consistent with the intermediate-mass driving sources we identify for 13 jets. The remaining jets emerge from opaque globules that obscure emission from the protostar. In many respects, the HH jets in Carina look like a scaled-up version of the jets driven by low-mass protostars. Altogether, these observations suggest that [Fe~{\sc ii}] emission is a reliable tracer of dense, irradiated jets driven by intermediate-mass protostars. We argue that highly collimated outflows are common to more massive protostars, and that they suggest the outflow physics inferred for low-mass stars formation scales up to at least $\sim 8$ M$_{\odot}$. | \label{s:ir_synth_intro} Understanding accretion and outflow in young stars is key to constraining the physics that govern their formation and early evolution. Accretion and outflow will shape the circumstellar environment around young stars where planet formation may already be ongoing, fostering or inhibiting the genesis of sub-stellar companions. Abundant low-mass sources in the solar neighborhood allow for detailed, multi-wavelength studies of the evolution of protostars from deeply embedded cores that are only accessible at long wavelengths \citep[e.g.][]{eno08,jor09} to the IR excess and strong optical emission lines characteristic of more evolved T~Tauri stars \citep[e.g.][]{eva03,harvey07,eva09}. For the nearby sources, high angular resolution observations can resolve the circumstellar geometry, clearly illustrating the importance of accretion disks, jets, and outflows for the formation of stars \citep[e.g.][]{bur96,kri98,mcc98,pad99}. In low-mass stars, disk material accretes along stellar magnetic field lines, ultimately splashing onto the stellar surface at high latitudes \citep[see, e.g. review by][]{bou07}. This process of magnetospheric accretion requires strong, large-scale stellar magnetic fields with a predominately dipolar topology to lift material from the inner edge of the disk and carry it along field lines to the star. Strong magnetic fields have been found in many T Tauri stars, supporting the magnetospheric accretion paradigm \citep[e.g.][]{joh99a,joh99b,joh04,joh13}. Whether a scaled-up version of this formation scenario applies to intermediate- and high-mass stars remains unclear. In particular, it is not settled whether intermediate- and high-mass stars generate magnetic fields of sufficient strength to support magnetospheric accretion. Surveys of Herbig Ae/Be stars find a low magnetic incidence of $\leq 10$\% \citep[see, e.g.][]{wad07}. Derived upper limits on the magnetic field strength are smaller than the minimum field strength required for magnetospheric accretion in both Herbig Ae and Be stars \citep[derived from the models of][]{joh99b}. More recent surveys with higher sensitivity to weaker fields further constrain the average field strength of intermediate-mass protostars to be an order of magnitude less than typically observed in T Tauri stars \citep[e.g.][]{ale13,hub15}. Evidence for circumstellar disks around intermediate- and high-mass protostars also argues for massive stars forming via a scaled-up version of low-mass star formation \citep[e.g.][]{tan03}. Direct detection is difficult, however, given the large median distances, high optical depths, and short timescales involved \citep[e.g.][]{beu09,kra10,pre11b,car12,joh15}. For this reason, indirect accretion indicators provide an important avenue to understand the evolution of intermediate-mass protostars. Jets are one such signpost as they require active disk accretion. Observed similarities in the physical properties of outflows from low- and high-mass stars suggest a common production mechanism regardless of protostellar mass \citep{ric00}. Alternate formation pathways, for example the coalescence of lower-mass cores, are unlikely to form collimated outflows \citep{bal05}. Thus, the detection of collimated jets provides compelling, though indirect, evidence of circumstellar disks \citep[e.g.][]{guz12}. Protostellar \textit{outflows} appear to be a ubiquitous feature of star formation \citep[e.g.][]{arc07}, and thus provide an avenue to identify accreting systems even at distances where the accretion geometry is not directly resolved. A well-collimated \textit{jet} launched near the protostar requires energy from disk accretion to produce a collimated stream of high-velocity gas \citep[e.g.][]{fer06}. An underlying jet, a wide-angle disk wind, or a combination of the two \citep[e.g.][]{bac95,san99,arc01b,yba06} may power the outflows typically studied at millimeter wavelengths. Outflows tend to have lower velocities and broader morphologies than the collimated jets that may be obscured inside the optically thick outflow lobe. This is especially true for high-mass protostars as they tend to form out of dense clumps that will birth a cluster of stars that have large columns of gas and dust that thoroughly enshroud the earliest evolutionary stages. Comparatively little attention has been paid to intermediate mass ($\sim 2-8$ M$_{\odot}$) stars, even though they sample the changes in stellar structure that may be related to a transition in accretion mechanisms between low- and high-mass stars. Unlike the highest mass sources, modest optical depths obscure intermediate-mass stars, permitting multi-wavelength observations of a variety of spatial and temporal scales. Employing similar observational techniques as low-mass star formation makes it easier to directly compare the results \citep[e.g.][]{cal04,vin05,men12}. This potential to link low- and high-mass star formation has led to growing interest in intermediate-mass stars. However, studies typically target only a few jets or outflows from intermediate-mass stars, providing a heterogeneous sample of objects observed in different regions and with different techniques \citep[e.g.][]{she03,ell13}. Ideally, multiple sources in a single region would be observed with the same technique to develop a coherent picture of accretion and outflow throughout the intermediate-mass range. \begin{table*} \caption[New WFC3-IR observations]{Observations} \vspace{5pt} \centering \vspace{3pt} \begin{tabular}{lllllll} \hline\hline \vspace{5pt} Target & $\alpha_{\mathrm{J2000}}$ & $\delta_{\mathrm{J2000}}$ & Date & Exp. time (s) & Comment \\ \hline HH~666 & 10:43:51.3 & -59:55:21 & 2009 Jul 24-29 & 2397/2797 & no cont.; see also \citet{rei13} \\ HH~901 & 10:44:03.5 & -59:31:02 & 2010 Feb 1-2 & 2797/3197 & no cont.; see also \citet{rei13} \\ HH~902 & 10:44:01.7 & -59:30:32 & 2010 Feb 1-2 & 2797/3197 & no cont.; see also \citet{rei13} \\ HH~1066 & 10:44:05.4 & -59:29:40 & 2010 Feb 1-2 & 2797/3197 & no cont.; see also \citet{rei13} \\ \hline HH~900 & 10:45:19.3 & -59:44:23 & 2013 Dec 28 & 2397 & see also \citet{rei15a}\\ HH~903 & 10:45:56.6 & -60:06:08 & 2014 Apr 17 & 2397 & \\ HH~1004 & 10:46:44.8 & -60:10:20 & 2014 Sep 28 & 2397 & \\ HH~1005 & 10:46:44.2 & -60:10:35 & 2014 Sep 28 & 2397 & \\ HH~1006 & 10:46:33.0 & -60:03:54 & 2014 Jun 05 & 2397 & \\ HH~1007 & 10:44:29.5 & -60:23:05 & 2014 Apr 17 & 2397 & \\ HH~1010 & 10:41:48.7 & -59:43:38 & 2014 Apr 18 & 2397 & \\ HH~1014 & 10:45:45.9 & -59:41:06 & 2015 Jan 16 & 2397 & \\ HH~1015 & 10:44:27.9 & -60:22:57 & 2014 Apr 17 & 2397 & \\ HH~c-3 & 10:45:04.6 & -60:03:02 & 2014 Feb 20 & 2397 & \\ HH~1159 & 10:45:08.3 & -60:02:31 & 2014 Feb 20 & 2397 & HH~c-4 in \citet{smi10} \\ HH~1160 & 10:45:09.3 & -60:01:59 & 2014 Feb 20 & 2397 & HH~c-5 in \citet{smi10} \\ HH~1161 & 10:45:09.3 & -60:02:26 & 2014 Feb 20 & 2397 & HH~c-6 in \citet{smi10} \\ HH~1162 & 10:45:13.4 & -60:02:55 & 2014 Feb 20 & 2397 & HH~c-7 in \citet{smi10} \\ HH~1163 & 10:45:12.2 & -60:03:09 & 2014 Feb 20 & 2397 & HH~c-8 in \citet{smi10} \\ HH~1164 & 10:45:10.5 & -60:02:42 & 2014 Feb 20 & 2397 & new jet identified in this work \\ HH~c-10 & 10:45:56.6 & -60:06:08 & 2014 Apr 17 & 2397 & \\ HH~1156 & 10:45:45.9 & -59:41:06 & 2015 Jan 16 & 2397 & HH~c-14 in \citet{smi10} \\ \hline \end{tabular} \label{t:ir_synth_obs} \end{table*} H~{\sc ii} regions offer one environment where jets from low- and intermediate-mass stars can be studied with similar techniques. Feedback from massive stars will have cleared much of the original molecular cloud, allowing UV radiation from nearby O-type stars to illuminate the jet body after it breaks free from its natal cloud. External irradiation lights up otherwise invisible components of the jet, including cold material that has not been excited in shocks and would therefore remain unseen in a quiescent region \citep[see, e.g.][]{rei98,bal01}. This more complete view allows for a better census of the mass in the jet. The physical properties of the jets can be calculated using the theory of photoionized gas, rather than complicated and time-dependent shock models \citep[e.g.][]{bal06}. These jets are bright in many of the same lines (e.g., H$\alpha$, [S~{\sc ii}]) as shock-excited Herbig-Haro (HH) objects that are now known to be associated with protostellar outflows \citep{her50,her51,har52,har53}, and are therefore called HH jets. Many HH jets have been seen emanating from low-mass stars in Orion \citep{rei98,bal00,bal01,bal06}, but few have been observed from intermediate-mass stars \citep[e.g.][]{ell13}. \citet{smi10} discovered 39 jets and candidate jets in the Carina Nebula in an H$\alpha$ imaging survey with \emph{HST}/ACS that imaged many of the brighter regions in the nebula with indications of ongoing star formation. Jet mass-loss rates, estimated from the H$\alpha$ emission measure (EM), are higher than those measured the same way for the jets in Orion, suggesting that the driving sources are intermediate-mass protostars. The high-luminosities of protostars identified along the jet axes support this hypothesis \citep[see][]{smi04,ohl12,rei13}. \citet{rei13} showed that bright [Fe~{\sc ii}] emission from these jets arises in high density, low ionization (or neutral) regions of the jets that are not bright in H$\alpha$ emission. While [Fe~{\sc ii}] is often assumed to be shock-excited, this is not necessarily the case in regions with significant photoexcitation. Regardless of the excitation mechanism, however, the survival of Fe$^+$ emission in the harsh UV environment created by $\sim 70$ O-type stars in the Carina Nebula requires a large column of neutral material to shield Fe$^+$ from further ionization by photons with energy $\geq$16.2~eV \citep{rei13}. Less energetic photons will penetrate deeper into the jet, producing [Fe~{\sc ii}] emission deeper in the jet core (the first ionization potential of Fe is 7.9~eV). Accounting for the neutral material in the jets increases the estimated mass-loss rate by as much as an order of magnitude, compared to that derived from the H$\alpha$ EM. This points to a distinct class of powerful outflows from intermediate-mass protostars. Several other factors point to near-IR [Fe~{\sc ii}] emission as a better tracer of irradiated, high mass-loss rate jets in H~{\sc ii} regions. The irradiated pillars from which many of the jets emerge are themselves bright in H$\alpha$, making it difficult to distinguish faint jet features from filamentary structures associated with the photoevaporative flow off the pillar. [Fe~{\sc ii}] emission from the jet provides better contrast between the jet and environment \citep[e.g.][]{smi04}, especially when offline-continuum images exist to subtract PDR emission that might otherwise obscure faint jet features \citep[see, e.g.][]{rei15a}. Near-IR [Fe~{\sc ii}] emission helps penetrate the dusty birthplaces of the jet-driving protostars, connecting the larger-scale H$\alpha$ outflow to the embedded IR source that drives it \citep[see, e.g.][]{smi04,rei13}. In addition, H$\alpha$ and [Fe~{\sc ii}] emission trace different morphologies and kinematics near the protostar in some jets with embedded driving sources \citep{rei15a,rei15b}. When the two emission lines trace different outflow components, [Fe~{\sc ii}] emission appears to be a better tracer of the protostellar \textit{jet}, while the broader morphology and slower kinematics of H$\alpha$ resemble those observed in entrained \textit{outflows}. In this paper, we present near-IR [Fe~{\sc ii}] images obtained with \emph{HST}/WFC3-IR of 18 jets, 2 HH objects, and one candidate jet in the Carina Nebula. We targeted 14 of the HH jets discovered by \citet{smi10} with a candidate driving source identified along the jet axis. Three additional candidate jets from \citet{smi10} and one new jet serendipitously fell within the imaged area. We confirm two of these as collimated jets based on their [Fe~{\sc ii}] morphology. Combined with earlier [Fe~{\sc ii}] imaging of four of the most powerful HH jets in Carina \citep{rei13}, this provides a sample of 18 jets driven by sources throughout the $\sim 2-8$ M$_{\odot}$ intermediate-mass range. | \label{s:ir_synth_conclusions} We present narrowband, near-IR [Fe~{\sc ii}] images obtained with \emph{HST}/WFC3-IR of 18 jets and 2 HH objects in the Carina Nebula. Bright [Fe~{\sc ii}] emission traces 18 separate collimated bipolar jets. This survey targets jets with a candidate driving source identified near the jet axis. [Fe~{\sc ii}] emission connects the larger scale H$\alpha$ jet to the intermediate-mass protostar that drives it in 13/18 sources. Jets without a detection of their driving source primarily emerge from small, dense globules. Simultaneous off-line continuum images allow us to remove PDR emission from the irradiated surface of the natal cloud and isolate emission from the jet. The dense cores of the jets traced by [Fe~{\sc ii}] appear highly collimated, while this is not always the case for H$\alpha$. In some cases, the two lines appear to trace different outflow components altogether. From these new [Fe~{\sc ii}] images, we report the discovery of two new jets, HH~1156 and HH~1164, that cannot be identified as such from H$\alpha$ images alone. Bright [Fe~{\sc ii}] emission in externally irradiated protostellar jets requires high densities to shield against further ionization in the H~{\sc ii} region. From this minimum density, we estimate high mass-loss rates that point to powerful jets. With these new and mass-loss rates and conservative estimates of the jet velocity, we find that the momentum of the jets is similar to the outflow momentum measured in molecular outflows from intermediate-mass stars \citep{bel08}. However, both the assumed velocities and estimated mass-loss rates are likely to be underestimates. The true jet momentum may be as much as an order of magnitude higher, suggesting that these jets are more than capable of entraining the molecular outflows more typically seen from intermediate-mass protostars. Altogether, these highly collimated jets look like a scaled-up version of the jets seen from low-mass stars. The harsh UV environment in the Carina Nebula offers a rare glimpse of collimated jets from intermediate-mass protostars. These jets remain invisible in the absence of external irradiation, but may well be a ubiquitous feature of star formation. If so, this offers strong evidence that similar accretion physics governs the formation of stars of all masses. | 16 | 9 | 1609.02607 |
1609 | 1609.05211_arXiv.txt | We present the results of SPT-GMOS, a spectroscopic survey with the Gemini Multi-Object Spectrograph (GMOS) on Gemini South. The targets of SPT-GMOS are galaxy clusters identified in the SPT-SZ survey, a millimeter-wave survey of 2500 deg$^{2}$ of the southern sky using the South Pole Telescope (SPT). Multi-object spectroscopic observations of 62 SPT-selected galaxy clusters were performed between January 2011 and December 2015, yielding spectra with radial velocity measurements for 2595 sources. We identify 2243 of these sources as galaxies, and 352 as stars. Of the galaxies, we identify 1579 as members of SPT-SZ galaxy clusters. The primary goal of these observations was to obtain spectra of cluster member galaxies to estimate cluster redshifts and velocity dispersions. We describe the full spectroscopic dataset and resulting data products, including galaxy redshifts, cluster redshifts and velocity dispersions, and measurements of several well-known spectral indices for each galaxy: the equivalent width, $W$, of [O {\small II}] $\lambda$$\lambda$3727,3729 and \hdelta, and the 4000\AA\ break strength, D4000. We use the spectral indices to classify galaxies by spectral type (i.e., passive, post-starburst, star-forming), and we match the spectra against photometric catalogs to characterize spectroscopically-observed cluster members as a function of brightness (relative to m$^{\star}$). Finally, we report several new measurements of redshifts for ten bright, strongly-lensed background galaxies in the cores of eight galaxy clusters. Combining the SPT-GMOS dataset with previous spectroscopic follow-up of SPT-SZ galaxy clusters results in spectroscopic measurements for $> 100$ clusters, or $\sim$20\% of the full SPT-SZ sample. | Precise spectroscopic measurements of the recession velocities of distant galaxies are among the most important cosmological observables available for studying large scale structure in the universe \citep{geller89,colless01,colless03,eisenstein05,geller05,drinkwater10,eisenstein11,geller14}. On cosmological scales, galaxy line-of-sight recession velocities increase monotonically, on average, with their distance; this bulk recession velocity is known as the Hubble Flow \citep{hubble31}. The line-of-sight velocities of individual galaxies are perturbed off of the Hubble Flow via two distinct kinds of gravitational interactions: gravitational redshifts, as described by general relativity \citep[e.g.,][]{chant30}, and peculiar velocities induced by local gradients in the matter density \citep[e.g.,][]{jackson72,kaiser87}. The former effect is typically very small \citep[$\sim 11$km s$^{-1}$][]{wojtak11,sadeh15} and rarely observed, but the latter is a standard tool for constraining the statistical properties of density fluctuations on large scales \citep[redshift space distortions, e.g.,][]{percival09} and for measuring the depths of the gravitational potential wells of individual large fluctuations, namely clusters of galaxies \citep{dressler99,rines03,white10,rines13,geller13,saro13,sifon13,ruel14,bocquet15,kirk15,sifon16}. The first large samples of galaxy clusters were identified as over-densities of galaxies \citep{abell58}, and have more recently been identified out to high redshift using optical and near-infrared observations \citep[e.g.;][]{gladders00,koester07a,eisenhardt08,wen12,rykoff14}. Galaxy clusters are also identifiable from the observational signatures associated with the hot, diffuse intracluster gas that accounts for the vast majority of their baryonic content, and there is a long history in the literature of galaxy cluster samples based on the characteristic extended X-ray emission that results from that hot intracluster gas \citep[e.g.;][]{edge90,ebeling98,rosati98,bohringer00,bohringer01,burenin07,pacaud16}. In recent years astronomers have been able to produce dedicated surveys at millimeter wavelengths that identify massive galaxy clusters via the Sunyaev Zel'dovich (SZ) effect \citep{sunyaev72,sunyaev80}. The {\it Planck} satellite \citep{planck13-XX}, the Atacama Cosmology Telescope \citep[ACT;][]{marriage11b,hasselfield2013}, and the South Pole Telescope \citep{staniszewski09,vanderlinde10,williamson11,reichardt13,bleem15} have all published SZ-based galaxy cluster catalogs. Galaxy cluster surveys that select clusters based on the SZ effect and have sufficient angular resolution to resolve galaxy clusters at all redshifts (e.g., SPT and ACT with $\sim$ 1\arcmin\ beams) benefit from an approximately flat selection in mass beyond $z \gtrsim 0.25$ \citep{carlstrom02}, which results in clean, mass-selected samples extending well beyond a redshift of $z = 1$. These SZ-selected galaxy cluster samples present us with new opportunities to characterize the properties of galaxy clusters in well-defined bins of mass and redshift. Such samples can be powerful tools for testing cosmological models via the growth of structure \citep[e.g.,][]{planck13-XX,dehaan16}, and for understanding the astrophysical processes that govern how galaxies evolve in the most overdense environments \citep[e.g.,][]{zenteno11,bayliss14c,chiu16,hennig16,mcdonald16,sifon16,zenteno16} In this work we present spectroscopic observations from SPT-GMOS --- a large NOAO survey program (11A-0034, PI: C. Stubbs) using the Gemini Multi-Object Spectrograph \citep[GMOS;][]{hook04} on Gemini-South. The objective of this program was to measure cosmological redshifts of cluster member galaxies and other galaxies along the line of sight toward galaxy clusters that were identified in the SPT-SZ survey \citep{bleem15}. In this work we describe observations of 62 galaxy clusters carried out between September 2011 and May 2015. This program can be combined with numerous smaller programs to obtain spectroscopic observations of SPT clusters \citep{brodwin10,foley11,stalder13,bayliss14c,ruel14} to produce a sample of $\sim100$ SPT clusters that have been followed up with multi-object spectroscopy (MOS). Throughout the paper, we assume a standard Lambda Cold Dark Matter ($\Lambda$CDM) cosmology with $\Omega_{M} = 0.3$, $\Omega_{\Lambda} = 0.7$, $\sigma_{8} = 0.8$, $H_{0} = 70$ km s$^{-1}$ Mpc$^{-1}$, and $h=H_{0}/100= 0.7$. All quoted magnitudes are in the AB system. \begin{figure}[t] \includegraphics[scale=0.56]{2500_mass_redshift_gemini.pdf} \caption{\scriptsize{ The full 2500 deg$^{2}$ SPT-SZ sample of 516 confirmed galaxy clusters (black dots) with the 62 SPT-GMOS clusters marked with red stars. Redshifts and masses for the full SPT-SZ sample are those described in \citet{bleem15}, where three clusters only have approximate redshift lower limits based on {\it Spitzer} infrared imaging.}} \label{fig:sample} \end{figure} | We present the full spectroscopic data release of the SPT-GMOS survey of 62 SPT-SZ galaxy clusters, which includes 2595 spectra with radial velocity measurements, 2243 of which are galaxies (1579 cluster members). Some of the SPT-SZ galaxy clusters are identified as strong-lensing systems in the available imaging, and we measure spectroscopic redshifts (or redshift constraints/limits) for candidate strongly-lensed background sources where possible. In addition to redshifts, we also measure standard spectral index measurements of the strength of the \oii\ doublet, \hdelta, and the 4000\AA\ break. These indices are useful for spectrally classifying galaxies, and introduce the potential to investigate the properties of SPT-SZ member galaxies as a function of galaxy type. The SPT-GMOS survey can be combined with previously published results from other spectroscopic programs \citep{sifon13,ruel14,sifon16} to provide $>$100 SPT-SZ galaxy clusters with spectroscopic follow-up (longslit or MOS), and more than 90 clusters with $N \geq 15$ member velocity dispersion measurements. These data contribute to a broad effort to obtain multi-wavelength follow-up of SPT-SZ galaxy clusters --- including extensive X-ray observations \citep{williamson11,mcdonald13,mcdonald14} and ongoing weak lensing measurements \citep[e.g.,][]{high12} --- that will inform future multi-wavelength efforts to cross-calibrate the SZ mass-observable relation, and thereby enable future cosmological studies using galaxy clusters. | 16 | 9 | 1609.05211 |
1609 | 1609.04398_arXiv.txt | Central galaxies make up the majority of the galaxy population, including the majority of the quiescent population at $\mathcal{M}_* > 10^{10}\mathrm{M}_\odot$. Thus, the mechanism(s) responsible for quenching central galaxies plays a crucial role in galaxy evolution as whole. We combine a high resolution cosmological $N$-body simulation with observed evolutionary trends of the ``star formation main sequence,'' quiescent fraction, and stellar mass function at $z < 1$ to construct a model that statistically tracks the star formation histories and quenching of central galaxies. Comparing this model to the distribution of central galaxy star formation rates in a group catalog of the SDSS Data Release 7, we constrain the timescales over which physical processes cease star formation in central galaxies. Over the stellar mass range $10^{9.5}$ to $10^{11} \mathrm{M}_\odot$ we infer quenching e-folding times that span $1.5$ to $0.5\; \mathrm{Gyr}$ with more massive central galaxies quenching faster. For $\mathcal{M}_* = 10^{10.5}\mathrm{M}_\odot$, this implies a total migration time of $\sim 4~\mathrm{Gyrs}$ from the star formation main sequence to quiescence. Compared to satellites, central galaxies take $\sim 2~\mathrm{Gyrs}$ longer to quench their star formation, suggesting that different mechanisms are responsible for quenching centrals versus satellites. Finally, the central galaxy quenching timescale we infer provides key constraints for proposed star formation quenching mechanisms. Our timescale is generally consistent with gas depletion timescales predicted by quenching through strangulation. However, the exact physical mechanism(s) responsible for this still remain unclear. | Observations of galaxies using large galaxy surveys such as the Sloan Digital Sky Survey (SDSS; \citealt{York:2000aa}), Cosmic Evolution Survey (COSMOS; \citealt{Scoville:2007aa}), and the PRIsm MUlti-object Survey (PRIMUS; \citealt{Coil:2011aa, Cool:2013aa}) have firmly established a global view of galaxy properties out to $z \sim 1$. Galaxies are broadly divided into two main classes: star forming and quiescent. Star forming galaxies are blue in color, forming stars, and typically disk-like in morphology. Meanwhile quiescent galaxies are red in color, have little to no star formation, and typically have elliptical morphologies (\citealt{Kauffmann:2003aa, Blanton:2003aa, Baldry:2006aa, Wyder:2007aa, Moustakas:2013aa}; for a recent review see \citealt{Blanton:2009aa}). Over the period $z < 1$, detailed observations of the stellar mass functions (SMF) reveal a significant decline in the number density of massive star forming galaxies accompanied by an increase in the number density of quiescent galaxies (\citealt{Blanton:2006aa, Borch:2006aa, Bundy:2006aa, Moustakas:2013aa}). The growth of the quiescent fraction with cosmic time also reflects this change in galaxy population (\citealt{Peng:2010aa, Tinker:2013aa, Hahn:2015aa}). Imprints of galaxy environment on the quiescent fraction (\citealt{Hubble:1936aa, Oemler:1974aa, Dressler:1980aa, Hermit:1996aa}; for a recent review see \citealt{Blanton:2009aa}) suggest that there is a significant correlation between environment and the cessation of star formation. In comparison to the field, high density environments have a higher quiescent fraction. However, observations find quiescent galaxies in the field (\citealt{Baldry:2006aa,Tinker:2011aa,Geha:2012aa}), at least for galaxies with stellar mass down to $10^9\mathrm{M}_\odot$ (\citealt{Geha:2012aa}), and as \cite{Hahn:2015aa} finds using PRIMUS, the quiescent fraction in both high density environments and the field increase significantly over time. Furthermore, galaxy environment is a subjective and heterogeneously defined quantity in the literature (\citealt{Muldrew:2012aa}). It can, however, be more objectively determined within the halo occupation context, which labels galaxies as `centrals' and `satellites' (\citealt{Zheng:2005aa, Weinmann:2006aa, Blanton:2007ab, Tinker:2011aa}). Central galaxies reside at the core of their host halos while satellite galaxies orbit around. % During their infall, satellite galaxies are likely to experience environmentally driven mechanisms such as ram pressure stripping (\citealt{Gunn:1972aa, Bekki:2009aa}), strangulation (\citealt{Larson:1980aa, Balogh:2000aa}), or harassment (\citealt{Moore:1998aa}). Central galaxies, within this context, are thought to cease their star formation through internal processes -- numerous mechanisms have been proposed and demonstrated on semi-analytic models (SAMs) and hydrodynamic simulations. One common proposal explains that hot gaseous coronae form in halos with masses above $\sim 10^{12}\mathrm{M}_\odot$ via virial shocks, which starve galaxies of cool gas required to fuel star formation (\citealt{Birnboim:2003aa, Keres:2005aa,Croton:2006aa,Cattaneo:2006aa, Dekel:2006aa}). Other have proposed galaxy merger induced starbursts and subsequent supermassive blackhole growth as possible mechanisms (\citealt{Springel:2005aa, DiMatteo:2005aa, Hopkins:2006aa, Hopkins:2008ab, Hopkins:2008aa}). Feedback from accreting active galactic nuclei (AGN) has also been suggested to contribute to quenching (sometimes in conjunction with other mechanisms; \citealt{Croton:2006aa,Cattaneo:2006aa,Gabor:2011aa}); so has internal morphological instabilities in the galactic disk or bar (\citealt{Cole:2000aa, Martig:2009aa}). With so many proposed mechanisms available, observational constraints are critical to test them. Several works have utilized the observed global trends of galaxy populations in order to construct empirical models for galaxy star formation histories and quenching (e.g. \citealt{Wetzel:2013aa, Schawinski:2014aa, Smethurst:2015aa}). Central galaxies constitute over $70\%$ of the $\mathcal{M}_* > 10^{9.7}\mathrm{M}_\odot$ galaxy population at $z = 0$. Moreover, the majority of the quiescent population at $\mathcal{M}_* > 10^{10}\mathrm{M}_\odot$ become quiescent as centrals (\citealt{Wetzel:2013aa}). The quenching of central galaxies plays a critical role in the evolution of massive galaxies. In this paper, we take a similar approach as \cite{Wetzel:2013aa} but for central galaxies. \cite{Wetzel:2013aa} quantify the star formation histories and quenching timescales in a statistical and empirical manner. Then using the observed SSFR distribution of satellite galaxies, they constrain the quenching timescale of satellites and illustrate the success of a ``delay-then-rapid'' quenching model, where a satellite begins to quench rapidly only after a significant delay time after it infalls onto its central halo. Extending to centrals, we use the global trends of the central galaxy population at $z < 1$ in order to construct a similarly statistical and empirical model for the star formation histories of central galaxies. While the initial conditions of the satellite galaxies in \cite{Wetzel:2013aa} (at the times of their infall) are taken from observed trends of the central galaxy population, our model for central galaxies must actually reproduce all of the multifaceted observations. This requires us to construct a more comprehensive model that marries all the significant observational trends. Then by comparing the mock catalogs generated using our model to observations, we constrain the star formation histories and quenching timescales of central galaxies. Quantifying the timescales of the physical mechanisms that quench star formation, not only gives us a means for discerning the numerous different proposed mechanisms, but it also provides important insights into the overall evolution of galaxies. We begin first in \S \ref{sec:sdss} by describing the observed central galaxy catalog at $z \approx 0$ that we construct from SDSS Data Release 7. Next, we describe the cosmological $N$-body simulation used to create a central galaxy mock catalog in \S \ref{sec:treepm}. We then develop parameterizations of the observed global trends of the galaxy population and describe how we incorporate them into the mock catalog in \S \ref{sec:model}. In \S \ref{sec:resultss}, we describe how we use our model and the observed central galaxy catalog in order to infer the quenching timescale of central galaxies. Finally in \S \ref{sec:discussion} and \S \ref{sec:summary} we discuss the implications of our results and summarize them. | \label{sec:discussion} \subsection{Central versus Satellite Quenching} One key result of the central galaxy quenching timescales we infer is its difference with the satellite galaxy quenching timescale from \cite{Wetzel:2013aa}. For the entire stellar masses range probed, the quenching timescale of central galaxies is $\sim 0.5\;\mathrm{Gyr}$ longer than that of satellite galaxies. This corresponds to central galaxies taking approximately $\sim 2 \;\mathrm{Gyrs}$ longer than satellite galaxies to transition from the SFMS to the quiescent peak. Moreover, this difference suggests that {\em quenching mechanisms responsible for the cessation of star formation in central galaxies are different from the ones in satellite galaxies}. At a glance, this difference in central and satellite quenching timescale is rather unexpected since the SSFR distribution of central (blue) and satellite (orange) galaxies of the SDSS DR7 Group Catalog in Figure \ref{fig:sdss_censat_ssfr}, show remarkably similar green valley heights. However, the similarity in green valley height is not determined by the quenching timescale alone. It reflects the combination of quenching timescale and the rate that star-forming galaxies transition to quenching. Since the satellite quenching timescale is shorter than that of centrals, star-forming satellites transition to quenching at a higher rate than star-forming centrals at $z = 0$. The difference in this transition rate is even higher than what the quenching timescale reflects because tidal disruption and mergers preferentially destroy quiescent satellite galaxies. The implication that satellites and centrals have different quenching mechanisms is broadly consistent with the currently favored dichotomy of quenching mechanisms: satellite galaxies undergo environmental quenching while central galaxies undergo internal quenching. It is also consistent with the significant difference in the structural properties of quiescent satellites versus centrals \citep{Woo:2016aa}, which also suggests different physical pathways for quenching satellites versus centrals. Furthermore, it explains the environment dependence in the quiescent fraction evolution in recent observations (\citealt{Hahn:2015aa, Darvish:2016aa}). Both central and satellite quenching contribute in high density environments while only central quenching contributes in the field causing the quiescent fraction to increase more significantly in high density environments. Additionally, combined with the \cite{Wetzel:2013aa} result that at $\mathcal{M}_* > 10^{10} \mathrm{M}_\odot$ central galaxy quenching is the dominant contributor to the growth of the quiescent population, we can also characterize mass regimes where environmental or internal quenching mechanisms dominate, similar to \cite{Peng:2010aa}. Below $\mathcal{M}_* < 10^{9} \mathrm{M}_\odot$, satellite quenching is the {\em only} mechanism \citep{Geha:2012aa} and internal quenching is ineffective. Until $\mathcal{M}_* < 10^{10} \mathrm{M}_\odot$, environmental quenching continues to be the dominant mechanism. At $\mathcal{M}_* > 10^{10} \mathrm{M}_\odot$ internal quenching dominates. \begin{figure} \begin{center} \includegraphics[width=0.5\textwidth]{SSFR_SDSS.pdf} \caption{SSFR distributions of the central galaxies versus the satellite galaxies in the SDSS DR7 Group Catalog with stellar mass between $10^{10.1}$ and $10^{10.5}\mathrm{M}_\odot$. Both SSFR distributions have similar green valley heights (green shaded region). Since central galaxies have significantly longer quenching timescales, satellite galaxies have a higher rate of transitioning from star-forming to quenching than central galaxies.} \label{fig:sdss_censat_ssfr} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics[width=0.45\textwidth]{t_quenching_comparison_z0_2.pdf} \caption{ Comparison of the central galaxy quenching migration time estimate we infer, ($t_\mathrm{mig}^\mathrm{cen}$; orange) with quenching time estimates for gas depletion absent accretion (strangulation) and morphological quenching. The width represents the 68 \% confidence region propagated from the posterior distributions of the $\taucen$ parameters. For strangulation, we include the gas depletion time at $z = 0.2$ derived from the star formation efficiency estimates in \cite{Popping:2015aa} (blue dash-dotted). The surrounding blue shaded region plots the range of gas depletion times at $z = 0.15$ (longer) to $0.25$ (shorter). We also include the quenching migration time inferred from the \cite{Peng:2015aa} gas regulation model (dashed). For morphological quenching we plot the quenching times taken from the star formation histories of the simulated galaxy in \cite{Martig:2009aa} (star). We also include the quenching times of the Milky Way in \cite{Haywood:2016aa} (triangle). The quenching timescale of strangulation exhibit a similar stellar mass dependence and is generally consistent with our central quenching timescales. Although its feasibility for a wider galaxy population is unexplored, the quenching timescale from morphological quenching is in good agreement with our timescale.} \label{fig:tquench_comp} \end{center} \end{figure} \subsection{Quenching Star Formation in Central Galaxies} Numerous physical processes have been proposed in the literature to explain the quenching of star formation. Observations, however, have yet to identify the primary driver of quenching or consistently narrowing down proposed mechanisms. The quenching timescale we derive for central galaxies provides a key constraint for any of the proposed mechanisms. Only processes that agree with our central galaxy quenching timescales, can be the main driver for quenching star formation in central galaxies. Merger driven quenching has often been proposed as a driving mechanism of star formation quenching (\citealt{Springel:2005aa, Hopkins:2006ab, Hopkins:2008ab, Hopkins:2008aa}). In this proposed mechanism, quenching is typically driven by gas-rich galaxy mergers which induce starburst and rapid black hole growth. Cosmological hydrodynamics simulations that examine mergers, however, conclude that quenching from mergers alone cannot produce a realistic red sequence (\citealt{Gabor:2010aa, Gabor:2011aa}. \cite{Gabor:2011aa} used an on-the-fly prescription to identify mergers and halos in order to test different prescriptions for quenching star formation. In addition to failing to produce a realistic red sequence, they find that mergers cannot sustain quiescence due to gas accretion from the inter-galactic medium, which refuels star formation after $1-2\;\mathrm{Gyr}$. The major mergers examined in the four high resolution zoom in cosmological hydrodynamic simulation of \cite{Sparre:2016aa} also fail to sustain quiescence after $1-2\;\mathrm{Gyr}$ (Sparre et al. in prep.). AGN feedback has also been proposed as a quenching mechanism (\citealt{Kauffmann:2000aa, Croton:2006aa, Hopkins:2008ab,van-de-Voort:2011aa}), sometimes in conjunction with mergers as a way to sustain quiescence or on its own. The feedback of the AGN deposit sufficient energy, which subsequently prevents additional gas from cooling. A number of more recent works have, however, cast doubt on the role of the AGN in quenching. \cite{Mendel:2013aa}, identified quenched galaxies, with selection criteria analogous to the selection of post-starburst galaxies, in the SDSS DR7 sample and found no excess of optical AGN in them, suggesting that AGN do not have defining role in quenching. \cite{Gabor:2014aa} further argue against AGN quenching by examining gas-rich, isolated disk galaxies in a suite of high resolution simulations where they find that the AGN outflows have little impact on the gas reservoir in the galaxy disk and furthermore fail to prevent gas inflow from the intergalactic medium. \cite{Yesuf:2014aa} examined post-starburst galaxies transitioning from the blue cloud to the red sequence to find a significant time delay between the AGN activity and starburst phase, which suggests that AGN do not play a primary role in triggering quenching. AGN may yet be responsible for quenching in conjunction with other mechanisms or have a role in sustaining quiescence. Besides mergers and AGN driven processes, another class of proposed mechanisms involves some process(es) that restrict the inflow of cold gas -- strangulation. With little inflow of cold gas, the galaxy quenches as it depletes its cold gas reservoir. One mechanism that has been proposed to prevent cold gas accretion is loosely referred to as ``halo quenching''. A hot gaseous coronae, which form in halos with masses above $\sim 10^{12}\mathrm{M}_\odot$ via virial shocks, starves galaxies of cold gas for star formation (\citealt{Birnboim:2003aa, Keres:2005aa, Cattaneo:2006aa, Dekel:2006aa, Birnboim:2007aa, Gabor:2012aa, Gabor:2015aa}). For these sorts of mechanisms, the quenching timescale is linked to the time it takes for the galaxy to deplete its cold gas reservoir -- the gas depletion timescale. In principle, the gas depletion time can be estimated from measurements of the total gas mass or gas fraction. In \cite{Popping:2015aa}, for instance, they derive ``star formation efficiency'' (SFE; inverse of the gas depletion time) by dividing the SFR of the SFMS by the total galaxy gas mass that they infer from their semi-empirical model. These sorts of gas depletion time estimates, however, have significant redshift dependence because the gas fraction of galaxies do not evolve significantly over $z < 1$ (\citealt{Stewart:2009aa, Santini:2014aa, Popping:2015aa}). Nevertheless, in Figure~\ref{fig:tquench_comp} we estimate the central quenching migration time ($t_\mathrm{mig}^\mathrm{cen}$; orange) -- the time it takes central galaxies to migrate from the SFMS to quiescent estimated from our $\taucen$ -- to the gas depletion times derived from the \cite{Popping:2015aa} SFEs (blue). For $t_\mathrm{mig}^\mathrm{cen}$, we compute the time it takes a quenching galaxy to transition from the SFMS to the quiescent peak of the SFR distribution at $z = 0.2$. We compute $t_\mathrm{mig}^\mathrm{cen}$ at $z = 0.2$ because this is approximately when the $z \approx 0$ green valley galaxies would have started quenching. For the gas depletion time, we invert the SFE at $z = 0.2$, interpolated between the $z = 0.$ and $z=0.5$ \cite{Popping:2015aa} SFEs (blue dot-dashed). The surrounding blue shaded region marks the range of gas depletion times from $z = 0.15$ (longer) to $0.25$ (shorter) to illustrate the significant redshift dependence. We also note that over the redshift range $z = 0.5$ to $0.$, at $\mathcal{M} = 10^{10}\mathrm{M}_\odot$, the \cite{Popping:2015aa} gas depletion time varies from $\sim 2.5$ to $7 \;\mathrm{Gyrs}$. The $t_\mathrm{mig}^\mathrm{cen}$ and gas depletion time in Figure \ref{fig:tquench_comp} are generally in agreement with each other and exhibit similar mass dependence. Beyond the estimates of gas depletion times from gas mass, recently \cite{Peng:2015aa}, using a gas regulation model (e.g. \citealt{Lilly:2013aa, Peng:2014aa}), explored the impact that different quenching mechanisms have on the stellar metallicity of local galaxies from the SDSS DR7 sample. To reproduce the stellar metallicity difference between quiescent and star forming galaxies in their galaxy sample, they conclude that the primary mechanism for quenching is gas depletion absent accretion and it a typical quenching migration time of $t_\mathrm{mig} \sim 4\;\mathrm{Gyr}$ for $\mathcal{M} < 10^{11}\mathrm{M}_\odot$. We infer the quenching migration time from Figure 2 of \cite{Peng:2015aa} and include it in Figure \ref{fig:tquench_comp} (dashed). The \cite{Peng:2015aa} migration time exhibits a similar mass dependence as our central quenching migration time. Furthermore, although slightly shorter at $\mathcal{M} > 5 \times 10^{10} \mathrm{M}_\odot$, the migration time is broadly consistent with our central quenching migration time. Overall, our $t_\mathrm{mig}^\mathrm{cen}$ is consistent with the migration time estimates of gas depletion mechanisms. In other words, our central galaxy quenching timescale is consistent with the timescales predicted by gas depletion absent accretion. One currently favored model for halting cold gas accretion -- halo quenching -- quenches galaxies that inhabit host halos with masses greater than some threshold $\sim 10^{12}\mathrm{M}_\odot$. Based on SHAM, this halo mass threshold corresponds to stellar masses of $\sim 10^{10.25} \mathrm{M}_\odot$. Yet, a significant fraction of the SDSS central galaxy population with stellar masses $< 10^{10.25} \mathrm{M}_\odot$ are quiescent. While, scatter in the halo mass threshold and the stellar mass to halo mass relation, combined, may help resolve this tension, halo quenching, faces a number of other challenges. For instance, the predictions of halo quenching models are difficult to reconcile with the observed scatter in the stellar mass to halo mass relation (\citealt{Tinker:2016aa}). Furthermore, models that rely only on such ‘halo quenching’ still must account for the hot gas in the inner region of the halo, which, because of its high density, often has short cooling times of just $1-2~\mathrm{Gyr}$. Of course, the challenges of halo quenching does {\em not} rule out quenching from gas depletion absent accretion since other mechanisms may also prevent cold gas from accreting onto the central galaxy Finally, morphological quenching has also been proposed as a mechanism responsible for quenching star formation. In the mechanism proposed by \cite{Martig:2009aa}, for instance, star formation in galactic disks are quenched once the galactic disks become dominated by a stellar bulge. This stabilizes the disk from fragmenting into bound, star forming clumps. In a cosmological zoom-in simulation of a $\sim 2 \times 10^{11} \mathrm{M}_\odot$ galaxy selected to examine such a mechanism, \cite{Martig:2009aa} finds that the galaxy quenches its star formation from $\sim 10~\mathrm{M}_\odot\mathrm{yr}^{-1}$ to $\sim 1.5~\mathrm{M}_\odot\mathrm{yr}^{-1}$ in $\sim 2.5\;\mathrm{Gyr}$ during the morphological quenching phase. A $\mathcal{M} \sim 2 \times 10^{11} \mathrm{M}_\odot$ galaxy with $\hat{t}_\mathrm{Q} \sim 2.5\;\mathrm{Gyr}$ (star; Figure \ref{fig:tquench_comp}) is in good agreement with $\hat{t}_\mathrm{Q}^\mathrm{cen}$. Despite this agreement, morphological quenching faces a number of challenges. There is little evidence from modern cosmological hydrodynamic simulations that suggest that morphological quenching can drive anything beyond short timescale fluctuations in gas fueling and SFR. Furthermore, proposed morphological quenching mechanisms face the ``cooling flow problem'' where they fail to prevent gas cooling onto a galaxy. Without addressing this issue, proposed morphological quenching mechanisms {\em cannot} maintain quiescence. Our own Milky Way galaxy, as \cite{Haywood:2016aa} finds, after forming its bar undergoes quenching. In the star formation history of the Milky Way that \cite{Haywood:2016aa} recovers, the SFR of the Milky Way decreases by an order of magnitude over the span of roughly $1.5\;\mathrm{Gyr}$. Converting to $\hat{t}_\mathrm{Q}$ in a similar fashion as our $\hat{t}_\mathrm{Q}^\mathrm{cen}$ estimates and assuming a Milky Way stellar mass of $\sim 6\times 10^{10}\mathrm{M}_\odot$ (\citealt{Licquia:2015aa, Haywood:2016aa}), we find remarkable agreement with our $\hat{t}_\mathrm{Q}^\mathrm{cen}$ (Figure \ref{fig:tquench_comp}). Motivated by the contemporaneous formation of the bar with quenching, \cite{Haywood:2016aa} suggest a bar driven (morphological) quenching mechanism that inhibits gas accretion through high level turbulence supported pressure that is generated from the shearing of the gaseous disk. Although, this proposal may resolve the cooling-flow problem, their arguments for the mechanism are qualitative and thus require more detailed investigation. Admittedly, however, this particular comparison is hastily made since quenching event occurs beyond the redshift probed by our simulation at $1 < z < 2$. Furthermore, after dramatic quenching episode, based on the star formation history that \cite{Haywood:2016aa} recovers, the Milky Way resumes star formation at a much lower level. The central quenching timescale we infer from our analysis provides key insight into the physical processes responsible for quenching star formation. It offers a means of assessing the feasibility of numerous quenching mechanisms, which operate on distinct timescale. Based on the latest models and simulations, merger driven quenching has fallen out of favor and AGN alone seem insufficient in triggering quenching. Mechanisms that halt cold gas accretion, such as halo quenching, predict quenching times generally consistent with our estimates from the central quenching timescale we derive. However, it fails to explain the significant low mass quiescent population of central galaxies. Morphological quenching, with its agreement in quenching time, may be a key physical mechanism in quenching star formation. However, more evidence is required that it can address the cooling flow problem and maintain quiescence. Furthermore, its role in the overall quenching of galaxy populations -- not just single simulated galaxies -- still remains to be explored. Understanding the physical mechanisms responsible for quenching star formation in galaxies has been a long standing challenge for hierarchical galaxy formation models. Following the success of \cite{Wetzel:2013aa} in constraining the quenching timescales of satellite galaxies, in this work, we focus on star formation quenching in central galaxies with a similar approach. Using a high resolution $N$-body simulation in conjunction with observations of the SMF, SFMS, and quiescent fraction at $z < 1$, we construct a model that statistically tracks the star formation histories of central galaxies. The free parameters of our model dictate the height of the green valley at the initial redshift, the correction to the quenching probability, and most importantly, the quenching timescale of central galaxies, Using ABC-PMC with our model, we infer parameter constraints that best reproduce the observations of the central galaxy SSFR distribution from the SDSS DR7 Group Catalog and the central galaxy quiescent fraction evolution. From the parameter constraints of our model, we find the following results: \begin{enumerate} \item The quenching timescale of central galaxies exhibit a significant mass dependence: more massive central galaxies have shorter quenching timescales. Over the stellar mass range $\mathcal{M} = 10^{9.5} - 10^{11.5}\mathrm{M}_\odot$, $\taucen \sim 1.2 - 0.5 \;\mathrm{Gyr}$. Based on these timescales, central galaxies take roughly $2$ to $5$ Gyrs to traverse the green valley. \item The quenching timescale of central galaxies is significantly longer than the quenching timescale of satellite galaxies. This result is robust for extreme prescriptions of the SMF evolution in our simulation and even for different parameterizations of the central quiescent fraction. \item The difference in quenching timescales of satellite and centrals suggest that different physical mechanisms are primary drivers of star formation quenching in satellites versus centrals. Satellite galaxies experience external ``environment quenching'' while central galaxies experience internal ``self quenching''. \item We compare the central quenching timescales we infer to the gas depletion timescales predicted by quenching through strangulation and find broad agreement. We also find good agreement with morphological quenching; however, its feasibility in maintaining quiescent and for a wider galaxy population remains to be explored. \end{enumerate} \noindent Ultimately, the central galaxy quenching timescale we obtain in our analysis provides a crucial constraint for any proposed mechanism for star formation quenching. One key component of our simulation is the use of SHAM to track evolution of stellar masses of central galaxies. As mentioned above, the central galaxy quenching timescale results we obtain remain unchanged if we use stellar mass growth from integrated SFR. However, the use of SHAM stellar masses neglects the connection between stellar mass growth and star formation history. To incorporate integrated SFR galaxy stellar mass growth in our simulation, however, a better understanding of the detailed relationship among stellar mass growth, host halo growth, and the observed stellar mass to halo mass relation is required. We will explore this in future work. | 16 | 9 | 1609.04398 |
1609 | 1609.01742_arXiv.txt | { Accretion of gas from the intergalactic medium is required to fuel star formation in galaxies. We have recently suggested that this process can be studied using host galaxies of gamma-ray bursts (GRBs).} {Our aim is to test this possibility by studying in detail the properties of gas in the closest galaxy hosting a GRB (980425). } {We obtained the first ever far-infrared (FIR) line observations of a GRB host, namely {\it Herschel}/PACS resolved {\cii} $158\,\micron$ and {\oi} $63\,\micron$ spectroscopy, as well as APEX/SHeFI CO(2-1) line detection and ALMA CO(1-0) observations of the GRB\,980425 host.} {The GRB\,980425 host has elevated {\cii}/FIR and {\oi}/FIR ratios and higher values of star formation rate (SFR) derived from line ({\cii}, {\oi}, H$\alpha$) than from continuum (UV, IR, radio) indicators. {\cii} emission exhibits a normal morphology, peaking at the galaxy center, whereas {\oi} is concentrated close to the GRB position and the nearby Wolf-Rayet region. The high {\oi} flux indicates high radiation field and gas density at these positions, as derived from Photo Dissociation Region modelling. The {\cii}/CO luminosity ratio of the GRB\,980425 host is close to the highest values found for local star-forming galaxies. Indeed, its CO-derived molecular gas mass is low given its SFR and metallicity, but the {\cii}-derived molecular gas mass is close to the expected value.} {The {\oi} and {\hi} concentrations as well as the high radiation field and density close to the GRB position are consistent with the hypothesis of a very recent (at most a few tens of Myr ago) inflow of atomic gas triggering star formation. In this scenario dust has not had time to build up (explaining high line-to-continuum ratios). Such a recent enhancement of star-formation activity would indeed manifest itself in high $\mbox{SFR}_{\rm line}/\mbox{SFR}_{\rm continuum}$ ratios, because the line indicators are sensitive only to recent ($\lesssim10\,$Myr) activity, whereas the continuum indicators measure the SFR averaged over much longer periods ($\sim100\,$Myr). Within a sample of 32 other GRB hosts, 20 exhibit $\mbox{SFR}_{\rm line}/\mbox{SFR}_{\rm continuum}>1$, with a mean ratio of $1.74\pm0.32$. This is consistent with a very recent enhancement of star formation being common among GRB hosts, so galaxies which have recently experienced inflow of gas may preferentially host stars exploding as GRBs. Therefore GRBs may be used to select unique samples of galaxies suitable for the investigation of recent gas accretion.} | 16 | 9 | 1609.01742 |
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1609 | 1609.03571_arXiv.txt | Understanding galaxy formation and evolution requires studying the interplay between the growth of galaxies and the growth of their black holes across cosmic time. Here we explore a sample of H$\alpha$-selected star-forming galaxies from the HiZELS survey and use the wealth of multi-wavelength data in the COSMOS field (X-rays, far-infrared and radio) to study the relative growth rates between typical galaxies and their central supermassive black holes, from $z=2.23$ to $z=0$. Typical star-forming galaxies at $z\sim1-2$ have black hole accretion rates ($\rm \dot{M}_{\rm BH}$) of 0.001-0.01M$_{\odot}$\,yr$^{-1}$ and star formation rates (SFRs) of $\sim$10-40 M$_{\odot}$\,yr$^{-1}$, and thus grow their stellar mass much quicker than their black hole mass (3.3$\pm$0.2 orders of magnitude faster). However, $\sim3$\% of the sample (the sources detected directly in the X-rays) show a significantly quicker growth of the black hole mass (up to 1.5 orders of magnitude quicker growth than the typical sources). $\rm \dot{M}_{\rm BH}$ falls from $z=2.23$ to $z=0$, with the decline resembling that of star formation rate density or the typical SFR (SFR$^*$). We find that the average black hole to galaxy growth ($\rm \dot{M}_{\rm BH}$/SFR) is approximately constant for star-forming galaxies in the last 11 Gyrs. The relatively constant $\rm \dot{M}_{\rm BH}$/SFR suggests that these two quantities evolve equivalently through cosmic time and with practically no delay between the two. | Understanding how galaxies form and evolve is a very challenging task, as there are a range of complex processes and quantities that need to be taken into account and that usually cannot be studied in isolation, such as gas abundances, dust, supernovae, radiative winds and relativistic jets \citep[e.g.][]{Illustris2015,Eagle2015}. Both the star formation history (SFH; e.g. \citealt{Lilly96,Karim2011,Sobral2013a}) and the black hole accretion history (BHAH; \citealt{Brandt2015}) are strongly influenced by the feedback effects of both star formation (SF) and black hole (BH) accretion, as they affect the ability of the host galaxy to convert molecular gas into stars. For example, an active galactic nucleus (AGN) is the result of the accretion of matter into the central supermassive black hole of a galaxy. A growing, massive BH releases copious amounts of energy so, provided that there is a strong coupling between radiation and the mechanical output of the BH and surrounding gas, the AGN may be able to disrupt the environment and in principle even quench the SF happening in the host galaxy \citep[e.g.][]{SilkRees1998, Bower2006}. This may happen mainly in two ways: i) radiatively-driven winds and ii) relativistic jets. Current studies cannot establish whether or not radiatively-driven winds have a significant effect on a galactic scale. Integral field unit (IFU) observations provide evidence for outflowing gas in local Seyferts \citep[e.g.][]{Davies2009, Storchi2010, Muller2011} on scales of $10-100$\,pc. Conversely, spectro-polarimetry of low redshift quasars shows high-velocity outflows close to the accretion disk \citep[e.g.][]{Young2007, GangulyBrotherton}. However, these winds are only observed along the line of sight and there are no direct constraints on the distribution of the outflowing gas, which makes it difficult to get a clear picture of how they affect the galaxy \citep[e.g.][]{Tremonti2007, Dunn2010, Harrison2012}. Relativistic jets are known to influence gas on a galactic scale, even reaching outside of the dark matter haloes of galaxies and, in addition, interact strongly with virialised hot atmospheres \citep[e.g.][]{Best2005, Nesvadba2006, Nesvadba2007, Nesvadba2008, McNamara2009, McNamara2011}. The accretion of matter into the central black hole leads to the emission of radiation from both the accretion disk and the relativistic jets and thus, in conjunction with star formation processes and gas dynamics, AGN are thought to be responsible for regulating the evolution of galaxies - but it may well be that AGN feedback mostly works as a maintenance mode \citep[e.g.][]{Best2005, Best2006} rather than be responsible for the actual quenching process. Stellar feedback also plays a major role in regulating star formation. This can happen through extreme events like strong stellar winds or shock waves of supernovae explosions \citep[]{Geach2014}. Typical outflows from star formation involve only small fractions of the molecular gas in Milky Way type galaxies (but are much more important for very low mass galaxies) and thus stellar feedback is generaly considered to be insufficient for the regulation without the contribution of an AGN. In order to understand how galaxies evolve, it is particularly important to understand how key properties such as the star formation rate (SFR) and the black hole accretion rate ($\rm \dot{M}_{\rm BH}$) in active galactic nuclei (AGN) evolve as a function of cosmic time. This can be done by examining the star formation and black hole accretion histories of galaxies. The latest surveys show that star formation activity peaks at $z\sim2$ \citep[e.g.][]{Sobral2013a,Madau2014} and then declines until today. As for the black hole accretion rates, the peak may happen at slightly lower redshifts than the peak of star formation, but the black hole activity may also decline more rapidly from $z\sim1$ to 0 \citep[e.g.][]{Aird2010}. However, studies taking into account the bolometric luminosity functions of AGN \citep[e.g.][]{Delvecchio2014} show that black hole accretion tracks the evolution of SF more closely, peaking at $z\sim2$. Most studies on the evolution of SF and BH accretion tend to focus on AGN selected samples. \cite{Stanley2015}, for example, found that while there is a strong evolution of the average SFR with redshift, the relation between SFR and AGN luminosity seems relatively flat for all redshifts. The authors interpreted this as being due to the effect of short time-scale variations in the mass accretion rates, which might erase any relation that might exist between the SFR and AGN luminosity. Nevertheless, there are also studies with star-forming selected samples: \cite{Delvecchio2015} analysed the relation of AGN accretion and SFR for star-forming galaxies up to $z\sim2.5$ and found that the ratio between the $\rm \dot{M}_{\rm BH}$ and the SFR evolves slightly with redshift, and has a lower value compared to what one would need to obtain the local M$\rm _{BH}$-M$\rm _{Bulge}$ relation. \cite{Lehmer2013} also investigated the $\rm \dot{M}_{\rm BH}$/SFR ratio using galaxy samples from both the field and a high-density structure (super-cluster of QSO from the 2QZ survey) at $z\sim2.23$. \cite{Lehmer2013} found that H$\alpha$ emitting galaxies in this structure have a relatively high fraction of AGN activity, leading to average $\rm \dot{M}_{\rm BH}$/SFR which are closer to what is typically measured for AGN. For more typical ``field'' H$\alpha$ emitters, the $\rm \dot{M}_{\rm BH}$/SFR was found to be typically an order of magnitude lower than for AGN and for H$\alpha$ emitters in the higher density region at $z\sim2$. These results suggest that SF galaxies are generally situated below the local relation (at least at redshifts of $z\sim2$) and that the activity of the AGN causes the ratio to rise high enough so that the galaxies approach a growth mode that could easily result in the observed local relation. However, much is still unknown, for typical, star-formation selected samples, regarding the relative growth of the black hole and the host galaxies, and particularly how such relative growth may vary with time, from the peak of the star formation history, at $z\sim2.5$ to $z\sim0$. In this paper we explore a sample of ``typical'' star-forming galaxies from HiZELS in the COSMOS field, selected in four different redshift slices in a self-consistent, homogenous way. We explore the wealth and variety of exquisite data in the COSMOS field to study the relative growth between the central black holes and their host galaxies, and how that varies across cosmic time. This paper is organised as follows: Section 2 presents the data and sample. Section 3 provides an overview of our selection of potential AGNs. Section 4 presents our stacking analysis in different bands. Section 5 presents the results: the relative supermassive black hole/galaxy growth and in section 6 we present the conclusions. In this paper, we use a Chabrier IMF \citep[]{Chabrier2003} and the following cosmology: H$_0$=70 km\,s\,$^{-1}$\,Mpc$^{-1}$, $\Omega_M$=0.3 and $\Omega_{\Lambda}$=0.7. | We have investigated the relative growth of H$\alpha$-selected star-forming galaxies and their supermassive black holes across a redshift range of $0.4\leq z \leq 2.23$ by making use of the HiZELS sample and the wealth of data available for the COSMOS field. We determined the black hole accretion rate of galaxies from their X-ray luminosities and their SFR from their luminosity in the far-infrared. In this manner, we were able to estimate the $\rm \dot{M}_{\rm BH}$/SFR ratio for typical star-forming galaxies and how that evolves with cosmic time. Only $\sim3$\% of the H$\alpha$-selected star-forming population are detected in the X-rays as AGN. Our results are in line with the results from the literature: \cite{Garn2010} found that only a few per cent of the H$\alpha$ emitters at $z=0.84$ are detected in the X-rays. \cite{Sobral2016} found similar results, with X-ray-detected AGN fractions that varied from 1\% to 2-3\% for redshifts $0.8 \leq z\leq 2.23$. Our X-ray AGN fractions are 3\% for the redshifts $z=0.4-1.47$ and 2\% for $z=2.23$. This implies that there is no significant evolution of the X-ray AGN fraction with redshift. Our results also complement those from \cite{Sobral2016}, who estimated AGN fractions at $z=0.84-2.23$ for the most luminous H$\alpha$ emitters and found little to no evolution with redshift. The FIR SFRs in our sample range from $\sim2$\,M$_{\odot}$\,yr$^{-1}$ to $\sim40$\,M\,$_{\odot}$\,yr$^{-1}$, from $z=0.4$ to $z=2.23$ \citep[][]{Alasdair}. This is in good agreement with the H$\alpha$ SFRs \citep[see e.g.][]{Swinbank2012,Sobral2014}. The $\rm \dot{M}_{\rm BH}$ we obtain are generally a thousandth of the SFRs of the galaxies we studied, in line with results from \cite{Lehmer2013} for star-forming galaxies at $z=2.23$. The black hole accretion rates rise with redshift from $\rm \dot{M}_{BH}\sim0.004$\,M$_{\odot}$\,yr$^{-1}$ at $z=0.8$ to $\rm \dot{M}_{BH}\sim0.03$\,M$_{\odot}$\,yr$^{-1}$ at $z=2.23$. The rising of the $\rm \dot{M}_{\rm BH}$ may be steeper until $z=1.47$. Interestingly, the SFRD evolves in a very similar way to the $\rm \dot{M}_{\rm BH}$, starting to stabilise at around the same redshifts: the $\rm \dot{M}_{\rm BH}$ evolution starts to ``flatten" at $1.47<z<2.23$ \citep[e.g.][]{Sobral2013a}, something that is supported in the literature, as \cite{Aird2010} has found that the peak of X-ray luminosity density is located at $z = 1.2 \pm 0.1$. Our $\rm \dot{M}_{\rm BH}$/SFR ratio is observed to have little to no evolution with redshift, being approximately $\sim10^{-3.3}$ between $z=0$ and $z=2.23$. This little to no evolution across redshift suggests that $\rm \dot{M}_{\rm BH}$ and SFRs of our typical star-forming galaxies evolve at similar rates across cosmic time. Our results are thus in good agreement with the ones in the literature. Several authors have noted that the $\rm \dot{M}_{\rm BH}$ and SFR ratio has been independent of cosmic time for the last $\sim10$\,Gyrs, with a value of $\sim10^{-3.2}$ \citep[see e.g.][]{Shankar2009, HopkinsBeacom2006, HeckmanBest2014}. It is worth noting that, although our results favor a scenario where the black holes and their host galaxies grow simultaneously as a whole, they do not imply that this is necessarily the case on a galaxy by galaxy basis. Nevertheless, the little to no evolution of $\rm \dot{M}_{\rm BH}$/SFR across cosmic time suggests that the processes that fuel $\rm \dot{M}_{\rm BH}$ and SFR have remained the essentially the same (or correlated) over cosmic time \citep[see, e.g.][]{Heckman2004, Mullaney2012}. However, understanding and explaining these physical processes in detail (feedback, gas stability and availability) is still a very important open question. We also find that $\rm \dot{M}_{\rm BH}$/SFR may decline slightly with increasing stellar mass, although very weakly. This specific relation is interesting because the canonical interpretation of the influence of AGN and star formation in galaxy evolution is that AGN generally dominate in more massive galaxies whereas in less massive galaxies star formation starts playing a more important role. The fact that $\rm \dot{M}_{\rm BH}$/SFR depends so little on galaxy mass could indicate that BH activity and SFR form a combined mechanism for the regulation of galaxy growth, as opposed to simply one mechanism taking over the other at set intervals in time, but this is currently very uncertain. As for the directly detected sources in the X-rays (X-ray AGN), they show very significant scatter. They seem to deviate from the behaviour of the full population, revealing $\rm \dot{M}_{\rm BH}$/SFR ratios of $>10^{-3.5}$ to $>10^{-1.2}$. This is not a surprising result, since AGN activity is highly variable and the BH growth may exceed SFR and vice-versa on short timescales \citep[e.g.][]{Alexander2008, Targett2012}. Future work would need to focus on extending this study to other surveys as well as trying to understand how SF and BH activity might constrain the evolution of the galaxies they happen in. The further use of ALMA to probe gas outflows in AGN and SF galaxies would allow us to get a much more detailed idea of whether these processes affect galaxies differently and let us better understand how AGN and SF influence galaxy growth and themselves. | 16 | 9 | 1609.03571 |
1609 | 1609.06448_arXiv.txt | {} {To gain insight into the expected gas dynamics at the interface of the Galactic bar and spiral arms in our own Milky Way galaxy, we examine as an extragalactic counterpart the evidence for multiple distinct velocity components in the cold, dense molecular gas populating a comparable region at the end of the bar in the nearby galaxy NGC 3627. } {We assemble a high resolution view of molecular gas kinematics traced by CO(2-1) emission and extract line-of-sight velocity profiles from regions of high and low gas velocity dispersion.} {The high velocity dispersions arise with often double-peaked or multiple line-profiles. We compare the centroids of the different velocity components to expectations based on orbital dynamics in the presence of bar and spiral potential perturbations. A model of the region as the interface of two gas-populated orbits families supporting the bar and the independently rotating spiral arms provides an overall good match to the data. An extent of the bar to the corotation radius of the galaxy is favored.} {Using NGC3627 as an extragalactic example, we expect situations like this to favor strong star formation events such as observed in our own Milky Way since gas can pile up at the crossings between the orbit families. The relative motions of the material following these orbits is likely even more important for the build up of high density in the region. The surface densities in NGC3627 are also so high that shear at the bar end is unlikely to significantly weaken the star formation activity. We speculate that scenarios in which the bar and spiral rotate at two different pattern speeds may be the most favorable for intense star formation at such interfaces.} | \label{intro} The interfaces of galactic bars and outer spiral arms represent some of most active star-forming environments in the local universe. In our own Milky Way, the overlap between the end of the Galactic bar and the inner Scutum-Centaurus spiral arm at longitudes of $\sim$30 degrees hosts the W43 mini-starburst with an approximate luminosity of $L\sim 3\times 10^6$\,L$_{\odot}$ (e.g., \citealt{blum1999,motte2003,bally2010,nguyen2011}). Questions about the nature of star formation in such bar-spiral interface regions remain puzzling, e.g., is it possible that clouds at different relative velocities physically interact and even may induce the star formation process this way. \citet{nguyen2011} estimate a star formation rate (SFR) between 0.01 and 0.1\,M$_{\odot}yr^{-1} \times \left(\frac{d}{6kpc}\right)^2$ (with d the distance) over the size of the W43 cloud complex of approximately 15\, (kpc)$^2$. One of the observational difficulties lies in the fact that gas kinematics are hard to constrain at these locations, both in our own Milky Way and in external galaxies. In the case of W43, several lines of evidence reveal the dynamics of the bar-spiral interaction and its effect on gas motions as the source of burst of star formation, which is thought to be the site of converging flows (e.g., \citealt{benjamin2005,lopez2007,rodriguez2008,nguyen2011,carlhoff2013,motte2014}). This region contains various evolutionary stages, from young infrared dark clouds to active star-forming cloud and a Wolf-Rayet cluster \citep{blum1999,beuther2012a}. A peculiar aspect of the W43 region is the existence of two prominent gas velocity components along the line of sight, the principle component at $\sim$100\,km\,s$^{-1}$, and a secondary at $\sim$50\,km\,s$^{-1}$. \citet{motte2014} discuss several converging gas flows in that region associated with kinematic CO and HI gas components between approximately 60 and 120\,km\,s$^{-1}$. In their picture, the 50\,km\,s$^{-1}$ component is not considered further because they do not identify associated converging velocity structures towards W43. Similarly, \citet{nguyen2011} and \citet{carlhoff2013} argue that the more prominent $\sim$100\,km\,s$^{-1}$ peak is the dominant one for the on-going star formation in the region, corresponding to the W43 complex, whereas the $\sim$50\,km\,s$^{-1}$ component may only be a chance alignment that could be attributed to the Perseus spiral arm. In contrast to this, \citet{beuther2012a} find both components in the $^{13}$CO(2--1) emission not just along the same sidelines but the two components appear in projection spatially connected. Furthermore, both components are also detected in dense gas tracers like N$_2$H$^+$, and again, both velocity components appear in mapping studies as connected gas structures \citep{beuther2012a}. While this may still be a chance alignment, it is nevertheless suggesting that both components may emerge from the same region. This part of our Galaxy is also almost the only region in the Milky Way that exhibits multiple velocity components in the ionized gas tracer through radio recombination lines \citep{anderson2011}. This can be interpreted as additional evidence for potentially interacting gas clouds. Due to our position in the Galaxy, however, it is currently not possible to accurately determine the distance of the two components, and thus to unambiguously determine whether the two gas components in W43 are either in fact interacting or just chance alignments in different parts of the Galaxy. Unambiguous proof will likely depend on future exact distance measurements via maser parallaxes of the Bessel project of both velocity components \citep{brunthaler2011}. While the 100\,km\,s$^{-1}$ component has recently been determined to be at a distance of $\sim 5.5$\,kpc via maser parallax measurements \citep{zhang2014}, the comparable measurement for the 50\,km\,s$^{-1}$ component is still missing. \begin{figure*}[ht] \includegraphics[width=0.9\textwidth]{heracles_mom1_v2.png} \caption{Herschel 70\,$\mu$m \citep{kennicutt2011} and HERACLES CO(2--1) data of NGC3627 \citep{leroy2009}. The left panel presents in color the 70\,$\mu$m emission (logarithmic stretch from 0.0001 to 0.1\,Jy\,pixel$^{-1}$) while the contours shows the integrated CO(2--1) emission from 5 to 55\,K\,km\,s$^{-1}$ in 5\,K\,km\,s$^{-1}$ steps. In the right panel, the color-scale presents the 1st moment map (intensity-weighted velocities), the contours again show the integrated CO(2--1) emission. Circles mark the locations and areas of the PdBI(2-1) primary beams for NGC3627N and NGC3627S. The central star and white line indicate the bar location following \citet{casasola2011}. A linear scale-bar assuming 11.1\,Mpc distance is shown in the bottom-left corner.} \label{heracles} \end{figure*} Hence, while proofing the spatial (dis)association of velocity components 50\,km\,s$^{-1}$ apart is currently not possible for the bar/spiral arm interface in the Milky Way, we want to test whether the scenario is in principle possible by means of studying a nearby galaxy with more favorable almost face-on geometry. Comparable regions in nearby galaxies can provide critical insight to the nature of Galactic environments like W43. Much of our understanding in this context derives from the study of \citet{kenney1991} who first linked star formation at the end of the bar in M83 to the molecular gas reservoir traced by CO. Their detailed examination of the properties and kinematics of the molecular gas at the time, although limited to rather coarse resolution, suggested that the change in orbit structure from the bar to the spiral may lead to the observed local build-up of gas, which might then favor a burst of star formation. Soon thereafter, \citet{rand1992} found supporting evidence for this picture, showing that the intense star formation observed at the end of the bar in M51 is linked to locally high (molecular) gas surface densities. Since then, numerous observational and theoretical studies have dealt with galactic bars and their dynamical importance for star formation as well as galactic dynamics (e.g., \citealt{martin1997,jogee2005,verley2007,athanassoula2013,zhou2015}). But it is still unclear how frequently star formation of this kind occurs, which types of bars and spirals may be most conducive, or whether it can explain environments like W43 in our own Milky Way. To develop this picture further requires in-depth study of the gas kinematics at more such interfaces, which are still poorly constrained in our Milky Way, as well as in external galaxies. In this paper, we seek to explore potential bar/spiral arm interactions in an exemplary external galaxy that allows a better identification of associated velocity components because of a geometry that is near to face-on. As a starting point we used the HERACLES database that provides sensitive CO(2--1) images of several tens of nearby galaxies \citep{leroy2009}. Additionally, all HERACLES galaxies have extensive multi-wavelength coverage from the X-ray to the radio regime from the SINGS \citep{kennicutt2003} and KINGFISH \citep{kennicutt2011} efforts. Among the barred galaxies in the HERACLES sample, only two galaxies show the desired geometry, i.e., a stellar bar with strong spiral arms emanating from the bar ends and associated massive star formation. NGC3627 is one of these two galaxies and has already high quality published molecular gas observations available \citep{paladino2008,leroy2009}. The well-known barred spiral galaxy NGC3627 exhibits strong burst signatures at the two bar/arm interfaces in the north and south as visible for example in the 70\,$\mu$m Herschel map (Fig.~\ref{heracles} left panel, \citealt{kennicutt2011}). These active bar/arm interaction zones resemble the structures found in W43 in our Milky Way well. Furthermore, the location of NGC3627 is very favorable for our study: the orientation is almost face-on (inclination angle of 65\,deg with a position angle $\theta_{PA}$=170$^o$, \citealt{chemin2003}), the object is relatively nearby at a distance of 11.1 Mpc (e.g., \citealt{saha1999}) where spatial resolution elements of $1''$ correspond to linear scales of $\sim$54\,pc, and the systemic velocity is $V_{sys}$ =744 km s$^{-1}$ \citep{casasola2011}. More details will be given in section \ref{dynamics}. Although these linear scales are obviously much larger than what can be achieved within our Milky Way, the almost face-on nature of this galaxy eases the interpretation of the data tremendously. Using near-infrared imaging from the Spitzer Survey for Stellar Structure (S$^4$G, \citealt{sheth2010}), \citet{buta2015} classified NGC3627 as a $\rm SB_x(s)b pec$, i.e. a strongly barred galaxy with a boxy/peanut bulge. NGC3627 has a stellar mass of $\rm log(M_{\star}(M_{\odot}))\approx10.8$ and a specific star formation rate ($\rm sSFR=SFR/M_{\star}$) of $\rm log(sSFR(yr^{-1}))\approx-10.3$, i.e., it lies on the local main sequence of star forming galaxies \citep{salim2007}. As we are interested in a qualitative comparison of signatures for the stellar bar/spiral arm region, an exact match in properties between NGC3627 and the Milky Way is not necessary. \begin{figure*}[ht] \includegraphics[width=0.99\textwidth]{mom_3627n_co21.png}\\ \includegraphics[width=0.99\textwidth]{mom_3627s_co21.png} \caption{Combined PdBI+30m CO(2-1) data toward NGC3627 north and south (top and bottom panels, respectively). The colors show in the left and right panels the 1st (intensity-weighted peak velocities) and 2nd moments (intensity-weighted line widths), respectively. The contours present the integrated intensities in the velocity regimes indicated above each panel from 5 to 95\% of the peak intensities (in 10\% steps). The stars in the right panels show the positions for spectra extraction. Example spectra are shown in Fig.~\ref{spectra}, and fit results are presented in Tables \ref{fits_n} and \ref{fits_s}.} \label{mom_co21} \end{figure*} The two interface regions between the bar and inner spiral arms at the northern and southern ends of the NGC3627's stellar bar have been observed with the Plateau de Bure Interferometer (PdBI) in the CO(1--0) and CO(2--1) emission by \citet{paladino2008}. While they concentrated on the connection between radio continuum, CO and 8\,$\mu$m emission, we now analyze the kinematics of the gas. We re-calibrate and re-image these data (see next section), and in particular we add the CO(2--1) short spacing information from the HERACLES data \citep{leroy2009} to minimize flux and imaging artifacts. Figure \ref{heracles} (right panel) presents the single-dish HERACLES CO(2--1) data as a first moment map (intensity weighted velocities) with the integrated intensity contours. This image shows the bar-spiral structure as well as the rotational velocities of the gas. The primary beams of the PdBI observations are marked as well. Using the PACS 70$\mu$m image from KINGFISH \citep{kennicutt2011}, we assess the star formation rate of the NGC3627 southeast bar end region. To do this, we convolve the PACS image to have a round Gaussian beam of FWHM $8\arcsec$. At this resolution ($\sim 350$~pc) the star-forming region is largely unresolved. For the 70$\mu$m-to-SFR conversion quoted by \citet{kennicutt2012}, the bar end has a SFR of $\approx 0.23$~M$_\odot$~yr$^{-1}$ inside the $8\arcsec$ Gaussian beam. This compares relatively well to the $\approx 0.01-0.1$\,M$_{\odot}$yr$^{-1}$ for W43 \citep{nguyen2011} given the degree of uncertainty in extragalactic star formation rate estimates, especially for individual regions. With the goal to better understand the dynamics of bar/arm interfaces in an external galaxy and set this into context to our Milky Way, we here study the nearby galaxy NGC3627 as an excellent example case with a comparable configuration to the Milky Way. This paper is structured as follows: Section 2 describes the combination of the Plateau de Bure Interferometer and 30\, single-dish data. Section 3 then outlines the basic morphological and spectral signatures of the spectral line data. Section 4 deals with the dynamical interpretation of the multiple velocity components at the bar/arm interface in the framework of crossing orbit families corresponding to the bar and arm. Finally, Section 5 discusses these results as potential reasons for enhanced star formation activities at bar/arm interfaces, as well as it sets it into context with our Milky Way and particularly W43. Section 6 then summarizes our results. | \label{conclusion} With the aim to gain insight into the nature of the Galactic bar/spiral arm interface region W43 in our Milky Way, we investigate as an extragalactic counterpart example region the kinematic properties of the molecular gas in the bar/interface region of the nearby, almost face-on galaxy NGC3627. Similar to our Milky Way, we also find several independent spectral velocity components in a large number of spectra toward the bar/spiral interface in NGC3627. Modeling these velocity components as being caused by different orbit families populating independently the bar and spiral of NGC3627, we find that solutions with the bar extending to the corotation radius give a reasonable fit to our data. The implications of this are manyfold. The similarity of the spectral signatures at the Milky Way bar/spiral interface compared with that of NGC3627 make it plausible thatt he multiple velocity components found toward W43 may indeed stem from interacting molecular clouds in this region, and not be located in different spiral arms. Furthermore, the extremely active star formation processes at the bar/spiral interface may exactly be caused by such crossing gas orbits and interacting/colliding gas clouds. The crossing gas streams may pile up significant amounts of dense gas which henceforth can collapse and undergo intense star formation activity. Furthermore, the gas surface densities in NGC3627 are so high that shear motions are unlikely capable to significantly reduce the star formation activity. While this scenario is suggestive, further investigations of more regions with respect to their gas kinematics as well as star formation activity are needed to further investigate the importance of such cloud-collision processes. | 16 | 9 | 1609.06448 |
1609 | 1609.04217_arXiv.txt | {} {We studied the characteristic physical properties and behavior of broadband microwave sub-second pulsations observed in an expanding coronal loop during the GOES~C2.4 solar flare on 2011~August~10.} {The complex microwave dynamic spectrum and the expanding loop images were analyzed with the~help of SDO/AIA/HMI, RHESSI, and the STEREO/SECCHI-EUVI data processing software, wavelet analysis methods, the GX~Simulator tool, and the NAFE method.} {We found sub-second pulsations and other different burst groups in the complex radio spectrum. The broadband (bandwidth about 1~GHz) sub-second pulsations (temporal period range 0.07--1.49\,s, no characteristic dominant period) lasted 70\,s in the frequency range 4-7\,GHz. These pulsations were not correlated at their individual frequencies, had no measurable frequency drift, and~zero polarization. In these pulsations, we found the signatures of fast sausage magnetoacoustic waves with the characteristic periods of 0.7 and 2\,s. The other radio bursts showed their characteristic frequency drifts in the range of -262--520\,MHz\,s$^{-1}$. They helped us to derive average values of 20--80\,G for the coronal magnetic field strength in the place of radio emission. It was revealed that the microwave event belongs to an expanding coronal loop with twisted sub-structures observed in the 131, 94, and 193\,\AA~SDO/AIA channels. Their slit-time diagrams were compared with the location of the radio source at 5.7\,GHz to realize that the EUV intensity of the expanding loop increased just before the radio source triggering. We reveal two EUV bidirectional flows that are linked with the start time of the loop expansion. Their positions were close to the radio source and propagated with velocities within a~range of 30--117\,km\,s$^{-1}$.} {We demonstrate that periodic regime of the electron acceleration in a~model of the quasi-periodic magnetic reconnection might be able to explain physical properties and behavior of the sub-second pulsations. The depolarization process of the microwave emission might be caused by a~plasma turbulence in the radio source. Finally, the observed EUV flows might be linked with reconnection outflows.} | The fine structures present in the flare radio emissions are studied because these phenomena might be an effective diagnostics of processes in flare plasma. Of the various fine structures observed in radio waves (e.g., Ji\v{r}i\v{c}ka et al. 2001), pulsations have been the subject of many papers, see the reviews, for instance, by Aschwanden (2003, 2004) and Nakariakov \&~Melnikov (2009). Generally, radio emissions can be classified into coherent and incoherent emission mechanisms (Aschwanden 2004). Incoherent emission results from continual processes such as~thermal particle distributions that produce free-free emission (bremsstrahlung) in microwave and mm wavelengths for low magnetic field strengths and~mildly relativistic electron distributions that generate gyrosynchrotron emission, which is naturally produced during flares. Coherent emission reflects kinetic instabilities from particle distributions. The most natural ways to produce these anisotropic particles are~velocity dispersion, which creates electron beams and thus plasma emission, and~mirroring in~magnetic traps, which produces loss-cone instabilities (electron-cyclotron emission). The most of coherent flare-related radio emissions are driven by bursty magnetic reconnection processes and the associated flare plasma dynamics. Pulsations with period $P>$~1\,s are frequently observed (e.g., Aschwanden 2003). Nevertheless, there are also several studies of sub-second pulsations, for example, in the period range 0.025--0.055\,s (Xie et al. 2003, Ma et al. 2003), 0.1\,s~(Karlicky et al. 2010), 0.07--0.08\,s (Fleishman et al. 1994), and 0.16--0.18\,s (Fu et al., 1990). There are rather exceptional observations at microwave frequencies (e.g., in the frequency range 5380--6250\,MHz in Fu et al., 1990). These sub-second pulsations are typically observed at individual single frequencies, where we can recognize spikes (Fleishman \&~Melnikov 1998, Fleishman 2004). On the other hand, we need to see radio dynamic spectra to recognize the~type of the fine structures with the sub-second pulsating phenomena, for instance, type III pulses in Meshalkina et al. 2012. Another problem is that radio dynamic spectra observed during solar flares can be very complex and show different types of bursts and fine structures. One possibility of studying these fine structures in detail is the separation method (M\'esz\'arosov\'a et al. 2011a), which is based on the wavelet analysis techniques. This method splits an original complex (radio) spectrum into two (or more) simpler dynamical spectra according to the temporal, frequency, and spatial components of individual bursts to simplify the analysis. This method is suitable when the original radio spectrum~consists of a~mixture of different fine structures or bursts that are observed at the same frequencies and during the same time interval, and when it is therefore difficult to recognize individual temporal or frequency components from each other. The method also works well~when weak bursts of the spectrum coincide with strong ones (then we can typically see only the strong component, while the weak one remains hidden) and~when we wish to detect or locate possible fast sausage magnetoacoustic waves. The properties of the impulsively generated sausage magnetoacoustic waves propagating along their waveguide (e.g., loops) were theoretically predicted by Roberts et al. (1983, 1984). Each of these fast sausage magnetoacoustic waves form wave trains that propagate along the waveguide. The time evolution of these trains forms a tadpole wavelet pattern with a~narrow tail that precedes a~broadband head (Nakariakov et al. 2004). The start of the wave decay phase corresponds to the tadpole head maximum. In solar radio observations, these wavelet tadpoles were recognized in the gyrosynchrotron radio bursts, for example (M\'esz\'arosov\'a et al. 2009a; tadpoles detected at the same time throughout the whole frequency range), in dm radio fiber bursts generated by the plasma emission processes (M\'esz\'arosov\'a et al. 2009b, 2011b; slowly drifting tadpoles corresponding to the frequency drift of the whole group of fiber bursts), and in sources of narrowband dm radio spikes (Karlick\'y et al. 2011). M\'esz\'arosov\'a et al. (2013) found these fast magnetoacoustic waves to propagate in the fan structure of the coronal magnetic null point. These studies were supported by MHD numerical simulations conducted by Jel\'inek \& Karlick\'y (2012), Pascoe et al. (2013), and M\'esz\'arosov\'a et al. (2014), for instance. Thus, the results of the separation method, the analysis of individual observed bursts, and MHD numerical models for the fast magnetoacoustic wave trains can help us to interpret our observational data and estimate flare plasma parameters. The goal of our study is to find a~possible explanation of the broadband microwave sub-second pulsations in a~dynamic spectrum that was obtained during the 2011~August~10 GOES C2.4 solar flare. This paper is organized as follows. In Sect.~2 we analyze the observed microwave dynamic spectrum with broadband sub-second pulsations to determine their characteristic physical properties. In Sect.~3 we study flare loops belonging to this radio event with the~help of imaging data (SDO/AIA, SDO/HMI, RHESSI, and STEREO/SECCHI-EUVI). Finally, a~discussion and conclusions are presented in Sect.~4. | We studied the solar microwave event observed at 9:33:57--9:35:07\,UT by the Badary Broadband Microwave Spectropolarimeter on 2011~August~10 during the GOES~C2.4 flare, which occurred in the active region NOAA~11236. The position of the background flaring radio source at 5.7\,GHz was obtained using the SSRT and RATAN-600 observation at this radio frequency (Kashapova et al. 2013a,~b). We revealed that the microwave radio dynamic spectrum (Fig.~1, top panel) observed in the frequency range (3797--8057\,MHz) with zero polarization consists of broadband (about 1\,GHz) sub-second pulsations and other different bursts (Fig.~2). Some bursts have frequency drifts in the range -262--2892\,MHz\,s$^{-1}$ (Table~1). We derived values of the magnetic field strength in the range 21--432\,G for these bursts with the frequency drift. The signatures (wavelet tadpole patterns) of fast sausage magnetoacoustic waves propagating in situ of the radio source were detected in our data. In the first case (Fig.~3), the wave characteristic period is 0.7\,s and the frequency drift of the tadpole head maxima is 2892\,MHz\,s$^{-1}$ , which is the same as the frequency drift of the pulses (Fig.~4) observed in the same time as the magnetoacoustic waves. In the second case (Fig.~5), the wave characteristic period is about 2\,s and there is no frequency drift of the tadpole head maxima. According to the SDO/AIA 131 and 94\,\AA~images, only two seemingly simple and faint loops were observed near to the limb before 9:32:21\,UT. From this moment, one of the loops (on the higher Y-coordinate values) expanded toward higher altitudes. The second loop remained more or less at its original position. The expanding loop spread to an increasingly greater area, and new loop sub-structures were created here eventually. This raises the~question why just this one loop of the two expanded. A~possible reason for this situation can be seen in the STEREO/SECCHI-EUVI top point of view of the active region shown in Fig.~10. This shows the situation (left column) of two very weak footpoint ribbons that are indicated with arrows~1 and~2. In the right column the later situation is shown, when both ribbons were linked with a~new flare structure marked by arrow~3. From this moment on, both ribbons (arrow~1 and~2) became highly excited and influenced the loop footpoint area. In this area the highest RHESSI X-ray source intensity (Fig.~9) was focused. It seems that the two footpoints of the expanding loop were excited at about 9:32:21\,UT. The SDO/AIA 131\,\AA~emission intensity increased from about 9:32:21\,UT, as shown by the time-slit diagram in Fig.~7. The radio source was triggered early after the start of the loop expansion, at 9:33:57\,UT (horizontal solid line in Fig.~7). The earlier EUV flows are presented in panel $c)$. This bidirectional perturbation was generated with the start time of the loop expansion (9:32:21\,UT) and propagated along the slit (vertical orange solid line in the left panel of Fig.~6) with a~velocity of 30 and 70\,km\,s$^{-1}$ toward the higher altitudes and the loop footpoint, respectively. Thus, the flow propagation in panel~$c)$ is significantly faster in the direction toward the footpoint. The later EUV flows (Fig.~7, panel~$b$) might be linked with triggering the radio source as well as with the generation of sausage magnetoacoustic waves. This bidirectional perturbation was generated just before the start time of the radio source emission (9:33:57\,UT) and propagated with a~velocity of 117 and 109\,km\,s$^{-1}$ toward the higher altitudes and the loop footpoint, respectively. These perturbation velocities (arrows~1 and~2) are similar to each other, and the propagation of these flows (in panel~$b)$ is significantly faster in both directions that the earlier flows (in panel~$c$). While the earlier perturbation propagated over the entire area of the expanding loop (Y~=~280--230\,arcsec), the later one was instead focused around the radio source. The main subject of our study was the origin of the broadband (bandwidth about 1\,GHz) sub-second pulsations (temporal period range 0.07--1.49\,s, no dominant period) that lasted 70\,s in microwaves (about 4--7\,GHz). Except for one (Fig.~4), these pulsations have no measurable frequency drift despite the high frequency range. These pulsations are not well cross-correlated at individual frequencies, and they have zero polarization. Furthermore, the equality between LCP and RCP polarization during the whole event might be caused by strong depolarization processes, for example, by a~strong plasma turbulence in the radio source. This turbulent plasma scenario is supported by the facts of no radio data correlation (Fig.~2, panel~$a$) and no characteristic dominant period in the period range 0.07--1.49\,s (Fig.~1, bottom panel). We tried to find the most likely possible interpretation of these pulsations in the very complex topology of the active region. Naturally, the microwave emission observed in the solar flares is frequently linked with the gyrosynchrotron emission of mildly relativistic electrons. This incoherent radio emission is shown in panel~$k$ (Fig.~2) at frequencies $>$~6\,GHz (radio continuum without frequency drift). The other types of the bursts in the left panels (Fig.2) need another explanation. We found that the radio fluxes in panels $a$~and~$c$ (Fig.2) correspond to the tadpole patterns shown in Figs. 3~and~5. We interpret these patterns found in the wavelet spectra of radio emission fluxes as a~signatures of the fast sausage magnetoacoustic wave trains moving along a~dense flare loop (waveguide) and passing through the radio source in the loop. These magnetoacoustic wave trains are characterized by the steady periodical tail and the quasi-periodical head that can be visualized with the~help of their wavelet power spectra. This characteristic wavelet tadpole pattern consists of the long-period spectral components (tadpole tail with a~characteristic period~$P$) propagating faster than the medium and short-period ones (tadpole head). Numerical simulations of these tadpole patterns can be found in Nakariakov et al. (2004) and M\'esz\'arosov\'a et al. (2014), for instance. Observed fast sausage magnetoacoustic waves with these tadpoles were presented by Katsiyannis et al. (2003) and M\'esz\'arosov\'a et al. (2009a, b; 2011a, b; 2013). We detected two cases with magnetoacoustic waves (Figs.~3 and~5) and tried to use a~model based on MHD oscillations (e.g., Roberts et al. 1984, Nakariakov~\&~Melnikov 2009). In this model the period of oscillations $\tau$ is proportional to the Alfv\'en transit time through the source: $\tau = 2.6(a/v_A)$, where $a$ is the small radius of the cylindrical loop. Considering the Alv\'en velocity $v_A$~=~1610\,km\,s$^{-1}$ and $\tau$~=~0.7\,s (Fig.~3), we obtained a very low value of $a$~=~433.5\,km for the radio source. It is doubtful whether this can produce our broadband pulsations. Only highly coherent plasma processes (when the brightness temperature is $T_b = 10^{14}-10^{16}$\,K) can solve this problem. Moreover, this model is commonly applied for pulsations with a~period greater than 1\,s (Nakariakov~\&~Melnikov 2009). Below, we search for other arguments to explain the magnetoacoustic waves in the active region. Therefore we discuss the~topology of this region in more detail. The expanding loop (Fig.~9) consisted of some temporal fine sub-structures observed, for example, by SDO/AIA in channels 131\,\AA~channel during 9:34:33--9:35:21\,UT, which are shown in Fig.~11 (processed with the NAFE method). The position of the radio source is marked by an arrow in all panels. While at 9:34:33\,UT the expanding loop is very compact and simple at the site of the radio source, the later situation is different. Immediately before the radio source activity (9:34:45\,UT), two substructures seem to be crossing in the~location of the radio source. During the time of the radio source activity (9:34:57 and 9:35:09\,UT), these individual sub-structures become increasingly complex and twisted (panels $b$--$c$ in Fig.~8 also show twisted magnetic field lines in this area). Finally, a~new sub-structure can be seen at 9:35:21\,UT (see the arrow in Fig.~11). Thus, we can postulate the~hypothesis that (some of) these temporal sub-structures might be reconnected and this process could be the~reason for the perturbations (bi-directional outflows) detected in the time-slit diagram (panels~$b$--$c$ of Fig.~7). (We note that a~similar time-slit diagram, but without the~separation according to individual characteristic temporal structures, was presented in Sim\~{o}es at al. (2015) and interpreted as the~result of reconnection). On the other hand, the actual data cadence and spatial resolution of the available observations as well as the absence of the z-coordinates of the event details do not allow us to make an unambiguous judgement. The~question remains why only one of the two loops was expanding. For this purpose we searched for the loop footpoint positions that might be connected with flare ribbons observed by both the SDO/AIA (panels~$b$ and $d$ in Fig.~10) and the STEREO/SECCHI-EUVI (panels~$e$--$h$ in Fig.~10) instruments. We found four such footpoints, which are marked by crosses A--D in Figs.~9 and~10. Footpoints~A and~B are clearly separated, both of them are connected with one of flare ribbon, and they were detected with~similar radial heights (1.4 and 1.5\,Mm), that is, they are located in the solar chromosphere. The situation of footpoints~C and~D is more complex. While footpoint~C is connected with the most active part of the ribbon (of the highest EUV intensity), footpoint~D was localized slightly aside of that ribbon part (see panel~$b$, Fig.~10). Footpoints~C and~D were detected instead at a coronal radial hight of 3.5 Mm and a chromospheric hight of 2.3 Mm, respectively. It seems that this very complex situation, which is connected with the ribbon marked by arrow~(2) in Fig.~10 and footpoint~C, might cause the loop expansion. The non-expanding loop seems to be connected instead with footpoint~D, which is localized next to the most active part of the ribbon. The flows detected in panels $b$--$c$ of Fig.~7 might be linked with the magnetic reconnection outflows. We can see the flows propagating in both direction along the slit (vertical orange solid line in Fig.~6). The 131 and 94\,\AA~flows start from about the location of the radio source center at 5700\,GHz (horizontal solid line in Fig.~7 for 131\,\AA). Moreover, the flows in panel $b)$ are limited to the vicinity of the radio source. (We note that the EUV time-slit diagram with reconnection inflows was studied in Yokoyama 2001). Therefore, some link between the EUV bidirectional flows and the reconnection outflows might be possible. We suggested an explanation of the solar event observed by the different instruments at different spectral ranges. To confirm the proposed complex scenario, observational data with a~higher spatial resolution are necessary. | 16 | 9 | 1609.04217 |
1609 | 1609.04021_arXiv.txt | Enormous Ly$\alpha$ Nebulae (ELANe), unique tracers of galaxy density peaks, are predicted to lie at the nodes and intersections of cosmic filamentary structures. Previous successful searches for ELANe have focused on wide-field narrowband surveys, or have targeted known sources such as ultraluminous quasi-stellar-objects (QSOs) or radio galaxies. Utilizing groups of coherently strong Ly$\alpha$ absorptions (CoSLAs), we have developed a new method to identify high-redshift galaxy overdensities and have identified an extremely massive overdensity, BOSS1441, at $z=2-3$ (Cai et al. 2016a). In its density peak, we discover an ELAN that is associated with a relatively faint continuum. To date, this object has the highest diffuse Ly$\alpha$ nebular luminosity of $L_{\rm{nebula}}=5.1\pm0.1\times10^{44}$ erg s$^{-1}$. Above the 2$\sigma$ surface brightness limit of SB$_{\rm{Ly\alpha}}= 4.8\times10^{-18}$ erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$, this nebula has an end-to-end spatial extent of 442 kpc. This radio-quiet source also has extended \civ\ $\lambda1549$ and \heii\ $\lambda1640$ emission on $\gtrsim30$ kpc scales. Note that the Ly$\alpha$, \heii\ and \civ\ emission all have double-peaked line profiles. Each velocity component has a full-width-half-maximum (FWHM) of $\approx700 - 1000$ km s$^{-1}$. We argue that this Ly$\alpha$ nebula could be powered by shocks due to an AGN-driven outflow or/and photoionization by a strongly obscured source. | During the peak epoch of galaxy formation at $z=2-3$ \citep[e.g.,][]{bouwens11}, most of the baryons in the Universe reside outside galaxies; they lie within the intergalactic medium (IGM) and circumgalactic medium (CGM) \cite[e.g.,][]{cen94, miralda96, hernquist96, rauch98}. The IGM and CGM provide a vast reservoir for fueling the star formation of galaxies and also serve as a ``sink" for metals driven from the galactic feedback \cite[e.g.,][]{prochaska11, tumlinson11}. On the other hand, the properties and structures of the IGM/CGM, such as kinematics, morphology, and metallicity, are increasingly reshaped by the energetic processes occuring in galaxies, and therefore the IGM/CGM acts as a laboratory to stringently constrain the physics of the galaxy formation \cite[e.g.,][]{fumagalli11}. Intergalactic/circumgalactic filaments have been studied via QSO absorption lines \cite[e.g.,][]{rauch98}. But QSO absorption studies are limited due to the sparseness of background QSOs. To reveal the connection of intergalactic gas to galaxies and their circumgalactic medium (i.e. on scales of $\sim$100 kpc), one must constrain the full three-dimensional intergalactic/circumgalactic material using more numerous, but fainter, background galaxy populations \cite[e.g.,][]{lee14} or directly map the faint diffuse emission of the intergalactic medium (IGM) or circumgalactic medium (CGM) \cite[e.g.,][]{cantalupo14, martin15, borisova16}. The Ly$\alpha$ line is the primary coolant of gas with $T\sim 10^4$ K and can be used to trace the CGM/IGM via emission. Such Ly$\alpha$ nebulae provide us an indispensable opportunity to study the CGM in emission. Theoretical models suggest that several mechanisms may generate circumgalactic Ly$\alpha$ emission: (1) recombination radiation following photoionization (fluorescence) powered by ultraviolet (UV) sources \citep{gould96, cantalupo05, geach09, kollmeier10}; (2) cooling radiation due to the gravitationally heated gas \citep{fardal01, yang06, dijkstra09, faucher10}; (3) radiation from shock-heated gas driven by the feedback of galactic outflow \cite[e.g.,][]{villar07, taniguchi00, wilman05}; and (4) resonant scattering of Ly$\alpha$ from the embedded source \citep{dijkstra09, cantalupo14}. The photoionization radiation is generated when the dense regions of the CGM are photoionized by strong ionizing sources and then recombine to emit Ly$\alpha$ photons. Cooling radiation is the Ly$\alpha$ photons released when gas settles into galactic potential wells \cite[e.g.,][]{yang06}. Shock-heating can be powered by supernovae, or by relativistic winds or jets resulting from gas accretion onto supermassive black holes (SMBHs). Ly$\alpha$ resonant scattering produces extended Ly$\alpha$ halos as Ly$\alpha$ photons propagate outward and is characterized by a double-peaked structure of the resonant emission lines \cite[e.g.,][]{yang14}. These mechanisms are believed to power the extended Ly$\alpha$ emission in high-density regions of the early Universe. The Ly$\alpha$ nebulae/blobs (LABs) are expected to occupy massive dark matter halos ($\sim$ 10$^{13}$ M$_\odot$), representing sites of the most active star formation and tracing large-scale mass overdensities \cite[e.g.,][]{steidel00, prescott09, yang09}. A few observational efforts have been made to search for Ly$\alpha$ nebulae/blobs at $z=2-3$. These successful searches include narrowband imaging surveys of random fields \cite[e.g.,][]{steidel00, francis01, palunas04, dey05, yang09, prescott09, yang10}, narrowband imaging of known overdensities \citep{matsuda05}, and targeting biased halo tracers, such as ultraluminous QSOs \citep[e.g.,][]{cantalupo14, hennawi15} and radio galaxies \cite[e.g.,][]{heckman91, villar07, miley08}. Using VLT/MUSE, \citet{borisova16} present a blind survey for Ly$\alpha$ nebulae associated with 17 brightest radio-quiet QSOs at $3 < z < 4$. They find that 100\% of the QSOs are associated with Ly$\alpha$ nebulae with linear sizes of $\sim100$ -- 320 kpc. In this sample, the relatively narrow Ly$\alpha$ FWHMs (300 -- 600 km s$^{-1}$) are consistent with a fluorescent powering mechanism. Increasing evidence has shown that the Ly$\alpha$ nebulae often lie in regions that contain both enhanced UV-radiation (or nearby UV sources) and gas overdensities \citep{hennawi13, hennawi15}. The extended \heii\ and \civ\ associated with Ly$\alpha$ nebulae contain crucial information about the powering mechnisms. The extended \civ\ line allows us to estimate the metallicity of the CGM gas and the size of the metal enriched halos \citep{arrigoni15a}. In turn, such metal line emission allows us to examine whether the shocks of the galactic outflow could power the LABs \cite[e.g.,][]{villar99, villar07, allen08, arrigoni15b}. Arrigoni-Battaia et al. (2015a) conducted a deep survey of 13 Ly$\alpha$ blobs in the SSA22 overdensity (Steidel et al. 2000; Matsuda et al. 2005), targeting the \heii\ $\lambda1640$ and \civ\ $\lambda1549$. These observations did not detect extended \heii\ and \civ\ emission in any of the LABs, suggesting that photoionization could be a major powering mechanism. \citet{borisova16} also did not detect strongly extended He II and C IV emission in their sample of the 17 ultraluminous QSOs, indicating a large fraction of the gas in massive QSO host halos at $z=3-4$ could be cold ($T\sim10^4$ K) and metal-poor ($Z < 0.1 Z_\odot$). \citet{prescott09} detect a LAB that has a spatial extent of 80 kpc at $z\approx1.67$ associated with extended \civ\ and \heii. The Ly$\alpha$, \civ, \heii\ and \ciii lines all show a coherent velocity gradient of 500 km s$^{-1}$, strongly indicating a 50 kpc large rotational disk illuminated by an AGN. Recently, two enormous Ly$\alpha$ nebulae (ELANe) have been discovered to have a large spatial extent of $\gtrsim400$ kpc \citep{cantalupo14, hennawi15}. These ELANe further offer excellent laboratories to detect and map the gas in the dense part of the intergalactic medium (IGM), and to study how the IGM feeds star formation in massive halos \citep{martin14, martin15}. \citet{arrigoni15a} conducted deep spectroscopic integrations targeting \heii\ and \civ\ emission and report a null detection, suggesting ELANe are mainly due to AGN photoionization on the cool, metal-poor CGM gas. In this paper, we report a discovery of another ultraluminous ELAN that resides near the density peak of our newly discovered massive overdensity BOSS1441 at $z=2.32\pm0.02$ (Cai et al. 2016a). This nebula has a projected linear size of $\approx 450$ kpc, comparable with the Slug nebula \citep{cantalupo14}, and remarkably extended \heii\ and \civ\ emission over $\gtrsim30$ kpc. The Ly$\alpha$, \heii\ and \civ\ lines all show double-peaked kinematics, with each component having the line widths of 700 $-$ 1000 km s$^{-1}$. The large spatial extent of Ly$\alpha$ emission, the strongly extended \heii\ and \civ, and the emission line structures and kinematics all make this ELAN unique. This Ly$\alpha$ nebula resides in an overdense field selected utilizing the largest QSO spectral library from the Baryon Oscillations Spectroscopic Survey (BOSS) \cite[e.g.,][]{dawson13}. It contains a group of extremely rare, high optical depth Ly$\alpha$ absorption (Cai et al. 2015) arising from the IGM overdensity and a rare QSO group \cite[e.g.,][]{cai16a}. We refer to this program as MApping the Most Massive Overdensity Through Hydrogen (MAMMOTH) (Cai et al. 2015). In this paper, we refer this nebula as MAMMOTH-1. This paper is structured as follows. In \S2, we introduce the selection of MAMMOTH-1 and our follow-up observations. In \S3, we discuss our observational results. In \S4, we discuss the physical properties and several powering mechanisms that could be responsible for such a unique ELAN. We also estimate the cool gas mass. We give a brief summary in \S 5. We convert redshifts to physical distances assuming a $\rm{\Lambda}$CDM cosmology with $\Omega_m= 0.3$, $\Omega_{\Lambda}=0.7$ and $h=0.70$ ($h_{70}$). Throughout this paper when measuring distances, we normally refer to physical separations or distances. We use cMpc to represent comoving Mpc, and kpc to represent physical kpc. | In the previous section, we showed that the ELAN MAMMOTH-1 has a Ly$\alpha$ spatial extent of $\approx440$ kpc and a total luminosity of $5.28\pm0.07\times10^{44}$ erg s$^{-1}$. This nebula resides in an extremely overdense galaxy environment previously discovered at $z=2.3$. Moreover, this radio-quiet nebula has the strongly extended \heii, \civ, and \ciii emission (Figure~4). The Ly$\alpha$, \heii, \civ\ line profiles are all double-peaked. In Table~3, we compare the properties of MAMMOTH-1 to other ELANe recently discovered. The Ly$\alpha$ spatial extent and the strong emission of \civ\ and \heii\ make MAMMOTH-1 unique. In this section, we derive the physical properties of MAMMOTH-1, and we discuss several possible physical explanations for powering this ELAN. \subsection{Ionizing Radiation} A comparison between hydrogen ionizing photons and helium ionizing photons constrains the hardness of the ionizing radiation. The number of H$^+$ ionizing photons can be expressed as: \begin{equation} Q(\rm{H})= \frac{L_{\rm{Ly\alpha, 15kpc}}}{h\nu_{\rm{Ly\alpha}}}\frac{1}{0.68}\approx 1.5\times10^{54}\ \rm{s}^{-1} \end{equation} where $f_{\rm{Ly\alpha},15kpc}=2.99\pm0.01\times10^{-16}$ erg s$^{-1}$ cm$^{-2}$, corresponding to $L_{\rm{Ly\alpha},15kpc}=1.7\times10^{43}$ erg s$^{-1}$. We have assumed that $\approx 68$\% of the ionizing photons are converted into Ly$\alpha$ emission (Spitzer 1978). This is a lower limit of Ly$\alpha$, because it may be destroyed by dust. Using the same spatial region, we measured that the \heii\ emission has a flux of $f_{\rm{HeII}}=7.8\pm0.2\times10^{-17} $ erg s$^{-1}$ ($L_{\rm{HeII}} = 3.2\pm0.1\times10^{42}$ erg s$^{-1}$). We calculated the He$^+$-ionizing photon number ($E_{\nu} \ge54.4$ eV) using the equation of: \begin{equation} Q(\rm{He^+})= \frac{L_{\rm{\lambda1640}}}{h\nu_{\rm{\lambda1640}}}\frac{\alpha^{\rm{eff}}_{HeII}}{\alpha^{1640}_{\rm{HeII}}}\approx 2.8\times10^{53}\ \rm{s}^{-1} \end{equation} where we assumed the case B recombination model, with a temperature of $T=10^4$ K. % Under this assumption, $\alpha_{\rm{HeII}}^{\rm{eff}}(T)= 1.53\times10^{-12}$ cm$^3$ s$^{-1}$ (Prescott et al. 2009). Therefore Q(He$^+$)/Q(H) is equal to 0.19. Note this is an upper limit for the Q(He$^+$)/Q(H) ratio because Ly$\alpha$ could be destroyed by dust. The Q(He$^+$)/Q(H) ratio suggests that the powering source of MAMMOTH-1 produces a hard ionizing radiation spectrum. In comparison, if we assume a typical Pop II stellar population with a Salpeter IMF, and a low metallicity of $Z=10^{-4}\ Z_\odot$, % then Q(He$^+$)/Q(H) equals 0.005 \citep{schaerer03, prescott09}, two orders of magnitude smaller than the value we estimated from MAMMOTH-1. This hard ionization ratio could arise because of significantly lower metallicity (e.g., Population III), a stellar population with a top-heavy IMF \citep{tumlinson03, schaerer03, cai11}, or an AGN. The detection of strong \civ\ and \ciii\ emission make this nebula unlikely to be powered by a low metallicity (e.g., Pop III) stars. Our current data support the conclusion that this ELAN is powered by one or more hard ionizing sources (e.g., AGN). \subsection{Sources of the enormous Ly$\alpha$, strong extended \civ, and \heii\ emission in a radio-quiet system} At least 15 Ly$\alpha$ nebulae with Ly$\alpha$ spatial extents larger than $150$ kpc have recently been discovered \cite[e.g.,][]{cantalupo14, hennawi15, borisova16}. But in none of these nebulae have strongly extended \heii\ and \civ\ been reported. We will discuss below several mechanisms that may power MAMMOTH-1. \subsubsection{Photoionization Model} In photoionization models, \civ\ emission is mainly powered by collisional excitation \cite[e.g.,][]{arrigoni15a}. The intensity of collisional excitation has a strong dependence on the temperature \cite[e.g.,][]{gurzadyan97}. A higher ionization parameter ($U$) yields a higher gas temperature, and thus the \civ\ intensity strongly depends on the ionization parameter. Collisional excitation also depends on the gas density and column density of \civ. The \heii\ emission is mainly due to recombination. The fraction of \heii\ emission reaches a peak at $U\sim-2.0$, where a larger fraction of the helium has been doubly ionized (e.g., Arrigoni-Batta et al. 2015b). Higher ionization parameters only modestly change the \heii\ intensity. The \ciii\ emission increases with the ionization parameter, and it is also highly sensitive to the metallicity. The \ciii\ emission peaks at a gas metallicity of $Z \sim 0.2\times Z_\odot$, and it decreases at both higher and lower metallicities (Erb et al. 2009). Therefore, the combination of \heii, \civ, and \ciii\ strongly constrains the physical properties of the CGM. Using CLOUDY ionization modeling \citep{ferland96}, \citet{arrigoni15a} have thoroughly investigated the \heii/ Ly$\alpha$ and \civ/Ly$\alpha$ ratios under different ionization parameters, gas densities ($n_{\rm{H}}$), and QSO ionizing luminosities ($L_{\nu_{{\rm{LL}}}}$) for the Slug nebula and nebulae in SSA22 protocluster. In \S3, we suggest that MAMMOTH-1 could be powered mainly by source B. Source B may be a strongly obscured source, e.g., a type-II AGN. The Ly$\alpha$ emission from a strongly obscured source may be complicated to interpret. In this section, we conduct a similar studies as \citet{arrigoni15a}, but focus on reproducing the \heii\ surface brightness and the \civ/\heii\ and \ciii/\heii\ line ratios. In our CLOUDY modeling, the AGN continuum follows the recipe in Matthews \& Ferland (1987). We assume that the CGM clouds have a constant hydrogen density ($n_{\rm{H}}$). We assume that the emitting gaseous clouds are uniformly distributed throughout the halo, and we further assume a standard plane-parallel geometry for these clouds. To match our measurements in \S3.3, we assume that the distance between the CGM cloud and the central QSO is $R\approx15$ kpc. In our CLOUDY models, we try combinations of different $n_{\rm{H}}$ values, with $n_{\rm{H}}= 0.01 - 10.0$ cm$^{-3}$ (steps of 0.5 dex); different ionization parameters, with Log $U= -3 -1$ (steps of 0.5 dex); different column densities of $N_{\rm{H}}=10^{19} - 10^{22}$ cm$^{-2}$ (steps of 0.5 dex), and metallicities with $Z=0.1 - 1.0\times Z_\odot$ (steps of $0.5\times Z_\odot$). We assume a gas covering fraction of $f_C=0.3$ \cite[e.g.,][]{cantalupo14}. % Our observed \heii\ surface brightness is $SB_{\rm{HeII}}\approx3.3\times10^{-17}$ erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$. We require that the parameter combinations yield a \heii\ surface brightness of $\approx 3.0-3.5\times10^{-17}$ erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$ to roughly match the observed \heii\ emission. In Figure~7, we present models that yield the observed \heii\ surface brightness, and present our observed value using a red dot with an error bar. Using the parameter combinations with ($N_{\rm{H}}$, $Z$, Log(U), $n_{\rm{H}}$)= (10$^{20}$ cm$^{-2}$, 0.5 $Z_\odot$, $-2$, 0.1 cm$^{-3}$) and ($10^{18}$ cm$^{-2}$, 1.0 $Z_\odot$, $-2$, 2.0 cm$^{-3}$) reproduce the observed intensities of \heii, \civ\ and \ciii, and the line ratios of \civ/\heii\ and \ciii/\heii\ within 1$\sigma$ errors (red error bars in Figure~7). Therefore, the \civ/\heii\ and \ciii/\heii\ line ratios are consistent with AGN photoionization. \figurenum{7} \begin{figure}[tbp] \epsscale{1.2} \plotone{cloudy_HeII.pdf} \caption{Simulation of the intensity ratios of \civ/\heii\ and \ciii/\heii\ powered by AGN. Colors represent different ionization parameters ($LogU$) and symbols represent different metallicities of the gaseous clouds. The observed value is marked with red points with an error bar. MAMMOTH-1 is consistent with the photoionization scenario, with an ionization parameter of Log U $\approx 2$ and a gas metallicity of 0.1 $Z_\odot$.} \end{figure} \subsubsection{\it Resonant Scatter} In \S3, we have shown that the Ly$\alpha$, \civ\ and \heii\ emission line profiles contain at least two major components. Double-peaked Ly$\alpha$ emission is predicted by the resonant scattering of Ly$\alpha$ photons \cite[e.g.][]{dijkstra06, yang14}. The key prediction of these radiative transfer (RT) calculations is that the Ly$\alpha$ spectrum is double peaked with an enhanced blue peak, producing a blueshift of the Ly$\alpha$ profile. Although it is true that this prediction matches the Ly$\alpha$ profile of MAMMOTH-1, the \heii\ emission has the same double-peaked structure as Ly$\alpha$. \heii\ is an optically-thin, non-resonant emission line whose photons escape the halo without radiative transfer effects \cite[e.g.,][]{yang14}. The non-resonant, optically thin emission lines should directly reflect the spatial distribution and kinematics of the gas. Thus, the emission-line structure of \heii\ strongly suggests that the double peaks are due to the actual kinematics (e.g., gas flows) rather than the radiative transfer effects. \subsubsection{\it Shocks due to a Gas Flow } The shocks due to flowing gas can also explain the double peaks of the emission lines. If the fast wind of an outflow is launched, then the shock could heat the surrounding interstellar gas over scales of $\gtrsim 50$ kpc (\citealt{debuhr12, harrison14}). Current galaxy formation simulations and observations suggest that high-velocity ($v_{\rm{max}}\sim1000$ km s$^{-1}$) galactic outflow can quench star formation in the most massive galaxies and eject heavy elements into the IGM \cite[e.g.,][]{taniguchi00, martin05, ho14}. Such galactic winds can be driven by (1) intense star formation or (2) relativistic winds or jets resulting from the gas accretion onto the supermassive black holes \cite[e.g.,][]{leitherer99, tombesi15}. \citet{wilman05} find a Ly$\alpha$ blob at $z=3.09$ in the SSA22 overdensity \citep{steidel00, matsuda05} whose double-peaked line profile is consistent with a simple outflow model. This model suggests that the Ly$\alpha$ emission is absorbed by a foreground shell of neutral gas that is pushed out up to a $\approx70$ kpc by an AGN-driven outflow. Using MAPPINGS \citep{dopita96} and CLOUDY \citep{ferland96} modeling, \citet{villar99, villar07} and \citet{moy02} suggest both shocks and AGN photoionization could power the extended Ly$\alpha$, \heii, and \civ\ observed in radio galaxies. Using hydrodynamical simulations, \citet{cabot16} further argue that the Ly$\alpha$, \heii\ and \civ\ emission in $z\approx3$ Ly$\alpha$ blobs could be primarily due to the shocks. Integral Field Spectrometer (IFS) observations suggest that the high-velocity ($v_{\rm{max}}\approx1000$ km s$^{-1}$) [OIII] outflows exist in a sample of 5 radio-quiet ULIRGs at $z\gtrsim2$. Such [OIII] outflows are consistent with the AGN-driven wind scenario \cite[e.g.,][]{alexander10, harrison12}. % MAMMOTH-1 has \ciii/\heii\ and \civ/\heii\ line ratios consistent with both photionization and shock models (see Figure~2 and Figure~3 of Villar-Martin et al. 1999). Further, the \civ/Ly$\alpha$ and \heii/Ly$\alpha$ ratios of MAMMOTH-1 are consistent with the predictions using shock models \citep{arrigoni15a}, with a gas denisty $n_H\sim 0.1-$ 1 cm$^{-3}$ and a shock velocity of $500$ -- 600 km s$^{-1}$. If the extended \heii\ and \civ\ are powered by shocks due to an AGN-driven outflow, then the double velocity peaks of emission lines can be naturally interpreted. Like \citet{harrison14}, we draw a schematic diagram to illustrate the outflow interpretation of the extended \civ\ and \heii\ (Figure~8). The velocity offsets between the two components and the spatial extent of emission lines strongly depend on the orientation of the outflow with respect to the line of sight: if the axis of the outflow is oriented along the line of sight, then a high-velocity offset and a small spatial extent should be observed; and conversely, if the axis of the outflow is in the plane of the sky, then a small velocity offset and a large spatial extent should be observed. From \S3.2, the offset between two velocity components is $\approx700$ km s$^{-1}$. These line structures are similar to ULIRG sample in \citet{harrison12}. If we assume the extended \civ\ and \heii\ are due to the AGN outflow, then we can estimate the energy of the outflow: \begin{equation} \dot{E}\approx 1.5\times10^{46}\ r_{10}^2\ v^3_{1000}\ n_{0.5} \ \rm{erg}\ \rm{s}^{-1} \end{equation} where $v_{1000}$ is the velocity offset between two components in units of 1000 km s$^{-1}$. $r_{10}$ is the radius of the observed of \civ\ emission in units of 10 kpc. The ambient density is the gas density ahead of the expanding bubble, in the units of 0.5 cm$^{-3}$. For MAMMOTH-1, if we assume that the extended \civ\ and \heii\ are completely powered by an AGN outflow, and further assume that the axis of the outflow is oriented 45 degrees with respect to the sight line, then $r_{10}=2$, $v_{1000}=0.7$. Taking these numbers into Equation (3), we establish that the spatially extended outflow in MAMMOTH-1 is potentially injecting energy into the circumgalactic medium at a considerable rate of $2\times10^{45-46}$ erg s$^{-1}$. Over a typical AGN duty cycle of 30 Myr \cite[e.g.,][]{hopkins05, harrison12}, the total energy injected reaches the order of $10^{60- 61}$ erg. According to \citet{nesvadba06}, the typical binding energy of a massive elliptical galaxy with a halo mass of $M_{\rm{halo}}\approx10^{12}$ M$_\odot$ is about $10^{60}$ erg. Thus, if MAMMOTH-1 is powered by an AGN outflow, then the outflow energy could be comparable or even an order of magnitude higher than this binding energy, making a vast AGN outflow possibly plays a major role in heating the ISM. % It has also long been suggested that jet-induced shocks can power extended metal-line emission, and extended \civ\ emission has been reported in a few radio-galaxies with strong radio continua \cite[e.g.,][]{mccarthy93, villar07}. We argue that our current data disfavour the model of jet-ISM interaction. From the FIRST radio catalog (Becker et al. 1995), we do not find any source with a radio flux at 1.4 GHz $>0.9\mu$Jy within a radius of 30 arcsec from MAMMOTH-1. Assuming a radio spectrum $S(\nu)\propto \nu^{-0.8}$, this 3-$\sigma$ upper limit corresponds to a luminosity density of $< 3.2 \times 10^{32}$ erg s$^{-1}$ Hz$^{-1}$ at rest-frame 1.4 GHz \citep{yang09}. This limit is two orders of magnitude lower than the radio continua of other Ly$\alpha$ nebulae powered by radio galaxies \cite[e.g.,][]{carilli97,reuland03}. \figurenum{8} \begin{figure}[tbp] \epsscale{1} \plotone{cartoon.pdf} \caption{A schematic diagram to demonstrate the outflow interpretation of the data. The \civ\ and \heii\ velocity offsets between the two components and the spatial extent of emission lines shown in Figure~5 strongly depend on the orientation of the outflow with respect to the line of sight. For a given AGN outflow, if the axis of the outflow is oriented along the line of sight, high-velocity offsets and a small spatial extent would be observed. Conversely, if the axis of the outflow is in the plane of the sky, a small velocity offset and a large spatial extent would be seen. } \end{figure} \subsubsection{\it Gravitational Cooling Radiation} Theoretical studies have suggested that Ly$\alpha$ nebula could result from the gravitational cooling radiation \cite[e.g.,][]{haiman01, dijkstra06, yang06, faucher10, rosdahl12}. % Several studies have predicted the \heii\ cooling radiation using hydrodynamical simulations. \citet{yang06} predict that the \heii\ line has the FWHM $\le 400$ km s$^{-1}$ even for the most massive halo at $z\approx2$ ($M\sim10^{14}\ M_\odot$). If our observed \heii\ line profile has two major velocity components as shown in Figure~5, then the \heii\ has a large FWHM of $714\pm100$ km s$^{-1}$ for the blue component and $909\pm130$ km s$^{-1}$ for the red component. The observed FWHMs are much wider than the predicted line width for cooling radiation. Also, using hydrodynamical simulations, \citet{fardal01} and \citet{yang06} point out that the \heii\ regions should be centrally-concentrated and the \heii\ cooling radiation may be too small to resolve using current ground-based telescopes. This size prediction of the \heii\ cooling radiation does not fit our observations. We have detected extended \heii\ emission over $\gtrsim30$ kpc scale. Further, if the Ly$\alpha$ emission results from the cooling inflow of the pristine gas in the intergalactic filaments, then we should expect no extended \civ\ being detected \cite[e.g.,][]{yang06, arrigoni15a}. Therefore, we conclude that our current observations do not fit with the cooling radiation picture. | 16 | 9 | 1609.04021 |
1609 | 1609.06801_arXiv.txt | Radial and azimuthal features (such as disc offsets and eccentric rings) seen in high resolution images of debris discs, provide us with the unique opportunity of finding potential planetary companions which betray their presence by gravitationally sculpting such asymmetric features. The young debris disc around HD~115600, imaged recently by the \emph{Gemini Planet Imager}, is such a disc with an eccentricity $e \sim 0.1-0.2$ and a projected offset from the star of $\sim 4$~AU. Using our modified N-body code which incorporates radiation forces, we firstly aim to determine the orbit of a hidden planetary companion potentially responsible for shaping the disc. We run a suite of simulations covering a broad range of planetary parameters using a \emph{Monte Carlo Markov Chain} sampling method and create synthetic images from which we extract the geometric disc parameters to be compared with the observed and model-derived quantities. We then repeat the study using a traditional grid to explore the planetary parameter space and aim secondly to compare the efficiency of both sampling methods. We find a planet of 7.8 Jupiter mass orbiting at 30 AU with an eccentricity of $e=0.2$ to be the best fit to the observations of HD~115600. Technically, such planet has a contrast detectable by direct imaging, however the system's orientation does not favour such detection. In this study, at equal number of explored planetary configurations, the Monte Carlo Markov Chain not only converges faster but provides a better fit than a traditional grid. | Planets can gravitationally perturb debris discs by various dynamical processes, such as secular interactions, where an eccentric or inclined planet can force the disc eccentricity or inclination \citep{1999ApJ...527..918W}, or resonance interactions, where the planet traps dust at a specific location, resulting in the creation of dust clumps in the disc \citep{2002ApJ...578L.149Q}. These processes inducing eccentricity, a disc position offset with respect to the star, or clumps into the disc can result in brightness asymmetries. Due to the limitations in the detection techniques, most of the confirmed exoplanets are located within 10~AU of their host star, and potential planets located beyond this limit (beyond Saturn in our solar system) remain undetected. However, even if those distant planets are too small to be detected with our current telescopes, they can still leave an observational signature by gravitationally perturbing the dust of their debris disc. Therefore investigating the dynamical relationship between debris discs and exoplanets can not only provide some insights on the origin of debris disc asymmetries, but also provides clues to the presence of hidden planets in the outer part of stellar systems, a region currently difficult to observe. HD~115600 is a young F2 type star at a distance of 110~pc in the Scorpius--Centaurus Association \citep{2007A&A...474..653V} of age $\sim$15 Myr \citep{2012ApJ...746..154P}. Although an IR excess was detected by \cite{2011ApJ...738..122C} using \textit{Spitzer/MIPS}, its debris disc was imaged for the first time in the H-band at $\lambda=1.6$~$\mu$m by \cite{2015ApJ...807L...7C} using the \emph{Gemini Planet Imager} (\emph{GPI}). The observation revealed a very broad nearly edge-on disc with an observed width to mean radius ratio $\Delta r$/$r_{0} \sim$ 0.37, which makes the HD~115600 debris disc one of the broadest ever observed -- see Table ~\ref{Table1} for the main parameters of HD~115600. \cite{2015ApJ...807L...7C} used the radiative transfer code GRaTeR \citep{1999A&A...348..557A} to model the disc emission. They found that the disc, most likely primarily constituted of ice-icy/silicate grains, appears eccentric with $0.1<e<0.2$ and its projected centre offset by $x_{off}=0.018^{\arcsec}$ and $y_{off}=0.029^{\arcsec}$ compared to the stellar location leading to a total offset of $r=\sqrt{x_{off}^{2}+y_{off}^{2}}=0.034^{\arcsec}$ or $3.75$~AU. They proposed that such disc eccentricity and offset could have been sculpted by a potential planetary companion. The absence of a direct detection of such a companion by \emph{GPI} places an upper limit of the mass of the potential companion of $m_{p}<7$~$M_{J}$ if it is ideally located on an orbit outside the coronograph mask. The authors point out that their model, however, respectively overestimates (underestimates) the disc flux at the southeast (southwest) corner. Using predictions from the gap opening model developed by \cite{2015ApJ...798...83N}, as well as the planet-stirring scenario established by \cite{2009MNRAS.399.1403M}, only very loose constraints on the potential planetary companion could be derived and the authors concluded that either a superjovian planet orbiting at $a<30$AU or a super-Earth located at the very inner edge of the disc could sculpt the disc. N-body simulations can be used to model the interaction between a debris disc and a planet. In these simulations, a disc, modeled by an ensemble of massless particles, orbits around a central body representing the star and feels the gravitational perturbation of another massive body. To test different planet configurations, a suite of these simulations must be run, and the planet parameter space (comprised of the planet mass and orbital elements) is traditionally explored by using a grid of set values \citep{2005ApJ...625..398D,2014A&A...563A..72F}. In this approach, the entire parameter space must be explored to isolate the best fit, and the precision of the best fit parameters directly depends on the size of the grid, and therefore a large number of simulations are required to reach high precision. Given the low number of currently resolved debris discs\footnote{The total resolved debris disc is 41 as referenced by http://www.circumstellardisks.org/ (accessed 25/07/16).}, N-body simulations have been so far used to study individual objects \citep{2014A&A...561A..43B,2015ApJ...815...61N}, however with the increased number of expected discoveries from the latest and next generation of instruments such as \emph{ALMA} and \emph{JWST}, a more efficient and statistical approach must be found. For example, the \textit{Monte Carlo Markov Chain} (MCMC) approach explores closely located points of the parameter space along a chain, and by accepting parameter space point resulting in better fits and rejecting point resulting in worse fits, the chain quickly converges toward the best fit region. This method has been used in astrophysics to estimate cosmological parameters with high precision \citep{2002PhRvD..66j3511L}, adjusting semi-analytic models of galaxy formation \citep{2013MNRAS.428.2001M} or fitting planetary orbital element from transit and radial velocity data \citep{2013PASP..125...83E}. \cite{2015NatCo...6E7599U} present the first study integrating N-body simulations within an \textit{MCMC} algorithm to estimate the pre-infall mass of the Carina galaxy before it joins the Milky Way satellites group. One focus of our study is to present a framework for testing if the \emph{MCMC} algorithm can be used to more efficiently probe the parameter space of N-body simulations of a planet shaping a debris disc than a traditional grid method. In this paper, we investigate the role of planets in determining the morphology of the HD~115600 debris disc. We dynamically model the interaction between an exoplanet and the HD~115600 disc using our modified N-body integrator, and explore the parameter space of the planets' orbit and mass using both the sampling method \textit{MCMC} and a traditional grid method. To compare the results of our numerical simulations with observations of HD~115600, we create synthetic images from the simulations at a similar wavelength and resolution as the \emph{GPI} image. Thus this study has two primary aims to both test the \textit{MCMC} algorithm for exploring the parameter space in N-body simulations and also provide information on a potentially hidden companion that planet hunters can use in the future searches. We first present our general method in Section 2. In order to derive the grain composition and properties required to turn our simulations into synthetic images, Section 3 presents our spectral modeling of the HD~115600 disc using the radiative transfer code \textit{MCFOST}. In Section 4, we introduce our numerical method for performing the dynamical simulations, before presenting our results in Section 5. A summary of our findings and conclusions are given in Section 6. \begin{table} \renewcommand{\arraystretch}{1.0} \caption{Properties for HD~115600 from Currie et al. (2015).} \label{Table1} \centering \begin{tabular}{cc} \hline Stellar properties & \\ \hline Spectral type & F2V/3V \\ Age & 15 Myr$^{a}$\\ Luminosity $L_{\ast}$ & $\sim$ 4.8~$L_{\odot}^{b}$ \\ Mass $M_{\ast}$ & $\sim$ $1.5~M_{\odot}$ \\ Distance & 110.5~pc$^{c}$ \\ \hline Disc properties & \\ \hline Width $\Delta r$ & 37.5--55~AU \\ Mean radius $r_{0}$ & $ 48 \pm 1.1$~AU\\ $\Delta r$/$r_{0}$ & 0.37 \\ Eccentricity $e$ & 0.1--0.2 \\ Mass & 0.05 $M_{\rm moon}$\\ Proj. offset $\delta$ & $3.7 \pm 1.5$~AU \\ Line-of-sight inclination $i$ & $79.5 \pm 0.5^{\circ}$\\ PA & $24 \pm 0.5^{\circ}$\\ \hline \end{tabular} \\ \small{ $^{a}$ Pecaut et al. (2012), $^{b}$ Chen et al. (2011), $^{c}$ van Leeuwen (2007).} \end{table} | In this work, we conducted a numerical search for a planet responsible for shaping the debris disc of HD~115600 recently imaged in the H band by \cite{2015ApJ...807L...7C} using \emph{GPI}. We first use the radiative transfer code \emph{MCFOST} with a parametric disc structure to derive the dust grain properties needed to fit the observed SED in order to create synthetic images. We then used a modified N-body integrator which incorporates radiation forces to dynamically model the interaction between the potential companion and the debris disc, and used \emph{MCFOST} to produce synthetic images to compare with observations. We explored the 3D parameter space ($a_{p}$,$e_{p}$ and $m_{p}$) of the potential planet using two different methods: a classic grid exploration over 360 grid points, and a \emph{MCMC} approach over 720 iterations. Our main results are as follows: \begin{itemize} \item From our SED modeling, and by selecting the Greenburg model where the grains are made of a core of silicate with a coating of water ice, the disc emission is best reproduced by a disc with a total dust mass of 0.2~$M_{\rm moon}$ with a minimal and maximal grain size of $0.05~\mu$m and $75~\mu$m. We however note that these parameters are not well constrained. \item From image modeling and using the \emph{MCMC} scheme to explore the parameter space, we reproduce the HD115600 disc eccentricity, projected offset, disc width and brightness peak with a $7.76~M_{\rm J}$ planet located at $a_{p}=31.07~$AU with $e_{p}=0.20$. Such a planet shapes the disc via a mix of secular interactions forcing the disc eccentricity, orientation and offset, as well as a set of planet resonances, at 4:3, 3:1 and 5:2, trapping dust at $a=38.5$, $48$ and $54$ AU respectively. \item While technically detectable by \emph{GPI}, the apparent and projected planet orbit is likely hidden by the disc emission as well as partially concealed by the coronograph mask due to the high inclination of the system. \item Using a same total number of simulations, we compared two methods of exploring the parameter space: a \emph{MCMC} sampling of the parameter space versus a grid method. We find that the \emph{MCMC} scheme not only finds a better fit to the observations, but also converges faster toward the best fit region. However we find that using a \emph{MCMC} scheme on such a short number of iterations presents some limitations: while our \emph{MCMC} implementation barely passed the convergence test such as the \cite{1992GelmanRubin}, it also only provides weak constraints on the confidence intervals. Increasing the numbers of iterations would increase the quality of the best fit estimation. We chose to conduct our study with a small number (720) of simulations for multiple reasons: first very few studies in the literature uses more than a few hundred dynamical simulations as they are computationally expensive and, secondly, after about a hundred iterations, the majority of subsequent models resulted in disc parameters comparable to the values obtained by \cite{2015ApJ...807L...7C} within the observational uncertainties. Finally our planetary parameters uncertainties estimated with 720 \emph{MCMC} iterations are well below the current uncertainties of parameters for planets detected via direct imaging. \end{itemize} For low dimensional problems (low $D<2-3$), like our study, a traditional grid of $M$ points only requires $M^{D}$ evaluations and presents the advantage of being trivially parallelized. For higher dimensional problems, it should be noted the \emph{MCMC} efficiently converges like $\sqrt{1/M}$, which is dimensionally independant and therefore a large advantage over the grid technique. In this study, we compare the efficiency of exploring our $D=3$ parameter space with a grid and a \emph{MCMC} algorithm. We conclude that this work demonstrates that the \emph{MCMC} scheme is a promising method to efficiently explore the parameter space of dynamical simulations and allows us to localize a better-fit region faster than the grid method, although we also stress that the limited number of simulations makes reaching the convergence state quite challenging. There are numerous schemes existing in the literature to explore multidimensional parameter spaces which could represent very good alternatives, such as the \emph{sparse grid MCMC} \citep{Menze2011} -- a scheme combining the use of both a grid and \emph{MCMC}, or the use of grids of different resolutions successively \citep{2013MNRAS.435.2033H}. The debris disc of HD~115600 shows interesting features which can be reproduced by simulating the gravitational influence of an inner massive planet on the disc structure. Additional observations of HD~115600 at different wavelengths could help constraining the planetary parameters furthermore. | 16 | 9 | 1609.06801 |
1609 | 1609.08507_arXiv.txt | We show that the effective theory describing single component continuous media with a linear and constant equation of state of the form $p=w\rho$ is invariant under a 1-parameter family of continuous disformal transformations. In the special case of $w=1/3$ (ultrarelativistic gas), such a family reduces to conformal transformations. As examples, perfect fluids, homogeneous and isotropic solids are discussed. | Disformal transformations have been considered in the framework of large-distance modification of gravity \cite{Bekenstein:1992pj}, and have become a very active field of research in modern cosmology and modified gravity, finding applications, for example, in Bekenstein’s TeVeS formalism \cite{Bekenstein:2004ne}, bimetric theories of gravity \cite{Milgrom:2009gv}, scalar-tensor theories \cite{Clifton:2011jh, Sakstein:2014isa} and disformal inflation \cite{Kaloper:2003yf}. Introduced in the context of Finsler geometry \cite{Bekenstein:1992pj}, these transformations describe the most general relation between two geometries in one and the same gravitational theory, preserving the causal structure and the weak equivalence principle. \\ More recently, it was discovered that the structure of Horndeski Lagrangian is invariant under a particular class of disformal transformations \cite{Bettoni:2013diz}. \\ As noted in Ref.\cite{Deruelle:2014zza}, the Einstein field equations are invariant under invertible disformal transformations, as well as more general scalar-tensor theories \cite{Arroja:2015wpa}\footnote{This is actually true for a generic non-singular field redefinition}. This fact has been used to show that some extensions of Horndeski theory, obtained by performing a general disformal transformation to the Horndeski Lagrangian, lead to the same equations of motion of the original theory and are thus free of ghost instabilities \cite{Zumalacarregui:2013pma}. On the other hand, if General Relativity (or a more general scalar-tensor theory) is reformulated in terms of an auxiliary metric, which is related with the original ``physical" metric by a non-invertible disformal transformation, a new degree of freedom of gravity is switched on \cite{Deruelle:2014zza, Arroja:2015wpa, Arroja:2015yvd}. This scalar degree of freedom behaves as an irrotational pressureless perfect fluid, i.e. it can mimic a cold dark matter component, or, more generally, irrotational dust. The resulting theory, called mimetic dark matter, was first proposed in \cite{Chamseddine:2013kea} and explored in \cite{Chamseddine:2014vna} (see also \cite{Hammer:2015pcx, Myrzakulov:2015kda, Cognola:2016gjy} and \cite{Ramazanov:2016xhp} for the relation with Ho\v{r}ava-Lifshitz gravity). Remarkably, disformal transformations have found other applications, for example they have been used in the context of primordial tensor modes during inflation \cite{Creminelli:2014wna}. \\ Furthermore, in a general fixed background even a free massless scalar field is invariant under a particular class of local disformal transformations~\cite{Falciano:2011rf} and disformal invariance of Maxwell's field equations was proved in \cite{Goulart:2013laa} while invariance of the Dirac equation was studied in~\cite{Bittencourt:2015ypa}. The goal of this paper is to analyze the general consequences of invariance under a disformal transformation for a rather large class of systems, namely continuous media, that are relevant for cosmology, modified gravity or analog gravity. Our analysis relies on the observation that the physics of fluids or solids can be derived by an unique Lagrangian \cite{Taub:1954zz, Schutz:1970my, Schutz:1977df}. This remarkable result has been investigated using the language of the effective field theory \cite{Dubovsky:2005xd,Dubovsky:2011sj,Nicolis:2011cs,Ballesteros:2012kv,Delacretaz:2014jka,Gripaios:2014yha} using the pull-back formalism, which had already been used to describe the dynamics of continuous media \cite{Carter:1987qr,Comer:1993zfa,Comer:1994tw,Andersson:2006nr}. Basically, the symmetries of the theory allow to extract all the dynamical information and the thermodynamics concerning the medium from an action principle. The paper is organized as follows. In Section \ref{Section:GeneralDisformal} we show that any Lagrangian invariant under this class of disformal transformations describes a medium with a linear equation of state. Then, as an example, in Section \ref{Section:PFDisformal} we show that the action for a perfect fluid with a linear equation of state is disformal invariant, the special case of an irrotational perfect fluid is discussed in Section \ref{Section:IPFDisformal}. In Section \ref{Section:SolidDisformal} we generalize this result to homogeneous and isotropic solids. Finally, in Section \ref{Section:Discussion}, we summarize and discuss our results. \textit{Notation}. Our signature is $(-+++)$; greek indices run from $0$ to $3$. Units are such that $\hbar=c=k_B=1$. | \label{Section:Discussion} In this work we have studied the invariance properties under a 1-parameter family class of disformal transformations (\ref{eq:generic_disformal_transformation}), that can be considered as a deformation of Weyl transformations. \\ Each family is characterized by a constant $w$ that has a manifest physical interpretation. Indeed, we have shown that every Lagrangian invariant under these disformal transformations is associated with an energy-momentum tensor characterized by a linear and equation of state of the form $p=w\rho$. \\ When $w=1/3$ the family of disformal transformations reduces to conformal ones and we recover the well-known conformal invariance of a Lagrangian describing ultra-relativistic matter. As explicit examples of our general analysis we have considered perfect fluids and solids, generalizing the analysis for a free scalar field given in \cite{Falciano:2011rf}. | 16 | 9 | 1609.08507 |
1609 | 1609.03565_arXiv.txt | The detection of gravitational waves from the merger of binary black holes by the LIGO Collaboration has opened a new window to astrophysics. With the sensitivities of ground based detectors in the coming years, we will principally detect local binary black hole mergers. The integrated merger rate can instead be probed by the gravitational-wave background, the incoherent superposition of the released energy in gravitational waves during binary-black-hole coalescence. Through that, the properties of the binary black holes can be studied. In this work we show that by measuring the energy density $\Omega_{GW}$ (in units of the cosmic critical density) of the gravitational-wave background, we can search for the rare $\sim 100 M_{\odot}$ massive black holes formed in the Universe. In addition, we can answer how often the least massive BHs of mass $\gsim 3 M_{\odot}$ form. Finally, if there are multiple channels for the formation of binary black holes and if any of them predicts a narrow mass range for the black holes, then the total $\Omega_{GW}$ spectrum may have features that with the future Einstein Telescope can be detected. | \label{sec:introduction} The observation of the coalescence of black holes (BHs) by the LIGO collaboration~\cite{Abbott:2016blz, Abbott:2016nmj, TheLIGOScientific:2016pea}, has generated great interest in gravitational wave (GW) physics and in the sources responsible for them. Many alternatives have been proposed regarding the progenitors of binary black holes (BBHs), including from BH as the end product of stellar evolution of massive stars \cite{Hosokawa:2015ena, Zhang:2016rli, Woosley:2016nnw, deMink:2016vkw, Hartwig:2016nde, Inayoshi:2016hco}, of BHs in globular clusters \cite{Rodriguez:2016kxx, Chatterjee:2016hxc, Rodriguez:2016avt, O'Leary:2016qkt}, or in centers of galaxies \cite{O'Leary:2008xt, Stone:2016wzz}, or as the result of primordial black holes capturing each other \cite{Bird:2016dcv, Clesse:2016vqa, Sasaki:2016jop}, all consistent with the observed BBH merger rates \cite{Abbott:2016nhf, TheLIGOScientific:2016pea}. In order to probe and discriminate among the various models for the BBH progenitors, different observables will be necessary. With LIGO, we expect that BH binaries of composite masses of 10 (20, 30) $M_{\odot}$ will be detectable as individual events, only up to redshifts of 0.3 (0.5, 0.7). However, with the future Einstein Telescope (ET) \cite{Sathyaprakash:2011bh} those redshifts may increase up to 11 (12, 11) respectively. In addition, the entire merging BBH population of the Universe, can be probed through the incoherent superposition of their released energy in GWs, giving the gravitational wave background \cite{Kosenko:1998mv, Ferrari:1998ut, Schneider:2000sg, Schneider:2000sg, Hogan:2001jn, Farmer:2003pa, Howell:2010hm, Regimbau:2011rp, Rosado:2011kv, Zhu:2011bd, Marassi:2011si, Wu:2013xfa, Regimbau:2014uia, TheLIGOScientific:2016wyq}. This background is affected, by both the BBH population mass and redshift distributions at the time of the merger. In turn these distributions depend on the environment where the BH binaries form. After its first run, advanced LIGO has detected two events, event GW150914 of $36.2^{+5.2}_{-3.8}$ and $29.1^{+3.7}_{-4.4}$ $M_{\odot}$ merging BHs, and event GW151226 of $14.2^{+8.3}_{-3.7}$ and $7.5^{+2.3}_{-2.3}$ $M_{\odot}$ , each with a significance larger than 5.3 $\sigma$. LIGO has also detected one possible event, LVT151012 of $23^{+18}_{-6}$ and $13^{+4}_{-5}$ $M_{\odot}$ with a significance of 1.7 $\sigma$ \cite{TheLIGOScientific:2016pea}. Merging BHs, during the last stages of their coalescence when most energy is radiated, emit GWs at frequencies and with amplitudes that depend on the combination of their masses. Using the first three events, and the estimated BBH merging rates, we can study the impact that uncertainties on individual BH mass and redshift distributions have on the gravitational wave background, and present how those properties can be further probed. This paper is organized as follows; in section~\ref{sec:Methodology} we give the basic set up for our calculations and in section~\ref{sec:PBHs_OmegaGW} we give our main results and discuss on the detectability of the gravitational wave background. Finally in section~\ref{sec:Conclusions} we give our conclusions. | \label{sec:Conclusions} The detection of GWs from the merger event of binary BHs has opened a new window in astrophysics. In this work we discuss the importance of the gravitational waves energy density on probing the properties of the BBHs and thus possibly their origin. While the current uncertainties after only three merger events are still very wide, there is a series of questions that can be asked. Since the GW energy density $\Omega_{GW}$ is the integrated merger rate of BBHs even at high redshifts where individual mergers can't be identified, its spectrum can give us information on the total BBH mass distribution. We find that at high frequencies ($O(10^{2})$ Hz) the contribution from the lightest BHs can be probed and thus help us understand how often such objects form (see Figure~\ref{fig:StochGWBack} and Figure~\ref{fig:StochGWBackMassAssup}). More interestingly, at frequencies as low as 10-50 Hz, we can indirectly search for a signal of the most massive BHs of stellar origin. If the initial stellar mass function extends to masses as large as $\sim 500 M_{\odot}$, resulting in BHs of $\gsim 100 M_{\odot}$ at the binaries, then a deviation from the expected $\Omega_{GW} \propto f^{2/3}$ spectrum behavior may be clearly observed with ET (see Figure~\ref{fig:StochGWBackMassAssup}). The gravitational wave energy density amplitude depends strongly both on the total local rate and its redshift profile, which in turn depends on the exact environment, the time of binary formation, and the time-delay between formation and merger of the binary. The $\Omega_{GW}$ is strongly degenerate to those assumptions (see Figure~\ref{fig:StochGWBackRateAssump2}). Yet, we can use the individual detected events from LIGO in the next years to measure the local value of $R_{m}$ and break some of these degeneracies. Finally, we discussed that if populations of BHs exist with narrow mass distributions as are those of PBHs \cite{Bird:2016dcv, Sasaki:2016jop, Clesse:2016vqa}, then mild spectral features may exist in the $\Omega_{GW}$, that future detectors can identify (see Figure~\ref{fig:StochPBHGWBack}). The measurement of the spectrum of the gravitational wave energy density should be considered an other tool of searches to understand the properties of the BBHs in the Universe. That would be complementary to other studies as for instance cross-correlations of GW maps with galaxy catalogues \cite{Raccanelli:2016cud, Namikawa:2016edr}, searches for high modes of GW emission \cite{Seto:2016wom, Nishizawa:2016jji, Cholis:2016kqi, Nishizawa:2016eza} or studies regarding the spins of the composite BHs \cite{Kalogera:1999tq, TheLIGOScientific:2016htt}. \bigskip {\it Acknowledgements}: The author would like to thank Yacine Ali-Ha\"{i}moud, Ely Kovetz, Marc Kamionkowski, Chris Moore, Julian Mu\~{n}oz, Alvise Raccanelli and especially Simeon Bird and Vuk Mandic for interesting discussions. This work is supported by NASA Grant NNX15AB18G and the Simons Foundation. | 16 | 9 | 1609.03565 |
1609 | 1609.03753_arXiv.txt | We build a simple physical model to study the high-redshift active galactic Nucleus (AGN) evolution within the co-evolution framework of central black holes (BHs) and their host galaxies. The correlation between the circular velocity of a dark halo $V_c$ and the velocity dispersion of a galaxy $\sigma$ is used to link the dark matter halo mass and BH mass. The dark matter halo mass function is converted to the BH mass function for any given redshift. The high-redshift optical AGN luminosity functions (LFs) are constructed. At $z\sim 4$, the flattening feature is not shown at the faint end of the optical AGN LF. This is consistent with observational results. If the optical AGN LF at $z\sim 6$ can be reproduced in the case in which central BHs have the Eddington-limited accretion, it is possible for the AGN lifetime to have a small value of $2\times 10^5$ yrs. The X-ray AGN LFs and X-ray AGN number counts are also calculated at $2.0<z<5.0$ and $z>3$, respectively, using the same parameters adopted in the calculation for the optical AGN LF at $z\sim 4$. It is estimated that about 30 AGNs per $\rm{deg}^2$ at $z>6$ can be detected with a flux limit of $3\times 10^{-17}~\rm{erg~cm^{-2}~s^{-1}}$ in the $0.5-2$ keV band. Additionally, the cosmic reionization is also investigated. The ultraviolet photons emitted from the high-redshift AGNs mainly contribute to the cosmic reionization, and the central BHs of the high-redshift AGNs have a mass range of $10^6-10^8M_\odot$. We also discuss some uncertainties in both the AGN LFs and AGN number counts originating from the $M_{\rm{BH}}-\sigma$ relation, Eddington ratio, AGN lifetime, and X-ray attenuation in our model. | Active galactic nucleus (AGN) evolution is one of the vital issues to investigate the central black hole (BH) accretion, galaxy formation, and large-scale structure of the universe. Some statistical results, such as luminosity functions (LFs) and number counts, can be obtained from multi-wavelength sky surveys. The optical LFs of quasi-stellar objects (QSOs) were obtained from the 2dF survey \citep{boyle00,croom04}. Using the data from ROSAT, {\it{Chandra}}, and XMM-{\it{Newton}} satellites, \citet{miyaji00}, \citet{miyaji01}, and \citet{hasinger05} constructed the soft X-ray AGN LFs in the $0.2-2$ keV band. The hard X-ray LFs and hard X-ray cosmic background in the $2-10$ keV band were studied as well \citep{cowie03,ueda03,barger05,lafranca05}. From these early studies, we know that neither density evolution nor luminosity evolution can fully describe AGN LF evolutionary properties. However, a downsizing feature has been reported, which is the number density of galaxies/AGNs peaking at low redshift \citep{cowie96,lemaux14,ueda14}. Thus, the crucial explorations of the AGN LFs in the optical band for the high-redshift universe, which have been performed during recent years, have become more important. The QSO LFs at $3.6<z<5.0$ from the Sloan Digital Sky Survey (SDSS) have been given \citep{fan01}. The AGN LFs at $3.5<z<5.2$ have been extended to the faint end of $M_{1450}\sim -21.5$ by the great observatories origins deeps survey (GOODS) high-redshift AGN sample \citep{cristiani04,fontanot07}. The faint type-1 AGN LFs have been given by \citet{bongiorno07} from the VIMOS-VLT deep survey. With the 2dF-SDSS data, the AGN LF at $0.4<z<2.6$ has been extended 2.5 mag fainter \citep{croom09} than the previous one. At $z\sim 4$, some faint end data points for QSO LF have been provided by the NOAO deep wide-field survey and the deep lens survey \citep{glikman10}. The AGN LFs at $z\sim 6$ were obtained by the SDSS deep survey \citep{jiang09} and the Canada-France high-redshift QSO survey \citep{willott10}. The Subaru high-redshift QSO survey has also discovered some faint AGNs at $z\sim 6$ \citep{kashikawa14}. High-redshift AGN detections in the X-ray band are also exciting. From the {\it XMM-Newton} medium-sensitivity survey, \citet{ebrero09} have derived AGN LFs ($0<z<3$) which can be described by a luminosity-dependent density evolution (LDDE) model. The AGN LF at $z\leq 5$ obtained from a faint {\it Chandra} sample has been reported by \citet{yencho09}. \citet{aird10} have found the high space density of low-luminosity AGNs at $z>2$ from the 2 Ms {\it Chandra} deep survey and the AEGIS-X 200 ks survey. The number counts of X-ray selected QSOs at $z>3$ have been obtained from the COSMOS survey and the Subaru/{\it XMM-Newton} deep survey \citep{brusa09,civano11,hiroi12}. The number density evolution of obscured AGNs has been mentioned by \citet{fiore08,fiore09}, \citet{brusa10}, and \citet{hiroi12}. AGNs with column densities above $10^{24}~\rm{cm^{-2}}$ are denoted as ``Compton thick'', and these heavily obscured AGNs represent a key phase of AGN-host galaxy co-evolution. It is quite interesting that two Compton-thick AGNs have been discovered in the {\it XMM}-{\it Newton} deep survey ($z=3.7$) and the 4 Ms {\it Chandra} deep field (CDF) survey ($z=4.76$), respectively \citep{comastri10a,gilli11}. The Compton-thick AGN surveys have been done by \citet{brightman14} and \citet{lanzuisi14}. The AGN number density and the cosmic X-ray background have been studied with large observational samples \citep{ueda14,aird15,miyaji15}. Some problems with the AGN LF have been raised by these new observations. For example, at $z>4$, a flattening feature at $M_{1450}>-23$ seen in the optical AGN LF \citep{fontanot07} was explained by the physics of central BH growth and AGN/supernova feedback \citep{lapi06,fontanot06}. However, the number density of faint optical AGNs ($-23<M_{1450}<-21$) reported by \citet{glikman10} is about 10 times larger than that of \citet{fontanot07}. With additional spectral identifications, \citet{glikman11} re-built the AGN LF at $z=4$. However, the number density of these faint AGNs is still two times that given by \citet{fontanot07}. This observational discrepancy was also mentioned by \citet{fiore10}. One possible reason for this discrepancy is as follows \citep{glikman10,glikman11}. \citet{fontanot07} used the QSO spectral template of \citet{cristiani90}, which empirically determines a distribution of continua blueward of Ly$\alpha$, and the power-law spectral template has a slope of 0.7; \citet{glikman10,glikman11} had the QSO spectral library template modified by a composite using the Gaussian distribution of power-law continua, and a slope of 0.5 is given in the spectral template. If the sample selected by \citet{glikman11} has better completeness than that selected by \citet{fontanot07}, the flattening feature given by \citet{fontanot07} would be significantly reduced. While Masters et al. (2012) built the optical LFs at $3<z<5$ from the COSMOS survey field. The space density of faint AGNs at $z\sim 4$ is lower than the result of Glikman et al. (2011) by a factor of $3\sim 4$. They suggested that this discrepancy may be due to the contamination of dwarf stars and high-z galaxies in the sample of Glikman et al. (2011), and spectroscopic follow-up identification is still challenging for this contamination constraint. Therefore, the final high-redshift AGN candidates are different due to different selection functions. Although the AGN LF at $z\sim 6$ has been extended to the faint end of $M_{\rm{1450}}\sim -22$, it seems that the AGN LF is still steep at the faint end \citep{willott10, kashikawa14}. One widely accepted issue of AGN evolution is that the AGN and its host galaxy have co-evolution characteristics \citep{richstone98}. A strong correlation was found between the central BH mass $M_{\rm{BH}}$ of a normal galaxy and the velocity dispersion $\sigma$ of a galactic bulge \citep{ferrarese00,gebhardt00,tremaine02,gultekin09,batcheldor10}. This $M_{\rm{BH}}-\sigma$ relation (presented as $logM_{\rm{BH}}=\alpha+\beta log(\sigma/200~\rm{km~s^{-1}})$, where $\alpha$ and $\beta$ are fitting parameters) is also valid for the AGN population \citep{shields03,shields06,greene07,wu07,woo10}. A correlation between a BH mass $M_{\rm{BH}}$ and the galactic spheroid mass $M_{\rm{sph}}$ \citep{magorrian98,marconi03,haring04,nelson04} also indicates the co-evolution feature of AGNs and their host galaxies. Moreover, the $M_{\rm{BH}}-\sigma$ relation evolves with redshift, and the ratio between the $M_{\rm{BH}}$ and $M_{\rm{sph}}$ increases with redshift \citep{shields06,mclure06,decarli10}. These evolution properties provide the possibility that the central BH growth could finish before its host spheroid formation. In other words, massive BHs grow rapidly in the early universe without commensurate growth of their host galaxies \citep{grupe04,shields06}. On the contrary, Schulze \& Wisotzki (2014) performed a fitting procedure of the BH-bulge relation with the Monte Carlo simulation test, in which the observational selection effects were considered. They did not find any cosmological evolution of the BH-bulge relation when the selection effects were corrected. On the other hand, \citet{loeb03} suggested that the circular velocity $V_{\rm{c}}$ of a dark matter halo potential well can be linked to the velocity dispersion $\sigma$ of a galactic bulge, and the theoretical relationship between $\sigma$ and $V_{\rm{c}}$ was also examined by observational data \citep{ferrarese02}. Therefore, we can link the physical processes of dark matter halos to those of baryons at a certain redshift. Theoretical investigations of co-evolution have been carried out between central BHs and their host galaxies \citep{silk98,fabian99,king03,king05,begelman05,croton09,nayakshin09,king10}. \citet{shankar09a} predicted the velocity dispersion functions of spheroid galaxies at $0<z<6$. Their results indicate a redshift evolution of the $M_{\rm{BH}}-\sigma$ relation. Similar evidence for the evolution of the $M_{\rm{BH}}-\sigma$ relation was given by numerical simulations \citep{robertson06}. The redshift evolution of a $M_{\rm{BH}}/M_{\rm{sph}}$ was also modeled \citep{somerville09,lamastra10}. \citet{haehnelt93} presented a QSO evolution model in which massive BHs are formed inside virialized dark matter halos. AGN LFs were studied within the framework of co-evolution between central BHs and their host galaxies, and the BH accretion history was explored in detail \citep{haehnelt98}. A linear relation between a dark matter halo mass and BH mass was used to derive the AGN LF \citep{haiman98,wyithe02}, and the processes of BH self-regulated growth were also considered \citep{wyithe03}. Several complicated models of QSO activity, including the BH accretion process \citep{mahmood05} and the BH merger process \citep{shen09}, were given as well. From numerical simulations, \citet{hopkins05} proposed a luminosity-dependent AGN lifetime to reproduce the AGN LFs. The AGN/supernova feedback processes were used to explain the observational downsizing feature of the AGNs/BHs \citep{croton06,fontanot06,lapi06,lapi14,marulli08,menci08}. \citet{lapi06} noticed that AGN shining occurs after dark matter halo virialization due to the growth of a central BH seed. Thus, a time delay between dark matter halo virialization and AGN shining should be considered. In this case, super-Eddington accretion is important for the central BH growth. Based on a semi-analytic model of the co-evolution between BHs and their hosts, Fanidakis et al. (2012) investigated the AGN evolution, considering both the thin-disk accretion and the ADAF model. The optical and X-ray AGN LFs were reproduced when the AGN obscuration form of Hasinger (2008) was taken into account. This model predicted a hierarchical buildup of BH mass, but the downsizing feature for different AGN populations was clearly shown due to the different accretion modes and the AGN obscuration. Hirschmann et al. (2012) comprehensively investigated some accretion modes. Standard accretion, varing sub-Eddington limit for the maximum accretion, and disk instability accretion were considered. The BH seed mass for the merger process was also considered. A cosmological numerical simulation for the BH growth was performed by Hirschmann et al. (2014). The downsizing feature of the AGN number density evolution was well explained when the gas density nearby the massive BH was included in their model. Thus, the processes of star formation and AGN/supernova feedback should be also involved. The star formation process was further explored by Enoki et al. (2014). In their semi-analytic model, the starburst is caused by an AGN merger, and the cold gas accretion triggers AGN shining. The amount of cold gas for the BH accretion decreases with cosmic time, and the AGN lifetime decreases with redshift. Then, the downsizing trend of the AGN evolution is shown. From above theoretical models, the observed downsizing feature of the AGN evolution can also be explained under the framework of the hierarchical structure formation. Some research efforts have been attempted toward explaining the faint end of the high-redshift AGN LFs. \citet{hopkins07} determined the bolometric AGN LF at $0<z<6$ using a large set of AGN LFs in different rest-frame wavelengths. The faint-end slope of the AGN LF was confirmed. \citet{shankar09,shankar10,shankar13} comprehensively studied bolometric LFs through the arrangements of BH accretion, radiative efficiency of AGNs, and AGN clustering. However, it was pointed out by \citet{willott10} that those LFs built by \citet{hopkins07} and \citet{shankar09} overestimated the number density of faint AGNs at $z=6$. For instance, in a luminosity range of $-25.5<M_{1450}<-24.5$, the AGN number density calculated by \citet{shankar09} is about five times larger than those given by \citet{jiang09} and \citet{willott10b}. Moreover, the predictions of high-redshift AGN number counts in the X-ray band are also uncertain. \citet{rhook08} proposed a dark matter halo merger model to drive AGN shining. \citet{marulli08} constructed a semi-analytic model of the co-evolution between BHs and host galaxies. It was assumed that central BHs continuously accrete surrounding hot gas for AGN shining. As reported by \citet{gilli10}, at $z>6$, with a flux limit of $3\times 10^{-17}~\rm{erg~cm^{-2}~s^{-1}}$ in the $0.2-2$ keV band, an optimistic detection of $500-600$ AGNs per $\rm{deg}^2$ and a pessimistic detection of $\sim$ 16 AGNs per $\rm{deg}^2$ were predicted by \citet{rhook08} and \citet{marulli08}, respectively. Because many obscured low-luminosity AGNs can be found at high redshifts \citep{lafranca05,hasinger08, menci08}, high-redshift AGN detections in the X-ray band are strongly encouraged by some satellite proposals. For example, the Wide Field X-ray Telescope (WFXT) can perform deep observations in 100 $\rm{deg}^2$ to a flux limit of $3\times 10^{-17}~\rm{erg~cm^{-2}~s^{-1}}$ in the $0.5-2$ keV band \citep{rosati10}. Those unobscured AGNs beyond redshift 6 can be effectively detected. Some obscured AGNs can also be explored up to $z\sim 4$ \citep{comastri10a,gilli10}. Therefore, modeling predictions of the high-redshift AGN number density in the X-ray band could also be important for future missions. The ultravoilet photons emitted by AGNs can effectively ionize the intergalactic medium (IGM). High-redshift AGN LFs are used to study cosmic reionization. The so-called Gunn-Peterson trough \citep{gunn65} seen in the optical spectra of the SDSS AGN sample provides excellent evidences to constrain the cosmic reionization epoch \citep{fan02,fan06}. It was estimated by \citet{fan06b} that the QSO contribution to the ionizing background is less than 30\% of the star-forming galaxy contribution. The AGN contribution to the cosmic reionization \citep{shankar07} was revisited by \citet{glikman10}. However, the Subaru high-redshift quasar survey has shown that the AGNs at redshift 6 still do not have enough photons to ionize the universe \citep{kashikawa14}. In this paper, as a consequent issue of the high-redshift AGN evolution, some rough estimations for the cosmic reionization are given. We build a simple analytic model to study high-redshift AGN evolution within the framework of joint evolution between central BHs and their host galaxies. Beginning from the dark matter halo mass function, we derive the AGN LFs by applying the $M_{\rm{BH}}-\sigma$ and $V_c-\sigma$ relations. High-redshift AGN number counts in the X-ray band are obtained as well. We compare our results to those observational data. The cosmic reionization is also examined. In our physical recipe, the Eddington ratio $\lambda$, AGN lifetime $\tau_{\rm{AGN}}$, $\alpha$, and $\beta$ in the $M_{\rm{BH}}-\sigma$ relation, are free parameters (see Table 1 for details). All of these parameters are within their observational constraints. We do not perform optimized fittings to those observational AGN LF data by adjusting the parameters in our model. Instead, we choose reasonable values for these parameters to produce the AGN LFs and AGN number counts by comparison with the observational data. Thus, some related physical processes can be further explored. Section 2.1 describes our physical model. The AGN LFs and AGN number counts are derived in Section 2.2. In Section 3, the contributions from the high-redshift AGNs to the cosmic reionization are estimated. Discussion and conclusions are given in Sections 4 and 5, respectively. Throughout the paper, we adopt the following cosmological parameters: $H_0=72~\rm{km~s^{-1}~Mpc^{-1}}$, $\Omega_{\rm{m}}=0.3$, and $\Omega_\Lambda=0.7$. | \begin{enumerate} \item With a moderate sub-Eddington ratio and an AGN lifetime of about $10^7$-$10^8$ years, optical and X-ray AGN LFs at high redshifts are produced. At $z\sim 4$, we do not obtain any flattening feature at the faint end of the optical AGN LF, consistent with observational results. \item The optical AGN LF at $z=6$ built by \citet{willott10,willott10b} and \citet{kashikawa14} can be reproduced with Eddington-limited accretion and an AGN lifetime of about $2\times 10^5$ yrs. It seems possible that these AGNs at $z=6$ are very young. \item We calculate the X-ray AGN LFs at $2.0<z<5.0$ and the X-ray AGN number counts at $z>3$ using the same parameters adopted for the calculation of the optical AGN LFs at $z\sim 4$. We estimate that, at $z>6$, there are about 30 AGNs per $\rm{deg}^2$ to the flux limit of $3\times 10^{-17}~\rm{erg~cm^{-2}~s^{-1}}$ in the $0.5-2$ keV band. \item High-redshift AGNs with central masses less than $10^8~M_{\odot}$ may dominate the cosmic reionization, though this domination is strongly dependent on the AGN LF, clumping factor, and escape fraction of ionizing photons. \end{enumerate} Although our AGN LFs and AGN number counts at high redshifts have uncertainties that originate from the $M_{\rm{BH}}-\sigma$ relation, Eddington ratio, AGN lifetime, and X-ray attenuation, they can be further constrained by optical and X-ray observations (Subaru/PFS, WFXT, eROSITA) in the future. | 16 | 9 | 1609.03753 |
1609 | 1609.02563_arXiv.txt | Being the first of its kind, the white dwarf WD\,1145+017 exhibits a complex system of disintegrating debris which offers a unique opportunity to study its disruption process in real time. Even with plenty of transit observations there are no clear constraints on the masses or eccentricities of such debris. Using $N$-body simulations we show that masses greater than $\simeq10^{20}$\,kg (a tenth of the mass of Ceres) or orbits that are not nearly circular ($\mathrm{eccentricity}>10^{-3}$) dramatically increase the chances of the system becoming unstable within two years, which would contrast with the observational data over this timespan. We also provide a direct comparison between transit phase shifts detected in the observations and by our numerical simulations. | Planets which survive the giant branch evolution of their hosts stars are expected to be rather common \citep{burleigh2002,villaver2007,mustil12,veras13}. This prediction is corroborated by the detection of photospheric metal pollution in a large fraction of all white dwarfs \citep{zuckerman03, zuckerman2010, koester14}. Dynamical interactions in evolved planetary systems can scatter planetary bodies near the Roche radii of the white dwarfs \citep{debes02,frewen2014,payne2016a,payne2016b} where they are tidally disrupted \citep{jura2003,debes2012,veras14a,veras15c}, forming detectable accretion discs \citep{zuckerman1987,boris2006,kilic2006,farihi2009,bergfors2014}, and ultimately accreting onto the white dwarf. Analysis of the photospheric trace metals provides detailed insight into the bulk chemical compositions of planetary systems \citep{zuckerman2007,boris2012,xu2014}, which in turn guides planet formation models (e.g. \citealt*{bond2012}). The current observational and theoretical progress on evolved planetary systems is summarised by \citet{farihi2016} and \citet{veras2016rev}. \cite{vanderburg1} announced transits recurring with a period of $\simeq4.5$\,h in the $K2$ light curve of the white dwarf WD\,1145+017, which also exhibits infrared excess from a circumstellar disk and photospheric metal pollution. The orbit of the transiting objects lies close to the disruption, or Roche, limit for rocky objects. Thus, WD\,1145+017 represents the first observational detection of planetesimals orbiting a white dwarf, opening a new window into the understanding of poorly-known processes such as disintegration, orbital circularisation, or the actual nature of those orbiting bodies \citep{veras14b,veras15b,veras2016rev}. In this work we derive constraints for the masses and eccentricities of the bodies orbiting the star from N-body simulations of the system. Section \ref{sec:system}, provides an overview of the WD\,1145+017 system and Sect. \ref{sec:simulation} outlines the setup of our simulations. In Sect. \ref{sec:mass} and \ref{sec:ecc} we present the results that set constraints on the mass and eccentricity of the orbiting debris. Section \ref{sec:shifts} is devoted to phase shifts, proving also a direct comparison between observational data and our simulations. We briefly discuss our results in Sect. \ref{sec:disc} and then conclude in Sect. \ref{sec:conc}. | \label{sec:conc} We have performed $N$-body simulations to derive constraints on mass and eccentricity of the planetary bodies orbiting WD\,1145+017. We found that either masses greater than $\simeq10^{20}$\,kg (0.1 the mass of Ceres) or orbits that are not nearly circular ($\mathrm{eccentricity}>10^{-3}$) increase the likelihood of dynamical instability over a timespan comparable to the baseline of the current set of observations. We also computed the phase shifts of the fragments with respect to the parent body, and found good agreement with the shifts measured by \cite{rappaport16}. Future work should include a detailed treatment of the actual disruption process, which would provide further insight into the physical properties of the disintegrating bodies, and allow an estimate of the expected duration of this phase. | 16 | 9 | 1609.02563 |
1609 | 1609.05175_arXiv.txt | {}{ We present a comparison of Gaia Data Release 1 (DR1) parallaxes with photometric parallaxes for a sample of 212 Galactic Cepheids at a median distance of 2~kpc, and explore their implications on the distance scale and the local value of the Hubble constant $ H_0 $. }{ The Cepheid distances are estimated from a recent calibration of the near-infrared Period-Luminosity (\PL) relation. The comparison is carried out in parallax space, where the DR1 parallax errors, with a median value of half the median parallax, are expected to be well-behaved. }{ With the exception of one outlier, the DR1 parallaxes are in remarkably good global agreement with the predictions, and there is an indication that the published errors may be conservatively overestimated by about 20\%. Our analysis suggests that the parallaxes of 9 Cepheids brighter than $G = 6$ may be systematically underestimated; {\it trigonometric} parallaxes measured with the Hubble Space Telescope Fine Guidance Sensor for three of these objects confirm this trend. If interpreted as an independent calibration of the Cepheid luminosities and assumed to be otherwise free of systematic uncertainties, DR1 parallaxes would imply a decrease of 0.3\% in the current estimate of the local Hubble constant, well within their statistical uncertainty, and corresponding to a value 2.5 $\sigma$ (3.5 $\sigma$ if the errors are scaled) higher than the value inferred from Planck CMB data used in conjunction with {\lcdm}. We also test for a zeropoint error in Gaia parallaxes and find none to a precision of $ \sim 20 \muas$. We caution however that with this early release, the complete systematic properties of the measurements may not be fully understood at the statistical level of the Cepheid sample mean, a level an order of magnitude below the individual uncertainties. The early results from DR1 demonstrate again the enormous impact that the full mission will likely have on fundamental questions in astrophysics and cosmology. }{} | The Gaia mission appears to be off to a tremendous start, and there is little doubt that the full mission will produce results of great import for cosmology. While individual parallaxes have been measured for a small number of Cepheids at better precision than Gaia DR1, the new and exciting feature of DR1 is the angular breadth of the measurements, providing for $\sim$ 300 $\mu$as precision for hundreds of classical Cepheids. Indeed, the comparison of the parallaxes predicted for $ \sim 200 $ of these Cepheids suggests that the Gaia DR1 uncertainties may have been conservatively {\it overestimated}. The dispersion of $V,I$ and $H$-band based Wesenheit magnitudes and log periods has been observed to be 0.08 magnitudes for over 1000 objects in the LMC \citep{macri15}, which would result in random, individual errors of just $\sim 20 $ \muas. The fact that the $\chi^2_{\nu}=0.63 $ ($N=202$) likely results from a 20\% overestimate of Gaia errors, as the errors in the predictions are too small to have any impact. The sample mean of the DR1 parallaxes for the Cepheids we consider has a nominal error of $ \sim 20 \muas $. {\it IF} there are no systematic errors at this level in the DR1 measurements, then these Cepheids would produce an independent calibration of the Cepheid distance scale with an uncertainty of 3.1\% (original errors) to 2.5\% (80\% errors), competitive with the best geometric calibrations from NGC 4258 (2.6\%), previous MW Cepheid parallaxes (2.1\%) and detached eclipsing binaries in the LMC (2.0\%) (R16). The factor of twenty or more improvement expected for Gaia parallaxes by mission end will push the uncertainty due to geometric distance calibration well below 1\%, assuming systematics can be kept under comparable control. However, the geometric calibration of Cepheids, central to measuring the Hubble constant, depends not on just the mean parallax precision of the sample but also on the ability to compare them photometrically to their cousins in distant galaxies. The photometry of extragalactic Cepheids in SN~Ia hosts can only be measured at present in space with {\HST} and has been achieved most extensively with WFC3. On the other hand, the photometry of the Gaia DR1 Cepheid sample analyzed here was obtained from various ground-based sources. Due to the high foreground extinction of the Milky Way fields and in external galaxies, the use of near-infrared magnitudes and colors is especially important. Ground-based NIR filter systems are based on natural (and nightly changing) breaks in water and OH emission and do not well match the space based system. This produces systematic uncertainties at the level of approximately 0.02 mag, including the relative uncertainties in NIR zeropoints and dereddened colors (R16). These uncertainties are currently below the precision of the geometric calibration of the distance scale, but will be well above the precision that can be achieved with Gaia full-mission results. One of the best ways to mitigate the systematic error resulting from comparing ground and space-based Cepheid photometry is to observe the MW Cepheids with {\HST}'s WFC3. We have undertaken a series of HST programs to measure the magnitudes of $\sim$ 50 MW Cepheids with relatively low extinction and we have employed rapid spatial scanning with {\HST} to avoid the saturation which would occur with direct imaging of such bright stars. In the future, the combination of these 50 parallaxes from Gaia and their {\HST} photometry in F555W, F814W, and F160W should produce a complete and effective calibration of extragalactic Cepheids with a mean error of $\sim$ 0.5 \%, and an anchor for a 1\% determination of the Hubble constant. We have chosen to use the Gaia DR1 parallaxes as a test rather than an augmentation of the current calibration of $H_0$ by R16 to avoid the complication of Lutz-Kelker type bias corrections that would be large and necessary for parallax measurements with mean SNR $ \sim 2 $, and in recognition that these parallaxes are expected to dramatically improve in the near term (thus reducing the need for such corrections as well). This is the start of an exciting phase of measurement and perhaps discovery in the long-lived field of parallax measurement, with the best yet to come. | 16 | 9 | 1609.05175 |
|
1609 | 1609.05707.txt | {Main sequence turn-off (MSTO) stars have advantages as indicators of Galactic evolution since their ages could be robustly estimated from atmospheric parameters. Hundreds of thousands of MSTO stars have been selected from the LAMOST Galactic survey to study the evolution of the Galaxy, and it is vital to derive accurate stellar parameters. In this work, we select 150 MSTO star candidates from the MSTO stars sample of Xiang that have asteroseismic parameters and determine accurate stellar parameters for these stars combing the asteroseismic parameters deduced from the $Kepler$ photometry and atmospheric parameters deduced from the LAMOST spectra. With this sample, we examine the age determination as well as the contamination rate of the MSTO stars sample. A comparison of age between this work and Xiang shows a mean difference of 0.53\,Gyr (7\%) and a dispersion of 2.71\,Gyr (28\%). The results show that 79 of the candidates are MSTO stars, while the others are contaminations from either main sequence or sub-giant stars. The contamination rate for the oldest stars is much higher than that for the younger stars. The main cause for the high contamination rate is found to be the relatively large systematic bias in the LAMOST surface gravity estimates. | \label{sect:intro} A star begins its evolution as a hydrogen-rich main-sequence star with a hydrogen-burning core. As core hydrogen burning finishes, hydrogen-shell burning starts and the star expands to larger radius, lower surface temperature and higher luminosity, %The core contracts and heats, and the star evolves into the sub-giant branch phase. Main sequence turn-off (MSTO) stars are stars that have reached the point of central hydrogen exhaustion at the end of the main-sequence phase. Given the metallicity, their effective temperatures are very sensitive to their ages, hence one can obtain reliable age estimates for MSTO stars given accurate measurements of effective temperatures. MSTO stars are widely used to determine ages of star clusters as they are easily identified from the color-magnitude diagrams (CMDs) \citep[e.g.][]{Mackey08, Goudfrooij09, Yang13}. Since member stars of a cluster are generally believed to form from the same gas cloud simultaneously, they have the same age. Unlike the MSTO stars in clusters, MSTO stars in the field are not easy to be identified from the CMDs. To identify field MSTO stars, accurate estimates of atmospheric parameters ($T_{\rm eff}$, $\log g$ and [Fe/H] ) are required. As the implementation of the LAMOST Experiment for Galactic Understanding and Exploration \citep[LEGUE;][]{Deng12, Zhao12, Liu14} and other spectroscopic surveys such as the Sloan Extension for Galactic Understanding and Exploration \citep[SDSS/SEGUE;][]{Yanny09}, the Radial Velocity Experiment \citep[RAVE; ][]{Steinmetz06} and the Apache Point Observatory Galactic Evolution Experiment \citep[APOGEE;][]{Majewski10}, stellar atmospheric parameters of millions of stars are delivered from the survey spectra. Typical accuracies of the LAMOST stellar atmospheric parameters reach 100 -- 150\,K for $T_{\rm eff}$, 0.20 -- 0.25\,dex for log\,$g$ and 0.1 -- 0.2\,dex for [Fe/H] (Xiang et al. 2015b, Wu et al. 2014, Luo et al. 2015, Gao et al. 2015). Hundreds of thousands of MSTO stars have been selected from the LAMOST survey by Xiang et al. (2015a) %(hereafter MSTO stars sample) based on stellar atmospheric parameters yielded by the LAMOST Stellar Parameter Pipeline at Peking University (LSP3; Xiang et al. 2015b). The ages of these MSTO stars are also estimated, with a claimed uncertainty of about 30 per cent. However, given the low spectral resolving power of LAMOST ($R\sim$1800; e.g. Cui et al. 2012; Deng et al. 2012), accurate stellar parameters, especially surface gravity, are difficult to yield from the spectra. Therefore, a careful sanity examination on the feasibility of the method to select the MSTO stars sample and on the accuracy of age estimation seems to be essential. Asteroseismology is a powerful tool to derive accurate stellar parameters \citep{Bi08,G10, Yang10, Chaplin11, Stello13, Tian15}. By asteroseismology, accurate stellar parameters of thousands of stars have been obtained \citep{Chaplin14, Huber14}. It is found that surface gravities yielded by the asteroseismology can be accurate to 0.01 -- 0.03\,dex \citep{Hekker13, Huber14}, much better than the spectroscopic estimates. Combing effective temperatures and metallicities from the LAMOST spectra with asteroseismic surface gravity yielded from the $Kepler$ photometry, MSTO stars can be well identified and their ages can also be accurately determined. In this paper, we determine fundamental stellar parameters ($M$, $R$, Age, $L$, $T_{\rm eff}$, $Z$, $\log g$) for 150 MSTO star candidates selected from the MSTO stars sample that have asteroseismic properties delivered from photometry of the $Kepler$ mission \citep{G10}. Meanwhile, we compare our results with previous studies by Huber et al.\ (2014) and Xiang et al.\ (2015a). We discuss the impact of uncertainties in atmospheric parameters on the measurement of ages, and examine the accuracy of the age estimates as well as the contamination rate of the MSTO stars sample. The paper is organized as follows. In Section\,2, we introduce how to select the sample of MSTO star candidates. In Section\,3, we describe the stellar model and how to obtain the stellar parameters. Results and discussion are presented in Section\,4 and a summary is shown in Section\,5. | %\subsection{Fundamental Parameters} Among the 179 MSTO star candidates, stellar parameters for 150 of them are successfully derived, and are listed in Table\,3, while the remaining 29 stars are falling outside of our model grids. For the 29 remaining stars, 25 stars are RGB stars according to their asteroseismic characteristics and the other 4 stars are metal-poor stars with $[\rm{Fe/H}] < -0.3\,\dex$. %The stellar parameters of 150 MSTO star candidates are determined by asteroseismology using maximum likelihood method are listed in Table~3. Figure~2 illustrates distributions of the derived mass, age and metallicity for the 150 MSTO star candidates. Their masses are in the range of $0.8$ -- $1.5\,\Msun$ and peak at about $1.1\,\Msun$. The ages are widely distributed in the range of $0$ -- $13\,\Gyr$, mostly in $2$ -- $8\,\Gyr$. The metallicities distributed in the range of $-0.3$ -- $0.3\,\dex$, with a moderate peak near the solar value. Besides, the typical uncertainties in $T_{\rm eff}$, $\log g$, [Fe/H], $M$ and $R$ are $60\,\rm{K}$, $0.009\,\dex$, $0.1\,\dex$, $0.04\,\Msun$ and $0.03\,\Rsun$, respectively. The uncertainty in $\log g$ is much smaller than that yielded by the LSP3 from the LAMOST spectra. And uncertainties in the stellar age vary from $0.4\,\Gyr$ for young stars to $1.3\,\Gyr$ for old stars, corresponding to a relative error about $9$ -- $10\,\%$. In fact, part of the stellar parameters for those $150$ MSTO star candidates are also provided by Huber et al. ~(2014). Based on the Dartmouth Stellar Evolution Database \citep[DSEP,][]{Dotter08}, Huber et al. (2014) derived fundamental parameters using the asteroseismic quantities and atmospheric parameters in the $Kepler$ input catalog (KIC), which are estimated from photometry for most stars. But they did not provide ages. % in the case of the mean [Fe/H] (-0.2 $\pm$ 0.3 dex) they used. By comparing the $\log g$, $M$ and $R$ derived by Huber et al.\ (2014) and those of our work, we find that our estimates of $\log g$ are consistent with those of Huber et al. very well, which yield a mean difference of only $0.0002\,\dex$, and a standard deviation of $0.013\,\dex$. However, there are systematic deviations of $R$ and $M$ between our estimates and those of Huber et al. Our values are systematically smaller than those of Huber et al., and the deviations increase with increasing $R$ and $M$. Typical difference of $R$ is 0.025 -- 0.05\,$R_{\odot}$ for stars with $R$\ $\sim$\ 2.0 $R_{\odot}$, and typical difference of $M$ is 0.1 -- 0.2\,$M_{\odot}$ for stars with $M$\,$\sim$\,1.5 $M_{\odot}$. Nevertheless, the dispersion of differences of $R$ and $M$ are small (after exclude systematic trends), with only 0.056\,$R_{\odot}$ in $R$, and 0.1\,$M_{\odot}$ in $M$. %The differences are about $0.1$ -- $0.2\,\Msun$ for stars around $1.5\,\Msun$. The systematic trends of differences in $R$ and $M$ are mainly caused by systematic differences in the effective temperatures adopted. In Figure\,4, we compare $T_{\rm eff}$ derived by the LSP3 and those of Huber et al. The figure exhibits similar trends to those for the mass in Figure\,3. As expected, there is strong correlation between the differences of mass and the differences of effective temperatures. Because the $T_{\rm eff}$ derived by the LSP3 are calibrated to the recently deduced metallicity-dependent color--temperature relation of Huang et al. \citep{15}, which is deduced based on stellar interferometry data sets, we believe our results of stellar mass are more reliable than those of Huber et al. In addition, the stellar metallicity could also affect the determination of stellar mass, but it has only a minor contribution compared to that from the effective temperature. %\subsection{Ages of MSTO stars} %Furthermore, the results can be used to examine age measurements derived by Xiang et al.\ (2015a). After that, in Figure\,5, we compare age estimates of this work with those of Xiang et al. (2015a). %order to compare the differences between age estimation of this work and those in Xiang et al. (2015a), we perform a comparison of age in Figure ~5. The left panel shows that though ages for the majority of stars agree well with each other, there are a considerable fraction of stars that our values are systematically much lower than those of Xiang et al. For stars older than 10\,Gyr based on Xiang et al.'s age estimates, about half of them are actually younger than 7\,Gyr according to our results. % there is a systematic trend between these two age estimation that %our values are systematically younger than the Xiang's. For ages greater than $10\,\Gyr$, the differences are relatively large %and cannot be ignored when study of Galactic structure. The right panel plots the distribution of the differences of age estimates. The distribution yields a mean difference of $0.53\,\Gyr$ ($7\,\%$), and a dispersion of $2.71\,\Gyr$ ($28\,\%$). It is found that the age discrepancy are mostly caused by systematic bias in the LSP3 $\log g$. For instance, KIC 5523099, the LSP3 atmospheric parameters ($5513\,\rm{K}$, $4.24\,\dex$, $0.03\,\dex$) yield an age of $12.5\,\Gyr$, while our atmospheric parameters ($5507\,\rm{K}$, $3.79\,\dex$, $0.05\,\dex$) yield $4.6\,\Gyr$, which is $6.9\,\Gyr$ younger due to a $0.45\,\dex$ overestimate of the LSP3 $\log g$. As the uncertainty of the LSP3 $\log g$ is the main cause of the differences in stellar ages, left panel in Figure\,6, we compare $\log g$ derived by the LSP3 with our values. The figure reveals that $\log g$ given by the LSP3 has a linear trend of deviation with our estimated values. The result is consistent with that of Ren et al.~(2016), who examined the LSP3 $\log g$ with asteroseismic values from Huber et al. (2014). To better characterize the bias in the LSP3 $\log g$, we display the histogram distribution of log\ $g$ differences in right panel in Figure\,6. The figure exhibits that the LSP3 $\log g$ is generally higher than our seismic values by about $0.1\,\dex$, with a calculated standard deviation of $0.16\,\dex$. %Generally, $\log g$ derived from asteroseismic parameters is more accurate than that derived from spectroscopy. We compare the $T_{\rm eff}$ -- $\log g$ diagram of the LSP3 and our work in Figure\,7 . The figure indicates that our work yields a sparser distribution, and that a considerable fraction of the stars are located in the sub-giant branch. Based on the definition of the MSTO stars of Xiang et al.(2015a), our revised atmospheric parameters indicate that only $79$ of the $150$ star candidates are MSTO stars, while the other $71$ are contaminations from either main sequence or sub-giant stars. The stellar ages for those 71 contamination stars are marked with red circles in Figure\,5. Considering the $29$ stars falling outside of our model grids, which 4 metal-poor ones maybe MSTO stars and the other 25 stars are certainly RGB stars, there are $46\,\%$ (83/179) stars in total are MSTO stars, while the others are contaminations from either main sequence or sub-giant stars. However, considering that the number of stars in our sample is still small, and that the asteroseismic sample from literature are probably biased to sub-giant stars because they are brighter and also have relatively larger oscillation amplitudes thus easier to be detected, our results have probably overestimated the contamination rate. | 16 | 9 | 1609.05707 |
1609 | 1609.09501_arXiv.txt | We present VLBI observations, carried out with the European Very Long Baseline Interferometry Network (EVN), of \src, a radio-loud narrow-line Seyfert 1 (RL~NLS1) characterized by a steep radio spectrum. The source, compact at Very Large Array (VLA) resolution, is resolved on the milliarcsec scale, showing a central region plus two extended structures. The relatively high brightness temperature of all components (5$\times$10$^6$-1.3$\times$10$^8$ K) supports the hypothesis that the radio emission is non-thermal and likely produced by a relativistic jet and/or small radio lobes. The observed radio morphology, the lack of a significant core and the presence of a low frequency (230 MHz) spectral turnover are reminiscent of the Compact Steep Spectrum sources (CSS). However, the linear size of the source ($\sim$0.5~kpc) measured from the EVN map is lower than the value predicted using the turnover/size relation valid for CSS sources ($\sim$6 kpc). This discrepancy can be explained by an additional component not detected in our observations, accounting for about a quarter of the total source flux density, combined to projection effects. The low core-dominance of the source (CD$<$0.29) confirms that \src\ is not a blazar, i.e. the relativistic jet is not pointing towards the observer. This supports the idea that \src\ may belong to the ``parent population'' of flat-spectrum RL~NLS1 and favours the hypothesis of a direct link between RL~NLS1 and compact, possibly young, radio galaxies. | Narrow-line Seyfert 1 (NLS1) galaxies represent a class of Active Galactic Nuclei (AGN) characterized by narrow ($<$2000 km s$^{-1}$) Balmer lines, weak [OIII]$\lambda$5007\AA\ emission compared to the Balmer lines ([OIII]$\lambda$5007\AA/H$\beta$ flux ratio below 3) and strong optical FeII emission (e.g. Osterbrock \& Pogge 1985; Goodrich 1989; Pogge 2000; Veron-Cetty et al. 2001). The optical properties of NLS1 are usually explained as the consequence of a combination of a low-mass ($\lesssim$10$^8$ M$_{\odot}$) central supermassive black-hole (SMBH) with a high accretion rate (close to the Eddington limit). Most of the NLS1 are radio-quiet (RQ) objects while a minority ($\sim$7 per cent, \citealt{Komossa2006}) are radio-loud (RL), using the common definition based on the 5~GHz to 4400\AA\ flux density ratio (R$_5$, where RL NLS1 have R$_5>$10) or an (almost) equivalent definition based on the 1.4~GHz flux density (R$_{1.4}$, where RL NLS1 have R$_{1.4}>$19, \citealt{Komossa2006}). The $\sim$110 RL~NLS1 discovered so far, have been discussed in a number of papers (e.g. \citealt{Komossa2006}; \citealt{Yuan2008}; \citealt{Foschini2015}; \citealt{Berton2015}; \citealt{Gu2015}). A peculiarity of the RL NLS1 discovered to date is that most of them present a compact radio emission (linear size below a few kpc, e.g. Doi et al. 2012 and references therein). Some of the RL NLS1 with the highest values of radio-loudness show strict similarities with blazars (BL Lac objects and flat spectrum radio quasar, FSRQ): a flat or inverted radio spectrum, high brightness temperatures ($T_B>$10$^{11}$ K, e.g. \citealt{Yuan2008}) and a detectable gamma-ray emission (in {\it Fermi}-LAT, \citealt{Abdo2009}; \citealt{Abdo2009a}; \citealt{Foschini2011}; \citealt{Foschini2015}; \citealt{Liao2015}; \citealt{Yao2015}; \citealt{Yao2015a}). Since blazars are usually believed to be radio galaxies whose relativistic jets are pointing towards the observer (e.g. \citealt{Urry1995}), a natural conclusion is that most of the RL NLS1 discovered so far should also have their jets aligned within small angles to the line of sight. If this picture is correct we expect a population of mis-oriented and unbeamed sources, the so-called {\it parent population}, that in the standard beaming model (e.g. \citealt{Urry1995}) is constituted by the class of lobe-dominated radio galaxies. To date, however, only in few RL NLS1 an extended emission has been detected (\citealt{Whalen2006}; \citealt{Anton2008}; \citealt{Doi2012}; \citealt{Richards2015}) and only one RL NLS1 (SDSSJ120014.08--004638.7) is a lobe-dominated radio galaxy (\citealt{Doi2012}). This may suggest that RL NLS1 are intrinsically lacking an extended radio emission component on large scales or that these structures are not detected due to selection effects (e.g. see \citealt{Richards2015}). Several hypotheses for the parent population have been recently considered and discussed by \citet{Berton2015} and \citet{Berton2016c}. An interesting possibility is that RL NLS1 are young or ``frustrated'' radio galaxies that either have not yet fully deployed their radio lobes on large scales (at least tens of kpc) or they will never be able to form them. This possibility was suggested on the basis of the similarities found between some RL NLS1 and Compact Steep-Spectrum (CSS) or GHz-Peaked Spectrum (GPS) sources (e.g. \citealt{Oshlack2001}; \citealt{Gallo2006}; \citealt{Komossa2006}; \citealt{Yuan2008}; \citealt{Caccianiga2014b}; \citealt{Gu2015}; \citealt{Gu2016}; \citealt{Schulz2016}) that are usually believed to be young radio galaxies (e.g. \citealt{Fanti1995}). A direct test of this hypothesis, however, is not simple. In sources with the jet oriented close to the line of sight, i.e. RL NLS1 with blazar properties, the analysis of any possible extended emission is difficult due to the dominance of the beamed nuclear emission. Conversely, if the sources have the jet axis close to the plane of the sky, the possible presence of obscuration in the optical and X-rays makes it difficult, if not impossible, to study the nuclear properties and, therefore, to establish the NLS1 nature. A direct test would only be possible by finding and studying sources oriented at intermediate angles, where the NLS1 nature can be established and, at the same time, the amplification of the nuclear emission is not too severe for the analysis of the extended radio properties to be fruitfully carried out. We believe that we have found at least one of such objects: \src, a new RL NLS1 that we have recently discussed (\citealt{Caccianiga2014b}, hereafter referred as C14) and which shows radio properties suggesting a non-blazar nature. In this second paper we present the results of a radio follow up at a resolution of $\sim$0.01 arcsecond carried out using the European VLBI Network (EVN) at 1.66~GHz. Throughout the paper spectral indices are given assuming S$_{\nu}\propto\nu^{-\alpha}$, and we assume a flat $\Lambda$CDM cosmology with H$_0$=71 km s$^{-1}$ Mpc$^{-1}$, $\Omega_{\Lambda}$=0.7 and $\Omega_{M}$=0.3. | We have presented VLBI observations carried out with EVN of \src, a steep spectrum RL~NLS1 that has been recently classified as {\bf a } possible CSS source (C14). The results can be summarized as follows: \begin{itemize} \item EVN observations have resolved \src\ which shows a quite complex structure without a clear morphology. The total flux density accounted for in the EVN image (34 mJy) is divided into 3 components: a central, more compact (but resolved), emission, containing more than half of the total correlated flux density, plus two extended structures. The lack of a strong unresolved component (core) is consistent with what is usually observed in steep-spectrum young radio sources. \item The high brightness temperature of the radio components detected in the EVN map (T$_B\sim$5$\times$10$^6$-1.3$\times$10$^8$ K) dis-favours the hypothesis that star-forming activity (detected in the mid-IR band) is the main origin of the observed radio emission and strongly supports a non-thermal origin. \item The size of the extended structure (100-150 m.a.s., corresponding to $\sim$0.5~kpc) is smaller than the value inferred from the linear size/turnover relation valid for the CSS/GPS galaxies. This is likely due to the non-detection of a low surface brightness component in the EVN map combined to projection effects. \end{itemize} Overall, the EVN observations support the idea that \src\ is a CSS source with the relativistic jet observed at larger angles than the flat-spectrum RL~NLS1 studied so far. The fact of observing directly the nuclear emission in the optical, without significant obscuration, suggests that \src\ is probably not oriented on the plane of the sky but at intermediate angles. VLBI observations at high frequencies would prove this hypothesis since they are expected to detect a stronger, mildly boosted, radio core. These results confirm that \src\ likely belongs to the parent population of the RL~NLS1 with a blazar spectrum and favour the idea that these sources can be directly related to young radio galaxies. A systematic follow-up at VLBI resolution, similar to the one discussed here, of all the RL~NLS1 will be fundamental to test this hypothesis on a firm statistical basis. | 16 | 9 | 1609.09501 |
1609 | 1609.04423_arXiv.txt | { We report the discovery that the known `changing look' AGN Mrk~1018 has changed spectral type for a second time. New VLT-MUSE data taken in 2015 as part of the Close AGN Reference Survey (CARS) shows that the AGN has returned to its original Seyfert 1.9 classification. The CARS sample is selected to contain only bright type 1 AGN, but Mrk~1018's broad emission lines and continuum, typical of type 1 AGN, have almost entirely disappeared. We use spectral fitting of the MUSE spectrum and previously available spectra to determine the drop in broad line flux and the Balmer decrement. We find that the broad line flux has decreased by a factor of $4.75 \pm 0.5$ in \ha\ since an SDSS spectrum was taken in 2000. The Balmer decrement has not changed significantly implying no enhanced reddening with time, but the remaining broad lines are more asymmetric than those present in the type 1 phase. We posit that the change is due to an intrinsic drop in flux from the accretion disk rather than variable extinction or a tidal disruption event. } | In this letter we presented evidence for the AGN Mrk~1018 returning to its Seyfert 1.9 state after $\sim$30 years as a Seyfert 1. Using MUSE data from the Close AGN Reference Survey alongside archival spectroscopic and photometric observations we explored the possible causes of this change: a decline in accretion rate or lack of fuel, a TDE, obscuration, or disruption of the accretion disk. We reason that the length and consistency of Mrk~1018's bright phase makes a TDE an unlikely explanation, but we cannot rule out a simple decline in accretion rate. The Balmer decrement between the Seyfert 1 and 1.9 phases implies that the obscuration along our line of sight has not increased, but a highly opaque column of gas selectively obscuring our view is still a possibility. In light of this exciting discovery we were awarded Chandra, HST, and VLA director's discretionary time to investigate how Mrk 1018 has changed since our MUSE observations. While the data presented in this paper cannot definitively tell us the nature of the change in Mrk 1018's nucleus, these newer observations in the UV, X-ray, and radio bands will provide further constraints. | 16 | 9 | 1609.04423 |
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1609 | 1609.06610_arXiv.txt | We present a discussion of the design issues and trade-offs that have been considered in putting together a new concept for MOSAIC\cite{Hammer14,Hammer16}, the multi-object spectrograph for the E-ELT. MOSAIC aims to address the combined science cases for E-ELT MOS that arose from the earlier studies of the multi-object and multi-adaptive optics instruments (see MOSAIC science requirements in [\cite{Evans16}]). MOSAIC combines the advantages of a highly-multiplexed instrument targeting single-point objects with one which has a more modest multiplex but can spatially resolve a source with high resolution (IFU). These will span across two wavebands: visible and near-infrared. | \label{sect:intro} % {MOSAIC} is the proposed multiple-object spectrograph for the E-ELT [\cite{Hammer14,Hammer16}]. The instrument will have both multiplex and multi-IFU capability and will utilise the widest possible field of view provided by the telescope. The {MOSAIC} top-level instrument requirements [\cite{Evans16}] were building on the comprehensive White Paper [\cite{WhitePaper}] on the scientific case for multi-object spectroscopy on the European ELT. In this paper we present the preliminary design concept and trade-off based on the actual top-level instrument requirements. Key to the concept are two design principles: firstly having a shared focal-plate with multi-function tiles which can serve as pick-offs for any of the modes and AO functions; and secondly utilising shared-slit spectrographs whereby the spectrograph optics and detectors can be re-used between the highly-multiplexed mode and the IFU mode. | 16 | 9 | 1609.06610 |
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1609 | 1609.08866_arXiv.txt | We present photometry and long-slit spectroscopy for 12 S0 and spiral galaxies selected from the Catalogue of Isolated Galaxies. The structural parameters of the sample galaxies are derived from the Sloan Digital Sky Survey $i$-band images by performing a two-dimensional photometric decomposition of the surface brightness distribution. This is assumed to be the sum of the contribution of a S\'ersic bulge, an exponential disc, and a Ferrers bar characterized by elliptical and concentric isophotes with constant ellipticity and position angles. The rotation curves and velocity dispersion profiles of the stellar component are measured from the spectra obtained along the major axis of galaxies. The radial profiles of the \Hb, Mg and Fe line-strength indices are derived too. Correlations between the central values of the \Mgd\ and \Fe\ line-strength indices and the velocity dispersion are found. The mean age, total metallicity and total $\alpha$/Fe enhancement of the stellar population in the centre and at the radius where the bulge gives the same contribution to the total surface brightness as the remaining components are obtained using stellar population models with variable element abundance ratios. We identify intermediate-age bulges with solar metallicity and old bulges with a large spread in metallicity. Most of the sample bulges display super-solar $\alpha$/Fe enhancement, no gradient in age and negative gradients of metallicity and $\alpha$/Fe enhancement. These findings support a formation scenario via dissipative collapse where environmental effects are remarkably less important than in the assembly of bulges of galaxies in groups and clusters. | \label{sec:introduction} Stellar populations are a powerful diagnostics to constrain the assembly history of galaxy bulges. In the current picture, dissipative collapse \citep[e.g.,][]{gilwys98}, merging and acquisition events \citep[e.g.,][]{coletal00}, and secular evolution \citep[e.g.,][]{korken04} are considered as possible processes driving the formation of bulges. According to theoretical models, these processes give rise to different properties of the stellar populations in galaxy centres and to different trends of age, metallicity, and star-formation timescale as a function of the galactocentric distance. For example, from the metallicity gradient it is possible to extract information about the gas dissipation processes and the importance of secular processes and merging history. Stars form at all galactocentric distances during the dissipative collapse of a protogalactic cloud and they remain on their orbits with little migration towards the center. On the contrary, the gas dissipates inward and it is continuously enriched by the evolving stars. In consequence of this, the stars formed in the outskirts of a galaxy are expected to have a lower metal contents with respect to those in the central regions. Also galactic winds induced by the supernovae \citep{aryo87,Creasey2013} have a relevant role in the evolution history of the galaxy. High-resolution simulations \citep{Hirschmann2013} demonstrated that the stellar accretion in galaxies with galactic winds is steepening the galactic gradient of about 0.2 dex \citep{Hirschmann2015}. These winds, indeed, eliminate the gas suppressing the fuel needed for star formation. The outer regions develop the winds before the central ones, where the star formation and chemical enrichment continue for a longer time. Strong negative gradients are expected in dissipative collapse models as both star formation and galactic winds act in steepening any incipient gradient. In hierarchical formation models, the situation is somewhat contradictory. Some authors suggest that clustering and wet or dry merging erase the metallicity gradient \citep[e.g.,][]{besh99,dimatteo2009}, while others argue that the metallicity gradient is moderately affected by interactions since the violent relaxation preserves the position of the stars in the local potential \citep[e.g.,][]{vanAlbada1982}. Such a dichotomy possibly depends on how the properties of the resulting galaxy are related to the gas-to-stellar mass ratio of the progenitors. If they are characterized by a large gas fraction, the resulting metallicity gradient is indeed steeper. In the secular evolution scenario, the bulge is the result of a redistribution of the disc stars due to the instabilities triggered by bars, ovals, and spiral arms. The theoretical model predictions for the metallicity gradient in these bulges are ambiguous. It could be erased as consequence of disc heating or amplified from the reduction of the scalelength of the final resulting spheroid \citep{mooretal06}. In the last decade, a major observational effort was performed to derive the stellar population properties in large number of bulges \citep[e.g.,][]{jabletal07, moreetal08, morelli2012, gonzalezdelgado2014, seidel2015, Wilkinson2015} to be compared to those of elliptical galaxies \citep[e.g.,][]{sancetal06p, annietal07, kuntschner2010, mcdermid2015} and galaxy disks \citep{sancetal14, morelli2015b}. Stellar populations of bulges show a complex variety of properties. The ages of bulges are spread between 1 and 15 Gyr. Such a large difference seems to be driven by the morphological type of the host galaxy with the late type younger than the early type \citep{gandetal07}. The timescale of the last major star-formation burst spans between 1 to 5 Gyr, as derived from the central values of $\alpha/$Fe abundance ratio \citep{thda06}. In general, $\alpha$/Fe is constant over the observed radial ranges and many bulges have a solar abundance ratio \citep{jabletal07, moreetal08, morelli2012}. Independently of their structural properties and whether they reside in low or high surface-brightness discs, most bulges are characterised by a negative metallicity gradient, which is one of the tighter predictions made by theoretical models for the dissipative collapse \citep{gilwys98,pipietal10}. On the other hand, the absence of stellar population gradients measured in some bulges is an clear indication that bulge stars were redistributed as a consequence of external and internal processes, like minor mergers and slow rearrangement of the disk material, respectively \citep{besh99, cobari99}. In many cases the difficulty in determining the mechanism driving the assembly history of the bulge is probably due to the fact that the dissipative collapse, minor and major mergers, and secular evolution are all having an effect in reshaping the structure of disk galaxies. Furthermore, phenomena driven by the environment like gas stripping, harassment, and strangulation are likely to play a role in mixing up the properties of the stellar populations \citep{labarbera2014}. However, to date the observational evidences on how the environment influences the stellar populations of bulges are sparse and the analysis of both the central values of age, metallicity, and star formation timescale \citep{denietal05,redaetal07} and their radial gradients \citep{katkov2015} does not lead to any firm conclusion. In addition, the comparison of the results obtained for galaxies in different environments is not straightforward. Part of the difficulty lies in addressing the relative importance of one-to-one interactions and the local galaxy density, and this reflects the lack of suitable control samples to which the properties of bulges of interacting and/or cluster galaxies can be compared. As a matter of fact, the samples of field galaxies studied so far include also galaxies in pairs and loose groups. A way to make simpler the observational picture is studying the bulges of isolated galaxies, for which the interactions with the surrounding environment or with other galaxies are likely to be negligible \citep{Hirschmann2013_is}. Therefore, it could be possible to use the stellar population diagnostics to disentangle between bulges formed from dissipative collapse and those assembled via secular evolution. To this aim, here we analyse the stellar populations of the bulges of a carefully selected sample of high surface-brightness isolated disc galaxies to be compared with the complementary samples of bulges in high surface-brightness cluster galaxies and giant low surface-brightness galaxies which we studied in in the past several years \citep{pizzetal08, moreetal08, morelli2012, morelli2015a}. The paper is organized as follows. We present the selection of the sample of isolated disc galaxies in Section~\ref{sec:sample}, and we describe the analysis of the photometric and spectroscopic data in Sections \ref{sec:photometry} and \ref{sec:spectroscopy}, respectively. We analysed the stellar population properties in Section~\ref{sec:populations}. We discuss conclusions and summarise results in Section~\ref{sec:conclusions}. | \label{sec:conclusions} We analysed the surface-brightness distribution, stellar kinematics, and stellar population properties of a sample of isolated galaxies selected from the CIG to constrain the dominant mechanism of the assembly of their bulges. To this aim the properties of stellar populations of the sample bulges were compared with those of bulges in galaxies residing in groups and clusters. A photometric decomposition of the SDSS $i$-band images was performed to obtain the structural parameters of the sample galaxies. We used the structural parameters to identify the bulge-dominated radial range of the sample galaxies by measuring the radius \rbd , where the bulge contribution to the galaxy surface brightness dominates over that of the remaining components. We measured the stellar kinematics and radial profiles of the \Mgb, \Mgd, \Hb, and \Fe\ line-strength indices from the major-axis spectra we obtained at TNG. The kinematics of all the sample galaxies is very regular giving further support to the idea that these objects are not suffering interactions with the neighbour galaxies. The correlations between the central values of the \Mgd\ and \Fe\ line-strength indices and velocity dispersion were found to be consistent with those for bulges of group and cluster galaxies \citep{idiaetal96, prugetal01, procetal02, moreetal08}. We obtained the stellar population properties of the bulges of the sample galaxies by deriving their central values of mean age, total metallicity, and total $\alpha/$Fe from stellar population models with variable element abundance ratios. The sample bulges are characterised by a bimodal age distribution with intermediate-age ($\sim3$ Gyr) and old systems ($\sim15$ Gyr), a large spread in metallicities ranging from sub- to super-solar values, and $\alpha$/Fe enhancements peaked at \aFe$\,=\,0.2$ dex. The higher \aFe\ ratios found for the bulges of isolated galaxies indicate a shorter star-formation timescale with respect their counterparts in high density environment \citep{thometal05}. On the contrary, the metallicity distribution is very similar for bulges residing in different environments. The absence of a correlation between the bulge stellar populations and galaxy morphology excludes a strong interplay between bulges and discs during their evolution. This conclusion is also supported by the findings of \citet{silchenko2012} and \citet{katkov2015} who formulate the hypothesis that the morphological type of a field galaxy is determined by the outer-gas accretion. Finally, we derived the gradients of the stellar population properties within the sample bulges. Most of them have a null age gradient and a negative metallicity gradient. This is in agreement with earlier findings for bulges in cluster \citep{jabletal07,moreetal08} and high surface-brightness galaxies \citep{morelli2012}. All the sample bulges show a negative gradient for the $\alpha/$Fe enhancement. This is a prediction of the dissipative collapse model of bulge formation and it was never been observed before. The stellar population gradients are believed to be flattened or even erased by merging and acquisition events. Therefore, we suggest that the gradients imprinted during the inside-out formation process are preserved in the bulges of isolated galaxies, which suffered a limited number of interactions and mergers, whereas the gradients are cancelled in the bulges of group and cluster galaxies as a consequence of phenomena driven by environment. | 16 | 9 | 1609.08866 |
1609 | 1609.01340_arXiv.txt | In a recent letter~\cite{Cunha:2015yba}, it was shown that the lensing of light around rotating boson stars and Kerr black holes with scalar hair can exhibit chaotic patterns. Since no separation of variables is known (or expected) for geodesic motion on these backgrounds, we examine the 2D effective potentials for photon trajectories, to obtain a deeper understanding of this phenomenon. We find that the emergence of \textit{stable light rings} on the background spacetimes, allows the formation of ``pockets" in one of the effective potentials, for open sets of impact parameters, leading to an effective trapping of some trajectories, dubbed \textit{quasi-bound orbits}. We conclude that pocket formation induces chaotic scattering, although not \textit{all} chaotic orbits are associated to pockets. These and other features are illustrated in a gallery of examples, obtained with a new ray-tracing code, \textsc{pyhole}, which includes tools for a simple, simultaneous visualization of the effective potential together with the spacetime trajectory, for any given point in a lensing image. An analysis of photon orbits allows us to further establish a positive correlation between photon orbits in chaotic regions and those with more than one turning point in the radial direction; we recall that the latter is not possible around Kerr black holes. Moreover, we observe that the existence of several light rings around a horizon (several \textit{fundamental orbits}, including a stable one), is a central ingredient for the existence of multiple shadows of a single hairy black hole. We also exhibit the lensing and shadows by Kerr black holes with scalar hair, observed away from the equatorial plane, obtained with \textsc{pyhole}. | The effect of gravitational lensing was considered by Einstein even prior to the completion of his General Theory of Relativity (GR)~(see~\cite{1997Sci...275..184R} for an historical account). In particular, in 1912, he derived the basic lensing equation and magnification factor for the intensity of the deflected light. These results, however, were only published in 1936, in a paper often considered the pioneering study on gravitational lensing~\cite{Einstein:1956zz}, where Einstein discusses that a gravitational lens can lead to both multiple images and ring shaped images (subsequently called \textit{Einstein rings}) of a star. Both these effects were actually discussed by other authors in the 1920s, the first one by Eddington~\cite{Eddington:1987tk} and the second by Chwolson~\cite{Chwolson}, thus before Einstein's 1936 paper~\cite{1997Sci...275..184R}. At the time of Einstein, the prospects for observing this type of lensing were dim. By contrast, the phenomenon at the origin of the gravitational lensing, $i.e.$ the bending of light by a gravitational field -- and in particular that caused by the Sun --, had been instrumental in establishing GR as a physical theory of the Universe. It was only with the discovery of quasars, in the 1960s~\cite{1963Natur.197.1040S}, that the subject of gravitational lensing was brought into the realm of observational astronomy. Being both very distant and very bright objects, quasars are ideal light sources for observing lensing effects, when a deflecting mass, typically a galaxy, is present along their line of sight. The first lensing effect of a distant quasar (a double image) was identified in 1979~\cite{1979Natur.279..381W} and, since then, many other systems with both multiple images and Einstein rings have been discovered (see $e.g.$~\cite{lensingcat}). The largest lensing effects that have been observed, at present, in astrophysical objects (and cosmological contexts), are of the order of tens of arc seconds (see $e.g.$~\cite{2003Natur.426..810I}), corresponding to tiny local light bendings by (typically) lensing galaxies. Ultra-compact objects can, on the other hand, cause much more extreme local deflections of light. Black holes (BHs), in particular, can possess \textit{light rings} and hence can bend light by an \textit{arbitrarily large angle}. For the paradigmatic Kerr BH spacetimes of GR, these light rings are \textit{unstable}. Their existence allows light to circle any number of times around the light ring before being scattered back to infinity (or fall into the BH). From the viewpoint of an observer which sees the BH lit by a distant celestial sphere, an infinite number of smaller and smaller copies of the whole celestial sphere accumulate near the edge of the absorption cross-section for light (at high frequencies) -- dubbed the~\textit{BH shadow}~\cite{Bardeen1973,Falcke:1999pj} -- in an organized self-similar structure -- see~\cite{Bohn:2014xxa} for striking visualizations of this effect in the Schwarzschild and Kerr BH spacetimes, and~\cite{Amarilla:2011fx,Yumoto:2012kz,Abdujabbarov:2012bn,Amarilla:2013sj,Nedkova:2013msa,Atamurotov:2013dpa,Atamurotov:2013sca,Li:2013jra,Tinchev:2013nba,Wei:2013kza,Tsukamoto:2014tja,Grenzebach:2014fha,Lu:2014zja,Papnoi:2014aaa,Sakai:2014pga,Psaltis:2014mca,Wei:2015dua,Abdolrahimi:2015rua,Moffat:2015kva,Grenzebach:2015uva,Vincent:2015xta,Grenzebach:2015oea,Abdujabbarov:2015xqa,Ortiz:2015rma,Ghasemi-Nodehi:2015raa,Ohgami:2015nra,Atamurotov:2015xfa, Perlick:2015vta,Bambi:2015rda,Atamurotov:2015nra,Yang:2015hwf,Tinchev:2015apf,Shipley:2016omi,Dolan:2016bxj,Amir:2016cen,Cunha:2015yba,Johannsen:2015hib,Abdujabbarov:2016hnw,Cunha:2016bpi,Huang:2016qnl,Dastan:2016vhb,Younsi:2016azx} for examples of recent investigations of BH shadows and lensing by compact objects in different models. \bigskip In a recent letter~\cite{Cunha:2015yba}, some of us have studied the lensing and shadows of a deformed type of Kerr BHs, known as Kerr BHs with scalar hair (KBHsSH)~\cite{Herdeiro:2014goa,Herdeiro:2015gia,Herdeiro:2014ima} (see also~\cite{Herdeiro:2014jaa,Brihaye:2014nba,Herdeiro:2015waa,Herdeiro:2015kha,Brito:2015pxa,Kleihaus:2015iea,Herdeiro:2015tia,Herdeiro:2016tmi,Herdeiro:2016gxs,Brihaye:2016vkv,Vincent:2016sjq,Ni:2016rhz,Delgado:2016zxv,Delgado:2016jxq,Dias:2011at} for generalizations and physical properties). These are solutions to Einstein's gravity minimally coupled to a simple and physically reasonable matter content: a complex, massive, free scalar field. KBHsSH interpolate between a (subset of) of vacuum Kerr BHs, when the scalar field vanishes, and horizonless, everywhere regular, gravitating scalar field configurations known as boson stars~\cite{Schunck:2003kk,Liebling:2012fv}, when the horizon vanishes. The lensing of both KBHsSH and their solitonic limit [rotating boson stars (RBSs)] was observed to exhibit chaotic patterns for solutions in some region of the parameter space, as illustrated by the example in Fig.~\ref{fig1}. Chaotic scattering in GR spacetimes has been observed and discussed in binary or multi-BH solutions -- see, $e.g.$,~\cite{Dettmann:1994dj,Yurtsever:1994yb,Dettmann:1995ex,Cornish:1996de,Sota:1995ms,deMoura:1999wf,deMoura:1999zd,Hanan:2006uf,Alonso:2007ts,Shipley:2016omi,Dolan:2016bxj} -- and is well known in the context of many body scattering in classical dynamics, for example the scattering of charged particles off magnetic dipoles~\cite{1992JPhA...25L.227A} and the 3-body problem (see $e.g.$~\cite{2011CeMDA.110...17M}). KBHsSH, or RBSs, provide an example of chaos in geodesic motion on the background of a single compact object, which moreover solves a simple and well defined matter model minimally coupled to GR.\footnote{Chaotic geodesic motion has also been reported around BHs surrounded by disks~\cite{Saa:1999je,Semerak:2012dw}. These models have some parallelism with KBHsSH, since the scalar field of the latter have a toroidal-type energy distribution, around the horizon.} Additionally, these objects possess a rich geometric structure, and may contain both multiple light rings~\cite{Cunha:2015yba}, including a stable one, as well as a structure of ergoregions~\cite{Herdeiro:2014jaa,Herdeiro:2016gxs}. The purpose of this paper is to investigate, in detail, chaotic scattering in this family of backgrounds and its interplay with the above geometric structure. \begin{figure}[ht] \begin{center} \includegraphics[width=6cm]{./pic-11.pdf}% \end{center} \caption{\small Example of a RBS exhibiting chaotic scattering, which can be clearly seen in some fringes on the right hand side (wherein neighbouring pixels present different colours). The setup for this figure is explained in~\cite{Cunha:2015yba} ($cf.$ Section~\ref{sec3} below), and this image corresponds to configuration 11 therein (zoomed).} \label{fig1} \end{figure} We start in Section~\ref{sec2} by performing an analysis of the effective potentials for (null) geodesic motion. We assume a stationary and axi-symmetric spacetime but no separation of variables; the latter is not known (or expected) in general for geodesic motion on RBSs or KBHsSH. Examining the 2D effective potentials for photon trajectories, we find that the emergence of \textit{stable light rings} on the background spacetimes, allows the formation of ``pockets" in one of the effective potentials, for open sets of impact parameters, leading to an effective trapping of the corresponding trajectories, dubbed \textit{quasi-bound orbits}. This analysis is analytical, with the exception of the explicit metric coefficients which are numerical for the examples exhibited. Comparing this analysis with some of the lensing images obtained in~\cite{Cunha:2015yba} allows us to establish a correspondence between pocket formation and the emergence of chaotic patterns in the images. Then, searching for features shared by all trajectories in chaotic patches, we observe that they exhibit a positive correlation to the number of radial turning points of the geodesic motion, and their time delay. Note in particular that in the Kerr BH background a photon can only have one radial turning point~\cite{Wilkins1972}, while in our family of backgrounds more than one radial turning point can occur, corresponding, generically, to chaotic motion. In Section~\ref{sec3} we exhibit a gallery of examples of lensing images obtained with a new ray-tracing code, \textsc{pyhole}, briefly described in Appendix~\ref{appendixb}. This code, based on \textsc{python}, includes tools for a simple, simultaneous visualization of the effective potential together with the spacetime trajectory, for any given point in a lensing image (and for an arbitrary numerical or analytical background metric). The results obtained with this code are in agreement with previous results~\cite{Cunha:2015yba,Vincent:2016sjq}, obtained with different ray-tracing codes, and it adds further tools that are useful for interpreting the results. In Section~\ref{sec4} we present some conclusions. In Appendix~\ref{appendixao}, we illustrate a trajectory in phase space of a trapped photon. In Appendix~\ref{appendixa} the effective potentials for Kerr are discussed, without using separation of variables, which are useful for a comparison with those shown in Section~\ref{sec2} for RBSs and KBHsSH. In Appendix~\ref{appendixa2} we introduce an acceleration field and describe its connection to the number of radial turning points. In Appendix~\ref{appendixb}, some details on \textsc{pyhole} are discussed, and, as an application, we also exhibit the lensing and shadows by KBHsSH, observed away from the equatorial plane. | \label{sec4} In this paper we have performed a detailed study of photon orbits in the background of KBHsSH and RBHs, extending and complementing the results in~\cite{Cunha:2015yba}. We now summarize some of our main results: \begin{description} \item[$\bullet$] For null geodesics, the Hamiltonian $\mathcal{H}=0$ restricts the motion of the light ray and sets a forbidden region in the phase space ($r,\theta$). The boundary of the latter can be studied in a systematic way by defining two potentials $h_\pm$, such that their countour lines delimit the boundary of the forbidden region for each value of the impact parameter $\eta$. \item[$\bullet$] For some configurations, this boundary forms a \textit{pocket} that can be closed for some interval of $\eta$, giving rise to \textit{bound} orbits. However, there is a open interval of $\eta$ values that can leave an arbitrarily small entrance to the pocket, leading to \textit{trapped} or \textit{quasi-bound} orbits. The formation of such pockets can be traced back to the presence of a \textit{stable light ring}, combined with at least one unstable light ring. The latter is associated to a ``throat'' (a pocket entrance) that connects the interior of the pocket with a different region of the allowed phase space. \item[$\bullet$] The existence of a pocket is strongly correlated to the existence of chaos in the motion of the light ray, leading to turbulent patterns in the gravitational lensed image of the configuration. However, despite inducing chaos, pockets are neither a necessary nor sufficient condition for a particular trajectory to lie in such a chaotic pattern. \item[$\bullet$] A common feature of chaotic orbits appears to be having \textit{more than one radial turning point}, a feature which embodies a deviation from Kerr spacetime \cite{Wilkins1972}. Nevertheless, it is still possible to have several turning points for a regular scattering, and hence this is not a sufficient condition for chaos. \item[$\bullet$] The ergoregion does not appear to play a major role in this context, despite enhancing the chaotic patterns in the image. \item[$\bullet$] If an event horizon and a pocket are both present, the existence of a two throat system may be the origin of the formation of disconnected shadows, first reported in \cite{Cunha:2015yba} for KBHsSH. \end{description} To conclude, and following the above observations, we would like to emphasize that: - not all KBHsSH display chaotic lensing. For instance, configuration II in~\cite{Cunha:2015yba} exhibits effective potentials very similar to those of Kerr ($cf.$ Appendix~\ref{appendixa}), even though the corresponding shadow is quite distinct. This also provides an example for which lack of integrability, in the sense of Liouville\footnote{Except for the corresponding Kerr boundary line (see Fig. \ref{fig_overview}), it is unlikely that any KBHsSH has a hidden constant of the motion (which exists in Kerr), and hence geodesic motion is almost certainly non-integrable in (almost) all the domain of existence.}, does not imply chaos; - an important part of our analysis in this paper relied on numerical ray tracing. The results obtained using different ray tracing codes agree, lending them credibility. Such numerical methods, however, have issues for very long term integrations. Thus, our discussion of the chaotic patterns is mostly focused on their emergence, rather than on their precise quantitative properties, for which numerical errors may become important; - finally, a similar analysis to that performed herein can certainly be pursued for other similar types of backgrounds, as, $e.g.$ the ones discussed in~\cite{Kleihaus:2005me,Brito:2015pxa,Kleihaus:2015iea,Herdeiro:2015tia,Herdeiro:2016tmi,Delgado:2016jxq}. \vspace{0.5cm} | 16 | 9 | 1609.01340 |
1609 | 1609.00493_arXiv.txt | In view of the new recent observation and measurement of the rotating and highly-magnetized white dwarf AR Scorpii \cite{Marsh:2016uhc}, we determine bounds of its moment of inertia, magnetic fields and radius. Moreover, we investigate the possibility of fast rotating and/or magnetized white dwarfs to be source of detectable gravitational wave (GW) emission. Numerical stellar models at different baryon masses are constructed. For each star configuration, we compute self-consistent relativistic solutions for white dwarfs endowed with poloidal magnetic fields by solving the Einstein-Maxwell field equations in a self-consistent way. The magnetic field supplies an anisotropic pressure, leading to the braking of the spherical symmetry of the star. In this case, we compute the quadrupole moment of the mass distribution. Next, we perform an estimate of the GW of such objects. Finally, we show that the new recent observation and measurement pulsar white dwarf AR Scorpii, as well as other stellar models, might generate gravitational wave radiation that lies in the bandwidth of the discussed next generation of space-based GW detectors DECI-hertz interferometer Gravitational wave Observatory (DECIGO) and Big Bang Observer (BBO). | Some white dwarfs (WD) are associated with strong magnetic fields. From observations, it was shown that the surface magnetic field in these stars can reach values up to $10^{9}\,$ G, see \cite{Terada:2007br,Reimers:1995ia,Schmidt:1995eh,Kemp:1970zz,putney1995three,angel1978magnetic}. However, the internal magnetic field in stars is very poorly constrained by observations and can be much stronger than the one at the surface. A virial-theorem based estimate by equating the magnetic field energy with the gravitational biding energy leads to an upper limit for the magnetic fields inside WD's of $\sim 10^{13}$ G \citep{shapiro2008black}. On the other hand, in the context of exploring overluminous type Ia supernovae and the possible existence of super-Chandrasekhar white dwarfs, different numerical calculations suggest that white dwarfs might have internal magnetic fields as large as $10^{12-16}\,$ G \citep{das2013new, Bera:2015yxa, Franzon:2015gda}. Due to their large radius compared to neutron stars, white dwarfs present a different scale in their macroscopic stellar properties, like the moment of inertia, magnetic moment, rotational frequency and quadruple moment. This, together with the fact that white dwarfs are found closer to earth, is one of the reasons why white dwarfs are much more understood than neutron stars. The main motivation of this work is provided by the recent binary system discovered by \cite{Marsh:2016uhc}. This system is composed of a main sequence star and a fast spinning and magnetized white dwarf with a mass that lies in the range $0.81M_{\odot}<M_{\rm{wd}}\leq1.29M_{\odot}$. The pulsating white dwarf is called AR Scorpii, AR Sco for short, and such a system has never been observed orbiting a cool red dwarf star. In the case of AR Sco, this was the first radio pulsations detected in any white dwarf system. In addition, due to its high magnetic field combined with rotation, such type of WD's are called `white dwarf pulsar'. The rapidly-spinning and magnetized stellar remnant AR Sco pulses across almost the entire electromagnetic spectrum, from X-ray to radio wavelengths. Up to now, pulsating stars were related to neutron stars (NS), which can be rotating and highly magnetized, emitting a beam of electromagnetic radiation. Typically, white dwarfs rotate with periods of days or even years. On the other hand, according to \cite{Mereghetti:2010id}, one of the fastest observed WD possesses a spin period of $13.2\,s$, a value similar to the ones observed in Soft Gamma Repeaters (SGR) and Anomalous X-ray pulsars (AXP), known as magnetars \citep{Duncan:1992hi, Thompson:1993hn}. A relation between WD's and magnetars was addressed by \cite{Malheiro:2015yda}, where the authors speculated that SGR's and AXP's with low surface magnetic field might be rotating magnetized white dwarfs. As in neutron stars, the origin of magnetic fields in white dwarfs is still under debate. While the magnetic flux conservation of a progenitor remains an attractive possibility, a likely origin of the such strong magnetic fields is a dynamo process that operates during the envelope evolution, see \cite{ferrario2016magnetic}. Recently, observations have shown that the formation of high magnetic white dwarfs can be related to strong binary interactions during post-main-sequence phases of stellar evolution \citep{nordhaus2011formation}. Whatever the origin of strong magnetic fields might be, they effect the stars in different ways. First, magnetic fields affect locally the microphysics of the equation of state through the Landau quantization of the energy levels of charged particles. However, as already shown by \cite{bera2014mass}, although equation of state of electron degenerate matter is strongly modified due to Landau quantization, this effect is negligible on the global properties of white dwarfs. In fact, we already shown that in NS's the contribution to the structure of the star when taking into account the magnetic field corrections in the equation of state is very small, see \cite{franzon2016self}. For this reason, we do not take into consideration a magnetic-field-dependent equation of state in our calculation. Secondly, magnetic fields are sources of the gravitational field equations through the Maxwell energy-momentum tensor. As a result, they make the pressure anisotropic, which requires a general treatment beyond the Tolman-Oppenheimer-Volkoff (TOV) solutions \citep{oppenheimer1939massive, tolman1939static}. In addition, the Lorentz force induced by magnetic fields change the structure of white dwarfs, which, in the case of poloidal fields, become oblate objects. This is the same effect as the one produced by rotation. In both cases, the star deformation with respect to the magnetic and/or rotation axis can be quantified by the stellar quadrupole moment. As predicted by \cite{einstein1916approximative}, gravitational waves are generated by objects that have quadrupole moment varying in time, such as colliding black holes, collapse of stellar cores, coalescing neutron stars, white dwarf stars, etc. Such systems disrupt the space-time producing GW that radiate from the source and travel at the speed of light through the Universe, carrying information about their sources, as well as the nature of gravity itself. Currently, the main ground-based gravitational waves interferometer operating is the twin Laser Interferometer Gravitational-wave Observatory (LIGO) which sensitivity is designed to detect GW amplitude of one part in $10^{21}$ within the frequency bandwidth in the range 30 - 7000 Hz. In the next years, a second generation of detectors, as for example, advanced-LIGO and advanced-Virgo, will be operating. Furthermore, the space-based gravitational waves detector Laser Interferometer Space Antenna (LISA) \citep{danzmann1996lisa} has been planning to be launched. LISA operates a space-based gravitational waves detector sensitive at frequencies between 0.03 mHz and 0.1 Hz. The Deci-Hertz Interferometer Gravitational Wave Observatory (DECIGO) \citep{seto2001possibility, kawamura2006japanese} is a plan of a future Japanese space mission for observing GW's in frequency bandwidth similar to LISA, however, at lower gravitational waves amplitudes. This fact, as we are going to see, makes DEGICO suitable to detect gravitational waves from fast rotating and/or magnetized white dwarfs. Meanwhile, another space-based interferometer has been proposed as a successor to LISA, the Big Bang Observer (BBO) \citep{phinney2003big}, with both frequency bandwidth and gravitational waves amplitudes similar to the ones of DECIGO. With this in mind, we make use of available data of AR Sco, as its distance from Earth, its rotation frequency and its mass range, to perform self-consistent rotating and magnetized white dwarf calculations and then determine bounds of its radius, moment of inertia, quadruple moment and magnetic fields. With these results, we investigate the possibility of rotating and magnetized white dwarfs to be sources of detectable GW emission. A white dwarf is a dense configuration supported by the electron degeneracy pressure against gravitational collapse. Here, we describe the stellar interior assuming that the star is predominately composed of carbon $^{12}C$ ($A/Z = 2$) in an electron background, see \cite{chandrasekhar1931maximum}. In fact, white dwarfs are much less compact stars than neutron stars, being easily deformed due to magnetic fields. Another important point is that white dwarfs can be considered the most closest astrophysical sources of gravitational waves. We organise the paper in the following way.In Sec. 2 we summarise the coupled Maxwell-Einstein equations and the hydrodynamic equations in presence of a magnetic field in general relativity. In Sec. 3, we describe the results concerning the influence of strong magnetic fields on the structure of white dwarfs, in particular to the AR Sco star. Sec. 4 describes the effects of rotation, combined also with magnetic fields, on the detectability of gravitational waves emitted by rotating and/or magnetized white dwarfs. Finally in Sec. 5, we give our conclusions. | In this work, we performed self-consistent and relativistic numerical calculations of axisymmetric rotating and magnetized white dwarf structure by means of a pseudo-spectral method, where the standard stress-energy tensor of a perfect fluid and the electromagnetic field were employed. First, we fixed the baryon stellar mass and we computed the quadrupole moment of the configuration, which was used to estimate the gravitational wave amplitudes of potential sources. In our case, white dwarfs can be rotating and/or endowed with a poloidal magnetic field. We showed that the moment of inertia of white dwarfs increase significantly due to magnetic fields and depend strongly on the stellar mass, where less massive WD's have higher moment of inertia, however, since they are less dense, they reach lower magnetic fields values than massive stars. Moreover, we gave bounds for the radius, magnetic fields, moment of inertia and quadrupole moment of the pulsar white dwarf AR Sco. These results relied on the assumption that the observed luminosity corresponds exactly to the spin-down power undergone by the white dwarf. Although we have assumed this approximation in this work, we do not expect qualitative changes in our conclusions, since according to Fig.~\ref{rc_luminosity} a higher luminosity implies just a smaller possible mass for AR Sco. More importantly, we also found that magnetic white dwarfs might lead to a detectable signal by the DECIGO and BBO gravitational wave detectors. The DECIGO and the BBO, both having the same sensitivity frequency band, perform better than LISA in detecting GW from magnetized white dwarfs. In addition, we saw that BBO is able to detect GW even from a purely rotating white dwarf (without magnetic fields) with $M_{B}=0.50\,M_{\odot}$ rotating at a frequency of 0.01 Hz, while DECIGO can potentially measure gravitation radiation from the magnetic counterpart of this star. A key fact is that the magnetic field (for the star $M_{B}=0.50\,M_{\odot}$) that corresponds to the minimum GW amplitude within the detectable range of DECIGO is close to observed ones, what indicates that magnetized white dwarfs are also likely sources of GW and could be detected by future space-based gravitational wave detectors. Furthermore, based on the GW amplitude, magnetic white dwarfs can emit gravitational radiation so intense as in strongly magnetized neutron stars. It is worth mentioning that the detection of white dwarfs with higher frequencies ($\sim$ 1 Hz) would make them better candidates of gravitational wave sources, since they would lie in the optimal band of DECIDO and BBO interferometers. Note that, we did not run out of all possible combinations of masses, rotation and magnetic field configurations. However, non-magnetized white dwarfs can reach (Keplerian limit) frequencies at most $\sim$ 1.50 Hz, see e.g. \cite{Franzon:2015gda}. As a consequence, we have a natural limit when looking for white dwarfs through gravitational waves emission. It is well known that simple magnetic field configurations with purely poloidal or purely toroidal components are unlikely to be stable \citep{tayler1973adiabatic, markey1973adiabatic, flowers1977evolution, braithwaite2006stable}. Note that the quadrupole distortion induced by toroidal magnetic fields would contribute negatively to the total stellar deformation. This is the case because poloidal magnetic fields make the stars more oblate, while toroidal fields make them more prolate. In this context, an estimate of the stellar quadrupole distortion assuming both poloidal and toroidal magnetic field components was perfomed by \cite{wentzel1960hydromagnetic, ostriker1969nature}. Accordingly, the stellar deformation could be reduced by $50\%$ when a mixture of poloidal and toroidal fields of similar strength are presented in the star. The distortion of the star scale with its quadrupole moment as $\epsilon \sim Q$ \citep{frieben2012equilibrium}. Therefore, we expect that the gravitational wave amplitude, which scale with $Q$ as $h_0\sim Q$, should be only roughly reduced by a factor of 2 compared to those obtained in this work. In addition, magnetized stars seem to carry an external dipole magnetic field as the one modeled in this work. Furthermore, even assuming for simplicity purely poloidal fields, we can have a fair idea of the maximum magnetic field strength that can be reached inside these stars and also understand the effects of strong magnetic fields both on the GW emission and on global structure of white dwarfs. In the future, we are going to include effects due to microphysics in our calculations as, for example, a more realistic equation of state which includes electron-ion interactions. Moreover, although we do not expect that our findings are going to change qualitatively, different particle composition of the star might lead to different gravitational wave amplitudes. | 16 | 9 | 1609.00493 |
1609 | 1609.02944_arXiv.txt | {NGC 1365 is a Seyfert 2 galaxy with a starburst ring in its nuclear region. In this work we look at the \xmm Reflection Grating Spectrometer (RGS) data from four 2012-13, three 2007 and two 2004 observations of NGC 1365, in order to analyse and characterise in a uniform way the soft X-ray narrow-line emitting gas in the nucleus.}{We characterise the narrow-line emitting gas visible by \xmm RGS and make comparisons between the 2012-13 spectra and those from 2004-07, already published.}{This source is usually absorbed within the soft X-ray band, with a typical neutral column density of $>$1.5 x 10$^{23}$ cm$^{-2}$, and only one observation of the nine we investigate shows low enough absorption for the continuum to emerge in the soft X-rays. We stack all observations from 2004-07, and separately three of the four observations from 2012-13, analysing the less absorbed observation separately. We first model the spectra using gaussian profiles representing the narrow line emission. We fit physically motivated models to the 2012-13 stacked spectra, with collisionally ionised components representing the starburst emission and photoionised line emission models representing the AGN line emission. The collisional and photoionised emission line models are fitted together (rather than holding either one constant), on top of a physical continuum and absorption model.}{The X-ray narrow emission line spectrum of NGC 1365 is well represented by a combination of two collisionally ionised (kT of 220$\pm10$ and 570$\pm15$\,eV) and three photoionised ($\log \xi$ of 1.5$\pm0.2$, 2.5$\pm0.2$, 1.1$\pm0.2$) phases of emitting gas, all with higher than solar nitrogen abundances. This physical model was fitted to the 2012-13 stacked spectrum, and yet also fits well to the 2004-07 stacked spectrum, without changing any characteristics of the emitting gas phases. Our 2004-07 results are consistent with previous emission line work using these data, with five additional emission lines detected in both this and the 2012-13 stacked spectra. We also estimate the distance of the X-ray line-emitting photoionised gas from the central source to be $<$300\,pc.}{} | \label{NGC1365_intro} \begin{table*} \begin{minipage}[t]{\hsize} \setlength{\extrarowheight}{3pt} \caption{\xmm and \chandra observations of the nuclear region of NGC 1365 and where the data have been analysed. The final four \xmm observations were taken simultaneously with \nustar.} \label{obs_table} \centering \renewcommand{\footnoterule}{} \begin{tabular}{l l c c | c} \hline \hline Telescope & Start of obs. & Obs. ID & {Duration (ks) \footnote{For \chandra observations the scheduled length is quoted}} & References \\ \hline \chandra & 2002-12-24 & 3554 & 15 & 1, 9 \\ \xmm & 2004-01-17 & 0205590301 & 59.7 & 2, 7, 5, 10 \\ \xmm & 2004-07-24 & 0205590401 & 68.8 & 2, 5, 10 \\ \chandra & 2006-04-17 & 6868 & 15 & 3, 4 \\ \chandra & 2006-04-20 & 6869 & 15 & 3, 4 \\ \chandra & 2006-04-23 & 6870 & 15 & 3, 4 \\ \chandra & 2006-04-10 & 6871 & 15 & 3, 4 \\ \chandra & 2006-04-12 & 6872 & 15 & 3, 4 \\ \chandra & 2006-04-12 & 6873 & 15 & 3, 4 \\ \xmm & 2007-06-30 & 0505140201 & 128.9 & 6, 5, 10 \\ \xmm & 2007-07-02 & 0505140401 & 131.1 & 6, 5, 10 \\ \xmm & 2007-07-04 & 0505140501 & 130.9 & 6, 5, 10 \\ \chandra & 2012-04-09 & 13920 & 90 & 11, 13 \\ \chandra & 2012-04-12 & 13920 & 120 & 11, 13 \\ \xmm & 2012-07-25 & 0692840201 & 138.5 & 8, 10, 12, 14 \\ \xmm & 2012-12-24 & 0692840301 & 126.2 & 10, 12, 14 \\ \xmm & 2013-01-23 & 0692840401 & 133.6 & 11, 10, 12, 14 \\ \xmm & 2013-02-12 & 0692840501 & 134.7 & 10, 12, 14 \\ \hline \hline \end{tabular} \tablebib{ (1)~\citet{Risaliti:2005dj}; (2) \citet{Risaliti:2005kd}; (3) \citet{2007ApJ...659L.111R}; (4) \citet{Wang:2009jh}; (5) \citet{Guainazzi:2009fv}; (6) \citet{Risaliti:2009ic}; (7) \citet{Risaliti:2009cx}; (8) \citet{2013Natur.494..449R}; (9) \citet{Connolly:2014ft}; (10) \citet{2014MNRAS.441.1817P}; (11) \citet{Braito:2014ct}; (12) \citet{Walton:2014fc}; (13) \citet{2015MNRAS.453.2558N}; (14) \citet{Rivers:2015fy} } \end{minipage} \end{table*} \object{NGC 1365} (z $=$ 0.0055) has an interesting observational classification history. Optically it has been called a Seyfert 1.5, 1.8 or 2 by different authors \citep[e.g.][respectively]{1980A&A....87..245V,1995ApJ...454...95M,1993ApJ...418..653T}. Most recent X-ray papers have classified NGC 1365 as a Seyfert 2 due to the column density of neutral material \citep[$>1.5 \times 10^{23}$ cm$^{-2}$,][]{2007ApJ...659L.111R,Risaliti:2009cx} covering its X-ray emission \citep[intrinsic L$_{2-10\,keV} \sim10^{42}$\,erg\,s$^{-1}$][]{Risaliti:2005dj}. Notably, especially for this work, there is a nuclear starburst with a diameter of 10'', which is resolved in optical wavelengths into multiple compact star clusters \citep[using the \hst Faint Object Camera, ][]{1997A&A...328..483K}. This is often referred to as a `ring', and we continue to do so in this work, although there is some evidence from radio emission that the ring is incomplete \citep{Beck:2005cb}. Starburst regions are known to produce soft X-rays primarily from collisionally excited, shock-heated gas, and hard X-rays mainly from accreting compact objects such as X-ray binaries. Any interpretation of soft X-ray emission from AGN photoionised gas in NGC 1365 must take this surrounding starburst emission into account. It is well established that the variability seen in the spectrum of NGC 1365 is caused by variations in photoelectric absorption. Recently, \cite{2014MNRAS.441.1817P} showed this in a model independent way by using Principal Component Analysis (PCA). Comparing PCA results of analysis of NGC 1365 to results from model spectra, varied in different physical ways, showed that variable absorption causes $>\,90\,\%$ of the variability in NGC 1365's observed spectra. The details of the complex phases of X-ray absorbing gas found in this source are summarised below. \textit{Emission line gas.} Gas photoionised by the central AGN of NGC 1365 has been studied in both optical and X-ray bands. Optical line ratios in an asymmetrical conical region suggests photoionisation by the AGN \citep{Veilleux:2003fe,1999A&A...346..764S}. NGC 1365 was the first AGN where high-quality, high-resolution soft X-ray data showed emission lines dominated by collisionally ionised gas \citep{Guainazzi:2009fv}. In their analysis of a $\sim$500\,ks stacked spectrum collected by RGS between 2004 and 2007, \cite{Guainazzi:2009fv} model the emission lines with two collisional components (kT$\sim$300 and $\sim$640\,eV) and one loosely constrained photoionised component ($N_H \geq 10^{22}$\,cm$^{-2}$, $\log$\,U\,$= 1.6^{+0.3}_{-0.4}$, $n_e \leq 10^{10}$\,cm$^{-3}$). Studies since \cite{Guainazzi:2009fv} have confirmed the two collisional phases of emission line gas. Characterising the photoionised emission in the presence of this collisional emission has been difficult, but restricting the spatial dimension of \chandra HETGS spectra allowed \cite{2015MNRAS.453.2558N} to reduce the contribution of collisional emission from the circumnuclear starburst ring in their spectra compared to previous analyses \citep[e.g.][]{Guainazzi:2009fv}. They confirm the presence of photoionised emission, as well as two collisionally ionised phases with different temperatures to those found by \cite{Guainazzi:2009fv} ($\sim$150\,eV and $\sim$1200\,eV as opposed to $\sim$300\,eV and $\sim$640\,eV). \cite{2015MNRAS.453.2558N} accept that the spectral quality of their data is limited by lack of photon counts and therefore a detailed characterisation of the photoionised emission lines cannot be done with this dataset. The authors loosely contrain the temperature and density of the emitting gas to $T < 3 \times 10^6$\,K and $n < 10^{13}-10^{14}$\,cm$^{-3}$ respectively. They could fit the spectrum with three photoionised emission models at ionisations of $\log \xi > 4.1, \sim3.1\pm0.3$ and $< 0.6$ but recommend interpretation of this as simply proof of the existence of a large range of ionisation states. Using the \chandra data, \cite{2015MNRAS.453.2558N} estimated the location of the photoionised gas to be `across the virtual BLR/NLR boundary', based on some evidence of broadening of the emission lines ($\sim1000\,$\kms). \cite{Guainazzi:2009fv} tentatively suggested the inner face of the photoionised gas could be $\geq 0.75$\,pc from the source, potentially placing it within the BLR. \cite{Braito:2014ct} use an \xmm observation in 2013 (RGS and EPIC) and also conclude that some emission line gas is located within the BLR, as they see the Mg\,XII\,Ly-$\alpha$ emission line increase in strength as their measured absorption decreases. They interpret this as either the uncovering of emission from within their most variable absorber ($r < 10^{17}$\,cm) or ionised gas responding to a change in its illuminating continuum, which (given the likely timescales) would have to be a compact region and then would again be likely located at $r \sim 10^{15}$\,cm from the source. Finally, \cite{Braito:2014ct} suggest that the Mg\,XII emission and absorption lines in the highest flux part of their observation are reminiscent of a classical P-Cygni profile, and therefore could hint at a common origin for both from an outflowing wind. \textit{Multiple layer X-ray absorbers.} The X-ray absorption complex within NGC 1365's nuclear region has been studied in detail. In addition to the original neutral absorber characterised by \cite{Risaliti:2005dj}, shown to cause the main variability seen from the source \citep[][]{Risaliti:2005dj,Risaliti:2009ic,2014MNRAS.441.1817P}, many other absorption layers have also been detected with X-ray data. \cite{Risaliti:2005kd} found absorption lines between 6.7 and 8.3\,keV with \xmm EPIC data of the source in a Compton-thin state, which they attribute to an absorber originating from an accretion disk wind. By analysing one 120\,ks (2013) \xmm observation in detail, \cite{Braito:2014ct} find at least two ionised absorber phases (and evidence for a third), which are needed to fit the RGS spectrum, as well as a neutral absorber needed to fit the EPIC spectrum (not statistically required in the RGS band). The lowest ionisation phase of these three is found to be partially covering and variable in column density over timescales as short as 40\,ks (within the 120\,ks observation). The three ionised absorber phases they use are each responsible for different signatures within the data. Their highest ionisation phase ($\log \xi = 3.8$), which causes the absorption features around the Fe\,K line complex \citep[the absorption lines found by][]{Risaliti:2005kd}, is outflowing by 3900\,\kms, and is only needed by the EPIC spectrum. Their mid ionisation phase ($\log \xi = 2.1$) produces Mg, Si and S absorption lines, fitted in both RGS and EPIC spectra, and with an RGS measured outflow velocity of 1200\,\kms. Their lowest ionisation phase ($\log \xi < 1$) causes spectral curvature in the EPIC spectrum and the Fe UTA in the RGS spectrum. \cite{Braito:2014ct} propose that the three ionised absorber phases are part of a disk wind, and the lowest ionisation phase could be identified as the partially covering neutral absorber previously detected by \cite{Risaliti:2005dj}, located around the distance of the BLR \cite[r\,$<\,10^{16}$\,cm; e.g.][]{Brenneman:2013kw,Risaliti:2005kd}. The same four 2012-13 joint \xmm and \nustar observations analysed by \cite{Walton:2014fc}, \cite{2013Natur.494..449R} and \cite{Braito:2014ct} were also studied by \cite{Rivers:2015fy}, to untangle any extra complexities and layers of neutral absorption. The \cite{Rivers:2015fy} model also includes absorption lines to represent the ionised absorption discovered around 6-8\,keV by \cite{Risaliti:2005kd}. They observed that when the source becomes uncovered by its high column density partially covering absorber (the covering fraction decreases), such as in observations 2, 3 and 4 of this set (in Dec 2012, Jan 2013 and Feb 2013 respectively), an additional layer of fully covering neutral absorption is needed to fit the spectrum. Their model for a partially covering layer of absorption varies substantially within and between observations 1, 3 and 4. Its behaviour during observations 1 and 4 is similar, with column density changes but no covering fraction changes, and here \cite{Rivers:2015fy} call it a ``partial-covering `high column density' absorber''. Its behaviour in observation 3 is very different, with a rapid drop of both covering factor and column density, which \cite{Rivers:2015fy} refer to as an uncovering of the source, and call this a ``patchy partial-covering'' absorber instead. They argue that these two different behaviours are evidence that the one partial covering model they use actually tracks different layers of the absorption, in reality distinct from each other. In this work we look at the RGS data from all four of these 2012-13 \xmm observations, and at the \xmm observations from 2004 and 2007, in order to analyse in a uniform way and further characterise the X-ray narrow-line emitting photoionised gas. This paper is structured as follows: in Sect. \ref{NGC1365_obsdata} we describe the observations and data reduction process; in Sect. \ref{NGC1365_mywork} we go on to present an analysis of the emission line spectrum from NGC 1365, firstly using gaussian line models (Sect. \ref{gaussian_fit}) before moving on to a combination of physically motivated emission models (Sect. \ref{physicalmodels_sect}). We discuss the implications of our findings in Sect. \ref{NGC1365_discussion}, and finally conclude in Sect. \ref{NGC1365_conclusion}. | \label{NGC1365_conclusion} This is the most detailed spectral description of the emission lines from NGC 1365's nucleus so far, enabled by the quantity of good quality data available in the \xmm archive. In this work we show that the X-ray narrow emission line spectrum of NGC 1365 is well represented by a combination of two collisionally ionised (kT of 220$\pm10$ and 570$\pm15$\,eV) and three photoionised ($\log \xi$ of 1.5$\pm0.2$, 2.5$\pm0.2$, 1.1$\pm0.2$) phases of emitting gas, all with higher than solar nitrogen abundances. We attribute the collisionally ionised gas to the starburst surrounding the nuclear region and the photoionised gas to the Seyfert 2 nucleus in the centre. This physical model is the best fit to the 2012-13 stacked spectrum, and yet also fits well to the 2004-07 stacked spectrum, without changing any characteristics of the emitting gas phases. Our finding of 4.5$\pm$0.5 times solar nitrogen abundance in the nuclear region of this system represents the second time an over abundance of nitrogen has been suggested in this source \citep[the first being][from optical measurements]{1999A&A...346..764S}. We find that the photoionised X-ray emitting gas is $0.5 \leq $ distance $ \leq 270$\,pc from the ionising continuum of the central source. | 16 | 9 | 1609.02944 |
1609 | 1609.00200_arXiv.txt | Kernel phase interferometry is an approach to high angular resolution imaging which enhances the performance of speckle imaging with adaptive optics. Kernel phases are self-calibrating observables that generalize the idea of closure phases from non-redundant arrays to telescopes with arbitrarily shaped pupils, by considering a matrix-based approximation to the diffraction problem. In this paper I discuss the recent history of kernel phase, in particular in the matrix-based study of sparse arrays, and propose an analogous generalization of the closure amplitude to kernel amplitudes. This new approach can self-calibrate throughput and scintillation errors in optical imaging, which extends the power of kernel phase-like methods to symmetric targets where amplitude and not phase calibration can be a significant limitation, and will enable further developments in high angular resolution astronomy. | \label{intro} In imaging stars and their environments from the ground, under most circumstances the chief limitation on resolution and on sensitivity to faint structure is imposed by the turbulence of the Earth's atmosphere. This `seeing' introduces random delays in the phase of incoming light, so that when it arrives at a ground-based telescope, the wavefront is distorted and generates blurry, speckled images. Furthermore, as a higher-order effect, this wavefront distortion induces focussing and defocussing of the light in the Fresnel regime, so that there is also generally amplitude aberration, or scintillation, which is the reason that stars appear to twinkle. This is a major challenge in doing optical astronomy from the ground at high angular resolution, and in this paper I will review the history of techniques for ameliorating the effects of the atmosphere from speckle imaging; early hardware developments in non-redundant masking, where the telescope aperture is selectively masked out to facilitate optical calibration; and through to the more recent computer post-processing technique of kernel phase, where such a masking procedure is simulated purely with software. I will then present a generalization of the kernel phase idea, to kernel amplitudes, and discuss its applicability to present and future adaptive optics systems and space telescopes. For mathematically modelling the atmospheric distortion of images, it is useful to consider any telescope, even one with a conventional filled aperture, as an interferometer, where light incident at different parts of the telescope is optically combined and caused to interfere. By measuring these interference fringes, the Van~Cittert-Zernike theorem \citep{1938Phy.....5..785Z} states that we can map out the Fourier transform of the intensity distribution of the source on the sky. This means that the Fourier plane is a natural representation for understanding optical imaging under most circumstances. Pairs of points in the telescope aperture are considered to form baselines, whose length and orientation determine the Fourier component to which the associated fringe is sensitive. Interferometers are classically considered to be either of the Michelson configuration, where the light is combined in the pupil plane, or the Fizeau configuration, where the light from all elements of the pupil is directly combined on a detector. In radio astronomy, it has long been possible to record the electric field received at each detector, and combine these pupil-plane signals in postprocessing via a correlator. In optical astronomy, because it is not possible to directly sample the waveform of the electric field as it is at radio frequencies, single-telescope filled-aperture imaging typically occurs in the Fizeau configuration. As a result, fringes from every pair of points in the pupil are superimposed to form the point spread function (PSF) of the telescope. This is true both of discrete sets of apertures, for example the double slit whose PSF is a sinusoidal fringe, and filled apertures, where the familiar circular telescope aperture's PSF is the Airy pattern. In the following, I will refer interchangeably to pupil elements and subapertures, and stations and antennae, using the appropriate terminology for specifically-optical applications and for historical radio applications respectively. Sophisticated techniques for analysing images degraded by atmospheric turbulence have long been in use. By modelling the effects of the atmosphere on Fourier components of the image, speckle interferometry \citep{1970A&A.....6...85L} and speckle masking \citep{1977OptCo..21...55W} have been used to resolve systems at very high angular resolution while ameliorating the effects of the atmosphere. These techniques rely on the fact that, while the PSF is degraded in potentially complicated ways, the complex visibilities in its Fourier transform can be represented simply. To achieve this, one must be able to `freeze the seeing', i.e. to take exposures with appropriate signal-to-noise at timescales shorter than the characteristic timescale of the atmosphere's variations. A successful solution to the problem of seeing has been the technique of aperture masking, first used by \citet{fizeau1868}, where sections of the telescope aperture are deliberately blocked out to leave a non-redundant pattern of holes, i.e. a pattern of holes in which no two are separated by the same baseline, in order to make the resulting fringe pattern more resilient to aberrations and easier to calibrate. In a redundant aperture, on the other hand, multiple sets of subapertures generate the same baseline, and it is not so easy to disentangle their contributions to the resulting visibilities. Aperture masking has yielded some of the highest-resolution astronomical images obtained with a single-mirror telescope \citep{1999Natur.398..487T,1999ApJ...525L..97M}, relying on the idea of closure phase \citep{1958MNRAS.118..276J}, an interferometric self-calibration technique originating in radio astronomy. Often in interferometry, the dominant source of uncertainty is from phase aberrations in the pupil plane (i.e. for discrete interferometers, delay errors at individual stations), which are in general very large, originating from the ionosphere in the context of radio astronomy, or from atmospheric turbulence in the optical regime. These are especially important because, since the Fourier transform is Hermitian, the Fourier phases of a nonnegative real source (i.e. any astronomical image) encode only information about the asymmetric component of an image, and the moduli about its point-symmetric component \citep{2007NewAR..51..604M}. Therefore in the absence of prior information it is crucial to have access to both; regularly in astronomy, the issue is therefore to restore phase information which is typically more-degraded by the atmosphere. In this paper, we will discuss the context of methods for doing this, and then show that these can be generalized to self-calibrating both phase and amplitude information. The key idea in interferometric self-calibration is the closure phase or (bispectral phase). These are sums of measured phases around closing triangles of baselines; because errors occur locally to each station, while astrophysical signals are encoded in correlations between stations, if you add the phases measured around such a triangle of baselines, the local phase errors cancel but the astrophysical signal adds. As a result, for a simple three-element interferometer, for the price of three phase observables corrupted by aberrations, one very stable observable can be obtained, which is often a significant advantage. This idea entered optical astronomy under the guise of `triple-correlation' speckle imaging \citep{1970A&A.....6...85L,1977OptCo..21...55W}, which was shown by \citet{1986OptCo..60..145R} to be the exact equivalent of the closure phase idea. While aperture masking in general requires, as with speckle imaging, that exposures are taken fast enough to freeze the seeing, adaptive optics can be used to dramatically increase the timescale of phase variations and effectively remove this limitation \citep{2006SPIE.6272E.103T}. In radio astronomy, successive generations of calibration schemes have been able to use closure information in conjunction with the phases and amplitudes recorded at each antenna for self-calibration. \citet{2011A&A...527A.106S} classifies these into first-generation schemes using closure phases but not using individual receiver phases directly, second-generation schemes which iteratively self-calibrate the phase and gain at each receiver, and third-generation schemes which use the radio interferometry measurement equation to include direction-dependent effects. Because the phases and amplitudes of individual aperture elements cannot at present be easily and directly measured, optical imaging does not yet benefit from these second-~and third-generation calibration schemes. As a result, we are still limited to the classical closure relations in self-calibration, and I therefore seek to obtain the fullest and most detailed understanding of these quantities as is possible. Kernel phase interferometry was proposed for this reason by \citet{2010ApJ...724..464M}, who also coined the term itself. The key idea was a generalization of closure phase, using a matrix approach to show that a wider class of telescopes possess linearly self-calibrating quantities that can be used to improve the imaging performance of telescopes at resolutions close to the diffraction limit. Closure phases are shown to be a special case of this formalism, which in general applies to any standard Fizeau imaging system subject to only small aberrations. This technique has been used both for space telescopes such as the \emph{Hubble Space Telescope} \citep{2013ApJ...767..110P}, and also for ground-based adaptive optics systems \citep{2016MNRAS.455.1647P}. In this paper, I discuss the closure and kernel quantities associated with general Fizeau interferometers and the relationship of previous methods to the more recent development of kernel phase interferometry. I propose the extension of this to kernel amplitudes, a natural generalization of the kernel phase theory which allows us to calibrate not only phase errors but also scintillation. | \label{conclusion} With kernel amplitudes and kernel phases, we now have a full formalism to describe all self-calibrating observables in a direct Fizeau imaging system, such as most full-aperture telescopes. This means that both even and odd symmetry components of an image reconstruction can now be directly based upon self-calibrating observations. By including both even and odd image components, we will be able to improve existing methods of imaging stars, circumstellar and protoplanetary disks, and other astrophysical sources with both extended symmetric structure and embedded inhomogeneities. This may be of limited use in standard imaging, but in specialist cases where scintillation is the limiting factor (such as in Section~\ref{discussion}) this may be a step forward. I hope that this will prove useful in forthcoming imaging campaigns with adaptive optics and space telescopes. The fundamental theorem of linear algebra also implies that similar self-calibrating observables may be discoverable for other linear imaging systems, whenever the relevant measurement basis (e.g. baselines) is of substantially higher dimension than the pupil samples which generate it. It will be of compelling future interest to establish the extent to which this is true of coronagraphic systems, whose sensitivity to small phase and amplitude aberrations is a key limiting factor in the search for exoplanets. In the interest of open science, \textsc{IPython} Notebooks and \textsc{Python} scripts implementing the simulations used in this paper are available at \url{https://github.com/benjaminpope/pysco}, under a GNU General Public License (v3). | 16 | 9 | 1609.00200 |
1609 | 1609.04825_arXiv.txt | {We study the capture of WIMP dark matter by the Sun in the non-relativistic effective theory of dark matter self-interactions.~The aim is to assess the impact of self-interactions on the expected neutrino flux from the annihilation of WIMPs trapped in the Sun in a model independent manner.~We consider all non-relativistic Galilean invariant self-interaction operators that can arise from the exchange of a heavy particle of spin less than or equal to 1 for WIMPs of spin equal to 0, 1/2 and 1.~We show that for interaction operators depending at most linearly on the momentum transfer, the WIMP-induced neutrino flux can be enhanced by several orders of magnitude compared to the same flux in absence of self-interactions.~This is true even for standard values of the thermally averaged annihilation cross-section.~This conclusion impacts the analysis of present and future observations performed at neutrino telescopes.} \begin{document} | Evidence for a dark matter component of the Universe has been gathered over a broad range of physical scales in the past decades~\cite{Jungman:1995df,Bergstrom00}.~In the paradigm of Weakly Interacting Massive Particles (WIMPs) as a dark matter candidate, WIMPs are expected to interact with nuclei via elastic scattering~\cite{Goodman:1984dc}.~This property of WIMPs has a variety of implications as far as dark matter particle detection is concerned~\cite{Bertone:2004pz}.~In particular, WIMPs could scatter to gravitationally bound orbits while crossing the solar interior, accumulate at the Sun's centre, and finally annihilate into Standard Model particles at an observable rate~\cite{Silk:1985ax}.~In this scenario, the physical observable is the flux of energetic neutrinos produced in the decay chain of WIMP primary annihilation products.~Neutrino telescopes such as IceCube, Super-Kamiokande, ANTARES and Baikal are currently searching for this as of yet hypothetical neutrino signal~\cite{Aartsen:2016exj,Choi:2015ara,Adrian-Martinez:2016gti,Avrorin:2014swy}. Progress in understanding the general properties of the capture of WIMPs by the Sun has recently been made through the use of effective theories~\cite{Catena:2015iea,Blumenthal:2014cwa,Liang:2013dsa,Guo:2013ypa}.~In particular, the non-relativistic effective theory of dark matter-nucleon interactions has allowed us to gain new insights on the actual complexity of the capture process~\cite{Catena:2015iea,Catena:2015uha}.~The effective theory of dark matter-nucleon interactions has been proposed in the context of dark matter direct detection~\cite{Chang:2009yt,Fan:2010gt,Fitzpatrick:2012ix,Fitzpatrick:2012ib}, and developed in~\cite{Fornengo:2011sz,Menendez:2012tm,Cirigliano:2012pq,Anand:2013yka,DelNobile:2013sia,Klos:2013rwa,Peter:2013aha,Hill:2013hoa,Catena:2014uqa,Catena:2014hla,Catena:2014epa,Gluscevic:2014vga,Panci:2014gga,Vietze:2014vsa,Barello:2014uda,Catena:2015uua,Schneck:2015eqa,Dent:2015zpa,Catena:2015vpa,Kavanagh:2015jma,D'Eramo:2016atc,Catena:2016hoj,Kahlhoefer:2016eds}.~It allows to compute elastic and inelastic WIMP-nucleus scattering cross-sections without assuming a specific coupling of dark matter to quarks or gluons.~Its application to the study of WIMP capture by the Sun is based upon the numerical shell-model calculations performed in~\cite{Catena:2015uha}, where all nuclear response functions predicted by the theory are computed and made publicly available for the most abundant elements in the Sun.~A variety of new phenomena have been identified pursuing this approach, both concerning the complementarity of direct detection experiments and the search for WIMPs at neutrino telescopes, and regarding the potential of neutrino telescopes themselves~\cite{Catena:2015iea,Catena:2015uha}. WIMPs can also be captured by the Sun via self-interaction, as shown in~\cite{Zentner:2009is}.~WIMPs self-interactions are particularly interesting in the context of dark matter searches at neutrino telescopes, since they can enhance the rate of WIMP capture by the Sun, and therefore amplify the associated WIMP-induced neutrino flux~\cite{Albuquerque:2013xna,Chen:2014oaa,Chen:2015uha}.~So far, the use of effective theory methods has been restricted to the capture of WIMPs via scattering by nuclei.~In this paper we perform the first calculation of the rate of dark matter capture by the Sun in the effective theory of short-range dark matter self-interactions, recently proposed in~\cite{Bellazzini:2013foa}.~In contrast to previous findings~\cite{Zentner:2009is}, we show that in the general effective theory of dark matter self-interactions large neutrino signal amplifications are expected, even for standard thermally averaged annihilation cross-sections and momentum/velocity independent dark matter self-interactions. The paper is organised as follows.~In Sec.~\ref{capture} we review the capture of WIMPs in the Sun via elastic scattering by nuclei and introduce the equations describing WIMPs capture via self-interaction.~Sec.~\ref{sec:theory} is devoted to the effective theory of dark matter-nucleon interactions and the effective theory of dark matter self-interactions.~The two theories will be used to calculate scattering and capture rates in the Sun in the subsequent section.~We present our results for the rate of dark matter capture by the Sun in the effective theory of dark matter self-interactions in Sec.~\ref{sec:results}.~We highlight the broad applicability of our results and conclude in Sec.~\ref{sec:conclusions}.~Key equations for the calculation of WIMP scattering and self-scattering cross-sections are in Appendix~\ref{sec:appDM}. | \label{sec:conclusions} We studied the capture of WIMP dark matter by the Sun in non-relativistic effective theories for dark matter-nucleon and dark matter self-interactions mediated by a heavy particle.~Whereas effective theories were already used previously to model the scattering of WIMPs by nuclei in the Sun, this is the first time that an effective theory approach to dark matter self-interactions is used in this context.~This general theoretical framework allowed us to perform a model independent analysis of the capture of dark matter particles by the Sun via self-interaction. Within this theoretical framework, we compared the total rate of dark matter capture by the Sun in presence of dark matter self-interactions to the same quantity when dark matter self-scattering in the solar interior is neglected.~The time dependent ratio of these two rates, denoted by $\beta$ in Eq.~(\ref{beta}), determines the relative enhancement of the neutrino flux from WIMP annihilation in the Sun due to dark matter self-interaction.~We computed this ratio at present time for all dark matter-nucleon and dark matter self-interaction operators in Tab.~\ref{tab:operators}.~Results were presented for selected dark matter-nucleon and self-interaction operators in the $\left(\sigma_{\chi N},\sigma_{\chi \chi}\right)$ plane, where $\sigma_{\chi N}$ and $\sigma_{\chi \chi}$ are the dark matter-nucleon scattering cross-section and dark matter self-scattering cross-section, respectively.~Limits from the LUX experiment, the Bullet cluster and halo shape analyses in N-body simulations were imposed on this parameter space. We found that for self-interaction operators with no dependence on the momentum transfer $\hat{\bf{q}}$, that is, $\hat{\mathcal{O}}_1$ and $\hat{\mathcal{O}}_4$, a signal amplification of several orders of magnitude is possible, even for standard thermally averaged annihilation cross-sections $\langle \sigma_{\rm ann} v_{\rm rel}\rangle$.~This is in contrast with previous findings~\cite{Zentner:2009is}, which at the same time do not seem to numerically reproduce the analytic dependence on the capture rate $C_c$ given in Eq.~(\ref{betaequilibriumsolution}) of this work, and in Eq.~(7) of~\cite{Zentner:2009is}.~This significant amplification is reported in Fig.~\ref{betalines-operator-1}.~We also found a large amplification for self-interaction operators with a linear dependence on the momentum transfer (those labelled by $k=7,8,9,10,11,12$).~Results for these operators are given in Fig.~\ref{betalines-operator-7}.~For the operators in Figs.~\ref{betalines-operator-1} and \ref{betalines-operator-7}, self-interactions could completely dominate the rate of WIMP capture by the Sun.~For operators with a quadratic dependence on the momentum transfer (those labelled by $k=3,5,6,13,14$), the Bullet cluster limit allows for a smaller signal amplification, whereas for the operator $\hat{\mathcal{O}}_{15}$, that exhibits an indirect cubic dependence on the momentum transfer through the operator ${\bf{\hat{v}}}^{\perp}$, the Bullet cluster limit excludes any signal amplification larger than a few percent.~The latter two cases are discussed in Fig.~\ref{betalines-operator-3} and Fig.~\ref{betalines-operator-15}, respectively. The results found in this investigation can be used to optimise present and future searches for dark matter self-interactions at neutrino telescopes.~At the same time, our findings lay the foundations for model independent studies of the dark matter capture by the Sun via self-interaction. \appendix | 16 | 9 | 1609.04825 |
1609 | 1609.03402_arXiv.txt | Accretion-driven luminosity outbursts are a vivid manifestation of variable mass accretion onto protostars. They are known as the so-called FU Orionis phenomenon in the context of low-mass protostars. More recently, this process has been found in models of primordial star formation. Using numerical radiation hydrodynamics simulations, we stress that present-day forming massive stars also experience variable accretion and show that this process is accompanied by luminous outbursts induced by the episodic accretion of gaseous clumps falling from the circumstellar disk onto the protostar. Consequently, the process of accretion-induced luminous flares is also conceivable in the high-mass regime of star formation and we propose to regard this phenomenon as a general mechanism that can affect protostars regardless of their mass and/or the chemical properties of the parent environment in which they form. In addition to the commonness of accretion-driven outbursts in the star formation machinery, we conjecture that luminous flares from regions hosting forming high-mass star may be an observational implication of the fragmentation of their accretion disks. | \label{sect:introduction} Stars form in reservoirs of gas and dust, which collapse under their own gravity. However, a significant fraction of pre-stellar gas, thanks to the conservation of the gas net angular momentum, lands onto a centrifugally balanced circumstellar disc rather than falling directly onto the forming protostar. The manner in which matter accretes from the disc onto the star is still poorly understood and, notably, early spherical collapse models~\citep{larson_mnras_145_1969,shu_apj_214_1977} that neglect the disc formation phase cannot explain the variety of mass accretion rates observed in present-day star-forming regions~\citep{vorobyov_apj_704_2009}. In particular, these models yield accretion luminosities that are factors of 10$-$100 greater than the mean luminosity measured for nearby star-forming regions. This so-called "luminosity problem"~\citep{kenyon_aj_99_1990} can be solved if the accretion history onto the protostar is not smooth or quasi-constant, as predicted by spherical collapse models, but highly time-variable, as it naturally occurs in self-consistent models that follow the transition from clouds to protostellar discs~\citep{dunham_apj_747_2012}. In these models, protostars spend most of their time in the quiescent phase with low rate of accretion, which is interspersed with short but intense accretion bursts~\citep[see][]{voroboyov_apj_650_2006,vorobyov_apj_714_2010, machida_apj_729_2011, zhu_apj_746_2012,vorobyov_apj_805_2015}. Spectacular examples of these burst systems are a special class of young stars called FU Orionis objects, which display outbursts of a factor of hundreds in luminosity which last several decades to hundreds of years. Such flares are thought to be due to drastic increases in the mass accretion rate of such young stars~\citep{kley_apj_461_1996}. Until recently, it was thought that FU-Orionis-type accretion and luminosity bursts were constrained to occur in the solar mass regime of present-day star formation~\citep{audard_2014}. However, recent numerical hydrodynamics simulations of primordial disc formation around the first very massive stars have also revealed the presence of accretion bursts caused by disc gravitational fragmentation followed by rapid migration of the fragments onto the protostar~\textcolor{black}{\citep{stacy_mnras_403_2010,greif_mnras_424_2012,smith_mnras_424_2012, vorobyov_apj_768_2013,hosokawa_2015}}. These studies have revealed highly variable protostellar accretion with multiple bursts, exceeding in numbers their present-day counterparts~\citep{desouza_mnras_540_2015}. The same process of bursts driven by disc fragmentation operates around primordial super-massive stars, relaxing the ultraviolet photon output and enabling the stellar growth to the limit where general-relativistic instability results in the formation of super-massive black holes~\citep{sakurai_mnras_549_2016}. \begin{figure*} \centering \begin{minipage}[b]{ 0.245\textwidth} \includegraphics[width=1.0\textwidth]{./rho_plot_letter_1813_legend.eps} \end{minipage} \begin{minipage}[b]{ 0.245\textwidth} \includegraphics[width=1.0\textwidth]{./rho_plot_letter_1828_legend.eps} \end{minipage} \begin{minipage}[b]{ 0.245\textwidth} \includegraphics[width=1.0\textwidth]{./rho_plot_letter_1841_legend.eps} \end{minipage} \begin{minipage}[b]{ 0.245\textwidth} \includegraphics[width=1.0\textwidth]{./rho_plot_letter_1859_legend.eps} \end{minipage} \caption{ Midplane density \textcolor{black}{in the center of the computational domain around} the time of the first outburst. (a) \textcolor{black}{The region within 800~AU} when a clump forms in a spiral arm $\sim200\, \rm AU$ \textcolor{black}{away from} the protostar, at a time $18.10\, \rm kyr$. Panel (b-c) display zooms to illustrate the migration and accretion of a part of the clump at times $18.28$, $18.30$ and $18.32\, \rm kyr$, respectively. The density is plotted in g/cm$^{3}$ on a logarithmic scale and the size of the panels is in AU. } \label{fig:disk_density_plots} \end{figure*} Consequently, the emerging question is, how universal is variable accretion with episodic bursts in star formation and whether it can be associated to a unique physical mechanism? Time-variability of accretion onto present-day massive stars at the early phase of their formation is a known \textcolor{black}{ process~\citep{krumholz_apj_656_2007,peters_apj_711_2010,kuiper_apj_732_2011,klassen_arXiv160307345K}. Those studies interpret this phenomenon as a natural consequence of the three-dimensional nature of their self-gravitating numerical simulations, while~\citet{kuiper_apj_772_2013} explains it by the interplay between mass accretion, stellar evolution, and radiative feedback. } They report how asymmetries can develop in self-gravitating discs and generate an azimuthal anisotropy in the accretion flow onto the protostars. One can particularly notice that in addition to its variable character, it is interspersed with several accretion peaks~\citep[see fig.~4 of][]{klassen_arXiv160307345K}. In the above cited references, the sharp increases of the accretion rate are generated in simulations assuming different pre-stellar core masses, ratio of kinetic by gravitational energy $\beta$, assuming either a {\it rigidly} rotating cloud or a turbulent pre-stellar core. \textcolor{black}{ The study of a maser outflow in the high-mass star forming region W75N equally conjectures that "short-lived outflows in massive protostars are probably related to episodic increases in the accretion rates, as observed in low-mass star formation"~\citep{Carrasco_sci_348_2015}. } Additionally, a luminosity outburst of the massive ($\approx 20\, \rm M_\odot$) young star S255IR-NIRS3 was reported in~\citet{fujisawa_atel_2015} by means of 6.7 GHz methanol maser emission. This emission line has been discovered by~\citet{menten_apj_380_1991} and constitutes today a well known-tracer of high-mass star forming regions~\citep[see][and references therein]{bartkiewicz_aa_587_2016}. \textcolor{black}{Recent observation of the same object show brightness variations that resemble strongly} FU-Orionis-type outbursts~\citep{stecklum_ATel_2016}. Motivated by the above listed numerical studies and observational arguments, we continue to investigate the burst phenomenon in the high-mass regime of star formation. We follow existing models showing accretion spikes in high-mass star formation, further analyze their nature in the context of the star-disc evolution and conjecture on possible observational implications. This study is organized as follows. In Section~\ref{sect:method}, we review the methods that we utilise to carry out our high-resolution \textcolor{black}{self-gravity radiation-hydrodynamical} simulation of the formation and evolution of a disc surrounding a growing present-day massive protostar generated by the collapse of a {\it non-rigidly} rotating pre-stellar core. Our outcomes are presented and discussed in Section~\ref{sect:results}. Particularly, our model also generates such outbursts and we show that they are caused by the rapid migration of disc fragments onto the protostar. Finally, we conclude on their significances in Section~\ref{section:cc}. | \label{section:cc} We have confirmed the presence of strong peaks in the variable accretion history of high-mass protostars, already present in the literature \textcolor{black}{for a wide range of initial conditions of the pre-stellar core. All models have a standard initial density distribution $\propto r^{-3/2}$ that is assumed in the absence of corresponding observations. All rotating models preceding our study assumed cores in sold-body rotation. Turbulent radiation-hydrodynamics simulations include~\citep{krumholz_apj_656_2007,peters_apj_711_2010,seifried_mnras_417_2011}, other studies neglected turbulence. Initial conditions of $M_{\rm c}$ and $\beta$-ratio are $100$$-$$200\, \rm M_{\odot}$ with $2\%$~\citep{krumholz_apj_656_2007}, $100\, \rm M_{\odot}$ with $2\%$~\citep{krumholz_sci_323_2009,kuiper_apj_732_2011}, $1000\, \rm M_{\odot}$ with $5\%$~\citep{peters_apj_711_2010}, $100\, \rm M_{\odot}$ with $4$$-$$20\%$~\citep{peters_apj_711_2010} and $100;200\, \rm M_{\odot}$ with $10.5;5.3\%$~\citep{klassen_arXiv160307345K}, respectively, while we use $100\, \rm M_{\odot}$ with $4\%$. } Our higher spatial resolution in the inner disc allows us to explicitly capture the fall of forming circumstellar clumps rather than modelling overdense filaments in the disc that wrap onto the star. It enables to study this process, well-known in the low-mass and primordial regime of star formation as the so-called episodic accretion-driven outbursts, which we conclude to be also present in the high-mass regime of contemporary star formation. \textcolor{black}{ To confirm this result, we have performed preliminary simulations varying the initial rotation curves of the pre-stellar core. } In the subsequent studies, numerical simulations with a smaller sink cell are needed to determine more in detail the final fate of the accreted clumps. However, we expect that the protostellar accretion history remains quantitatively similar in models with sink radii varied by a factor of two, as was earlier shown for low-mass star formation~\citep[see][and references therein]{vorobyov_apj_805_2015}. \textcolor{black}{We obtain} the protostellar accretion history which is highly time-variable and shows sudden accretion spikes, as was found in several previous models of massive-star-forming pre-stellar cores and interpreted as caused by azimuthal asymmetries in the accretion flow. The higher spatial resolution of our model reveals that, in addition to variable accretion indeed caused by the asymmetric character of its disc, the growing massive protostar can accrete material of gaseous clumps formed in spiral arms owing to disc gravitational fragmentation, which rapidly migrate towards the protostar and induce luminous protostellar outbursts. A similar rapid migration of dense clumps is present in gravitationally unstable discs around solar-mass stars, in primordial discs around the first stars and when high-mass planets form~\citep{2011MNRAS.416.1971B,vorobyov_aa_552_2013}. Our work indicates that this also applies to the high-mass regime of star formation, which implies a change in the paradigm which, to the best of our knowledge, considered episodic accretion-induced protostellar outbursts as inherent to low-mass and primordial star formation only. Our study shows that it concerns star formation in general, for a wide range of the physical properties such as the initial mass, $\beta$-ratio, angular momentum distribution or chemical composition of the parent environment in which stars form. It supports the consideration of star formation as a process ruled by a common set of mechanisms leading to circum-protostellar structures similarly organized, but scaled-up with respect to each other as a function of the initial properties of their parental pre-stellar cores, as observationally suggested~\citep{shepherd_apj_472_1996, fuente_aa_366_2001,testi_2003,keto_mnras_406_2010,johnston_apj_813_2015}. Finally, we propose to consider flares from high-mass protostellar objects as a possible tracer of the fragmentation of their accretion discs. This may apply to the young star S255IR-NIRS3 that has recently been associated to a 6.7 GHz methanol maser outburst~\citep{fujisawa_atel_2015,stecklum_ATel_2016}, but also to the other regions of high-mass star formation from which originated similar flares~\citep{menten_apj_380_1991} and which are showing evidences of accretion flow associated to massive protostars, see e.g. \textcolor{black}{in} W3(OH)~\citep{hirsch_apj_757_2012}, W51~\citep{keto_apj_678_2008,zapata_apj_698_2009} and W75~\citep{Carrasco_sci_348_2015}. | 16 | 9 | 1609.03402 |
1609 | 1609.04014_arXiv.txt | We present a new procedure for the internal (night-to-night) calibration of time series spectra, with specific applications to optical AGN reverberation mapping data. The traditional calibration technique assumes that the narrow \oiii\ emission line profile is constant in time; given a reference \oiii\ line profile, nightly spectra are aligned by fitting for a wavelength shift, a flux rescaling factor, and a change in the spectroscopic resolution. We propose the following modifications to this procedure: 1) we stipulate a constant spectral resolution for the final calibrated spectra, 2) we employ a more flexible model for changes in the spectral resolution, and 3) we use a Bayesian modeling framework to assess uncertainties in the calibration. In a test case using data for MCG+08-11-011, these modifications result in a calibration precision of $\sim\! 1$ millimagnitude, which is approximately a factor of five improvement over the traditional technique. At this level, other systematic issues (e.g., the nightly sensitivity functions and Fe{\sc ii} contamination) limit the final precision of the observed light curves. We implement this procedure as a {\tt python} package ({\tt mapspec}), which we make available to the community. | Reverberation mapping \citep[RM,][]{Blandford1982, Peterson1993, Peterson2014} is a very successful way of exploring the spatially unresolved structures in active galactic nuclei (AGN). The conspicuous broad emission lines observed in Seyfert 1 and quasar spectra respond to continuum variations on weekly to monthly time scales. Measurements of the time delay between the continuum signal and the emission line ``echoes'' establish the characteristic size of the line-emitting gas. This technique has become a primary means of estimating the masses of super-massive black holes that are associated with AGN activity \citep{Peterson2004, Bentz2015}. On shorter or longer time scales (less than a few days or greater than a month), lags between the UV, optical, and IR continua provide a means of applying RM to the accretion disk or the ``dusty torus'' (e.g., \citealt{Kishimoto2007, Shappee2014, Vazquez2015, Edelson2015, Fausnaugh2016}). On even longer times scales (several years to decades), narrow emission line reverberations can probe structures up to several tens of parsecs across \citep{Peterson2013}. Crucial to RM measurements is a precise estimate of the intrinsic variability of the AGN. Such estimates require a treatment of extrinsic sources of variability, such as those created by differences in observing conditions from night to night. Studies that fail to do this will attribute extrinsic variability to the intrinsic AGN emission. \citet{Barth2016} analyze an example of such a problem in detail. The usual approach is to model and remove these extrinsic variations by assuming that some component of the AGN spectrum is constant over the full time series. The narrow \oiii\ emission line serves as a practical choice, since it originates in an extended region of the AGN (tens to hundreds of light years across) and should be constant over the course of a typical RM campaign (a few months). It is also relatively uncontaminated with other spectral features, although blending with variable Fe{\sc ii} emission and the red wing of H$\beta$ can sometimes be problematic. The traditional implementation of the rescaling model is that of \citet[hereinafter GW92]{vanGroningen1992}. The GW92 model uses an empirical template to correct a series of observations for differences in wavelength solution, attenuation, and spectral resolution, and routinely reaches night-to-night precisions of 3--5\%. As RM data have improved (e.g., \citealt{Denney2010, Grier2012, Du2016}), it has been possible to reach precisions closer to 1--3\%, and sometimes even better (0.5--0.7\%, \citealt{Barth2015}). Over the last 25 years, only minor modifications have been applied to the original GW92 approach. For example, \citet{Barth2015} updated the GW92 optimization procedure from a grid-search to a down-hill simplex algorithm. Occasionally, studies bypass the rescaling procedure all together; \citet{Kaspi2000} and \citet{Du2014} corrected all extrinsic variations using simultaneous observations of comparison stars. Another approach is to forgo the empirical template and model the narrow line emission with parametric functions. This is the approach adopted by the Sloan Digital Sky Survey Reverberation Mapping project \citep{Shen2015,Shen2016} using the {\tt PrepSpec} software developed by Keith Horne. \citet{Hu2016} recently employed a similar modeling technique to improve the calibration of RM data taken in 2008 of MCG-6-30-15 from 2\% to 0.5\%. Considering the gains in computing resources over the last two decades and the rise of alternative model-fitting techniques, we decided to investigate more substantial modifications to the GW92 procedure. In \S2 we review the main elements of the GW92 rescaling model and propose three improvements. We then discuss a new model and fitting procedure to implement these modifications, and we make our implementation available to the community as a {\tt python} package called {\tt mapspec} ({\bf M}CMC {\bf A}lgorithm for {\bf P}arameters of {\bf Spec}tra).\footnote{\url{https://github.com/mmfausnaugh/mapspec}} In \S3, we assess our method by applying it to new RM data for MCG+08-11-011 (UCG 3374) that has been presented more completely elsewhere (\citealt{Fausnaugh2017b}). We find that the precision of the night-to-night calibration increases by roughly a factor of five using our new approach, and the final light-curve uncertainties are dominated by intrinsic systematic effects that require more complicated methods to address. In \S4, we summarize these results, and we include a brief appendix that discusses the influence of correlated errors on our results. | We have developed a new procedure for night-to-night calibration of time-series spectra. The main innovations of our method are 1) a common and consistently defined resolution, 2) a more flexible smoothing kernel, and 3) a Bayesian formalism for fitting the line profiles and estimating parameter uncertainties. We have shown that the method improves the alignment of the [O{\sc iii}] line profiles, decreasing spurious variability in the rms spectrum and integrated \oiii\ line light curve. These improvements help isolate the variable broad emission-line profiles and reduce night-to-night calibration uncertainties. Other systematic effects limit the final precision of the light curves, such as the calculation of nightly sensitivity functions and contamination from additional spectral components such as Fe{\sc ii} emission. MMF thanks Richard Pogge for the suggestion to improve the GW92 method, Chris Kochanek for useful discussions about statistics, and Brad Peterson for general guidance. MMF also thanks Kelly Denney, Gisella de Rosa, Catherine Grier, Kevin Croxall, Richard Pogge, and Brad Peterson for tips on reducing and analyzing spectroscopic data. MMF acknowledges financial support from NSF grant AST-1008882 and a Presidential Fellowship awarded by The Ohio State University Graduate School. \facility{McGraw-Hill} \software{ Astropy \citep{astropy}, Matplotlib \citep{matplotlib}, Numpy \citep{numpy}, Scipy \citep{scipy} } \begin{figure} \includegraphics[width=0.5\textwidth]{lc_corr} \caption{Differences between the continuum and H$\beta$ light curves from different calibration procedures (red points minus black points in Figure \ref{fig:lc}) as a function of \oiii\ line flux. \oiii\ line fluxes from the GW92 procedure are shown with solid points, \oiii\ line fluxes from {\tt mapspec} are shown with open points. The Pearson $r$ correlation coefficients are shown in the legends. These correlations show that errors in the GW92 \oiii\ calibration introduce noise in the continuum and line light curves.\label{fig:lc_corr}} \end{figure} | 16 | 9 | 1609.04014 |
1609 | 1609.01294_arXiv.txt | The double red clump (RC) observed in the Milky Way bulge is widely interpreted as evidence for an X-shaped structure. We have recently suggested, however, an alternative interpretation based on the multiple population phenomenon, where the bright RC is from helium enhanced second-generation stars (G2), while the faint RC is representing first-generation stars (G1) with normal helium abundance. Here our RC models are constructed in a large parameter space to see the effects of metallicity, age, and helium abundance on the double RC feature. Our models show that the luminosity of RC stars is mainly affected by helium abundance, while the RC color is primarily affected by metallicity. The effect of age is relatively small, unless it is older than 12 Gyr or much younger than 6 Gyr. The observed double RC feature can therefore be reproduced in a relatively large parameter space, once $\Delta$Y between G2 and G1 is assumed to be greater than $\sim$0.10. We further show that the longitude dependence of the double RC feature at $b \approx -8\degr$, which was pointed out by \citet{gon15} as a potential problem of our model, is well explained in our scenario by a classical bulge embedded in a tilted bar. | Some years ago, the presence of two red clumps (RCs) was discovered in the high-latitude ($|b| \gtrsim 6\degr$) fields of the Milky Way bulge \citep{mcw10,nat10}. The origin of this double RC, however, is currently under intense debate. It was initially interpreted as evidence for an X-shaped structure that originated from the disk and bar instabilities \citep{mcw10,sai11,li12,weg13}. In this picture, the two RCs separated by $\sim$0.5 mag is due to the difference in distance between the two arms of the X-shaped structure. We have recently suggested \citep[hereafter \citetalias{lee15}]{lee15}, however, a drastically different interpretation based on the multiple stellar population phenomenon, which is widely observed in globular clusters (GCs) including metal-rich bulge GCs Terzan~5, NGC~6388, and NGC~6441 \citep{lee99,cal07,yoo08,car09b,fer09,gra12}. In this model, the brighter RC (bRC) is from helium enhanced second-generation stars (G2), which are intrinsically brighter, while the faint RC (fRC) is originated from the first-generation stars (G1) with normal helium abundance.\footnotemark[1] \footnotetext[1]{ As discussed in Paper I, we are not arguing against the bar dominated bulge in the low latitude ($|b| \lesssim 6 \degr$) fields. The question is whether this pseudo bulge characteristic is extended even to the high latitude region as suggested by the X-shaped structure interpretation of the double RC phenomenon. In our model, low-latitude fields are dominated by the most metal-rich bar population, while relatively metal-poor classical bulge (CB) population becomes more and more important at higher latitudes. While the low latitude fields show cylindrical rotation, stars in high latitude fields rotate more slowly \citep{zoc14}. Furthermore, \citet{sah12} showed that an initially non-rotating CB could absorb a significant fraction of the angular momentum from the bar within a few Gyr, which suggests that the cylindrical rotation is not necessarily an evidence against the coexistence of CB. \citet{zoc14} also pointed out that many early-type galaxies and the bulges originated from clumps \citep{elm08} are fast rotators. Note also that a three-dimensional density map of \citet{weg13} is based on the X-shaped structure interpretation of the double RC. Therefore, whether the high latitude field is also dominated by the bar population or not depends largely on the interpretation of the double RC. } Soon after our suggestion, two counterarguments were presented. Firstly, the longitude dependence of the double RC feature at $b \approx -8\degr$ was pointed out by \citet{gon15} as a potential problem of our model. Secondly, by employing the WISE mid-IR image, \citet{nes16} report a direct detection of a faint X-shaped structure in the Milky Way bulge. However, each of them can be rebutted. In a composite bulge, where a classical bulge is embedded in a tilted bar \citep[e.g.,][]{bab10,hil11,sah12,sah16,roj14,zoc14,erw15,sah15}, we have already shown in \citetalias{lee15} that our models can reproduce the longitude dependence well, which is also discussed in Section~3 of this paper with more realistic treatments. The second argument on the presence of a faint X-shaped structure is highly questioned as well, because when an ellipsoid is subtracted from a boxy structure, as has been done by \citet{nes16}, an artificial X-shaped structure always remains (D. Han \& Y.-W. Lee 2017, in preparation; see also \citealt{lop16}). Furthermore, if the X-shaped structure is solely responsible for the observed double RC, $\sim$45$\%$ of stars in the bulge are predicted to be on the orbits that make this structure \citep{por15}. However, even if real, the stellar density in the claimed X-shaped structure of \citet{nes16} appears to be way too low to be observed as a strong double RC at $l=0\degr$. A crucial evidence against the X-shaped bulge was also presented by \citet{lop16} from the analysis of the main-sequence (MS) stars in the bulge fields. Without critical distance information, therefore, the origin of the double RC phenomenon is still an open question, and the multiple population scenario merits more detailed investigations. The purpose of this paper is to extend the parameter space in our multiple population models to see the effects of metallicity, age, and helium abundance on the double RC feature. We have also used these models to illustrate how the point raised by \citet{gon15} can be explained in our scenario. \advance\textheight +24pt | In the multiple population paradigm, we have shown that the magnitude difference between the two RCs is mostly affected by the difference in helium abundance between G2 and G1, and the observed double RC feature can be reproduced if $\Delta Y_{\rm G2-G1} \approx 0.10-0.13$ at around solar metallicity. As illustrated in Figure~\ref{fig3}, this is obtained if the helium abundance for G2 increases with metallicity following a helium enrichment parameter $\Delta Y/\Delta Z = 6.0$, while G1 follows a standard value $\Delta Y/\Delta Z = 2.0$. Chemical evolution models (J. Kim \& Y.-W. Lee 2017, in preparation) confirm that this trend for G2 is predicted if the gas that formed G2 was locally enriched within the protogalactic subsystems by the winds of massive stars and the winds and ejecta from low and intermediate mass asymptotic-giant-branch stars. Disruption of these ``$building~blocks$" in a hierarchical merging paradigm would have provided stars (G1 and G2) to form a classical bulge component in the early stage of the Milky Way formation. One crucial condition required to obtain this result is to assume that most of the supernova ejecta could escape from these relatively less massive systems without expelling the pre-enriched gas inside \citep[see, e.g.,][]{rom10,ten15}. Because of the strong metallicity dependence of helium yield from the winds of massive stars \citep{mae92,mey08}, helium abundance of G2 in these models would then increase rapidly with metallicity. In our models, the helium abundance of G2, following $\Delta Y/\Delta Z = 6.0$, would be relatively low $\rm (Y = 0.24 - 0.25)$ at metal-poor regime (i.e., halo GCs), while it is very high $\rm (Y \approx 0.40)$ at solar metallicity where the double RC is observed (see Fig. 11 of \citealt{lee16}). Therefore, G2 in our models would correspond to ``$Na-intermediate$" population defined by \citet{car09a}. Very Na-rich and O-poor stars (``$Extreme$" population) are defined as G3 (3rd and later generations) in our models, which, if any, are more likely to be trapped in bulge GCs as in the metal-poor halo GCs \citep{der08}, and thus we do not expect many of them in the bulge fields. Nevertheless, at around solar metallicity, some significant spread in [Na/Fe] $(\Delta \rm [Na/Fe] \approx 0.4 - 0.5 ~dex)$ is observed in the bulge (see Figs. 15 \& 16 of \citealt{joh14}; Fig. 7 of \citealt{lec07}), which is clearly larger than that of the disk $(\Delta \rm [Na/Fe] \approx 0.1 ~dex)$ and halo $(\Delta \rm [Na/Fe] \approx 0.25 ~dex)$ field populations (see Fig. 11 of \citealt{vil17}), suggesting that the bulge contains more stars from G2 and later generations. \citet{lec07} even reports some indication of Na-O anticorrelation, although this has not been confirmed by \citet{joh14}. In the relatively metal-poor regime ([Fe/H] $\approx -1.1$) of the Milky Way bulge, \citet{pie15} discovered two sequences of RR Lyrae stars on the period-amplitude diagram. Recently, \citet{lee16} suggested a common origin for this phenomenon and the double RC observed in the metal-rich regime of the bulge. They have shown that the period-shift between these two populations of RR Lyrae stars is due to a small difference in helium abundance ($\Delta$Y $\approx 0.01$) between the first- and second-generation stars. As discussed above, this is expected because $\Delta$Y between G2 and G1 would be an order of magnitude smaller amount at this low metallicity regime compared to the metal-rich bulge where the double RC is observed. Therefore, it appears quite possible that the two populations of RR Lyrae stars and the double RC observed in the Milky Way bulge might be different manifestations of the same multiple population phenomenon in the metal-poor and metal-rich regimes respectively. It is important to note that the double RC originated from multiple population phenomenon is also observed in a metal-rich bulge GC Terzan~5 \citep{fer09}. In Figure~\ref{fig8}, we estimate a helium difference of $\Delta$Y $\approx 0.07$ between the two RCs in Terzan~5, which is roughly consistent with the value expected from a $\Delta Y/\Delta Z = 6.0$ trend at the metallicity of this GC ([Fe/H] = $-$0.2; \citealt{har96}). At lower metallicity, $\Delta$Y between G2 and G1 would be smaller and consequently the magnitude separation between the two RCs would be also narrower, or the two RCs could be merged into one with a vertically extended feature (see Figure~\ref{fig3}). Interestingly, the RC part of the HB in NGC~6441, another bulge GC with [Fe/H] = $-$0.5 \citep{pio02,har96}, shows just this feature, and \citet[][see their Fig. 6]{cal07} indeed estimate a smaller $\Delta$Y between G2 and G1 ($\Delta$Y $\approx 0.05$) from the RC luminosity function. As stressed in \citetalias{lee15}, Gaia trigonometric parallax distances can soon provide a crucial test as to the origin of the double RC observed in the Milky Way bulge. This will in turn reveal whether a non-negligible fraction of the classical bulge population is embedded in a bar structure of the Milky Way or not. Since the stellar populations in the classical bulge component of the Milky Way is considered as the nearest example of those in elliptical galaxies, this will also severely impact our understanding of stellar populations and formation of early-type galaxies. | 16 | 9 | 1609.01294 |
1609 | 1609.01588_arXiv.txt | We investigate primordial black hole formation in the matter-dominated phase of the Universe, where nonspherical effects in gravitational collapse play a crucial role. This is in contrast to the black hole formation in a radiation-dominated era. We apply the Zel'dovich approximation, Thorne's hoop conjecture, and Doroshkevich's probability distribution and subsequently derive the production probability $\beta_{0}$ of primordial black holes. The numerical result obtained is applicable even if the density fluctuation $\sigma$ at horizon entry is of the order of unity. For $\sigma\ll 1$, we find a semi-analytic formula $\beta_{0}\simeq 0.05556 \sigma^{5}$, which is comparable with the Khlopov-Polnarev formula. We find that the production probability in the matter-dominated era is much larger than that in the radiation-dominated era for $\sigma\alt 0.05$, while they are comparable with each other for $\sigma\agt 0.05$. We also discuss how $\sigma$ can be written in terms of primordial curvature perturbations. | Primordial black holes are becoming a very important area of study at the intersection of cosmology, astrophysics, high-energy physics, and gravitation. See \citet{Carr:2003bj} and \citet{Khlopov:2008qy} for recent reviews. The abundance of primordial black holes is severely constrained observationally \citep{Carr:1975qj,Carr:2009jm,Carr:2016hva} and this fact has rich implications to the early Universe and other relevant fields of physics. Furthermore, recently, LIGO has reported gravitational wave observation GW150914 \citep{Abbott:2016blz} and it has been argued \citep{Sasaki:2016jop} that a binary system of primordial black holes can be a source of gravitational waves of this event. The theoretical prediction of the abundance of primordial black holes based on the physical theory of black hole formation is a key issue from the theoretical side. Khlopov and Polnarev \citep{Khlopov:1980mg,Polnarev:1982} pioneered primordial black hole formation in the matter-dominated era of the Universe. They argued that if stable superheavy particles predicted in the grand unified theories dominate the Universe, the pressure of the matter field can be effectively neglected and the production of primordial black holes is significantly enhanced. More recently, \citet{Alabidi:2009bk} and \citet{Alabidi:2012ex,Alabidi:2013wtp} showed that in the so-called hill-top type inflation scenario, density perturbations of large amplitude can arise on small scales and lead to an enhanced formation of primordial black holes in an effectively matter-dominated phase of the Universe before the reheating phase. The formation of primordial black holes had been conventionally studied in the radiation-dominated era until recently. In this case, the threshold $\tilde{\delta}_{c}$ of the amplitude of the density perturbation in the comoving slicing at horizon entry is determined by the Jeans criterion. The production probability $\beta_{0}$ of primordial black holes is given by $\beta_{0}\sim \sqrt{2/\pi}(\sigma/\tilde{\delta}_{c}) \exp(-\tilde{\delta}_{c}^{2}/2\sigma^{2})$, where $\sigma$ is the standard deviation of the density perturbations at the relevant mass scale at horizon entry. The results of numerical relativity simulations in spherical symmetry give the threshold $\tilde{\delta}_{c}\simeq 0.42-0.50$~\citep{Shibata:1999zs,Musco:2004ak,Polnarev:2006aa,Musco:2012au,Harada:2015yda}. Since the threshold value is of the order of unity, gravitational instability leads to the formation of a black hole shortly after the horizon entry. For the equation of state $p=w\rho c^{2}$, the analytic formula for the threshold gives $\tilde{\delta}_{c}\simeq [3(1+w)/(5+3w)]\sin^{2}[\pi\sqrt{w}/(1+3w)]$~\citep{Harada:2013epa} showing a good agreement with the numerical results for $0.01\le w\le 0.6$~\citep{Musco:2012au}. In the limit of $w\to 0$, we have $\tilde{\delta}_{c}\to 0$, i.e., the region which is only slightly overdense would necessarily collapse to a black hole. This argument clearly overestimates $\beta_{0}$ because it neglects nonspherical effects. For a density perturbation of small amplitude to collapse to a black hole, it must shrink to a radius much smaller than that at the maximum expansion so that a deviation from spherical symmetry can significantly grow. This instability generally leads to a ``pancake'' collapse \citep{Lin:1965,Zeldovich:1969sb}. \citet{Khlopov:1980mg} and \citet{Polnarev:1982} discussed that a nonspherical effect significantly suppresses primordial black hole formation and obtained a compact analytic formula for $\beta_{0}$ under the assumption of the small density perturbations. Nonspherical effects on primordial black holes have also recently been discussed by \citet{Harada:2015ewt} and \citet{Kuhnel:2016exn}. The purpose of the current paper is to estimate $\beta_{0}$ even for a large fluctuation of perturbations and a large deviation from spherical symmetry based on a physical argument and also to reproduce the formula by Khlopov and Polnarev in some sense by adopting the approximation of small fluctuation. We apply the Zel'dovich approximation~\citep{Zeldovich:1969sb}, which is a well-established analytic approximation to describe the nonlinear evolution of density perturbations. See \citet{White:2014gfa} and references therein for its validity, application, and limitation. See also \citet{Russ:1995eu} for its general relativistic generalization. We adopt the hoop conjecture proposed by \citet{Thorne:1972ji} for the formation of a black hole horizon, which has not yet been proved for general situations but shown to hold even for highly distorted horizons~\citep{Yoshino:2007yb}. See also \citet{Malec:2015oza} for a recent proof for a special case. However, see~\citet{East:2016anr} for its possible violation in the presence of a negative energy density. As for the probability distribution of nonspherical perturbations, we adopt Doroshkevich's one~\citep{Doroshkevich:1970}, which was derived under a least number of natural assumptions. This paper is organized as follows. In Sec. II, we apply the Zel'dovich approximation to the nonlinear evolution of the density perturbations and obtain the criterion of the black hole formation based on Thorne's hoop conjecture. In Sec. III, we introduce the probability distribution for nonspherical perturbations by Doroshkevich, derive an integral expression for the production probability of primordial black holes without assuming the small fluctuation approximation. Moreover, we obtain a semi-analytic formula under the small fluctuation approximation. In Sec. IV we discuss our results followed by conclusions in Sec. V. We keep both the gravitational constant $G$ and the speed of light $c$ throughout this paper. | We have studied primordial black hole formation in the matter-dominated era of the Universe. In this epoch, in the absence of relativistic pressure, nonspherical effects play a crucial role and gravitational collapse does not necessarily lead to black hole formation. We have applied the Zel'dovich approximation to the nonlinear evolution of density perturbations in an expanding universe, Thorne's hoop conjecture for the formation of a black hole horizon, and Doroshkevich's probability distribution for the eigenvalues of the deformation tensor. We have succeeded in obtaining an integral expression for the probability of black hole formation, which allows for a large fluctuation of density perturbations and a large deviation from spherical symmetry. We have plotted the result of the numerical integration for the production probability as a function of the density fluctuation. Moreover, we have obtained a compact semi-analytic formula for a small fluctuation, which is comparable with Khlopov and Polnarev's formula with some nontrivial identification of parameters. We have also analytically obtained lower and upper bounds for a small fluctuation. This implies that the current analysis has essentially refined Khlopov and Polnarev's heuristic argument and generalized it to a large deviation from spherical symmetry and a large fluctuation of density perturbations. Both the integral expression and semi-analytic formula are applicable for the estimate of abundance of primordial black holes in the matter-dominated era of the Universe, such as the first-order phase transition, the ending phase of inflation before reheating and the late-time matter-dominated era following the matter-radiation equality. We have compared the new estimate of the production rate with that in the radiation-dominated phase of the Universe and found that the matter dominance strongly enhances primordial black hole formation for small density fluctuation, while it does not for larger density fluctuation. We have also presented a formula which gives the initial density fluctuation in terms of primordial curvature perturbation. | 16 | 9 | 1609.01588 |
1609 | 1609.03896_arXiv.txt | We map the \hi\, distribution of galaxies in a $\sim 1.5^\circ \times 2.5^\circ$ region located at the virial radius south of the Virgo cluster using the KAT$-$7 and the WSRT interferometers. Because of the different beam sizes of the two telescopes, a similar column density sensitivity of $\nhi\sim 1\e{18}\,\acm$ was reached with the two observations over 16.5 \kms. We pioneer a new approach to combine the observations and take advantage of their sensitivity to both the large and small scale structures. Out to an unprecedented extent, we detect an \HI\, tail of $\sim 60$ kpc being stripped off NGC 4424, a peculiar spiral galaxy. The properties of the galaxy, together with the shape of the tail, suggest that NGC 4424 is a post-merger galaxy undergoing a ram pressure stripping as it falls towards the centre of the Virgo Cluster. We detect a total of 14 galaxies and 3 \hi\, clouds lacking optical counterparts. One of the clouds is a new detection with an \hi\, mass of $7\e{7}\, \Mo$ and a strong \hi\, profile with $W_{50} = 73$ \kms. We find that 10 out of the 14 galaxies present \hi\, deficiencies not higher than those of the cluster's late spirals, suggesting that the environmental effects are not more pronounced in the region than elsewhere in the cluster. | When a galaxy resides in a dense region such as a cluster or a group, it undergoes different mechanisms that determine its morphology \citep[e.g.][]{Dressler1980} and gas properties \citep{Cayatte1990}. Galaxies evolving in dense environments tend to be \HI\, deficient with respect to their morphological counterparts evolving in less dense regions \citep{Haynes1984}. More specifically in clusters of galaxies, the small scale structure interstellar medium (ISM) of spiral galaxies interacts with the large scale structure intracluster medium (ICM) through hydrodynamical processes that then drive the evolution of those galaxies in clusters. Perhaps the most important mechanism at work is the ram pressure (RP) stripping \citep[e.g.][]{Gunn1972,Vollmer2001}. It occurs when a galaxy moves through the ICM of a galaxy cluster and the external force felt by the ISM is greater than the gravitational restoring force from the galaxy disk. It is known to be partly responsible for the \HI\, deficiency \citep{Bothun1982,Giovanelli1985,Vollmer2001} and star formation quenching \citep[e.g.][]{Balogh2000}. Typical examples of galaxies in the Virgo cluster undergoing RP stripping include NGC 4388 \citep{Oosterloo2005}, NGC 4522 \citep{Kenney2004a,Vollmer2004}, NGC 4402 \citep{Crowl2005} and NGC 4438 \citep{Chemin2005}. Although this effect is strongest in the central regions of clusters, cosmological simulations reveal that it remains an important mechanism of gas stripping of galaxies out to the virial radius of clusters \citep{Tonnesen2007}. While the optical characteristics of galaxies in dense environments seem well understood, we are still far from a complete picture of galaxy evolution. Observations of the neutral atomic gas in dense environments are key to our understanding of the growth and depletion of gas disks, as well as star formation quenching in galaxies. Further, they provide tests for numerical simulations and constraints for modelling galaxy evolution \citep[e.g.][]{Dave2013}. In particular the neutral gas provides an opportunity to map the outer regions of galaxies and their surrounding environment, allowing us to directly probe their interactions with the IGM and with their neighbours. To date, about 1300 galaxies have been identified, based on their morphology and radial velocities, as true members of the Virgo Cluster \citep[e.g.][]{Sandage1985,Binggeli1987}. Located at 16.8 Mpc \citep[distance of M87,][]{Neill2014}, the recession velocity of the cluster is $\sim1050$ \kms, and its velocity dispersion is $\sim700$ \kms\, \citep{Binggeli1993}. Detailed X-ray observations of the hot cluster gas \citep{Bohringer1994} revealed several substructures, suggesting that the cluster is not virialised, as seen in other clusters \citep[see e.g. for the Coma \& Antlia clusters,][]{Briel1992, Hess2015a}. The Virgo Cluster, instead, is still growing. Subclusters around the ellipticals M86 and M49 \citep[whose systemic velocities are respectively -181 and 950 \kms,][]{Kim2014} are merging with the main cluster around the central elliptical M87. Several \hi\, imaging surveys of the cluster revealed that the \hi\, disks of its central late-type galaxies are truncated to well within the optical disks, suggesting that ICM - ISM interactions play an important role in driving the evolution of galaxies in the inner region of the cluster \citep{Warmels1988a, Cayatte1990, Chung2009, Boselli2014}. Wide-area \hi\, surveys like HIPASS \citep[\hi\, Parkes All-Sky Survey,][]{Barnes2001}, ALFALFA \citep[Arecibo Legacy Fast ALFA,][]{Giovanelli2005} and AGES \citep[Arecibo Galaxy Environment Survey,][]{Auld2006} done with single-dish telescopes have helped detect many low \hi\, mass galaxies such as early-type and late-type dwarf galaxies, but also starless ``dark" galaxies and several \hi\, clouds \citep[e.g.,][]{Alighieri2007, Kent2007}. In particular, ALFALFA observations allowed the detection of complex structures associated with Virgo galaxies \citep[e.g.][]{Koopmann2008}, showing probable signs of interactions in the cluster. We use the KAT-7 and the WSRT to study galaxies located in an X-ray filament to the South-West of the cluster connecting the main cluster with the substructure associated with M49. We observe a $\sim 1.5^\circ \times 2.5^\circ$ region in the M49 subcluster. It is located south of the Virgo Cluster, $\sim3\dg$ away from the elliptical M87, and contains the elliptical M49 (see Fig. \ref{fig:virgo-rosat}). The field also contains the one-sided \hi\, tail galaxy, NGC 4424, previously observed using the VLA \citep{Chung2007,Chung2009}. Taking advantage of the short baselines of the KAT-7 telescope sensitive to extended structures and the high spatial resolution of the WSRT telescope, we map late-type galaxies in the region down to low column densities. Given the large difference in the resolutions of the two arrays, we develop a new technique to combine the data from the two telescopes. We begin with a description of the observations with the two telescopes, as well as the technique adopted for the data combination in section \ref{sec:ODR}. The results are presented in section \ref{sec:res} where the \hi\, map of the region as well as the \hi\, parameters of the detections are given. In section \ref{sec:dis} we discuss the results in light of the cluster environment effects, and give a summary in section \ref{sec:summary}. The contours and \hi\, profiles of all the detections are presented in the Appendix. \begin{figure} \hspace{-50pt} \includegraphics[width=1.5\columnwidth]{rosat-vir.eps} \caption{X-ray map of the Virgo Cluster \citep[$0.5-2.0$ keV, {\it ROSAT};][]{Bohringer1994}. The circle shows the virial radius of the cluster \citep[$\sim3.7\dg$ or 1.08 Mpc,][]{Arnaud2005, Urban2011a} around M87, and the box is the region observed in the present work. The labelled plus signs show the major ellipticals of the cluster, and the cross indicates the position of the \HI-tailed galaxy NGC 4424.}\label{fig:virgo-rosat} \end{figure} | \label{sec:summary} In this work we used the KAT-7 and WSRT telescopes to observe a region of $\sim 2.5\dg\times1.5\dg$ located in the Virgo Cluster, $\sim3\dg$ away from the centre of the cluster and containing the elliptical M49. The distribution of the hot X-ray gas in the field suggests a filamentary structure joining the M49 subcluster to the Virgo cluster. With a total of $\sim 78$ and 48 hours of observations respectively with the KAT-7 and WSRT telescopes, we reached similar column densities sensitivities with the two telescopes. To detect both the low and high resolution features and benefit from the advantages of both telescopes, we combined the two observations. However, because of the large difference in the point source flux sensitivities in the two datasets, the combination could not be done in the Fourier plane, as is widely practised. We have pioneered a new approach, which consists of combining the data in the image plane after converting the cubes from units of flux density to units of column density. This provided us a dataset highlighting features of both the large and small scale structures, and in which we reach an improved $1\sigma$ sensitivity of $\sim8\e{17}\,\rm cm^{-2}$ over 16.5 \kms. A total of 14 galaxies and 3 \hi\, clouds with \hi\, masses $M_\HI > 10^7\,\Mo$ were detected, including the one-sided \hi-tailed spiral NGC 4424. 10 out of the 14 galaxies were found to be \hi-deficient. Compared to both a sample of other Virgo spirals and field galaxies, most of the detected galaxies are found to be no more \hi-deficient than typical Virgo galaxies, suggesting that gas stripping processes in the region are not more pronounced than elsewhere in the cluster. In particular, NGC 4424 has an \hi-deficiency typical of the cluster galaxies and exhibits a tail observed to be 60 kpc, three times longer than previous observations with the VLA have revealed \citep{Chung2007}. The morphology of the tail, as well as the asymmetry and the \hi\, deficiency observed in other galaxies in the region suggest that RP is most likely the primary mechanism responsible for the tail. A high velocity collision was also found to be a possible cause of the tail, although the companion remains unidentified. | 16 | 9 | 1609.03896 |
1609 | 1609.02859_arXiv.txt | The origin of the very red optical and infrared colours of intermediate-age ($\sim$10--500~Myr) L-type dwarfs remains unknown. It has been suggested that low-gravity atmospheres containing large amounts of dust may account for the observed reddish nature. We explored an alternative scenario by simulating protoplanetary and debris discs around G\,196-3\,B, which is an L3 young brown dwarf with a mass of $\sim 15$~$M_{\rm Jup}$ and an age in the interval 20--300~Myr. The best-fit solution to G\,196-3\,B's photometric spectral energy distribution from optical wavelengths through 24~$\mu$m corresponds to the combination of an unreddened L3 atmosphere ($T_{\rm eff} \approx 1870$~K) and a warm ($\approx$~1280~K), narrow ($\approx$~{0.07--0.11}~R$_{\odot}$) debris disc located at very close distances ($\approx$~0.12--0.20~R$_{\odot}$) from the central brown dwarf. This putative, optically thick, dusty belt, whose presence is compatible with the relatively young system age, would have a mass $\ge 7\times 10^{-10}$~M$_{\oplus}$ comprised of sub-micron/micron characteristic dusty particles with temperatures close to the sublimation threshold of silicates. Considering the derived global properties of the belt and the disc-to-brown dwarf mass ratio, the dusty ring around G\,196-3\,B may resemble the rings of Neptune and Jupiter, except for its high temperature and thick vertical height ($\approx 6 \times 10^3$~km). Our inferred debris disc model is able to reproduce G\,196-3\,B's spectral energy distribution to a satisfactory level of achievement. | \label{introduction} To date, more than 1000 L-, T-, and the recently discovered Y-type dwarfs have been {identified over the past 15 years (e.g. \citealt{Kirk99, Kirk00, Kirk11, Kirk13, martin99, Burgasser99, cushing11, tinney12, beichman13, Pinfield14, masters12}). About 10~per~cent of the field L dwarfs show spectroscopic signatures of low-to-intermediate} gravity and youth (\citealt{mcgovern04,Kirk06, Cruz09}), usually accompanied by near- and mid-infrared colours redder than those of normal field sources of similar spectral classification (e.g. \citealt{Looper08,ZO10, Gizis12,Fah13,Liu13,Sch14,gauza15,gizis15}). Although novel synthetic spectra tend to explain these infrared flux excesses by the combining effects of low pressure conditions and thick dust clouds of the atmospheres (e.g. \citealt{barman11,marley12}), it is a fact that not all young and low gravity L dwarfs show markedly red indices, in particular at the very young ages ($\le$10 Myr, e.g. \citealt{martin01a,Lodieu08,pena15}), and not all very red L dwarfs display the full list of spectroscopic signposts indicative of low gravity (e.g. \citealt{marocco14,kellogg15}). In \cite{osorio14}, the authors derived ages in the interval $\approx$~10--500~Myr for a sample of field, highly reddened L dwarfs with clear spectroscopic evidence for low-to-intermediate gravity atmospheres. According to evolutionary models (e.g. \citealt{Chabrier00}), these dwarfs likely have substellar masses below the hydrogen burning-mass limit at 0.072~M$_{\odot}$ (for solar metallicity). Free-floating brown dwarfs in young star forming regions show the typical signatures associated with the presence of protoplanetary discs of gas and dust (strong and broad H$\alpha$ and other emission lines, marked infrared flux excesses), from which some objects are actually accreting material (e.g. \citealt{jayawardhana01,muzerolle03a}; see review by \citealt{luhman12}). Also, very young, isolated planetary-mass objects below the deuterium burning mass limit at 0.012~M$_\odot$ ($\approx 13$~$M_{\rm Jup}$) can host primordial discs (e.g. \citealt{luhman05,luhman08,osorio07}). The modelling of the observed spectral energy distributions suggests that the properties and grain growth of the circum(sub)stellar discs are quite similar to those related to T\,Tauri stars, scaled down to the smaller masses of the central objects (e.g. \citealt{Natta2001,Apai2008,Ricci2012,Ricci2013,Ricci2014}). \cite{luhman12b} concluded that primordial discs lifetimes are larger at lower stellar masses, and that a significant fraction of gas discs of low-mass objects survive for at least $\approx$~10--20~Myr (see also \citealt{Riaz09} and \citealt{ribas14}). After the gas is cleared out, dust accretes into planets and moons and/or remains as debris material circling the central object. According to the {\sl Herschel} observations conducted by \citet{riaz14}, the discs surrounding very young free-floating brown dwarfs appear to have transitioned from primordial to the debris phase by the age of $\sim$40--50~Myr. Therefore, debris discs are thought to occur around brown dwarfs and planetary-mass objects, although none has been unambiguously confirmed so far, partly because the dwarfs' low luminosity makes the thermal emission and scattered light from their discs more difficult to detect. Also, brown dwarf and planetary-mass companions to stars are capable of sustaining their own discs (see \citealt[and references therein]{Wu15}). \cite{mamajek12} and \cite{werkhoven14} suggested that the 16-Myr old star 1SWASP\,J140747.93$-$394542.6 has an unresolved substellar companion with a large ring system comprised of dusty particles, which may be responsible for the complex series of eclipses seen in the stellar light curve. On the contrary, the study of the {\sl Kepler} light curves of 21 hot-Jupiter planets, most likely with ages of Gyr, revealed no evidence for ringed exoplanets \citep{Heising15}. Here, we provide an alternative interpretation for the very red near- and mid-infrared colours of the young, early-L dwarf G\,196-3\,B \citep{Rebolo98}, which is conceptually different to the proposed low gravity, enshrouded atmosphere. G\,196-3\,B is separated by $\approx$~390~au from the primary, active M2.5 star G\,196-3\,A. As discussed by \cite{Rebolo98} and \cite{ZO10,osorio14}, the system has an age in the interval 20--300~Myr, with a probable value around 50--90~Myr. The substellar companion, which has a mass of $15^{+30}_{-4}$~$M_{\rm Jup}$ near the deuterium-burning mass limit, shows redder colours at all wavelengths from 1.6 up to 24 $\mu$m than expected for its spectral type determined at L1--L3 from optical and near-infrared spectra \citep{martin99,kirk01,Cruz09,allers13}. The working hypothesis is that, given the relatively young age, G\,196--3\,B's flux excesses may mostly originate in a surrounding disc. We fit the observed photometric energy distribution from the optical through 24~$\mu$m using a debris disc model. Our objectives are to explore whether physically possible fits can be obtained and to discuss a likely picture that accounts for the reddish properties of G\,196-3\,B. With plain assumptions on disc geometry and disc plane orientation, we found that a ring (debris) model reproduces many of the observed infrared fluxes. The paper is organised as follows: In Section~\ref{model}, we describe the modelling procedure for the disc. Results and their implications for the properties of G\,196-3\,B are presented in Section~\ref{results}. Finally, our conclusions and final remarks appear in Section~\ref{conclusions}. | \label{conclusions} We investigated the prospect of the presence of a debris disc surrounding G\,196-3\,B, one $\sim 15$~$M_{\rm Jup}$, L3 young brown dwarf with near- and mid-infrared colour excesses, by fitting its observed spectral energy distribution from the visible through 24~$\mu$m. The computations showed that the debris disc model is capable of delivering physically possible solutions. The best-fit solution yields a warm ($\approx$~1280~K), quite narrow, optically thick debris ring (width of $\approx$~0.07--0.11~R$_\odot$) located very close to the central brown dwarf (separation of $\approx$~0.12--0.20~R$_\odot$). The model also suggests a debris disc mass $\ge 7\times 10^{-10}$~M$_{\oplus}$ containing sub-micron/micron characteristic dusty particles with temperatures near the sublimation threshold of silicates, but below the sublimation temperature of carbon particles. Considering the derived location and size of the belt and the disc-to-brown dwarf mass ratio, the dusty ring around G\,196-3\,B resembles the rings of Neptune and Jupiter (except for the high temperature and likely thick vertical height of $\approx 6 \times 10^3$~km). With the data currently available, some parameters, like the surface density profile of the disc and the inclination angle of the system, cannot be properly constrained, and only warm and inner discs have been modelled in detail; to study the presence of outer, colder discs, data at wavelengths longer than 24~$\mu$m are required. The debris disc scenario provides a better reproduction of G\,196-3\,B's SED than the solar-metallicity, low-gravity BT-Settl model atmosphere corresponding to the effective temperature of 1800 K (typical of L3 dwarfs). The existence of debris discs surrounding intermediate-age, red L-type dwarfs may account for the colour flux excesses at near- and mid-infrared wavelengths, and may represent an alternative scenario to that of low-gravity, enshrouded atmospheres. The origin of this putative debris belt around G\,196-3\,B is unknown. It might result from the direct leftovers of the original disc made of gas and dust. At the time when the gas-to-dust ratio was of the order of 0.1--10 in the disc, the ``small" amount of gas might have organised the dusty particles into a narrow ring \citep{LyraKuchner2013}. Planets or proto-planets formed from the disc material sweep their orbits and may accumulate debris at certain locations within the planetary system (similarly to the Kuiper Belt in the Solar System), or produce a cut-off of the outer edge of the rings (e.g. \citealt{Thebault2012,Ertel12}). Alternatively, the hot dust component may arise in an asteroid belt undergoing collisional destruction or in massive collisions in ongoing terrestrial planet formation. In the latter picture, the high luminosities and temperatures of the debris material resulting from terrestrial planet formation may survive for around a few to several ten~Myr after the impacts \citep{jackson12}, with considerable levels of emission at $\sim$24~$\mu$m that might be readily seen above the intrinsic, faint photospheric flux of low-luminous and cool central objects. | 16 | 9 | 1609.02859 |
1609 | 1609.04829.txt | The extragalactic $\gamma$-ray sky is dominated by emission from blazars, a peculiar class of active galactic nuclei (AGNs). Many of the $\gamma$-ray sources included in \fer\ -Large Area Telescope Third Source catalog (3FGL) are classified as a blazar candidate of uncertain type (BCU) because there is no optical spectra available in the literature to confirm their nature. In 2013 we started a spectroscopic campaign to look for the optical counterparts of the BCUs and of the Unidentified $\gamma$-ray Sources. The main goal of our investigation is to confirm the blazar nature of these sources having peculiar properties as compact radio emission and/or selected on the basis of their infrared (IR) colors. Whenever possible we also determine their redshifts. Here we present the results of the observations carried out in the Northern hemisphere in 2013 and 2014 at Telescopio Nazionale Galilleo (TNG), Kitt Peak National Observatory (KPNO) and Observatorio Astron\'omico Nacional (OAN) in San Pedro M\'artir. In this paper we describe the optical spectra of 25 sources. We confirmed that all the 15 BCUs observed in our campaign and included in our sample are blazars and we estimated the redshift for 3 of them. In addition, we present the spectra for 3 sources classified as BL Lacs in the literature but with no optical spectra available to date. We found that one of them is a quasar (QSO) at a redshift $z$ = 0.208 and the other 2 are BL Lacs. Moreover, we also present 7 new spectra for known blazars listed in the \bzcat\ having an uncertain redshift or being classified as BL Lac candidates. We found that one of them, 5BZB J0724+2621 is a `changing look' blazar. According to the spectrum available in the literature it was classified as a BL Lac but in our observation we clearly detected a broad emission line that lead to classify this source as a QSO at $z$=1.17. | \label{sec:intro} Blazars are radio-loud active galactic nuclei (AGNs) characterised by non-thermal emission over the entire electromagnetic spectrum, from the radio band to $\gamma$ rays \citep[see e.g. ][]{giommi13}. They show rapid variability from hours timescales in the optical band up to minutes in the $\gamma$ rays (see e.g. Aharonian 2000; Homan et al. 2002), high linear polarization from the radio to the optical frequencies \citep[see e.g.][]{marscher10,agudo14}, compact radio emission (see e.g. Taylor et al. 2007; Lister et al. 2009), flat radio spectra and superluminal motions (see e.g. Vermeulen \& Cohen 1994; Kellermann et al. 2013 and references therein). The spectral energy distribution is characterised by a double bump, the first component peaking in infrared (IR)/optical wavelengths and the second one in X-rays (for more details see e.g. Giommi \& Padovani 1994, Inoue \& Takahara 1996). They are strong $\gamma$-ray emitters reaching luminosities up to $10^{49}\ erg\ s^{-1}$ as reported in both the \fer -LAT First Source Catalog \citep{abdo10} and the \fer -LAT Second Source Catalog \citep{nolan12}. According to Stickel et al. (1991) blazars are divided into two main subclasses: BL Lac objects which present featureless optical spectra or with emission/absorption lines of rest frame equivalent width $EW < 5\ \AA$, and flat spectrum radio quasars that show quasar-like optical spectra with broad emission lines ($EW > 5\, \AA$). In the following we label the former class as BZBs and the latter as BZQ according to the nomenclature adopted in \bzcat\ `Multifrequency Catalog of BLAZARS' \citep{bzcat4}. In this catalogue there are listed BL Lac candidates as sources claimed to be BL Lacs in the literature but no optical spectra was found to confirm their classification. There are also sources classified as blazars of uncertain type (BZUs), adopted for sources with peculiar characteristics, similar to those previously mentioned but also showing blazar activity like occasional presence/absence of broad spectral lines, transition objects between a radio galaxy and a BL Lac or galaxies hosting a low luminosity radio nucleus. In the latest version of the \bzcat\ \citep{5bzcat} there is one more class, BL Lacs whose optical spectra exhibit a typical elliptical galaxy spectrum with a low Ca H\&K break contrast, indicated as BZGs. With a density of the order of 0.1 sources/degree$^2$, blazars constitute the most numerous population of extragalactic $\gamma$-ray sources, about $38\%$. However, almost $20\%$ of the sources above 100 MeV in the \fer -LAT Third Source Catalog \citep{abdo14} are blazar candidates of uncertain type (BCUs). They present flat radio spectra and/or X-ray counterpart and have a multifrequency behaviour similar to blazars but there is no optical spectra to precisely allow this classification \citep{ackermann12}. In addition, Unidentified $\gamma$-ray Sources (UGSs) represent $\sim$ $33\%$ of the \fer\ -LAT Third Source Catalog and a large fraction of these sources can be associated to blazars \citep{paper4}. Knowing how much of the emission in $\gamma$-rays comes from blazars is important to set constraints on dark matter scenarios (Mirabal et al. 2012; Berlin \& Hooper 2014), to discover new classes of $\gamma$-ray emitters, to resolve the $\gamma$-ray sky and to determine the origin of the extragalactic $\gamma$-ray background \citep{ajello15}. For this purpose, several methods to recognise blazars as the low-energy counterparts of UGSs have been developed. For example, in the 3-dimensional IR color space generated by WISE photometry $\gamma$-ray emitting blazars lie in a region distinct from those where most of the other extragalactic sources dominated by thermal emission \citep[][]{ugs2,wibrals} are located. In addition, radio follow up observations of the Fermi UGSs (e.g., Kovalev 2009; Hovatta et al. 2012, 2014; Petrov et al. 2013; Schinzel et al. 2014) correlation of the peculiar IR colors with existing radio databases \citep{ugs3} and X-ray follow-up observations looking for X-ray counterparts (Paggi et al. 2013; Takeuchi et al. 2013) have been performed. Statistical studies based on $\gamma$-ray source properties have also allowed us to recognise the nature of the potential counterparts for UGSs (e.g., Ackermann et al. 2012; Mirabal et al. 2012; Hassan et al. 2013; Doert \& Errando 2014). However none of these methods can be conclusive without optical spectroscopic confirmation for both BCUs and UGSs. Since 2013 we have been carrying out a spectroscopic campaign to observe the blazar-like sources of uncertain classification as well as those selected according to the methods previously listed. In this fifth paper of the series, we present the results of optical spectroscopic observations of BCUs carried out in the Northern hemisphere at Kitt Peak National Observatory (KPNO) in Tucson (USA), Telescopio Nazionale Galileo (TNG) in La Palma (Spain) and Observatorio Astron\'omico Nacional (OAN) in San Pedro M\'artir (Mexico) between October 2013 and July 2014. Exploratory program obtained with TNG, OAN and Multiple Mirror Telescope (MMT) were described in Paggi et al. (2014); in addition, results for observations carried out in 2013 with SOAR and KPNO were presented in Landoni et al. (2015), Massaro et al. (2015b,2015c) and Ricci et al. (2015). In this paper we focus mainly on BCUs, although we also had the opportunity to observe \bzcat\ sources. The paper is organised as follows: Section~\ref{sec:sample} contains the sample selection. We present our dataset and discuss the data reduction procedures in Section ~\ref{sec:obs}. Then in Section ~\ref{sec:results} we report the details on the cross-matches with multifrequency databases and catalogs of the observed targets and present the results of our analysis for different types of sources. Finally Section ~\ref{sec:conclusions} is devoted to our summary and conclusions. We use cgs units unless otherwise stated. Spectral indices, $\alpha$, are defined by flux density $S_\nu \propto \nu^{-\alpha}$. Flat spectra are defined as $\alpha < 0.5$. | \label{sec:conclusions} We present the results of our 2013 and 2014 optical spectroscopic campaign in the Northern hemisphere with the Telescopio Nazionale Galileo (TNG), Kitt Peak National Observatory (KPNO) and Observatorio Astron\'omico Nacional (OAN) in San Pedro M\'artir. The main goal of our program is to use optical spectroscopy to confirm the nature of sources selected among the BCUs for having low radio frequency spectra (i.e. below $\sim$1 GHz) or peculiar IR colours. Confirmation of blazar nature among these objects will improve and refine future associations for the \fer\ catalog. Also, once our campaign is completed, this will yield to understand the efficiency and completeness of the association method based on IR colours. One more aim is to search for redshift estimates of the potential UGS counterparts. During our campaign we also observed several active galaxies of uncertain type as defined according to the \fer\ catalogs (Ackerman et al. 2011a; Nolan et al. 2012; Abdo et al. 2014) to verify if they are blazars. In addition we observed several sources that already belong to the \bzcat\ because either there were no optical spectra available in the literature, or their estimated redshifts were still uncertain when the catalog was released. The total number of targets presented is 25. The results of this part of the spectroscopic campaign can be reported as follows: \begin{itemize} \item In the BCU subsample, all of the sources have a blazar nature. One of them, namely WISE J014935.28+860115.4 is dominated by absorption of the host galaxy, and were able to detect absorption lines in the optical spectrum leading to a redshift measurement of $z$ = 0.15. We have also been able to set a lower limit for WISE J065344.26+281547.5 of 0.45 thanks to the detection of a Mg II intervening system. \item We obtained the spectra of 3 sources classified as BL Lacs in the literature but with no spectra published at the time of the observations. We found that 2 of them are indeed BL Lacs but the optical spectrum of WISE J101336.51+344003.6 shows this source is a QSO at $z$ = 0.208. \item For the 5 BZBs listed in the \bzcat\ with uncertain redshift estimation we were not able to obtain any z value with our observations. \item We also analysed 2 BL Lac candidates listed in the \bzcat. According to our results 5BZB J0814-1012 is confirmed as a BZB. The spectra of the source 5BZB J0724+2621 observed by White et al. (2000) showed a featureless continuum corresponding to the classification as a BL Lac, but in our observations we detected a broad emission line. This strongly indicates that the source was previously observed during a state dominated by non-thermal radiation that did not allow to detect emission lines. During our observation we observed this previously classified BL Lac showing a broad emission line that led to a QSO classification. It is a `changing look' blazar (see e.g. Giommi et al. 2012). and we classify it as a QSO at a redshift $z$ = 1.17. It has been suggested that this transition could happen due to a change in the bulk Lorentz factor of the jet \citep{bianchin09}. Other interpretation is that these blazars are instead FSRQs, whose emission lines are swamped by the relativistically boosted jet flux \citep{ghisellini12}. \end{itemize} % | 16 | 9 | 1609.04829 |
1609 | 1609.09520_arXiv.txt | We present a model for the dynamical evolution of subhaloes based on an approach combining numerical and analytical methods. Our method is based on tracking subhaloes in an N-body simulation up to the last point that it can be resolved, and applying an analytic prescription for its merger timescale that takes dynamical friction and tidal disruption into account. When applied to cosmological N-body simulations with mass resolutions that differ by two orders of magnitude, the technique produces halo occupation distributions that agree to within 3\%. | The evolution of the Universe in the standard cold dark matter model is characterized by hierarchical structure formation where small haloes form first, and subsequently merge to form larger haloes. High resolution N-body simulations have indicated that massive haloes retain a substantial amount of substructure \citep{klypin99,moore99,springel01}, consisting of bound dark matter clumps orbiting within the potential of their host halo. Evidently, such subhaloes were themselves independent, self-contained haloes in the past, before merging with a more massive halo. If sufficiently massive, these subhaloes were sites of baryon dissipation and star formation in the past. There are many indications, from studies of the statistical properties of how galaxies and sub-structures populate haloes, that galaxies in groups and clusters are in fact the observational counterparts of subhaloes. For example, \cite{colin99} and \cite{kravtsov04} show that the auto correlation functions of substructures in high resoution N-body simulations are in good agreement with the observed auto correlation functions of galaxies. On the theory side, \cite{kravtsov04} find that the distribution of subhaloes in high resolution N-body simulations is similar to that of smoothed particle hydrodynamics (SPH) galaxies in \cite{berlind03} and \cite{zheng05}, and \citep{simha12} find good agreement between the properties of galaxies in their SPH simulation, and the properties of halos in their matched N-body simulation. Using N-body simulations to study galaxy formation requires a framework for populating dark matter halos with galaxies. One approach is to employ semi-analytic models which use analytic techniques and phenomenological recipes to follow the evolution of baryons within dark matter halos. An alternative is to eschew assumptions about baryonic physics and use an empirical approach to relate observed galaxy properties to dark matter halo properties. One popular approach in this class of models is abundance matching which assumes a monotonic relationship between galaxy luminosity and halo mass. A key aspect of studying galaxy formation within the cold dark matter paradigm is to understand the fate of galaxies following halo mergers - how and when galaxy mergers happen, how and when galaxies are tidally disrupted and what ultimately happens to galaxies that fall in to more massive haloes. In this paper, we model the dynamical evolution of subhaloes and their galaxies using a combination of numerical and analytical methods. The formation of dark matter haloes through the growth of dark matter perturbations can be studied numerically using dissipationless cosmological simulations. But haloes do not evolve in isolation from each other. When a halo enters the virial radius of a more massive halo, its evolution becomes more complex than that of independent haloes. After falling in to a more massive halo, (sub)haloes experience tidal forces which cause mass loss, and even complete disruption under extreme circumstances. Furthermore, satellite subhaloes orbiting within a host halo lose energy and angular momentum through dynamical friction which causes their orbits to sink towards the halo centre. Galaxy formation models use two principal approaches to model the dynamical evolution of subhaloes and satellite galaxies. The first is to use analytically calculated or physically motivated empirical formulae for various aspects of the dynamical evolution of subhaloes such as the timescale for merging through dynamical friction, tidal stripping, tidal destruction, etc. \citep[e.g.][]{lc,bk08,jiang08}. An alternative approach, that avoids simplifying assumptions, is to use an N-body simulation to follow the dynamic evolution of subhaloes. N-body simulations capture the complexity of the physics of tidal disruption and dynamical friction, and do not require simplifying assumptions, either about the physical processes or the distribution of orbital parameters. However, subhalo merging and disruption are affected by finite force and mass resolution. Insufficiently resolved subhaloes disrupt artificially and on shorter timescales than well resolved haloes \citep{klypin99}. Using a fixed subhalo mass resolution limit, regardless of infall mass, leads to lower mass subhaloes being artificially disrupted more quickly. In subhalo abundance matching (SHAM) models, which assume a monotonic relationship between subhalo mass at infall and galaxy luminosity, it is assumed that each galaxy survives as long as its subhalo can be identified in an N-body simulation above a fixed resolution threshold. Some models allow galaxies to survive for a period of time after the disruption of their host subhaloes \citep{saro08,moster10}, while in contrast, \cite{stewart09} allows satellite galaxies to be disrupted even while their subhaloes still exist. In contrast, the GALFORM semi-analytic model uses an analytical formula to calculate the merger timescale for a satellite galaxy \citep{cole00}. Following a halo merger, it is assumed that the galaxy hosted by the less massive halo enters the host halo on an orbit with orbital parameters randomly drawn from a distribution. The merger timescale is then computed using the analytical formulae of \cite{lc} in the GALFORM model of \cite{gon14} and the analytical formulae of \cite{jiang08} in the GALFORM model of \cite{lacey15}. Once this time has elapsed, the galaxy hosted by this subhalo is considered to have merged with the central galaxy of the more massive host halo. In this paper, we employ a hybrid approach to follow the dynamical evolution of subhaloes. We follow subhaloes in an N-body simulation until the point when they can no longer be resolved. We then calculate a merger timescale using its orbital parameters and mass at the epoch that it was last resolved in the N-body simulation. Our formula to calculate the merger timescale is based on \cite{lc}, with parameters suitably modified to match our N-body simulation results. Our scheme is faithful to the underlying N-body simulation, minimising the reliance on analytically determined orbits. Instead of making assumptions about the orbital parameters of satellites, we track the positions of their associated subhaloes. Our goal is to provide a simple model for the dynamical evolution of subhaloes that uses the information in an N-body simulation, but can produce results that are not affected by artificial disruption of subhaloes due to limited resolution. While our model is primarily intended for application in semi-analytic models, it can also be used in other models of galaxy formation that use N-body simulations like SHAM models. We assume that once a subhalo reaches the centre of its host halo, the galaxy associated with the subhalo merges with the central galaxy of the host halo. We also assume that once a subhalo is tidally disrupted, the galaxy it hosts is also tidally disrupted. Therefore, within the context of this paper, subhalo mergers and tidal disruption are synonymous with galaxy mergers and galaxy tidal disruption. In \S2, we describe our simulation and models for populating our subhaloes with galaxies. In \S3, we describe our model for dynamical friction and tidal disruption. In \S4, we discuss our results. In \S5, we discuss the implications of our model on halo occupation distributions and galaxy clustering. In \S6, we summarise our results. | We present a model for the dynamical evolution of subhaloes based on an approach that combines numerical and analytical methods. Our method is based on tracking subhaloes in an N-body simulation up to the point that it can be resolved, and applying an analytic prescription for its subsequent merger timescale that takes dynamical friction and tidal disruption into account. When applied to cosmological N-body simulations with mass resolutions that differ by two orders of magnitude, the technique presented in this paper produces halo occupation distributions that agree to within 3\%. Modelling galaxy mergers within dark matter haloes is an important ingredient of galaxy formation models. Precise estimates of galaxy merger timescales are required for modelling galaxy clustering, mass assembly of galaxies, properties of satellite galaxies and black hole merger rates. While subhaloes that approach the host halo too closely can be tidally destroyed in our model, we do not model mass loss due to tidal stripping and its effects on the dynamical friction timescale. We also ignore satellite-satellite interactions which, in any case, are rare. Our model can be applied to generate mock galaxy catalogues from N-body simulations. Furthermore, it can also be applied to build mock galaxy catalogues from Monte-Carlo or other kinds of merger trees by drawing the energy and angular momentum of each subhalo from distributions similar to Fig. \ref{fig:sub6}, and then applying equation \ref{oureq} to determine the merger timescale. \cite{campbell15} apply our model for subhalo evolution to the GALFORM semi-analytic model with galaxy stellar masses matched to observationally inferred stellar masses and find that it produces better agreement with the observed small scale clustering in SDSS at $z=0.1$ and GAMA at $z=0.2$ (see Figures 7 and 8 of \citealt{campbell15}). \cite{mcc16} apply our model to an N-body simulation that is similar to the Millennium Simulation, but with cosmological parameters determined by the PLANCK mission \citep{planck15}. They examine the halo occupation distributions and galaxy clustering and find better agreement with data from SDSS compared to GALFORM-GP14. Our results are based on examining dark matter only simulations. Our model does not include the effect of baryons. Although stellar mass typically constitutes less than 10\% of the halo virial mass, baryons are more strongly concentrated than dark matter and more dense than dark matter at a given scale. As a result, they are more resistant to disruption. While including baryons reduces the likelihood of tidal disruption, it shortens the dynamical friction timescale. By comparing simulations with and without stellar bulges, \cite{bk09} find that the effect of baryons on merger time scales is typically less than 10\%. To shed further light on these issues, we plan to compare our prescription with hydrodynamic cosmological simulations in future work. We emphasise that the model presented in this paper for the dynamical evolution of subhaloes uses the information in an N-body simulation, but can produce results that are not affected by artificial disruption of subhaloes due to limited resolution. | 16 | 9 | 1609.09520 |
1609 | 1609.09716_arXiv.txt | In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfv\'en waves. Due to its localised nature, a direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction, recent observations indicate that in the low amplitude regime such transverse MHD waves can also appear decay-less, a yet unsolved phenomenon. Recent numerical work has shown that Kelvin-Helmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modelling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decay-less oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfv\'en waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows to estimate the density contrast at the boundary. | Research in the last decade has shown that waves and oscillations permeate the solar atmosphere and constitute coronal heating candidates. Of particular interest among these waves are transverse MHD waves. Their characteristic fast damping, particularly for strong amplitudes \citep{Aschwanden_1999ApJ...520..880A,Nakariakov_1999Sci...285..862N,Arregui_2012LRSP....9....2A, DeMoortel_Nakariakov_2012RSPTA.370.3193D,Verwichte_2013AA...552A.138V,Goddard_2016AA...590L...5G} is successfully explained by resonant absorption and mode coupling. Resonant absorption (or mode coupling for propagating waves) is an ideal process of energy transfer between different wave modes \citep{Ionson_1978ApJ...226..650I, Goossens_2002AA...394L..39G,Goossens_2011SSRv..158..289G,Pascoe_2010ApJ...711..990P,DeMoortel_2016PPCF...58a4001D}, which has been shown to be very efficient and robust \citep{DeMoortel_Nakariakov_2012RSPTA.370.3193D,Pascoe_etal_2011ApJ...731...73P,Terradas_2008ApJ...679.1611T}. This mechanism predicts that in the classical picture of coronal loops with a smooth density gradient between the inside and the outside of the flux tube the global transverse mode can resonantly couple to local Alfv\'en waves of azimuthal character. The global transverse mode, which consists of a purely transverse displacement of the loop core, then behaves as azimuthal Alfv\'en waves at the boundary for most of the oscillation time. This means that most of the displacement (and thus the energy) in such waves is azimuthal and local rather than transverse and global, making resonant absorption extremely difficult to observe directly. Recently, decay-less transverse oscillations have been reported \citep{Nistico_2013AA...552A..57N, Anfinogentov_2013AA...560A.107A, Anfinogentov_2015AA...583A.136A,Goddard_2016AA...585A.137G}, apparently at odds with resonant absorption theory. These events have a rather ubiquitous character in active regions and correspond well to fundamental (standing) kink modes. The clearly decay-less cases seem to occur on long loops with small perturbation amplitudes that on average are less than $1\%$ of the kink speed. Numerical simulations in 3D MHD have shown that transverse MHD waves can become unstable to KHI due to shear motions at the boundary of flux tubes \citep{Karpen_1993ApJ...403..769K,Ofman_1994GeoRL..21.2259O,Poedts_1997SoPh..172...45P, Terradas_2008ApJ...687L.115T,Antolin_2014ApJ...787L..22A, Zaqarashvili_2015ApJ...813..123Z}. The KHI associated with transverse MHD waves leads to the generation of a myriad of vortices and current sheets along the flux tube, so called TWIKH (Transverse Wave Induced Kelvin-Helmholtz) rolls. The mixing and the heating produced by the KHI, combined with the compressive nature of the vortices, leads to strand-like structure in intensity images in coronal loops \citep{Antolin_2014ApJ...787L..22A}, and thread-like structure in prominences \citep{Antolin_2015ApJ...809...72A}. Furthermore, the combination of resonant absorption (and phase mixing) and the KHI leads to anti-phase behaviour between the line-of-sight (LOS) velocity and the (transverse) plane-of-the-sky (POS) motion, a characteristic observed recently in a prominence by \textit{Hinode}/SOT and \textit{IRIS} \citep{Okamoto_2015ApJ...809...71O}. Here we show that the combination of resonant absorption and the KHI can be readily seen in current coronal imaging instruments as small amplitude decay-less transverse oscillations, thus providing an explanation for the recent observations. We further demonstrate a potential MHD seismology application. | \label{discussion} In this paper, we have investigated imaging signatures of the transverse MHD wave derived from 3D MHD numerical simulations and forward modelling. The main factors affecting the intensity modulation in the host loops are the KHI and resonant absorption. Importantly, the KHI vortices (TWIKH rolls) carry over characteristics of the resonant absorption and phase-mixing mechanisms, allowing these to be detected with current instrumentation. We have found that the KHI produces significant intensity changes and that emission lines with different temperature sensitivity to either the loop core or the external medium provide insights into different wave modes. At high spatial resolution and especially in the hot line, the fine strand-like structure generated by the TWIKH rolls can be observed, as described in \citet{Antolin_2014ApJ...787L..22A}. At a lower spatial resolution corresponding to AIA, we have shown that the detected damping and period can vary depending on the emission line, which can lead to an out-of-phase behaviour between core and boundary lines. These results can be understood from the fact that the boundary line is more sensitive to the KHI dynamics, to resonant absorption and phase mixing. A decay-less oscillation is obtained in the boundary line for any LOS angle and this is the result of periodic brightenings and the coherent motion of the vortices. The vortices, in turn, result from unstable azimuthal Alfv\'en waves. Therefore, this decay-less oscillation reflects more the Alfv\'en waves coupled resonantly to the kink mode than the global kink mode itself. Resonant absorption transfers the energy of the kink mode to the Alfv\'en waves, whose damping is expected to be much lower than that of the kink mode since it relies on phase mixing and the turbulence resulting from the instability. The Alfv\'en waves act therefore as energy reservoir for the TWIKH rolls, which persist over time leading to the decay-less oscillation. A shorter period is found for the boundary line and is due to phase mixing. Indeed, the azimuthal Alfv\'en waves in the boundary layer have an increasingly higher phase speed the farther they are from the loop core. Since it is these waves that are enhanced due to resonant absorption and which become K-H unstable, their signal becomes dominant in the boundary line. The fit to the density from the numerical model ends up with a shorter period than that obtained from the core line. This is because the density profile is influenced by the KHI dynamics, which broaden the flux tube, even though the small-scale structure produced by the instability is unresolved. Accordingly, when fitting only the central section of the flux tube along the oscillation axis, which is minimally influenced by resonant absorption and by the KHI, we obtain a period of 256~sec, closer to that obtained from the core line. The out-of-phase behaviour between the core and boundary lines is ultimately the same effect as that leading to the out-of-phase behaviour between the LOS velocity and the POS motion seen in the core line \citep{Antolin_2015ApJ...809...72A}, explaining the observations by \citet{Okamoto_2015ApJ...809...71O}. The difference in oscillation period between core and boundary lines can be used to obtain an estimate of the density at location of emission in the boundary layer and also to estimate the density contrast between the loop and the external corona. The period observed with the boundary line (here \ion{Fe}{12}~193~\AA) satisfies $P_{b}=2L/v_{A_b}$, corresponding to the period of azimuthal Alfv\'en waves dominating the signal, propagating with speed $v_{A_b}=B/\sqrt{4\pi\rho_b}$. Then $\rho_{b}=B^2 P_{b}^2/(16\pi L^2)$. Since the plasma $\beta$ is low, we can approximate the kink speed as $c_k=\sqrt{2/(1+\rho_e/\rho_i)}v_{A_i}$ and we have $P_k=2L/c_k$, where $P_k$ is the period of the kink speed, which is to a large accuracy the observed period with the core line. Using these equations to replace the magnetic field we obtain: \begin{equation}\label{rob2} \frac{\rho_b}{\rho_i}=\frac{1}{2}\left(1+\frac{\rho_e}{\rho_i}\right)\left(\frac{P_b}{P_k}\right)^2. \end{equation} Replacing with the observed values for $P_b$ and $P_k$, and assuming that $\rho_e$ and $\rho_i$ are known, we obtain $\rho_b\approx1.73\times10^{9}\mu m_p$~g~cm$^{-3}$. The average location (in time and angles) in the boundary corresponding to this density has a temperature of $1.83\times10^{6}~$K, very close to the maximum formation temperature of the line. From Eq.~\ref{rob2} we can provide an upper limit to the density contrast: \begin{equation}\label{rob3} \frac{\rho_e}{\rho_i}<\min\left\{\frac{(P_b/P_k)^2}{2-(P_b/P_k)^2}, \frac{2-(P_b/P_k)^2}{(P_b/P_k)^2}\right\} \end{equation} which gives a lowest upper limit of 0.76 (the true value being 0.34). These results open several possibilities for MHD seismology of the loop shell structure. Indeed, the KHI broadens the density profile, regardless of its initial shape, and the plasma emissivity at a particular temperature in the boundary ends up coming from a small dynamic range. Multiple periods can thus be detected using multiple channels sensitive to different temperatures in the boundary, leading to a temperature dependent density and the radial structure of a loop \citep[as suggested also by][]{Verth_2010ApJ...714.1637V, Fedun_2011ApJ...740L..46F}. Therefore, this technique also allows to probe the difference in temperature between loops and their surroundings. Our model assumes that the loop is colder than the ambient corona. Note that this model differs minimally from a model in which the loop is both hotter and denser than the ambient corona. Indeed, both the resonant properties and KHI onset in the loop remain largely the same. For example, in a model with an ambient temperature of $1$~MK and an internal loop temperature of $1.5$~MK, similar forward modelling results would be obtained with the same pair of emission lines, except that the results corresponding here to the core and boundary lines would be switched. The loop core and boundary would be better visualised with the \ion{Fe}{12} line and the \ion{Fe}{9} line, respectively. The observed transverse displacement and periods in our model match those observed exhibiting the decay-less kink mode oscillations in coronal loops \citep{Nistico_2013AA...552A..57N,Anfinogentov_2013AA...560A.107A,Anfinogentov_2015AA...583A.136A,Goddard_2016AA...585A.137G}. Our results therefore provide an explanation for these observations. Unfortunately in these studies only the \ion{Fe}{9}~171~\AA~line has been used and it is uncertain how multi-thermal these loops are and what the temperature difference is with the external corona. The loops shown in these studies present significant intensity changes during their oscillation, in a similar way to the changes observed in our model. Furthermore, the oscillations in our model can appear non-sinusoidal, especially in the first few periods. Such non sinusoidal and rather pointy oscillations can be seen in several of the examples provided by \citet{Anfinogentov_2013AA...560A.107A,Anfinogentov_2015AA...583A.136A,Goddard_2016AA...585A.137G}. The presence of the KHI and resonant absorption have been demonstrated to be quite robust with respect to density and longitudinal magnetic field variation across the loop, perturbation amplitudes, thickness of the boundary layer, longitudinal flows and magnetic twist \citep{Antolin_2014ApJ...787L..22A, Murawski_2016MNRAS.459.2566M, Terradas_etal_2016}. The described decay-less effect is however limited and will not be observed for strong perturbation amplitudes. This is because the TWIKH rolls that are associated with resonant absorption are always around the flux tube. The combined effect from the coherent motion of vortices and periodic brightening is therefore confined to a transverse layer equal to the loop width, which may explain why such decay-less oscillations are only seen for low amplitudes. On the other hand, for large amplitudes a negative correlation between damping time and perturbation amplitude has been found by \citet{Goddard_2016AA...590L...5G}, suggesting that non-linear effects such as those described here may still play an important role in the observed overall dynamics of the loop. | 16 | 9 | 1609.09716 |
1609 | 1609.02632_arXiv.txt | The dynamics and evolution of any galactic structure are strongly influenced by the properties of the orbits that constitute it. In this paper, we compare two orbit classification schemes, one by Laskar (NAFF) , and the other by Carpintero and Aguilar (CA), by applying both of them to orbits obtained by following individual particles in a numerical simulation of a barred galaxy. We find that, at least for our case and some provisos, the main frequencies calculated by the two methods are in good agreement: for $80\%$ of the orbits the difference between the results of the two methods is less than $5\%$ for all three main frequencies. However, it is difficult to evaluate the amount of regular or chaotic bar orbits in a given system. The fraction of regular orbits obtained by the NAFF method strongly depends on the critical frequency drift parameter, while in the CA method the number of fundamental frequencies strongly depends on the frequency difference parameter $L_{\rm r}$ and the maximum integer used for searching the linear independence of the fundamental frequencies. We also find that, for a given particle, in general the projection of its motion along the bar minor axis is more regular than the other two projections, while the projection along the intermediate axis is the least regular. | Nearly two-thirds of spiral galaxies in the Universe have a bar structure \citep[e.g.,][]{2012ApJ...745..125L, 2010ApJS..190..147B, 2015ApJS..217...32B}. Bars are one of the main drivers for the secular evolution of disc galaxies (see \citealt{2013seg..book..305A} for a review), and can transport material from the bar region to the center and redistribute angular momentum within the galaxy. This is emitted by the resonant regions in the bar and its vicinity, and absorbed by the outer parts of the disc and, mainly, by the spheroidal components (halo and bulge). Moreover, there is a strong correlation between the strength of the bar and the amount of angular momentum thus redistributed \citep{2003MNRAS.341.1179A}. Therefore, understanding the structure and the dynamical properties of bars is one of the most important issues in the formation and evolution of disc galaxies. Orbits are the fundamental building blocks of any galactic structure and therefore their properties greatly influence those of the structure. Moreover, it is difficult to describe the phase-space distribution for the chaotic orbits, which can not be adopted to construct torus models \citep{2008MNRAS.390..429M}. The orbit families and, more generally, the orbital structure in a fixed bar potential have been considered by many studies \citep{1980A&A....92...33C,1996MNRAS.283..149Z,2000MNRAS.314..433H,2011MNRAS.415..629M,2012MNRAS.427.1429W,2013MNRAS.435.3437W}. Different methods of orbit classification have been used: The Lyapunov exponent method \citep[see e.g. ][for a description]{1976PhRvA..14.2338B,1978CRASB.286..431B}. The Lyapunov exponents describe the time-averaged exponential rate of divergence of two orbits with close initial conditions in the phase space. Orbits with significantly non-zero Lyapunov exponents are chaotic. The Small ALignment Index method (SALI, \citealt{2001JPhA...3410029S,2002MNRAS.337..619V,2004JPhA...37.6269S,2014MNRAS.438.2871C}). This method can be considered as an extension of the Lyapunov one, as it relies on the properties of two arbitrary different initial deviation vectors of an orbit, in order to distinguish efficiently between chaotic and regular orbits. The Generalized ALignment Index \citep[GALI,][]{2007PhyD..231...30S} is similar to SALI, but uses a set of at least three initially linearly independent deviation vectors. The NAFF method, short for Numerical Analysis of Fundamental Frequencies, relies on the fact that the regular orbits move on a torus-like manifold and are thus quasi-periodic (\citealt{1990Icar...88..266L,1993PhyD...67..257L}). We will describe it further in Sect. 3.1. The spectral analysis method uses the Fourier transform of the time series of each coordinate of a given orbit (\citealt{1998MNRAS.298....1C}, hereafter CA98). We will hereafter refer to this method as CA, from the initials of its authors, and describe it further in Sect. 3.2. While each method has its advantages, each also suffers from disadvantages. For example, the Lyapunov method necessitates very long integration times and the fraction of chaotic orbits also depends on the integration time ~\citep{1996ApJ...460..136M}; the SALI method also needs relatively long integration times, albeit much shorter than the Lyapunov method. The CA method has some problems for rotating systems \citep{2003CeMDA..85..247C} and depends strongly on the orbit integration time \citep{2012MNRAS.427.1429W}. Finally in the NAFF method whether an orbit is regular or not depends on the drift of its frequencies, so that a critical value needs to be adopted (See Sect. 5 in the present paper). Compared to other methods, CA and NAFF have an important advantage, namely they give more information for the regular orbits, such as their fundamental frequencies, from the ratios of which it is possible to define orbital families. Both of them have been successfully applied to various potential systems \citep[e.g.][]{1998A&A...329..451P,2010MNRAS.403..525V,2012MNRAS.422.1863B,2016ApJ...818..141V}. Most studies so far have relied on simple analytic potentials, which, however, are not very realistic. In particular, real bars as well as N-body bars are composed of two parts: an inner part which is thick both horizontally and vertically, and an outer part which is thin in both these directions, while as yet no analytical potential with such a property has been developed (see \citealt{2016ASSL..418..391A} for a review). N-body bar potentials, however, are much more complex to use and there are therefore relatively few studies relying on them, compared to the large number of studies relying on analytic potentials. \cite{2014MNRAS.438.2201M} and \cite{2016MNRAS.458.3578M} took an intermediate path, using analytical time-dependent potentials modelled after an N-body simulation of a strongly barred galaxy. The disadvantage of this approach is that both the disc and the bar potentials are rigid and have not responded to each other, which is not realistic. An alternative route, much nearer to the N-bodies, is to freeze the simulation potential at a representative time and then follow in it orbits with initial conditions obtained from the positions and velocities of the simulation particles at that chosen time \citep{2002ApJ...569L..83A, 2003MNRAS.341.1179A, 2005NYASA1045..168A, 2006ApJ...637..214M, 2007MNRAS.381..757V, 2009A&A...494...11W, 2012MNRAS.419.1951V, 2016ApJ...818..141V}. This approach has a number of advantages. The corresponding potentials are realistic, and allow for orbital structure studies in bars with a thick inner part and a thin outer part. It also provides a unique and correct definition of the orbital sample which will be used, whereas in rigid potentials this sample is arbitrary, thus rendering any estimate of the fraction of chaos in a given system also entirely arbitrary. Indeed, whether a given orbit is regular or chaotic depends on its location within the galaxy's phase space, and different samples may populate this space differently. This severe drawback of analytical potentials is easily avoided by relying on the simulation to provide the initial conditions of the orbits. Concerning disadvantages, let us mention that a correct description of the potential from the simulation particles is not trivial and also that the potential has been frozen i.e. does not depend on time. It is nevertheless possible to obtain information on time evolution by considering a series of consecutive times and of corresponding frozen potentials. Thus full time information can be obtained, but in a very time consuming manner. A third alternative is to use directly the orbits of a preselected number of particles during the simulation \citep{2007MNRAS.379.1155C, 2015arXiv151104253G, 2016arXiv160600322G}. This attractively straightforward way has a number of difficulties, not the least being the fact that most of the available techniques and information on orbital structure have been obtained for non-evolving potentials. As we will show here, however, this third alternative can still be very useful if one chooses carefully the time interval over which one follows the orbits so that it has as little evolution as possible. In this paper, we will give a detailed comparison of the CA and NAFF orbit classification methods by studying orbits in a simulated bar. The outline of the paper is as follows. In \S 2 we describe briefly our numerically simulated bar. In \S 3 we outline different methods of orbit classifications. In \S 4 we present the main frequencies from two methods. In \S 5 we present the fraction of regular orbits from different classification schemes. In \S 6 we give a brief discussion. In \S 7 we present the summary and conclusions. | Individual particle orbits are the backbone of any structure. It is thus important for understanding the formation and evolution of this structure to know whether the orbits that constitute it are chaotic or regular and, in the latter case, what family they are associated with. Bars, in particular, are a favourite field for such tests and thus many studies have addressed the orbital structure in bars. Most of them, however, use an analytic potential and are thus not very realistic \citep[see e.g.][ for a review]{2016ASSL..418..391A}. A further disadvantage of such studies is that it is not trivial to choose the initial conditions for the orbits and the result can depend critically on this choice. Instead, we used here orbits taken directly from the simulation. This means that they have very realistic potentials, but at the expense of some noise and, particularly, some evolution of the potential. As a first step towards understanding the orbital structure in bars, we compare in this paper two methods, the NAFF method of \cite{1990Icar...88..266L} and the method of \cite{1998MNRAS.298....1C}. We show how the main frequencies depend on the maximum extracted line number $L_{\rm max}$ and on the parameter to distinguish two main frequencies $L_{\rm r}$. We find that only a small number $(<0.1\%)$ of the main frequencies in NAFF have been changed when using different values of $L_{\rm max}$, while about $6\%$ of the main frequencies have been changed in CA. If we change $L_{\rm r}$ from $2\times10^{-4}$ to $2\times 10^{-3}$, then around $6\%$ and $1.5\%$ of the orbits have a different main frequency in the NAFF and CA methods, respectively. We find that, at least for our case, the main frequencies calculated by the two methods are in good agreement provided we use the same definitions and values for $L_{\rm max}$ and $L_{\rm r}$: for $80\%$ of the orbits the differences between the results of the two methods are less than $5\%$ for all three main frequencies. We also find that there are two clear peaks in the histogram of the ratios of the three main frequencies in both methods. The highest peak is 1:1, and the second highest is 2:3 for the face-on view $(x,y)$. The two edge-on views, $(y,z)$ and $(x,z)$ also have two clear peaks, one at 4:5 and the other at 4:7. We find that the fraction of the regular orbits strongly depends on two parameters $L_{\rm r}$ and $I_{\rm n}$ in the CA method. The former is used to determinate whether the two frequencies are the same and whether there are resonances among the main frequencies. The fraction of the regular orbits increases with increasing $L_{\rm r}$ or $I_{\rm n}$. In the NAFF methods, the fraction of the regular orbits strongly depends on the critical frequency drift parameter. The regular fraction is increased with increasing this parameter. However, it is difficult to give certain values of these parameters in both methods. The fact that there is no abrupt change from chaotic to regular reflects the fact that there is stickiness and confined chaos. We also find that, for a given particle, in general the projection of its motion along the bar minor axis is more regular than the other two projections, while the projection along the intermediate axis is the least regular. Increasing the number of particles in the simulation will decrease the noise. In a future paper we plan to use a simulation with a considerably larger number of particles, to determine how noise may influence the results. \begin{figure} \includegraphics[angle=0, width=80mm]{fig22.eps} \caption{Same as the left panel of Figure ~\ref{fig:orbit2745}, but for orbit 160, a orbit looks regular in the x-y and x-z planes, but chaotic in the y-z plane.} \label{fig:orbit160} \end{figure} \begin{figure} \includegraphics[angle=0, width=80mm]{fig23.eps} \caption{Same as the left panel of Figure ~\ref{fig:orbit2745}, but for orbit 865, a orbit being regular in each interval, but the shape changing with time.} \label{fig:orbit865} \end{figure} | 16 | 9 | 1609.02632 |
1609 | 1609.04634_arXiv.txt | Dense plasma fragments were observed to fall back on the solar surface by the Solar Dynamics Observatory after an eruption on 7 June 2011, producing strong EUV brightenings. Previous studies investigated impacts in regions of weak magnetic field. Here we model the $\sim~300$ km/s impact of fragments channelled by the magnetic field close to active regions. In the observations, the magnetic channel brightens before the fragment impact. We use a 3D-MHD model of spherical blobs downfalling in a magnetized atmosphere. The blob parameters are constrained from the observation. We run numerical simulations with different ambient density and magnetic field intensity. We compare the model emission in the 171\AA~ channel of the Atmospheric Imaging Assembly with the observed one. We find that a model of downfall channelled in a $\sim~1$MK coronal loop confined by a magnetic field of $\sim~10-20$G, best explains qualitatively and quantitatively the observed evolution. The blobs are highly deformed, further fragmented, when the ram pressure becomes comparable to the local magnetic pressure and they are deviated to be channelled by the field, because of the differential stress applied by the perturbed magnetic field. Ahead of them, in the relatively dense coronal medium, shock fronts propagate, heat and brighten the channel between the cold falling plasma and the solar surface. This study shows a new mechanism which brightens downflows channelled by the magnetic field, such as in accreting young stars, and also works as a probe of the ambient atmosphere, providing information about the local plasma density and magnetic field. | In the process of accretion in young stars, dense plasma flows through magnetic channels, which link the star with its disk, and impacts the stellar surface \citep{Uchietal1984,Bertetal1988}. An emission excess and associated high plasma densities have been observed in high energy bands, and have been related to the accretion process \citep{Kastetal2002,Tellesetal2007,Argiretal2007,Argiretal2011,Testetal2004}. The formation of shocks after the impact could explain this excess \citep{Orletal2010} and also the complexity of the magnetic field in the impact region can influence the process. Impacts of dense plasma have been observed also in the solar corona with local brightenings in the EUV band that recall the emission excess in young stars. On the Sun we can study the process in great detail (e.g., \citealt{Xiaetal2016}) and we can characterize the role of each player, e.g., magnetic field, downfalling plasma, and shocks. In a solar eruption triggered by a flare on 7 June 2011, a large amount of fragments of an original dense and cold filament fall back spreading far from the original place all around on the solar surface \citep{Carletal2014,Doletal2014,Drietal2014,Innetal2012,Reaetal2013,Reaetal2014}. Part of the dense fragments falls in quiet Sun where the magnetic field was weak. Their impacts on the solar surface were bright in the EUV band observed with SDO/AIA. These brightenings are consistently reproduced by hydrodynamic modelling and recall the excess of high energy emission observed in accreting young stars \citep{Reaetal2013}. The fragments we analysed in \cite{Reaetal2013} were shown to travel along ballistic trajectories, and, therefore, the magnetic field had a minor role throughout their evolution. Many other fragments however appear to fall in regions where the magnetic field is much stronger, and even inside active regions. These fragments show a different evolution and destiny. In particular, we no longer see bright impacts but the fragments are deviated, channelled and the whole final segment of the channels is activated into bright thinner filaments. In this work we address this different class of downfalling fragments. It is clear from the observations that here the magnetic field plays a different and critical role in determining the evolution of the blobs and, thus, the mechanism that produces the excess of the emission is not necessary the same as that indicated in the previous work. So it is interesting to explore these cases in which the interaction of the blobs with the magnetic field is important. Our approach is similar to that of \cite{Reaetal2013} though here we need to include the description of an appropriate ambient magnetic field and therefore a full magnetohydrodynamic model. The fragments do not follow a simple trajectory but they are deviated as they move deeper and deeper in the low corona, confirming a non-trivial interaction with the more and more intense magnetic field. Another different and fundamental ingredient is that the downfalling fragments are eventually forced to propagate inside an already dense and hot medium, that is the plasma confined inside active region loops. This plasma will be strongly perturbed and activated by the infalling material, which will then act also as a probe for the ambient corona. This case represents a unique opportunity to probe active region conditions and their reaction to strong perturbations coming from outside. On the other hand, this is also closer to the conditions in star forming regions, where the flows coming from the circumstellar disk are believed to be funneled by the magnetic channels that link the disk to the young stars. In summary, this is an excellent opportunity to study the funneling of downfalling plasma and its interaction with the possible dense corona close to the stellar surface. The observed phenomenon is presented in Section 2, the model is described in Section 3, the simulations and the results in Section 4, and we discuss them in Section 5. | We studied the downfall of blobs of plasma channelled by the magnetic field toward an active region. These blobs were erupted by a M-class flare event on 7 June 2011, and showed a ballistic motion while still far from the active region. We see the blobs in absorption and we constrain their density to be around $1 - 2 \times 10^{10}$ cm$^{-3}$, according to the method in \cite{LaneRea2013}. As the interaction with the magnetic field becomes strong, they are deviated from their trajectory and channelled by a magnetic flux channel. During the channelling, the flux tube brightens in the 171 \AA~ EUV channel of the AIA instrument, and the blobs disappear. We investigated the channelling process with the aim to explain the brightening of the magnetic channel. We considered a model of a magnetized atmosphere with a curved topology of the magnetic field and a complete solar atmosphere from the chromosphere to the corona, and included all the physical terms of interest, in particular, gravity, radiative losses, thermal conduction along the field lines, and magnetic induction. The model solved numerically the magneto-hydrodynamic equations in 3D Cartesian geometry, implemented in the PLUTO parallel code. The blobs are modelled as spheres with a downward velocity of $300$ km/s not aligned with the magnetic field, different radii ($1.4-2 \times 10^8$ cm), density ($1-2 \times 10^{10}$ cm$^{-3}$), and a temperature of $10^4$ K. We tested the role of the atmosphere as well as of the magnetic field by exploring ambient atmosphere with three different ambient densities and two different magnetic field intensities, with the same topology. The blobs started to fall vertically in all the models, but only in the case in which the magnetic field is strong (170G in transition region and 15G at initial blobs position) they are channelled and deviated from their trajectory. In the case of weak magnetic field, the blobs simply fall without any deviation, similar to \cite{Reaetal2013}. This case is far from our target evolution and provides a lower limit to the conditions of the ambient magnetic field. The initial velocity of the blobs largely exceed the ambient sound speed, so shocks are generated. The behaviour of these shocks depends on the physical condition of the model explored, but with a common dynamics: they propagate ahead of the blobs inside the magnetic flux tube, in which the blobs are channelled, along the field lines. Another effect of the dynamics is that the blobs are strongly deformed, even further fragmented, during their motion. Two factors contribute to this effect: a) the field lines are chaotically displaced downwards and then back upwards, thus being mixed and determining braiding and a differential stress on the blobs, b) the blobs are squashed in the direction of motion. The former effect is common to all the confined models, while the latter depends strongly on the density and pressure of the ambient atmosphere, the larger the density (pressure) the stronger is the compression, and it is also affected by the compression of the magnetic field lines in the initial stage of the evolution. By synthesizing the emission in the 171 \AA~ EUV band, we identified the post-shock region as the main source of the brightening ahead of the blobs. The emission depends on the density and temperature of the ambient atmosphere. The former heavily influences the intensity, because of the dependence on the square of the density, the latter acts more on the shape and size of the emission because of the narrow temperature range of channel sensitivity. As a consequence, for the simulation with high ambient density the intensity of the emission produced is too high and its profile along the field lines does not match what we observe. Instead, for the other two densities, the cooler and tenuous atmospheres give a shape and intensity that better agrees with the observations, best for the one that we called the reference model (RM). The simulations show that the emission comes not only from the the post-shock region, but the whole magnetic channel between the blobs and the chromosphere is activated, well before the shock arrives at the chromosphere. The reason is that the shock compresses and heats the medium it crosses, and the heat front propagates downwards faster than the shock, making the unperturbed medium enter more in the AIA sensitivity range, with this assumption for $\phi$ for coronal condition \citep{Orletal2005}. This makes the emission contrast between the pre-shock and post-shock medium lower. More important, the shock are ultimately never visible as well-defined fronts in our scenario, for another reason. Each fragment or blob produces its own shock front, and, since the blobs are different and not aligned along the line of sight, also the shock are misaligned in time and space and washed out along the line of sight. Overall, our reference model provides the best match with the evolution of the channelled fragment that we selected in the observation. The parameters, i.e. size and density, of the blobs that we assumed in this simulation are well within the constraints provided by the data analysis. Therefore, we obtain a self-consistent scenario. Moreover, within our limited exploration of space of the parameters, our modeling provides us with constraints on, and therefore probes, the ambient medium, and in particular on the ambient coronal magnetic field ($\sim 10$ G) and density ($\sim 10^8$ cm$^{-3}$). Several general considerations descend from this study. We find that falling fragments are disrupted because of the chaotic interaction with a strong ambient magnetic field. The disruption occurs just when the fragments are deviated and channelled by the field. The ram pressure of the fragments displaces and compresses differentially the field lines, which react back and shuffle the blobs. Therefore, a misalignment of dense falling plasma with the local more intense magnetic field lead to a disruption of falling clouds. This evolution also becomes a signature of a strong local perturbation of the magnetic field. We considered simplified spherical blobs with homogeneous density, but in the reality they can be highly inhomogeneous, thus making the mixing and fragmentation even more chaotic. Indeed analogous effects are expected even for more continuous streams, instead of a set of blobs. The magnetic field lines can still be chaotically displaced downwards and the plasma can be squashed in the direction of the motion, depending on the magnetic field topology and on the trajectory of the stream. As a result, an initially continuous stream can be fragmented or become density-structured after interacting with the curved magnetic structures. This fact can be relevant for the accretion on young stars, which occurs along magnetic flux tubes between the disk and the stellar surface. It is plausible that even if an accretion stream is almost continuous in proximity of the disk, it may interact with the more complex magnetic field topology of the stellar corona when approaching the star surface, thus experimenting the effects described above. We may expect, therefore, that accretion streams in young stars may be commonly density-structured at impact regions. Regarding the emission, this study shows another mechanism that lead to an excess of emission in high energy bands. 1D/2D accretion models show higher emission due to a stationary shock produced by a continuous accretion column on the stellar surface \citep{Saccetal2010,Orletal2010,Orletal2013}. \cite{Reaetal2013,Reaetal2014} show that the impact of massive but isolated fragments also lead to hot brightenings. Here we show that falling fragments eventually channelled by the magnetic field do not brighten themselves, rather they activate the channel and make it bright, because of shock propagation and heating. This early further fragmentation and activation of the magnetic channel is certainly a considerable difference from the evolution studied in fragments that do not interact so strongly with the magnetic field. As described in \cite{Reaetal2013,Reaetal2014}, in that case the disruption of the fragments and the brightening are due exclusively to the impact on the dense chromosphere. One important implication for stellar accretion is that we might have emission excess also if the accretion flow interacts with a coronal magnetic field that is not strictly aligned to the flow, e.g. with a solar-like corona with intense active regions. In this study, we have assumed that the initial vertical trajectory of blobs is on the symmetry vertical plane of the magnetic field. We expect possible important effects in cases in which the falling fragments are ``out of axis" and stress the magnetic field in a non-symmetric way. This is to be investigated in a future study. | 16 | 9 | 1609.04634 |
1609 | 1609.01227_arXiv.txt | Vacuum perturbations of the Kerr metric can be reconstructed from the corresponding perturbation in either of the two Weyl scalars $\psi_0$ or $\psi_4$, using a procedure described by Chrzanowski and others in the 1970s. More recent work, motivated within the context of self-force physics, extends the procedure to metric perturbations sourced by a particle in a bound geodesic orbit. However, the existing procedure leaves undetermined a certain stationary, axially-symmetric piece of the metric perturbation. In the vacuum region away from the particle, this ``completion'' piece corresponds simply to mass and angular-momentum perturbations of the Kerr background, with amplitudes that are, however, a priori unknown. Here we present and implement a rigorous method for finding the completion piece. The key idea is to impose continuity, off the particle, of certain gauge-invariant fields constructed from the full (completed) perturbation, in order to determine the unknown amplitude parameters of the completion piece. We implement this method in full for bound (eccentric) geodesic orbits in the equatorial plane of the Kerr black hole. Our results provide a rigorous underpinning of recent results by Friedman {\it et al.}\ for circular orbits, and extend them to non-circular orbits. | Gravitational perturbations of the Kerr geometry are often studied within the null-tetrad framework of Newman and Penrose, using Teukolsky's formalism \cite{Teuk}. In this approach one does not work with the metric perturbation directly, but instead one considers the perturbations in the Weyl curvature scalars $\psi_0$ or $\psi_4$ as proxies. The perturbation equations governing these scalars are fully separable by means of a (spin-weighted) spheroidal-harmonic and Fourier decomposition, and thus conveniently reduce to a set of decoupled ordinary differential equations. In some problems, however, one is interested in the metric perturbation itself. One such problem of contemporary interest is that of calculating the gravitational self-force acting on an orbiting particle \citep{poisson,Barack:2009ux}, in which knowledge of the full local metric perturbation near the particle is required. In such problems one faces the challenge of {\em metric reconstruction}: Given the (harmonic modes of the) perturbation in $\psi_0$ or $\psi_4$, how does one recover the corresponding metric perturbation? A reconstruction procedure for {\em vacuum} perturbations was developed long ago in papers by Chrzanowski \citep{chrza} and Cohen and Kegeles \citep{cohen79}, with further contributions from Wald \citep{Waldrec}, Stewart \citep{Stewart:1978tm}, and (more recently) Lousto and Whiting \citep{Lousto:2002em}; in keeping with common nomenclature we shall refer to it here as the CCK procedure. The procedure yields a vacuum metric perturbation in (one of two) particular, traceless ``radiation'' gauges [cf.\ Eq.\ (\ref{gaugecondition})]. The reconstructed perturbation is determined only up to a 4-parameter family of Petrov type D vacuum perturbations \citep{waldtheo}, representing (i) perturbations into Kerr geometries of a different mass or (ii) a different angular-momentum, and perturbations away from Kerr into (iii) Kerr-Newman-Tamburino-Unti (Kerr-NUT) or (iv) C-metric geometries. These perturbations are all stationary and axisymmetric. In the vacuum case, Kerr-NUT and C-metric perturbations are ruled out based on regularity \citep{waldtheo}, but the mass and angular-momentum perturbations remain arbitrary within the CCK procedure. These two ``missing'' pieces of the metric perturbation must be determined separately [e.g., in the vacuum problem, through conditions imposed on the total Arnowitt--Deser--Misner (ADM) mass and angular momentum of the spacetime]. We shall refer to the task of fixing the missing pieces as the {\em completion} of the reconstruction procedure, and to the missing pieces themselves as the ``completion'' part of the perturbation. The CCK procedure is no longer directly applicable in the non-vacuum case, with the root cause of complication being the inconsistency of the (traceless) radiation gauge condition with the linearized Einstein's equations when matter sources are present \citep{PriceThesis,Price:2006ke}. Notably, in the presence of sources, the (mode-sum based) CCK procedure fails to return a valid solution not only within the matter region but also at vacuum points {\em away} from any sources \cite{barack1,Ori:2002uv,BMP1}. With the self-force problem as a prime motivation, Ori \citep{Ori:2002uv} devised a reconstruction procedure for perturbations sourced by a point particle in a bound orbit around a Kerr black hole. Specifically, he prescribed the reconstruction of a (radiation-gauge) metric perturbation in the vacuum regions $r>r_{\rm p}(t)$ and $r_{+}<r<r_{\rm p}(t)$, where $r=r_{\rm p}(t)$ is the radial location of the particle and $r=r_{+}$ the horizon's radius; we hereafter adopt standard Boyer-Linquist coordinates $\{t,r,\theta,\varphi\}$. Ori showed that the analytical extension of the solution from either vacuum region across $r=r_{\rm p}(t)$ produces a string-like gauge singularity that extends radially from the particle into the opposite vacuum domain. Later, Friedman, Keidl, Shah (FKS) and collaborators \citep{Keidlhom,friedman1,friedman2,friedman3} prescribed an alternative reconstruction, specialized to circular equatorial orbits of radius $r=r_0$, in which the singularities were replaced with a gauge discontinuity (and a delta function) on the sphere $r=r_0$.\footnote{The irregularity of the FKS reconstructed metric on the sphere $r=r_0$ was highlighted in Ref.\ \citep{BMP1}, referring to the FKS gauge as the ``no-string'' gauge.} The procedure was recently generalized by Van de Meent and Shah to any bound equatorial orbits \cite{vandeMeent:2015lxa}, using the method of extended homogeneous solutions \cite{Barack:2008ms}. Motivated by these developments, Pound {\it et al.}~\citep{BMP1} obtained a rigorous formulation of the self-force, complete with a practical mode-sum calculation formula, starting from a reconstructed metric perturbation in either Ori's or FKS's approach. The self-force formulation of Ref.\ \citep{BMP1} assumes that one knows how to complete the metric reconstruction; in general, the completion piece has an important contribution to the local self-force experienced by the particle. However, how to obtain the completion piece remains an open problem, in general.\footnote{The two recent numerical implementations of the Pound {\it et al.} formulation---by Merlin and Shah \cite{MerSha} in Schwarzschild and by Van de Meent \cite{vandeMeent:2016pee} in Kerr---apply the completion determined in the current paper.} Keidl {\it et al.} show, in \citep{Keidlhom,friedman1}, that Kerr-NUT and C-metric perturbations must be excluded for regularity reasons even in the particle case; and they derive the remaining, physical completion piece in the case of circular equatorial geodesic orbits. However, their calculation is restricted to that class of orbits, and their method relies on certain assumptions that are yet to be confirmed (see below). Our goal here is to describe a general, rigorous method for deriving the completion piece for bound orbits in Kerr geometry, and we will go on to implement it for generic (bound) orbits in the equatorial plane. We will thereby confirm and extend the results of Keidl {\it et al.}, and supply a necessary ingredient to enable self-force calculations from a reconstructed metric. For a particle in a bound orbit, the task of completion takes the following simple form. Let ${\cal S}^+$ and ${\cal S}^-$ denote, respectively, the two vacuum regions $r>r_{\rm p}(t)$ and $r_+\leq r<r_{\rm p}(t)$, and let $h^{\rm rec\pm}_{\alpha\beta}$ represent the piece of the metric perturbation obtained by applying the reconstruction procedure in the respective domains ${\cal S}^{\pm}$ (with the usual, retarded boundary conditions). We refer here specifically to an FKS-like ``no-string'' reconstruction (as implemented most recently in \cite{MerSha,vandeMeent:2015lxa,vandeMeent:2016pee}), in which $h^{\rm rec\pm}_{\alpha\beta}$ are each regular in their respective vacuum domains. The full, completed metric perturbation in each of ${\cal S}^{\pm}$ is given by \begin{equation} h^{\pm}_{\alpha\beta}=h^{\rm rec\pm}_{\alpha\beta}+h^{\rm comp\pm}_{\alpha\beta}, \end{equation} where $h^{\rm comp\pm}_{\alpha\beta}$ are the completion pieces in the respective domains. The latter have the form \begin{equation}\label{h_comp} h^{\rm comp\pm}_{\alpha\beta}= {\cal E}^{\pm}h^{(\delta M)}_{\alpha\beta}+{\cal J}^{\pm}h^{(\delta J)}_{\alpha\beta}, \end{equation} where ${\cal E}^{\pm}$ and ${\cal J}^{\pm}$ are constant coefficients (depending only on the details of the orbit), and $h^{(\delta M)}_{\alpha\beta}$ and $h^{(\delta J)}_{\alpha\beta}$ are certain homogeneous, stationary and axisymmetric perturbations representing, respectively, mass and angular-momentum perturbations of the Kerr geometry. These two perturbations can be readily written down in analytic form (fixing the gauge and the overall normalization), as we do in Eqs.\ (\ref{eq:dMexplicit}) and (\ref{eq:dJexplicit}) below. The problem of completion thus reduces to that of determining the values of the four coefficients ${\cal E}^{\pm},{\cal J}^{\pm}$. In fact, ${\cal E}^+$ and ${\cal J}^+$ may be readily deduced from global conditions on the total mass and angular-momentum contents of the system (this will be described in Sec.\ \ref{s:asymp}), so the problem further reduces to that of determining ${\cal E}^{-}$ and ${\cal J}^{-}$ alone, or, equivalently, the two differences \begin{equation}\label{diffEJ} [{\cal E}]:={\cal E}^{+}-{\cal E}^{-}, \quad\quad [{\cal J}]:={\cal J}^{+}-{\cal J}^{-}. \end{equation} In this work we propose and implement a new strategy for determining $[{\cal E}]$ and $[{\cal J}]$. The basic idea is as follows. Let $\cal S$ represent the (2+1-dimensional) surface $r=r_p(t)$ that is the interface between ${\cal S}^+$ and $\cal S^{-}$. The particle's orbit traces a timelike curve $\gamma$ in $\cal S$, and we let $\check{\cal S}:={\cal S}-\gamma$, i.e.\ $\check{\cal S}$ is the part of $\cal S$ excluding the particle's orbit. {\em Our strategy is based on the expectation that gauge-invariant fields constructed from the full, physical perturbation must be smooth everywhere but on the particle, and, in particular, they must be smooth on $\check{\cal S}$}. Thus, we construct a suitable set of (real) invariant fields ${\cal I}_n^{\pm}$ ($n=1,2,\ldots$) corresponding to the full perturbation $h^{\pm}_{\alpha\beta}$, and require that ${\cal I}_n^{+}={\cal I}_n^{-}$ on $\check{\cal S}$, for each $n$. This continuity requirement translates to a set of simple algebraic equations for $[{\cal E}]$ and $[{\cal J}]$, which are then solved. Since there are two unknowns, we require two independent matching conditions. This can be achieved by imposing ${\cal I}_n^{+}={\cal I}_n^{-}$ for a pair of independent invariants (say ${\cal I}_1$ and ${\cal I}_2$) at an arbitrarily chosen point of $\check{\cal S}$; or, possibly, by imposing continuity of a single invariant (say ${\cal I}_1$) at two different longitudinal points of $\check{\cal S}$. We shall confirm that the two procedures give identical results, and, indeed, that they each automatically guarantee the continuity of all invariants ${\cal I}_n$ on the entire surface $\check{\cal S}$. Since the completion piece $h^{\rm comp\pm}_{\alpha\beta}$ is stationary and axisymmetric, in the above calculation we need only concern ourselves with the stationary and axisymmetric piece of $h^{\pm}_{\alpha\beta}$. Since $h^{\rm comp\pm}_{\alpha\beta}$ is given in a simple analytic form, the main calculation task, therefore, is to derive the stationary and axisymmetric piece of the reconstructed metric $h^{\rm rec\pm}_{\alpha\beta}$. The reconstruction procedure yields individual multipole ($\ell$-)modes of $h^{\rm rec\pm}_{\alpha\beta}$, and the main challenge is in the evaluation of the sum of multipole contributions. We show how this can be done analytically. In fact, the stationarity and axial symmetry of the relevant perturbation enable us to perform the entire calculation analytically, even for non-circular orbits. We note the distinction between the task of completion and the (more ambitious) task of constructing a metric perturbation $h_{\alpha\beta}$ in a gauge in which it is globally smooth (except on the particle). Even after completion, our perturbation will in general fail to be continuous on $\check{\cal S}$. This discontinuity can, in principle, be removed with a suitable gauge transformation, but here we do not pursue this additional task of ``gauge regularization''. Whether a gauge regularization is required in practice depends on the particular application, and sometimes it suffices to gauge-regularize only some relevant piece of the perturbation; we shall discuss a few examples in the concluding section of this paper. We intend to present a systematic treatment of gauge regularization in a future work. Finally, we note that our calculation, and the completion perturbation that comes out of it, apply specifically for a reconstruction done in the so-called ``ingoing'' radiation gauge [see Eq.\ (\ref{gaugecondition})]. To determine the completion for a reconstruction in the companion ``outgoing'' gauge would require a separate calculation, which we have not carried out (though we expect it to be entirely analogous to the calculation presented here). The structure of this paper is as follows. In Sec.\ \ref{s:transpsi2} we present our set of auxiliary gauge-invariant quantities ${\cal I}_n$. In Sec.\ \ref{s:Schcir}, as a warm-up exercise, we perform our completion calculation and determine $[{\cal E}]$ and $[{\cal J}]$ for circular geodesic orbits in Schwarzschild spacetime. Section \ref{s:Kerrcirc} extends the calculation to circular equatorial geodesic orbits in Kerr spacetime, and Sec.\ \ref{s:ecceqorbits} extends it further to all bound (eccentric) geodesic orbits in the equatorial plane in Kerr. In Section \ref{s:asymp} we use asymptotic analysis at spatial infinity in order to determine the completion amplitudes ${\cal E}^+$ and ${\cal J}^+$, and consequently, using our now-known values of $[{\cal E}]$ and $[{\cal J}]$, also the amplitudes ${\cal E}^-$ and ${\cal J}^-$. Section \ref{s:summary} contains a summary and a discussion of remaining issues and generalizations. Some of the technical details of our calculation are relegated to appendices. Our conventions for the Newman-Penrose formalism and for the reconstruction procedure follow those of Ref.\ \cite{vandeMeent:2015lxa}. In particular, we adopt the metric signature ${-}{+}{+}{+}$ (unlike, e.g., FKS and much of the early Newman-Penrose literature). For convenience, we give in Appendix \ref{a:KerrBack} a full review of vacuum reconstruction using our conventions. We use geometrized units with $G=c=1$ throughout. In the rest of this introduction we review previous attempts at the completion problem, and describe some other relevant work. We highlight the way in which our method differs from that of earlier work. \subsection{Survey of previous, related work} An initial investigation of the completion problem for particle sources was carried out by L.\ Price (unpublished thesis, \citep{PriceThesis}). Specializing to a Schwarzschild background, Price attempted to determine the completion piece through the requirement that $h^{\rm comp+}_{\alpha\beta}$ matched smoothly with $h^{\rm comp-}_{\alpha\beta}$ on $\check{\cal S}$ (allowing for arbitrary gauge transformations on either sides of the surface). In Kerr, this procedure only makes sense under the unproven assumption that the reconstructed part $h^{\rm rec}_{\alpha\beta}$ is itself smooth on $\check{\cal S}$ (up to a gauge transformation). In our method we instead impose continuity (up to gauge) of the {\it full} (completed) perturbation, so need not resort to making such an assumption. Also, as described above, we impose continuity of certain invariant fields and not of the (gauge dependent) metric perturbation. This way we evade the arduous task of gauge regularization, which is unnecessary for the sole purpose of determining $h^{\rm comp}_{\alpha\beta}$. In their series of papers pioneering the radiation-gauge approach to the self-force, FKS have tackled the problem of determining the completion piece for circular geodesic orbits in the equatorial plane (first in Schwarzschild \citep{Keidlhom,friedman1,friedman2} and later in Kerr \citep{friedman3}). Their treatment invokes the Komar definitions of energy and angular momentum as applied to the stationary and axisymmetric piece of the perturbed spacetime: The amplitudes ${\cal E}^{\pm}$ and ${\cal J}^{\pm}$ are determined (essentially) by fixing the Komar mass and angular momentum of the perturbed spacetime at $r\to\infty$ and on the black hole's horizon. It is implicitly assumed, however, that the reconstructed piece $h^{\rm rec}_{\alpha\beta}$ has no contribution to the Komar quantities. This is readily justified in the Schwarzschild case, where the mass and angular momentum content of the perturbation is contained entirely in its monopole and dipole modes (which have no contribution from $h^{\rm rec}_{\alpha\beta}$). But, to the best of our knowledge, the assumption remains unproven in the Kerr case. The calculation to be presented in the current paper will indirectly establish the validity of FKS's assumption. In a slightly different context, Dolan and Barack \citep{dolan3}\footnote{Ref.\ \citep{dolan3} discusses a direct calculation of the metric perturbation (in the Lorenz gauge) via numerical time evolution of the linearized Einstein's equations. The problem of completion takes a different form within this treatment, the main issue being the mitigation of gauge instabilities that affect the stationary and axisymmetric part of the perturbation.} recently discussed an alternative method for determining the mass and angular-momentum content of an arbitrary region of perturbed space, building on work by Abbott and Deser \citep{AbbDes}. The Abbott--Deser formulation relies only on the existence of time-translation and rotational Killing symmetries in the {\it background} spacetime, and is thus applicable to a general perturbed Kerr geometry. The method prescribes certain conserved quantities (one for each background Killing field), which are constructed from the metric perturbation and its first derivatives, integrated over a closed 2-surface on a spacelike hypersurface. This provides a quasi-local definition of the energy and angular-momentum content of the volume enclosed within the surface, which can be shown to coincide with standard definitions (e.g., ADM's) in the appropriate limits. One can imagine using this method to determine the completion amplitudes ${\cal E}^{\pm}$ and ${\cal J}^{\pm}$ by fixing the Abbott--Deser mass and angular momentum of the completed perturbation at infinity and on the horizon. We have attempted this approach, but found the necessary surface integrals, and summation over modes, very hard to evaluate in practice (except at infinity). Thus, we have not been able to use this method for determining ${\cal E}^{\pm}$ and ${\cal J}^{\pm}$. Nonetheless, we think that, with some further development, the approach may provide a viable alternative to (and a check on) our method. An essentially equivalent completion problem was recently studied by Sano and Tagoshi, who considered the stationary and axisymmetric configuration of a rotating circular mass ring around a Schwarzschild \citep{SaTa} or a Kerr \citep{SaTa2} black hole. Their analysis, like ours, seeks to obtain $[{\cal E}]$ and $[{\cal J}]$ from continuity conditions imposed outside the matter source. However, Sano and Tagoshi do not employ gauge-invariant quantities as in our method, and instead require continuity of the metric perturbation and of the (gauge dependent) Weyl scalars $\psi_1$, $\psi_2$ and $\psi_3$. In their construction, the completed metric perturbation and Weyl scalars are smooth on the sphere $r=r_0$ (where $r_0$ is the ring's radius), off the ring itself, but are singular on the equatorial plane outside the ring. Due to the remaining singularity, it remains unclear whether the prescribed completion is unique. As we will demonstrate in the current paper (for a point particle source), the completion is determined uniquely by looking at invariant quantities that must be smooth everywhere in the vacuum region. | \label{s:summary} We have determined the completion piece of the metric perturbation for any bound geodesic orbit in Schwarzschild spacetime or in the equatorial plane of a Kerr black hole. Recalling (\ref{h_comp}) with (\ref{EJ+}) and (\ref{EJ-}), our main result is that \begin{equation}\label{mainresult} h^{\rm comp\pm}_{\alpha\beta}= \left\{ \begin{array}{ll} E h^{(\delta M)}_{\alpha\beta}+Lh^{(\delta J)}_{\alpha\beta} & \text{in ${\cal S}^+$}, \\ 0 & \text{in ${\cal S}^-$}, \end{array} \right. \end{equation} for any such orbit. Here $h^{(\delta M)}_{\alpha\beta}$ and $h^{(\delta J)}_{\alpha\beta}$ are the vacuum perturbations given explicitly in Eqs.\ (\ref{eq:dMexplicit}) and (\ref{eq:dJexplicit}), and $E$ and $L$ are the conserved energy and angular momentum associated with the geodesic orbit. The result (\ref{mainresult}) assumes that the total energy and angular momentum contents of the perturbation are fixed as in Eq.\ (\ref{AD_total}). {\em Independently of this assumption}, we find that the jump across $\cal S$ in the completion piece of the metric perturbation is given by \begin{equation}\label{[hcomp]} [h^{\rm comp}_{\alpha\beta}]=E h^{(\delta M)}_{\alpha\beta}+Lh^{(\delta J)}_{\alpha\beta}. \end{equation} As a consequence (and a corollary) of (\ref{[hcomp]}), we find that the {\it reconstructed} piece of the metric perturbation contains no mass or angular momentum (either in or out of $\cal S$), in a sense expressed in Eq.\ (\ref{MLin}). Our method consists in demanding that certain gauge-invariant fields constructed from the completed metric perturbation (and its derivatives) are continuous anywhere away from sources. This is a necessary condition that the perturbation must satisfy in order to solve the linear field equations anywhere in the vacuum (the reconstructed piece of the perturbation, by itself, fails to do so). As we have seen, imposing this continuity condition on suitably chosen invariant field(s) determines the completion piece of the perturbation completely and uniquely (up to gauge perturbations). It is expected from uniqueness that our completion renders the invariant fields {\em smooth} (and not just continuous), although we have not confirmed that with an explicit calculation. Our final results, as expressed in Eqs.\ (\ref{mainresult}), (\ref{[hcomp]}) and (\ref{MLin}), are extremely simple despite the long calculation leading to them. This is striking, and begs an explanation. In particular, one naturally wonders whether the fact that the reconstructed perturbation does not contain mass or angular momentum could be arrived at based on a more general argument (but one that is nonetheless as mathematically rigorous), without resorting to a detailed calculation. We have not been able to devise such an argument so far (except in the trivial, Schwarzschild case). One way to approach the problem would be via a direct evaluation of the Abbott-Deser mass and angular momentum contents of $h_{\alpha\beta}^{{\rm rec}\pm}$ in ${\cal S}^-$, which we have not been able to do analytically for Kerr, so far. If in the future a simple method is found to perform such a calculation in the Kerr case, it could offer a more direct route to the completion problem, and perhaps hint at the reasons for the simplicity of the results. The work presented here takes an important step towards a complete formulation of a practical scheme for calculating the gravitational self-force in astrophysically motivated inspiral problems, conveniently starting from solutions of the Teukolsky equation. Two important tasks remain. First, and most obvious, our analysis must be extended to encompass {\it non-equatorial} geodesic orbits in Kerr spacetime. We envisage using a similar methodology to the one applied here. One could start with the special subset of circular inclined (``spherical'') orbits, for which the energy-momentum source is supported on $r=r_0$ and $\pi-\theta_1\leq \theta\leq\theta_1$ with some constant $r_0$ and $0<\theta_1<\pi/2$. In this case, one would require continuity of the invariant fields across $r=r_0$ for $0\leq\theta<\theta_1$ and $\pi-\theta_1\leq\theta<\pi$. For orbits that are both inclined and eccentric, which are generically ergodic, the key step will be the formulation of a suitable decomposition of the energy-momentum source into simple partial elements (spherical sections?) that are each energy conserving, following our strategy in Sec.\ \ref{s:Kerrcirc}. The special cases of polar orbits and of resonant orbits would need to be considered separately. The second remaining task is that of {\it gauge regularization}. While our completion procedure guarantees the continuity of invariant fields at vacuum points, it does not guarantee the continuity of the metric perturbation itself. In fact, our completed metric perturbation will generally have a gauge discontinuity across $\cal S$, even off the particle (see, for example, the explicit calculation in Ref.\ \cite{vandeMeent:2015lxa}). This can be a problem in applications that require perturbation information on both sides of $\cal S$, such as a self-force calculation based on the simpler of the two methods formulated in Ref.\ \citep{BMP1}. Typically, for the results of a calculation to have a clear physical interpretation, one must place certain conditions on the gauge. For instance, one usually requires asymptotic flatness, and, for periodic orbits, also a particular periodicity. In the latter case, one must be able to relate the frequency (or frequencies) of the perturbation in and out of $\cal S$, and, for that purpose, one must be able to relate the coordinate times and angles in and out of that surface. A continuity of the perturbation across $\cal S$ is necessary for ``passing on'' such (and other) essential gauge information from the exterior to the interior. The goal of gauge regularization is to locally remove the gauge discontinuity in the neighbourhood of the particle, via a suitable, discontinuous gauge transformation. Optimally, one would aim to construct a perturbation that is entirely continuous across $\check{\cal S}$, at least near the particle. However, depending on the application, it might be sufficient to gauge-regularize only certain relevant pieces of the perturbation. For example, a partial gauge regularization of the SAS piece of the completed perturbation was performed recently in Refs.\ \citep{Shah:2015nva} (for circular orbits in Schwarzschild) and \citep{vandeMeent:ISCO} (for circular equatorial orbits in Kerr), sufficient for the purpose of calculating ``invariant'' frequencies (that is, frequencies with respect to asymptotic time $t$). This gauge regularization should now be extended to more general orbits; our partial-ring approach should offer an easy route. Other applications may require further gauge regularization of other pieces of the perturbation. For instance, one may need to work in a ``center-of-mass'' gauge (as defined via a condition on the mass dipole moment of the perturbed spacetime) in order to allow comparison with certain results from the post-Newtonian theory. This would require going beyond the SAS part, and gauge-regularizing also the $m=\pm 1$ azimuthal modes of the completed perturbation. Such a calculation is yet to be done. Other pieces of the perturbation may need to be gauge-regularized for other foreseeable applications. | 16 | 9 | 1609.01227 |
1609 | 1609.04128_arXiv.txt | The determination of exoplanet properties and occurrence rates using {\it Kepler} data critically depends on our knowledge of the fundamental properties (such as temperature, radius and mass) of the observed stars. We present revised stellar properties for 197,096 {\it Kepler} targets observed between Quarters 1--17 (Q1--17), which were used for the final transiting planet search run by the {\it Kepler} Mission (Data Release 25, DR25). Similar to the Q1--16 catalog by Huber et al.\ the classifications are based on conditioning published atmospheric parameters on a grid of Dartmouth isochrones, with significant improvements in the adopted methodology and over 29,000 new sources for temperatures, surface gravities or metallicities. In addition to fundamental stellar properties the new catalog also includes distances and extinctions, and we provide posterior samples for each stellar parameter of each star. Typical uncertainties are $\sim$\,27\% in radius, $\sim$\,17\% in mass, and $\sim$\,51\% in density, which is somewhat smaller than previous catalogs due to the larger number of improved \logg\ constraints and the inclusion of isochrone weighting when deriving stellar posterior distributions. On average, the catalog includes a significantly larger number of evolved solar-type stars, with an increase of 43.5\% in the number of subgiants. We discuss the overall changes of radii and masses of {\it Kepler} targets as a function of spectral type, with particular focus on exoplanet host stars. | Since the launch of the NASA {\it Kepler} mission \citep{2010Sci...327..977B,2010ApJ...713L..79K} in 2009, a tremendous number of discoveries in exoplanet science have been made possible thanks to the near-continuous, high-precision photometric data collected for over four years. To date 4,706 planet-candidates have been identified, over 49\,\% of which have been confirmed or validated \citep{2014ApJ...784...45R,2016ApJ...822...86M} This large number of detections allowed statistical studies of planet occurrence rates \citep[e.g.][]{2012ApJS..201...15H,2013ApJ...766...81F,2015ApJ...807...45D,2015ApJ...809....8B, 2015ApJ...799..180S} as well as numerous individual discoveries such as \kep's first rocky exoplanet, Kepler-10b \citep{2011ApJ...729...27B}, circumbinary planets \citep[e.g.][]{2012ApJ...758...87O,2014ApJ...784...14K,2015ApJ...809...26W}, or the detection of planets in or near the habitable zone \citep[e.g.][]{2013ApJ...773...98B,2013Natur.494..452B,2013Sci...340..587B,2015ApJ...800...99T,2016ApJ...830....1K}. Stellar astrophysics also benefited from the exquisite data of {\it Kepler} with a large number of breakthrough discoveries, such as the asteroseismic measurement of the internal rotation \citep{2012Natur.481...55B, 2012ApJ...756...19D,2012A&A...548A..10M, 2014A&A...564A..27D} and magnetic fields \citep{2015Sci...350..423F, 2016Natur.529..364S} of subgiants and red giants, the detection of surface rotation and its relation to ages of solar-like stars \citep[e.g.][]{2014A&A...572A..34G,2014ApJS..211...24M, 2016MNRAS.456..119C, 2016Natur.529..181V}, as well as the measurement of magnetic activity of main-sequence stars \citep[e.g.][]{2014A&A...562A.124M,2015ApJ...807..109A,2016A&A...589A.118S}. Asteroseismic data of red giants are now also being used to perform galactic archeology by combining them with high-resolution spectroscopy \citep[e.g.][]{2014ApJS..215...19P,2014MNRAS.445.2758R,2015MNRAS.451.2230M}. Since the transit technique measures planet properties only relative to the host star, it is crucial to characterize the parameters of the host stars to derive precise parameters of the planets. Before the launch of the mission, the {\it Kepler} Input Catalog \citep[KIC][]{2011AJ....142..112B} was constructed based on broadband photometry, with the primary purpose to select targets for observations \citep{2010ApJ...713L.109B} and provide an initial classification of planet candidates. In order to improve the KIC, \citet{2014ApJS..211....2H} presented revised stellar properties for 196,468 {\it Kepler} targets, which were used for the Q1-16 Transit Planet Search and Data Validation run \citep{2014ApJS..211....6T}. The catalog was based on atmospheric properties (temperature $T_{\rm eff}$, surface gravity $\log g$, and metallicity [Fe/H]) published in the literature using a variety of methods (asteroseismology, spectroscopy, exoplanet transits, photometry), which were then homogeneously fitted to a grid of Dartmouth (DSEP) isochrones \citep{2008ApJS..178...89D}. The catalog was updated in early 2015 for a Q1-17 transit detection run \citep[Data Release 24\footnote{\url{ http://exoplanetarchive.ipac.caltech.edu/docs/KeplerStellar\_Q1\_17\_documentation.pdf}}, DR24, ][]{Huber2014} based on the latest classifications of {\it Kepler} targets in the literature and using the same methodology as \citet{2014ApJS..211....2H}. { We discarded the stars observed only in Q0 as the transit search pipeline does not investigate the data from the commissioning phase for planets.} { However we note that 180 stars with only Q0 data have slipped into the catalog during the input data consolidation.}% \begin{figure*}[htbp] \begin{center} \includegraphics[width=5.8cm, trim=2cm 0.5cm 2cm 0]{Figures/HRD_surveys_density_0.pdf} \includegraphics[width=5.8cm, trim=2cm 0.5cm 2cm 0]{Figures/HRD_surveys_density_1.pdf} \includegraphics[width=5.8cm, trim=2cm 0.5cm 2cm 0]{Figures/HRD_surveys_density_2.pdf} \includegraphics[width=5.8cm, trim=2cm 0.5cm 2cm 0]{Figures/HRD_surveys_density_3.pdf} \includegraphics[width=5.8cm, trim=2cm 0.5cm 2cm 0]{Figures/HRD_surveys_density_4.pdf} \includegraphics[width=5.8cm, trim=2cm 0.5cm 2cm 0]{Figures/HRD_surveys_density_5.pdf} \caption{Input surface gravity and effective temperature for the full catalog (top left panel) and for the five largest sources of new input values (see legend on the top of each panel). Color-coding denotes the logarithmic number density as shown in the color bar in the top left panel.} \label{Fig1} \end{center} \end{figure*} In this work we present another major update of the \kep\ stellar properties catalog for 197,096 {\it Kepler} targets. The catalog was developed to support the final transit detection run (Data Release 25, hereafter DR25) prior to the close-out of the {\it Kepler} mission. Initial plans for the catalog included a homogeneous reclassification based on broadband colors only (i.e.\ without relying on classifications from the KIC, see Section 9 in H14). { However, the limited sensitivity of available broadband colors and the complexity of constructing priors that accurately reproduce the {\it Kepler} target selection function made such a classification scheme unfeasible for the delivery of the catalog.} Thus, similar to previous versions, the updated catalog presented here is based on the consolidation of atmospheric properties (temperature \teff, surface gravity \logg, metallicity \feh) that were either published in the literature or provided by the {\it Kepler} community follow-up program \citep[CFOP,][]{2010arXiv1001.0352G}, with input values taken from different methods such as asteroseismology, spectroscopy, { Flicker}, and photometry. | \subsection{Quality Control Tests} \subsubsection{Comparison of Input and Output Values} The first quality control test was to compare the input and output values for a well characterized sample of stars that have asteroseismic gravities or spectroscopic effective temperatures. Large deviations between input and output \teff\ or \logg\ values may indicate potential misclassifications due to problems with the adopted input values or the isochrone fitting methodology. Asteroseismic gravities are available for 16,947 stars (red giants and dwarfs) while spectroscopic temperatures were obtained for 14,813 stars. Figure~\ref{complogg} shows the difference between the input values of $\logg$ and $T_{\rm eff}$ and the DR25 values for the subsample of aforementioned stars. We see that for $\log g$ most of the output values agree with the seismic values within 1$\sigma$ and 5 stars disagree by more than 1$\sigma$. The largest disagreement concerns stars with $\log g$ values between 2 and 3, i.e. red giants including red clump stars. This can be explained by the fact that the DSEP models do not include helium-burning red giant models, as pointed out by H14. The effective temperature comparison (bottom panel of Figure~\ref{complogg}) shows that in most cases the values provided in the catalog agree with the spectroscopic input values within 1$\sigma$. A large number of stars with $T_{\rm eff}$ between 3500K and 5500K disagree by more than 1$\sigma$. These stars are again mostly red giants. { We note that 11} stars disagree by more than 5\,$\sigma$. Among them, three stars (KIC 8714886, 10536147, and 10797526) have $T_{\rm eff} >$\,15,000\,K, well beyond our grid of models { (and out of the plot)}, so we reported their DR24 stellar parameters for which the effective temperatures are close to 16,000\,K. The remaining nine stars have input values that are slightly off the model grid, thus the code converges to the parameter space that is significantly different than the input values. Three of these stars (KIC 2585447, 3968716, and 8559125) are new red giants with seismic $\log g$ and spectroscopic $T_{\rm eff}$. The first two stars are flagged in \citet{2016ApJ...827...50M} as a possible blend. This means that either the oscillation detection comes from another close-by star or that the blend has an impact on the estimate of the effective temperature in the spectroscopic analysis. KIC 8559125 is not a misclassified red giant anymore as it was removed from the list after the delivery of the DR25 catalog as explained in Section 5.3. The last five stars (KIC 3335176, 3346584, 4078024, 4263398, 8710336) have seismic and/or spectroscopic input values but are slightly off the grid, which explains the large difference between the input and the output values. \begin{figure} \begin{center} \includegraphics[width=9cm]{Figures/comp_logg_inout_ast.pdf} \includegraphics[width=9cm]{Figures/comp_teff_inout_spe.pdf} \caption{Top panel: differences between input and output $\log g$ values in units of $\sigma$ for stars with asteroseismic input values for $\log g$. The adopted typical uncertainty for asteroseismic $\log g$ values is 0.03\,dex. Bottom panel: Same as top panel but for stars with spectroscopic $T_{\rm eff}$. The adopted uncertainty is 2\%. } \label{complogg} \end{center} \end{figure} \subsubsection{Comparison to Previous Catalogs} Figure~\ref{Fig3} shows the surface gravity versus temperature distribution for DR25 (left panel) and DR24 (right panel). It is evident that the DR25 catalog contains a significantly larger fraction of subgiants, mostly due to the inclusion of the LAMOST and Flicker surface gravities. Using the equations (8) and (9) from \citet{2016ApJS..224....2H}, we computed the number of subgiants and found that DR25 contains 15,893 subgiants compared to 11,078 in DR24, a 43.5\% increase. % While these updates generally only affect the brighter {\it Kepler} targets ($Kp \lesssim 13$), this indicates that the DR25 catalog should be less prone to the systematic underestimation of radii for solar-type dwarfs than previous catalogs. \begin{figure*} \begin{center} \includegraphics[width=17cm]{Figures/numdens3.pdf} \caption{Surface gravity versus effective temperature for all classified stars in this catalog (DR25, left panel) and the previous catalog (DR24, right panel). Color denotes the logarithmic number density of stars.} \label{Fig3} \end{center} \end{figure*} Figures~\ref{compR} and \ref{compM} show the ratios of DR24 to DR25 radii and masses. These plots represent the logarithm of the number density of stars for different effective temperatures and gravity bins. Figures \ref{compR} and \ref{compM} are included for all stars (upper left) as well as the samples highlighted in Section 2.2. Figure~\ref{compR} shows that the highest density of stars is close to the $R_{\rm DR24}/R_{\rm DR25}$=1 line, which means their radii did not change. The stars with the most significant changes in the stellar parameters correspond to stars with new input values, as expected. Stars with LAMOST and Flicker inputs have a larger number density of stars slightly below the ratio equals 1 line, which means that these stars have become larger (up to a factor of 2). Stars with APOGEE inputs are on both sides of the 1 line with higher number density above 1 (i.e. smaller radii in the DR25). Finally, the new red giants have a radius ratio close to 0, corresponding to a large increase of the size of the star from a dwarf to a red giant. Some of these cases are also present in the APOGEE sample. \begin{figure*} \begin{center} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_R_surveys_density_0.pdf} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_R_surveys_density_1.pdf} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_R_surveys_density_2.pdf} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_R_surveys_density_3.pdf} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_R_surveys_density_4.pdf} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_R_surveys_density_5.pdf} \caption{Ratio of radii from DR24 and DR25 for full sample (top left panel), the LAMOST sample (top middle panel), the APOGEE sample (top right panel), the sample with Flicker \logg (bottom left panel), the sample of stars with CFOP spectroscopy (bottom middle panel), and the sample of new red giants (bottom right panel). Color denotes the number density of stars.} \label{compR} \end{center} \end{figure*} \begin{figure*}[htbp] \begin{center} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_M_surveys_density_0.pdf} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_M_surveys_density_1.pdf} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_M_surveys_density_2.pdf} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_M_surveys_density_3.pdf} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_M_surveys_density_4.pdf} \includegraphics[width=5.9cm, trim=2cm 0.5cm 2cm 0]{Figures/ratio_M_surveys_density_5.pdf} \caption{Same as Figure \ref{compR} but for stellar mass.} \label{compM} \end{center} \end{figure*} The mass comparison also shows that the highest number density of stars is close to 1:1 line. Stars with Flicker and CFOP inputs see their masses change by less than a factor of 2. The new inputs from LAMOST and APOGEE show a similar behaviour except that they also lead to smaller masses for stars with $\teff \sim 5000$\,K. In both Figures \ref{compR} and \ref{compM} we see a group of cool stars ($T_{\rm eff} <$\,3250\,K) which systematically fall below the 1:1 line. These are stars that were erroneously classified as giants in the H14 catalog and corrected using the dwarf classifications by \citet{2012ApJ...753...90M} in the DR25 catalog, as further explained in Section 5.3. After completion of DR25 catalog, \citet[][hereafter G16]{2016MNRAS.457.2877G} published the revised properties of 4216 M dwarfs observed by {\it Kepler}. A total of 699 stars in G16 are not included in the DR25 catalog since they were only observed during Q17 and { neither had KIC values available nor spectroscopic inputs. For 68 stars spectroscopic parameters were also published by \citet{2016A&A...594A..39F}}. For the stars in common between G16 and DR25, the two temperature scales are close for cool stars below 3500K, although the temperatures from G16 are on average 200K hotter for 63 stars. Above 3500K, the temperatures from G16 are cooler compared to the DR25 values with differences larger than 200K (up to 2000K) for 487 stars. We found that 54 stars in G16 are { classified} as red giants in the DR25. A small sample of these stars (16) were classified as red giants from seismology so the detection of oscillations does not agree with the dwarf classification of G16. A majority of the stars with DR25 temperatures hotter than 4000K have a $T_{\rm eff}$ provenance from the KIC and PHO54. Given that the analysis by G16 was specifically tailored towards cool dwarfs some of these stars may be misclassified in the DR25 catalog, and hence the classifications by G16 should be preferred over the DR25 catalog. We list these potentially misclassified stars in Appendix C, Table~\ref{tab:Mdwarfs}. \subsubsection{Effects on Planet Host Star Parameters} As a final test, we looked in particular at planet host stars parameters as they directly impact the size inferred for the planets. Figure~\ref{compRM_planet} compares the radii and masses of the planet host stars computed in this work with the DR24 catalog. It is comforting to see that stars where we used the same inputs as the DR24 catalog (black diamonds in the figure) fall on or are very close to the line $R_{Q1-17}$/$R_{\rm new}$=1, indicating that the radii of these stars changed by a few percent at most. The small change can be explained by the updated isochrone grid that was used in this work. As expected, the largest changes affected stars with new input values. Many stars with new CFOP parameters have a different evolutionary stage. Indeed, we aforementioned that a fraction of stars moved from main sequence stars to more evolved subgiants. This explains the number of stars that now have a larger radius than the previous catalog (cyan symbols). This is also the case for the star with the Flicker input (blue symbol) and some of the individual new inputs (pink symbols). For stars cooler than ~4500K, we notice that a significant number of host stars become smaller and less massive. Specifically, for eight host stars the spectroscopic classification by \citet{2014ApJ...784...45R} was subsequently shown to lead to systematically overestimated effective temperatures and radii, and hence led to biased estimates in the DR24 catalog. To correct this, we adopted the inputs from H14 for these stars for the DR25 catalog. \begin{figure}[htbp] \begin{center} \includegraphics[width=9cm]{Figures/compR_confirmed_planets2.pdf} \includegraphics[width=9cm]{Figures/compM_confirmed_planets2.pdf} \caption{Comparison of radii and masses of planet host stars showing the different subsamples where we used either new inputs values or the same input values as in the previous catalog.} \label{compRM_planet} \end{center} \end{figure} The following is a list of specific host stars with significant changes in their stellar parameters:% 1) The radii of the K-dwarfs KIC 5640085 (KOI-448 and Kepler-148) and KIC 10027323 (KOI-1596 and Kepler-309) decreased by $\sim\,40-50$\% due to the correction of the spectroscopic input values from \citet{2014ApJ...784...45R}, as discussed above. The input parameters were reversed back to the H14 catalog, which were based on \citet{2012ApJ...750L..37M}. 2) KIC 7529266 (KOI-680, Kepler-635) is a solar-type star ($\sim$\,6000K) and shows that the largest change in radius ($R_{\rm Q1-17}/R_{\rm new}$\,$\sim$\,0.3). We adopted updated input values from \citet{2015AA...575A..71A}, which lists a $\logg$ of 3.5\,dex compared to 4.35\,dex in the KIC where the $\log g$, leading to a large increase in radius. It is not surprising to see this change given that the original KIC had known shortcomings regarding the classification of subgiants. 3) KIC 8733898 (KOI-2842, Kepler-446), with $T_{\rm eff}\sim$3500K and $R_{\rm Q1-17}$/$R_{\rm new}\sim$\,1.4, had its input values changed from \citet{2013ApJ...767...95D} to \citet{2015ApJ...801...18M}, leading to a smaller radius. The spectroscopic input should be more reliable than the photometric classification in the previous catalog. \subsection{Distances and extinction} In addition to stellar parameters, the DR25 catalog also includes distances and extinction values for $\sim$\,196,850 stars (see Section 5.3 for more details). Figure~\ref{histDW_RG} shows the distribution of distances for dwarfs (left panel) and for red giants (right panel) observed by {\it Kepler}. As expected, red giants observed by \kep\ are on average more distant than dwarfs. \begin{figure}[htbp] \begin{center} \includegraphics[width=6.5cm, angle=90]{Figures/hist_dist_DW.pdf} \includegraphics[width=6.5cm, angle=90]{Figures/hist_dist_RG.pdf} \caption{Distribution of distances for dwarfs (top panel) and red giants (bottom panel) in the DR25 catalog.} \label{histDW_RG} \end{center} \end{figure} We also compared our catalog distances to \citet[][hereafter R14]{2014MNRAS.445.2758R}, who combined asteroseismology with APOGEE spectra to derive distances and extinctions for a sample of $\sim$\,2000 \kep\ red giants. The comparison showed that the catalog distances are systematically larger by up to \,50\%, which is due to the fact that our model grid does not include He-core burning models for low-mass stars, and hence giants are preferentially fitted to higher-mass, more luminous and hence more distant models. This bias was already pointed out in H14, and should be kept in mind when using catalog results for red giant stars. We emphasize that this distance bias is not expected to be relevant for dwarfs and subgiant stars, which form the majority of the {\it Kepler} target sample. Finally, a comparison of extinction values to \citet[][]{2014MNRAS.445.2758R} showed that the catalog values for giants are systematically larger by $\sim$0.1--0.3\,mag on average, similar to the results found for the KIC (see Figure 17 of R14). This is most likely due to the simplified 3D reddening model adopted in this work and the KIC compared to the method adopted by R14, which derives reddening values by comparing synthetic to observed photometry on a star-by-star basis. Since this method is only effective if \teff-\logg-\feh\ can be derived independently from photometry, it cannot be applied to the full {\it Kepler} sample at this point. \subsection{Catalog Shortcomings} While this paper provides important improvements over previous {\it Kepler} stellar properties catalogs, several shortcomings remain. In particular: \begin{itemize} \item For stars with input values that fall off the Dartmouth isochrone grid (e.g. very cool dwarfs) we adopted the input and output values from H14. There are also 3 stars where we adopted the published values (KIC 5807616, 5868793 and 10001893). Indeed these three stars fall out of the grid because they are too hot with a temperature above 25,000K. These stars do not have distances and extinction values. The provenance for the mass, radius and density is MULT as they come from a different method. \item Unlike in previous deliveries we did not override catalog values with published solutions that provide better estimates for radii and masses (e.g. from asteroseismology) in order to homogeneously derive posterior distributions (including distances) for all stars. This means that for some stars better estimates for radii and masses may be available in the literature. % \item Similar to H14, the adopted isochrone grid does not include He-core burning models for low-mass stars and hence derived properties for red giants (such as radius, mass, and distances) will be systematically biased towards higher-mass stars (and more distant for red giants). Users are strongly encouraged to adopt values from dedicated Kepler red-giant classification programs such as the APOKASC \citep[e.g.][]{2014ApJS..215...19P} or SAGA \citep{2014ApJ...787..110C} surveys for such stars, or use the {\bf provided} \teff, \logg\ and \feh\ values in this catalog as input for deriving more accurate stellar properties. \item The new catalog also includes several corrections that were pointed out by the community since the release of the H14 catalog. Due to a coding error, every star in the Q1-16 catalog with input $T_{\rm eff}$\,<\,3250K was automatically classified as a dwarf using BT-Settl models even if the input $T_{\rm eff}$ indicated that it was a giant. To correct this, we revisited all dwarfs that have been classified using BT-Settl models and verified their evolutionary state using the \citet{2012ApJ...753...90M} spectroscopic classifications. When this was verified, we adopted the Q1-16 BT-Settl solution. These stars do not have distances and extinction values. The provenance for the mass, radius and density is BTSL. \item The number of misclassified red giants reported in \citet{2016ApJ...827...50M} is of 854 while in this delivery the misclassified red giants represent 835 stars. Between the delivery of the catalog and the finalization of the misclassified red giants some stars were dropped due to the pollution from nearby known red giants while others were added. Hence, there is a discrepancy of 51 stars. % \item For the vast majority of targets the input classifications assumed that all the stars are single systems, which can lead to biased stellar parameters if the targets are in fact multiple star systems. While we expect that this effect is small compared to the typical uncertainties in the derived stellar properties, future catalog releases will attempt to take into account information from various high-resolution imaging programs \citep[e.g.][]{2012AJ....144...42A,2014AJ....148...78D,2014AA...566A.103L,2016AJ....152...18B,2016arXiv161202392F,2016AJ....152....8K} for stellar classifications. \end{itemize} | 16 | 9 | 1609.04128 |
1609 | 1609.04402_arXiv.txt | Given a galaxy's stellar mass, its host halo mass has a lower limit from the cosmic baryon fraction and known baryonic physics. At $z>4$, galaxy stellar mass functions place lower limits on halo number densities that approach expected $\Lambda$CDM halo mass functions. High-redshift galaxy stellar mass functions can thus place interesting limits on number densities of massive haloes, which are otherwise very difficult to measure. Although halo mass functions at $z<8$ are consistent with observed galaxy stellar masses if galaxy baryonic conversion efficiencies increase with redshift, \textit{JWST} and \textit{WFIRST} will more than double the redshift range over which useful constraints are available. We calculate maximum galaxy stellar masses as a function of redshift given expected halo number densities from $\Lambda$CDM. We apply similar arguments to black holes. If their virial mass estimates are accurate, number density constraints alone suggest that the quasars SDSS J1044$-$0125 and SDSS J010013.02$+$280225.8 likely have black hole mass --- stellar mass ratios higher than the median $z=0$ relation, confirming the expectation from Lauer bias. Finally, we present a public code to evaluate the probability of an apparently $\Lambda$CDM-inconsistent high-mass halo being detected given the combined effects of multiple surveys and observational errors. | \label{s:introduction} In the framework of Lambda Cold Dark Matter ($\Lambda$CDM), galaxies form at the centres of dark matter haloes \citep[see][for reviews]{Silk12,Somerville15}. The ratio of galaxy stellar mass to halo mass has an absolute maximum at the cosmic baryon fraction ($f_b \sim 0.16$; \citealt{Planck15}). In practice, stellar feedback processes limit the maximum fraction of baryons converted to $\lesssim 40\%$ \citep{moster-09,Moster12,Moster18,Behroozi10,BWC13} even when adopting a \cite{Salpeter55} initial mass function (IMF). At $z<4$, this maximum fraction is never achieved for massive haloes ($M_h>10^{12}\Msun$), due to inefficient cooling \citep{Lu11b} and feedback from supermassive black holes \citep{Silk98}. At $z>4$, however, comparisons of galaxy and halo number densities suggest that massive haloes can reach from 10--40\% typical integrated efficiencies in converting baryons into stars, again depending on assumptions for the IMF and luminosity---stellar mass conversions \citep{BWC13,BehrooziHighZ,Finkelstein15,Sun16,Moster18}. Conversely, an observed galaxy mass ($M_\star$) places a lower limit on its host halo mass ($M_h$). $\Lambda$CDM alone implies that $M_h > M_\star / f_b \sim 6.3 M_\star$, and known baryonic physics would give more stringent limits depending on the assumed maximum conversion efficiency. This fact has been used in \cite{Steinhardt16} to argue that galaxy number densities at $z\sim5-6$ are already inconsistent with $\Lambda$CDM. Although we disagree with their assumptions (especially that the $M_\star / M_h$ ratio cannot increase at $z>4$) and therefore also their conclusions, the basic principle that galaxy number densities constrain halo number densities is well-established. As galaxy number densities are consistent with halo number densities for redshifts $z\lesssim 8$ \citep{BWC13}, we compute galaxy mass limits corresponding to expectations from % typical $\Lambda$CDM baryon fraction limits over $7<z<20$, observable with future infrared space-based telescopes (e.g., \textit{JWST}, the \textit{James Webb Space Telescope}, and \textit{WFIRST}, the \textit{Wide-Field InfraRed Survey Telescope}). Similarly, useful physical thresholds can be calculated for supermassive black holes (SMBHs). The number density of a given quasar sample places a lower limit on the number density of their host haloes, which in turn limits the maximum average host halo mass in $\Lambda$CDM \citep[see also][]{Haiman01}. This then limits the maximum average host galaxy mass (via $M_\star < f_b M_h$). Hence, given the number density of black holes above a certain mass, we can derive a lower limit for their $M_\bullet / M_\star$ ratios without requiring observations of the host galaxy. The current claimed maximum $M_\bullet / M_\star$ ratio is 15\% \citep{vdBosch12,Seth14}. In comparison, the highest median relations for the $M_\bullet / M_\star$ ratio at $z=0$ \citep{Kormendy13,Savorgnan16} give $\sim 0.4$\% for $M_\mathrm{bulge} = 10^{11}\Msun$ (after conversion to a \citealt{Salpeter55} IMF). Throughout, we assume a flat, $\Lambda$CDM cosmology with $\Omega_M = 0.309$, $\Omega_b = 0.0486$, $\sigma_8=0.816$, $h=0.678$, $n_s = 0.967$, corresponding to the best-fit \textit{Planck} cosmology \citep{Planck15}, as well as a \cite{Salpeter55} IMF. For halo masses, we use the virial overdensity definition of \cite{mvir_conv}. \begin{figure} \vspace{-5ex} \plotgrace{graphs/smhm_comp_mauro_biggest}\\[-5ex] \caption{Median stellar mass--baryonic mass ratios at $z=4-8$ reach up to 10-40\%. With a scatter of even 0.2 dex (as at low redshifts), it is plausible that individual galaxies can reach ratios near unity. Results have been converted to a \protect\cite{Salpeter55} IMF and to Planck cosmology where appropriate. \protect\cite{BWC13}, \protect\cite{Stefanon17}, and \protect\cite{Moster18} use abundance matching; \protect\cite{Harikane16} uses halo occupation distribution modeling of angular correlation functions.} \label{f:smhm} \end{figure} \begin{figure*} \vspace{-6ex} \plotgrace{graphs/sm_nd_lcdm} \plotgrace{graphs/sm_limit6}\\[-7ex] \plotgrace{graphs/sm_limit8}% \plotgrace{graphs/sm_limit_obs}\\[-5ex] \caption{\textbf{Top-left} panel: Cumulative number density thresholds as a function of stellar mass and redshift; observed galaxy cumulative number densities are expected to be below these thresholds in Planck $\Lambda$CDM, subject to sample variance and observational errors (see Appendix \ref{a:code}). Colored solid lines correspond to different stellar mass thresholds; the \textit{brown} line corresponds to the $10^{11.7}\Msun$ mass estimated for the massive galaxy in \protect\cite{Stefanon15}. Colored dotted lines correspond to expected number density limits for the \textit{JWST} and \textit{WFIRST} missions. \textbf{Top-right} panel: threshold stellar masses for a cumulative number density of $\Phi = 10^{-6}$ Mpc$^{-3}$. If a survey found that galaxies with stellar masses larger than the \textit{black} line had a cumulative number density higher than $10^{-6}$ Mpc$^{-3}$ with significant confidence (see Appendix \ref{a:code}), it would rule out $\Lambda$CDM. \textbf{Bottom-left} panel: same, for a cumulative number density threshold of $\Phi = 10^{-8}$ Mpc$^{-3}$. \textbf{Bottom-right} panel: same, for the entire observable Universe (i.e., all sky survey with $z_\mathrm{min} < z < \infty$).} \vspace{-5ex} \label{f:mass} \end{figure*} \begin{figure*} \vspace{-3ex} \plotgrace{graphs/bh_limit9} \plotgrace{graphs/bh_limit11}\\[-5ex] \caption{\textbf{Left} panel: threshold black hole masses for a cumulative number density of $\Phi = 10^{-9.5}$ Mpc$^{-3}$. If a survey found black holes with masses above the \textit{red} line and cumulative number densities above $10^{-9.5}$ Mpc$^{-3}$, those black holes would exceed the current record $z=0$ black hole mass---stellar mass ratio. Similarly, if a survey found black holes with masses above the \textit{blue} line and cumulative number densities above $10^{-9.5}$ Mpc$^{-3}$, those black holes would exceed all current determinations of the median $z=0$ black hole mass---stellar mass ratio. \textbf{Right} panel: same, for a cumulative number density threshold of $\Phi = 10^{-11}$ Mpc$^{-3}$. Solid data points indicate the most massive black holes found to date in surveys of the respective volume; open data points indicate less-massive black holes.} \label{f:mass_bh} \end{figure*} | \label{s:conclusions} Several factors limit attempts to rule out $\Lambda$CDM with galaxy or black hole masses, including observational errors and multiple comparisons (see Appendix \ref{a:code}). For galaxies, there are significant uncertainties in converting luminosity to stellar mass \citep{Conroy09,Behroozi10}; besides systematic offsets, these also induce Eddington/Malmquist bias \citep{Eddington13,Malmquist22} that artificially inflates the number densities of massive galaxies \citep{Behroozi10,Caputi11,Grazian15}. Also present are uncertainties in photo-$z$ codes and priors; improperly chosen, the latter can similarly inflate massive galaxy counts \citep{Stefanon15}. Just as problematic are multiple peaks in the posterior distribution of $z$, as for the massive galaxy in \cite{Stefanon15}. We note also the relatively high lensing optical depth at $z>8$, which further boosts the apparent number of massive galaxies \citep{Mason15}. For a full discussion of other sources of systematic error affecting the stellar mass -- halo mass relation, we refer readers to \cite{Behroozi10}. Black hole masses are also subject to many uncertainties \citep[see][for a review]{Peterson14}, and virial masses in particular may be overestimates \citep{Shankar16}. Selecting the largest black holes from a sample with uncertain masses also imposes Eddington bias. Nonetheless, our limits agree with other approaches that infer large black hole mass --- stellar mass ratios \citep{Targett12,Venemans16}, which are expected due to selecting for luminous, massive black holes \citep{Lauer07,Volonteri11}. We note in passing that blazars are also subject to the same number density constraints; however, estimates of their number densities are made more complicated due to uncertain beaming factors \citep{Ghisellini09}. Even so, it is exciting that the highest stellar masses observed in Fig.\ \ref{f:mass} are so close to the limits expected for $\Lambda$CDM. This suggests that high-redshift galaxy surveys will give lower bounds on the evolution of the halo mass function at $z>8$, which is otherwise very difficult to measure. Combined with constraints on primordial non-Gaussianities and dark matter from faint galaxies \citep{Habouzit14,Governato15}, \textit{JWST} and \textit{WFIRST} will place very interesting limits on early Universe cosmology. For SMBHs, Fig.\ \ref{f:mass_bh} provides a simple estimate of whether a given $M_\bullet$ requires an anomalously high $M_\bullet / M_\star$ ratio, potentially bolstering the case for follow-up observations. Finally, we cite examples of ``unusual'' physics that could be invoked if future observations cross the thresholds outlined here. We refer to ideas beyond usual prescriptions for supernova feedback and AGN (active galactic nuclei) quenching that limit star formation in current cosmological and zoom-in simulations. Specifically, we mention positive feedback from AGN (as a precursor to the negative feedback observed via AGN-driven massive gas outflows; \citealt{Gaibler12,Ishibashi12,Silk13,Wagner16}), examples of which are beginning to be found \citep{Zinn13,Cresci15,Salome15}, and a significant duty cycle of hyper-Eddington accretion, increasingly invoked to solve SMBH growth problems at high redshift \citep{Jiang14,Volonteri15,Inayoshi16}. These processes may be able to increase the ratio of stellar mass or black hole mass to total baryonic mass up to the limit imposed by $\Lambda$CDM (i.e., the cosmic baryon fraction). Unusual physics that allows accelerated halo growth in overdense regions (e.g., non-gaussianities as in \citealt{Pillepich10}, although standard models are now strongly limited by \citealt{PlanckNonGaussianity}) could also result in overmassive galaxies and black holes that exceed standard $\Lambda$CDM limits. | 16 | 9 | 1609.04402 |
1609 | 1609.08240_arXiv.txt | The Central Molecular Zone (CMZ), usually referring to the inner 500 pc of the Galaxy, contains a dozen of massive ($\sim$10$^5$~$M_\odot$) molecular clouds. Are these clouds going to actively form stars like Sgr~B2? How are they affected by the extreme physical conditions in the CMZ, such as strong turbulence? Here we present a first step towards answering these questions. Using high-sensitivity, high angular resolution radio and (sub)millimeter observations, we studied deeply embedded star formation in six massive clouds in the CMZ, including the 20 and 50 km\,s$^{-1}$ clouds, Sgr B1~off (as known as dust ridge clouds e/f), Sgr~C, Sgr~D, and G0.253$-$0.016. The VLA water maser observations suggest a population of deeply embedded protostellar candidates, many of which are new detections. The SMA 1.3 mm continuum observations reveal peaks in dust emission associated with the masers, suggesting the existence of dense cores. While our findings confirm that clouds such as G0.253$-$0.016 lack internal compact substructures and are quiescent in terms of star formation, two clouds (the 20 km\,s$^{-1}$ cloud and Sgr~C) stand out with clusters of water masers with associated dense cores which may suggest a population of deeply embedded protostars at early evolutionary phases. Follow-up observations with VLA and ALMA are necessary to confirm their protostellar nature. | Massive molecular clouds in the Central Molecular Zone (CMZ) of the Galaxy are known to be inactive in star formation (e.g., \cite[Lis et al.~1994]{lis1994}; \cite[Immer et al.~2012]{immer2012}) and the overall star formation rate of the CMZ is estimated to be an order of magnitude lower than expected from the Kennicutt-Schmidt relations (\cite[Longmore et al.~2013]{longmore2013}). One case of inactive star forming clouds in the CMZ is G0.253$-$0.025, which contains $>$10$^5$~$M_\odot$ of molecular gas (\cite[Longmore et al.~2012]{longmore2012}) but one weak H$_2$O maser associated with a dense core has been found so far (\cite[Lis et al.~1994]{lis1994}; \cite[Kauffmann et al.~2013]{kauffmann2013}; \cite[Johnston et al.~2014]{johnston2014}; \cite[Rathborne et al.~2015]{rathborne2015}). \cite[Kruijssen et al.~(2014)]{kruijssen2014} have proposed that star formation in the CMZ may proceed episodically, in which case it is currently at a low point of star formation cycles. Strong turbulence in the CMZ clouds inhibits collapse of dense gas, hence suppresses star formation in the clouds (\cite[Kruijssen et al.~2014]{kruijssen2014}; \cite[Krumholz \& Kruijssen 2015]{krumholz2015}; \cite[Krumholz et al.~2016]{krumholz2016}). Meanwhile, once gravitational collapse starts, subsequent star formation seems to proceed within normal time scales (\cite[Kruijssen et al.~2015]{kruijssen2015}). To explore the new generation of star formation in the CMZ expected by the episodic star formation model, we started to search for deeply embedded protostellar population at very early evolutionary phases in massive molecular clouds. We selected six clouds with column densities above 10$^{23}$~cm$^{-2}$, hence containing large amount of dense gas and the most likely star forming regions (Fig.\,\ref{fig1}). In \cite[Lu et al.~(2015)]{lu2015b}, we have reported the discovery of a number of protostellar candidates traced by H$_2$O masers and associated dense cores in one of the clouds, the 20 km\,s$^{-1}$ cloud. Here we continued to report our progress on searching for protostellar candidates in all the six clouds. \begin{figure}[!t] \begin{center} \includegraphics[width=6.0in]{CMZ_overview_BGPS.eps} \caption{Overview of the six massive molecular clouds in the CMZ. The background image shows the BGPS 1.2~mm continuum emission (\cite[Ginsburg et al.~2013]{ginsburg2013}). The six clouds are marked by red arrows. Sgr~A* and Sgr~B2, which are not covered in our observations, are also marked by black arrows.} \label{fig1} \end{center} \end{figure} | As we stressed above, the H$_2$O masers and dense cores only represent protostellar `candidates', since there are still debates on the nature of the H$_2$O masers found in the CMZ. To verify their protostellar nature, it is necessary to obtain supplementary observations of, e.g., class II CH$_3$OH masers, centimeter continuum, or hot core tracers such as CH$_3$CN. These observations would be useful for confirming the existence of deeply embedded star formation in forms of ultra-compact H\,{\sc ii} regions or hot molecular cores. Therefore, future high sensitivity, high angular resolution VLA and ALMA observations of these protostellar candidates are critical. Once confirmed as protostellar, these masers and dense cores could be used to estimate star formation rates of the clouds in a short time scale of 10$^5$ years. This time scale corresponds to the characteristic evolutionary time before (compact) H\,{\sc ii} regions emerge (\cite[Gerner et al.~2014]{gerner2014}) as well as the typical life time of the class 0 phase of protostars (\cite[Dunham et al.~2014]{dunham2014}). On a qualitative level, the 18 protostellar candidates in the 20~km\,s$^{-1}$ cloud seems to suggest a more active star formation in the last 10$^5$ years than that traced by a single H\,{\sc ii} region in a time scale of 10$^6$ years (\cite[Peters et al.~2010]{peters2010}). This may suggest an increase of star formation activities in the last 10$^5$ years than in the last 10$^6$ years in this cloud. | 16 | 9 | 1609.08240 |
1609 | 1609.08289_arXiv.txt | WR 148 (HD 197406) is an extreme runaway system considered to be a potential candidate for a short-period (4.3173 d) rare WR + compact object binary. Provided with new high resolution, high signal-to-noise spectra from the Keck observatory, we determine the orbital parameters for both the primary WR and the secondary, yielding respective projected orbital velocity amplitudes of $88.1\pm3.8$\,\kms and $79.2\pm3.1$\,\kms and implying a mass ratio of $1.1\pm0.1$. We then apply the shift-and-add technique to disentangle the spectra and obtain spectra compatible with a WN7ha and an O4-6 star. Considering an orbital inclination of $\sim67^\circ$, derived from previous polarimetry observations, the system's total mass would be a mere 2-3 Msol, an unprecedented result for a putative massive binary system. However, a system comprising a $37\Msol$ secondary (typical mass of an O5V star) and a $33\Msol$ primary (given the mass ratio) would infer an inclination of $\sim18^\circ$. We therefore reconsider the previous methods of deriving the orbital inclination based on time-dependent polarimetry and photometry. While the polarimetric results are inconclusive requiring better data, the photometric results favour low inclinations. Finally, we compute WR 148's space velocity and retrace the runaway's trajectory back to the Galactic plane (GP). With an ejection velocity of $198\pm27$\,\kms and a travel time of $4.7\pm0.8$\,Myr to reach its current location, WR 148 was most likely ejected via dynamical interactions in a young cluster. | Current massive-star evolution theories agree that Wolf-Rayet (WR) stars originate from O-type main sequence stars \citep{Crowther}. Thus, we expect a commonplace O+O binary system to evolve into an O+cc (compact companion), i.e. a high mass X-ray binary (HMXRB) if they remain bound after the first supernova explosion (SN). Recent population synthesis models suggest that roughly 80-95\,\% of the O+O binaries are disrupted subsequent to the SN \citep{Eldridge,lrr}. The surviving O+cc systems are then expected to progess to a WR+cc system. Yet, while the number of known O + cc sytems is significant, the number of detected WR+cc systems is much lower than predicted. In fact, while there are a total of 114 confirmed HMXRBs \citep{HMXRB} in our Galaxy, there is only a single confirmed WR+cc binary, Cyg X-3 \citep{CygX3}, compared to the $\sim10$ expected based on the Galactic fraction of WR- to O- stars \citep{VH7}. HD 197406 (WR 148) is a well known candidate for such WR+cc systems. It is a single-lined spectroscopic binary with a well established $\sim4.3173$ d orbital period where the unseen companion was suspected to be either a low mass B2-B5 V-III star or a black hole (BH) \citep{Marchenko}. Found at roughly 800 pc above the Galactic plane \citep{Rosslowe}, HD 197406 is an extreme runaway with a high peculiar velocity. The compact companion is therefore an interesting possibility, as the recoil of the supernova explosion could have ejected the binary from the Galactic plane without breaking it up. The major shortfall of this hypothesis is the presence of a thermal X-ray spectrum \citep{XMM}, typical for WR+O colliding wind binaires, rather than a hard spectrum generally observed in accreting massive X-ray binaries. The purpose of this investigation is therefore to determine the nature of the secondary in WR 148 and understand the evolutionary path of WR 148 as a unique runaway WR binary. In order to do so, we have acquired high resolution, very high signal-to-noise spectra at the Keck Observatory at both quadratures, complemented with a dozen lower quality spectra at the Observatoire du Mont M\'{e}gantic (OMM) during the summers of 2014 and 2015. The OMM data will serve mostly to refine the system's orbital parameters based on the bright primary WR component, whereas the Keck data will be used in an attempt to determine the nature of the companion. The rest of the paper is organized as follows: We begin by describing the details of the observations in section \ref{Data}. This is followed by a thorough analysis of the observational data in section \ref{Analysis}. Finally, in section \ref{Conclusion}, we briefly summarize the results. | \label{Conclusion} We summarize our findings briefly as follows: \begin{itemize} \item WR 148 is found to be a normal, massive, close WR+O binary system: the primary is a H-burning WN7ha star and the secondary is an O5V star. \item This confirms the colliding wind binary scenario, rejecting once again the WR+cc scenario proposed in the past. \item Orbital solution is refined: P = 4.317336 d and time for phase zero (WR in front at inferior conjunction) of E = 2 444 825.04 HJD. \item We obtain a mass ratio of $1.1\pm0.1$. Assuming a mass of 37 $\Msol$ for the O star, the WR component has a mass of 33 $\Msol$ and the system has an orbital inclination of $18\pm4{^\circ}$. \item Regarding the previously determined inclination angle of 67${^\circ}$, we re-examine past polarimetric and photometric observations. Via a more appropriate error assessment, the polarimetric results are at best inconclusive requiring better data. The light curve is also now found to behave normally for an atmospheric eclipse of the O-star as it orbits in the WR wind with a low inclinations. \item We deduce a O/WR wind momentum ratio of 0$.51\pm0.13$ from analyzing the excess emission arising from CWs. Adopting typical mass loss rates and terminal velocities for an O5V star, we obtain for the WR component $\log \Mdot (\,\Msol \yr \, )=-5.4\pm0.3$. This is consistent with the mass loss rate derived from polarimetry. \item Runaway status is confirmed. Most likely ejected via dynamical interactions, WR 148 is an extreme runaway with a current peculiar velocity of $\sim197$\,\kms. \item WR 148 is currently $\sim800$\,pc from the Galactic plane. It took $\sim5$\,Myr to reach this position starting from the plane, which is marginally acceptable for massive-star lifetimes. \item The runaway's space velocity is not enough to allow for WR 148 to escape the Galactic potential; however, after the SN explosion of the current primary, two single massive runaways could result, with one or both able to escape the Galaxy. \item We find a projected rotational velocity of $\varv \sin i = 60_{-10}^{+20}$\kms for the O star and $\varv \sin i \lesssim 150$\,\kms for the WR star. Adopting $\sin i$ from the orbit, leads to high rotation speeds for both stars. Though the system has definitely circularized, we cannot confirm whether it has synchronized. \end{itemize} | 16 | 9 | 1609.08289 |
1609 | 1609.03963_arXiv.txt | {3C273, the nearest bright quasar, comprises a strong nuclear core and a bright, one-sided jet extending $\sim$23 arcseconds to the SW. The source has been the subject of imaging campaigns in all wavebands. Extensive observations of this source have been made with the Very Large Array and other telescopes as part of a campaign to understand the jet emission mechanisms. Partial results from the VLA radio campaign have been published, but to date, the complete set of VLA imaging results has not been made available. } {We have utilized the VLA to determine the radio structure of 3C273 in Stokes I, Q, and U, over the widest possible frequency and resolution range.} {The VLA observed the source in all four of its configurations, and with all eight of its frequency bands, spanning 73.8 MHz to 43 GHz. The data were taken in a pseudo-spectral line mode to minimize the VLA's correlator errors, and were fully calibrated with subsequent self-calibration techniques to maximise image fidelity.} {Images in Stokes parameters I, Q, and U, spanning a resolution range from 6 arcseconds to 88 milliarcseconds are presented. Spectral index images, showing the evolution of the jet component are shown. Polarimetry demonstrates the direction of the magnetic fields responsible for the emission, and rotation measure maps show the RM to be very small with no discernible trend along or across the jet. This paper presents a small subset of these images to demonstrate the major characteristics of the source emission. A library of all $\sim$ 500 images has been made available for open, free access by interested parties.} {} | 3C273 (J1229+0203), the first identified quasar \citep{S63}, is one of the closest and most luminous of all quasars. Imaging of this source shows that at all wavebands, 3C273 comprises a bright, flat-spectrum nuceus with highly variable flux density, and a one-sided, highly polarized, narrow jet extending $\sim$23 arcseconds to the SW of the nucleus. Since its discovery, and due to its relative proximity ($z=0.158$, so 3.4 arcsecond $\sim$ 1 kpc) and angular size, 3C273 has been observed by a wide range of instruments from long-wavelength radio through X-ray. 3C273 was the target of an extensive and comprehensive observational campaign spanning many wavebands and utilizing many telescopes from 1995 through 2005. Key results from this campaign are to be found in \citet{Jester05}, and references within, which presents results from observations made with the VLA from 8 through 43 GHz, along with HST observations from the near-ultraviolet through near-infrared. However, the radio images shown in this paper are a small selection of those available from the suite of VLA observations of this source. The purpose of this paper is to present an overview of the key results from all the VLA imaging of 3C273, from the data taken between 1987 and 1999. | The Very Large Array has been utilized to generate high-fidelity radio images of the iconic quasar 3C273. Major features found by this work include: \begin{itemize} \item A previously unknown low-brightness steep-spectrum diffuse halo, of extent 30 x 45 arcseconds, primarily on the northern and western side of the bright nucleus and jet. \item A bright, narrow, nearly straight inner jet, of 11 arcseconds length, joining the bright nucleus to the outer jet. The transition in width from the narrow to wider jet is abrupt. \item The inner jet comprising three elongated regions of enhanced brightness, the outer two of which are oppositely tilted by about 5 degrees from the jet axis, suggestive of an oscillatory or sinusoidal underlying structure of period $\sim$ 5 arcseconds. \item The outer jet, of width $\sim 2.5$ arcseconds, which also comprises an oscillatory structure, with a similar period, but significantly larger amplitude. \item The outer jet is highly linearly polarized, with the polarization fraction reaching 55\% along the jet boundaries. The fractional polarization in the central regions of the outer jet is much lower. The projected magnetic field accurately follows the lines of constant brightness, including curling around the leading edge of the jet. \item The inner jet is also highly polarized, with the magnetic field lines oriented along the jet axis. \item The bright radio hotspot `H2' is fully resolved with $\sim$0.09 arcsecond (300 pc) resolution. \item The spectrum of the outermost regions of the radio jet sharply steepens above 5 GHz. The inner jet's spectrum is flatter than that of the outer jet. \item The rotation measure of the jet is uniform, with no visible gradient either across or along the jet. \end{itemize} Despite the detailed information on the structure of this source provided by this work, much remains uncertain, or poorly determined. We note, in particular: \begin{itemize} \item The structure of the newly-discovered halo is very uncertain. While we are confident in the existence of this emission, the differences in structures suggested by comparison of Figures 1 to 3 are unlikely to be real. \item The current images are noise limited at all the higher frequencies, particularly in polarization. Hence, details of the jet structure and polarization at high frequencies and at high resolution are poorly determined. \item The polarization of the inner jet is only approximately known, since the high-fidelity data taken in 1987 and 1991 were in a single-polarization mode. \end{itemize} The recent upgrade of the Very Large Array can address all these, and other issues. With the dramatic increase in bandwidth, improved receiver sensitivies, and especially with the implementation of a much more powerful correlator, much superior imaging of this source -- and other such sources -- is easily in range. | 16 | 9 | 1609.03963 |
1609 | 1609.01157_arXiv.txt | {Submillimetre galaxies (SMGs) in the early universe are the potential antecedents of the most massive galaxies we see in the present-day universe. An important step towards quantifying this galactic evolutionary connection is to investigate the fundamental physical properties of SMGs, like their stellar mass content ($M_{\star}$) and star formation rate (SFR).} {We attempt to characterise the physical nature of a 1.1~mm-selected, flux-limited, and interferometrically followed up sample of SMGs in the COSMOS field.} {We used the latest release of the {\tt MAGPHYS} code to fit the multiwavelength (UV to radio) spectral energy distributions (SEDs) of 16 of the target SMGs, which lie at redshifts $z \simeq 1.6-5.3$. We also constructed the pure radio SEDs of our SMGs using three different radio bands (325~MHz, 1.4~GHz, and 3~GHz). Moreover, since two SMGs in our sample, AzTEC1 and AzTEC3, benefit from previous $^{12}$C$^{16}$O line observations, we studied their properties in more detail.} {The median and 16th--84th percentile ranges of $M_{\star}$, infrared ($8-1\,000~\mu$m) luminosity ($L_{\rm IR}$), SFR, dust temperature ($T_{\rm dust}$), and dust mass ($M_{\rm dust}$) were derived to be $\log(M_{\star}/{\rm M}_{\sun})=10.96^{+0.34}_{-0.19}$, $\log(L_{\rm IR}/{\rm L}_{\sun})=12.93^{+0.09}_{-0.19}$, ${\rm SFR}=856^{+191}_{-310}$~${\rm M}_{\sun}~{\rm yr}^{-1}$, $T_{\rm dust}=40.6^{+7.5}_{-8.1}$~K, and $\log(M_{\rm dust}/{\rm M}_{\sun})=9.17^{+0.03}_{-0.33}$, respectively. We found that $63\%$ of our target SMGs lie above the galaxy main-sequence by more than a factor of 3, and hence are starbursts. The 3~GHz radio sizes we have previously measured for the target SMGs were compared with the present $M_{\star}$ estimates, and we found that the $z>3$ SMGs are fairly consistent with the mass--size relationship of $z\sim2$ compact, quiescent galaxies (cQGs). The median radio spectral index is found to be $\alpha=-0.77^{+0.28}_{-0.42}$. The median IR-radio correlation parameter is found to be $q=2.27^{+0.27}_{-0.13}$, which is lower than measured locally (median $q=2.64$). The gas-to-dust mass ratio for AzTEC1 is derived to be $\delta_{\rm gdr}=90^{+23}_{-19}$, while that for AzTEC3 is $33^{+28}_{-18}$. AzTEC1 is found to have a sub-Eddington SFR surface density (by a factor of $2.6^{+0.2}_{-0.1}$), while AzTEC3 appears to be an Eddington-limited starburster. The gas reservoir in these two high-$z$ SMGs would be exhausted in only $\sim86$ and $19$~Myr at the current SFR, respectively.} {A comparison of the {\tt MAGPHYS}-based properties of our SMGs with those of equally bright 870~$\mu$m-selected, ALMA followed-up SMGs in the ECDFS field (the ALESS SMGs), suggests that the two populations share fairly similar physical characteristics, including the $q$ parameter. The somewhat higher $L_{\rm dust}$ for our sources (factor of $1.9^{+9.3}_{-1.6}$ on average) can originate in the longer selection wavelength of 1.1~mm. Although the derived median $\alpha$ is consistent with a canonical synchrotron spectral index, some of our SMGs exhibit spectral flattening or steepening, which can be attributed to different cosmic-ray energy gain and loss mechanisms. A hint of negative correlation is found between the 3~GHz size and the level of starburstiness, and hence cosmic-ray electrons in more compact starbursts might be more susceptible to free-free absorption. Some of the derived low and high $q$ values (compared to the local median) could be the result of a specific merger/post-starburst phase of galaxy evolution. Overall, our results, like the $M_{\star}$--3~GHz radio size analysis and comparison with the stellar masses of $z\sim2$ cQGs, in concert with the star formation properties of AzTEC1 and 3, support the scenario where $z>3$ SMGs evolve into today's giant, gas-poor ellipticals.} | Submillimetre galaxies or SMGs (e.g. \cite{smail1997}; \cite{hughes1998}; \cite{barger1998}; \cite{eales1999}) are a population of some of the most extreme, dusty star-forming galaxies in the universe, and have become one of the prime targets for studying massive galaxy evolution across cosmic time (for a recent review, see \cite{casey2014}). Abundant evidence has emerged that high-redshift ($z\gtrsim3$) SMGs are the potential antecedents of the $z \sim 2$ compact, quiescent galaxies (cQGs), which ultimately evolve into the present-day massive ($M_{\star}\geq10^{11}$~M$_{\odot}$), gas-poor elliptical galaxies (e.g. \cite{swinbank2006}; \cite{fu2013}; \cite{toft2014}; \cite{simpson2014}). A better, quantitative understanding of the interconnected physical processes that drive the aforementioned massive galaxy evolution requires us to determine the key physical properties of SMGs, like the stellar mass ($M_{\star}$) and star formation rate (SFR). Fitting the observed multiwavelength spectral energy distributions (SEDs) of SMGs provides an important tool for this purpose. The physical characteristics derived through SED fitting for a well-defined sample of SMGs -- as done in the present study -- can provide new, valuable insights into the evolutionary path from the $z\gtrsim3$ SMG phase to local massive ellipticals. However, these studies are exacerbated by the fact that high-redshift SMGs are also the most dust-obscured objects in the early universe (e.g. \cite{dye2008}; \cite{simpson2014}). Further insight into the nature of SMGs can be gained by studying the infrared (IR)-radio correlation (e.g. \cite{helou1985}; \cite{yun2001}) of this galaxy population. On the basis of the relative strength of the continuum emission in the IR and radio wavebands, the IR-radio correlation can provide clues to the evolutionary (merger) stage of a starbursting SMG (\cite{bressan2002}), or it can help identify radio-excess active galactic nuclei (AGN) in SMGs (e.g. \cite{delmoro2013}). Moreover, because submillimetre-selected galaxies have been identified over a wide redshift range, from $z\sim0.1$ (e.g. \cite{chapman2005}) to $z=6.34$ (\cite{riechers2013}), it is possible to examine whether the IR-radio correlation of SMGs has evolved across cosmic time. A potentially important bias in the IR-radio correlation studies is the assumption of a single radio spectral index (usually the synchrotron spectral index ranging from $\alpha=-0.8$ to $-0.7$, where $\alpha$ is defined at the end of this section) for all individual sources in the sample. Hence, the sources that have steep ($\alpha \lesssim -1$), flat ($\alpha \approx 0$), or inverted ($\alpha >0$) radio spectra will be mistreated under the simplified assumption of a canonical synchrotron spectral index (see e.g. \cite{thomson2014}). As done in the present work, this can be circumvented by constructing the radio SEDs of the sources when there are enough radio data points available, and derive the radio spectral index values for each individual source. Ultimately, a better understanding of the physics of star formation in SMGs (and galaxies in general) requires us to investigate the properties of their molecular gas content -- the raw material for star formation. Two of our target SMGs benefit from previous $^{12}$C$^{16}$O spectral line observations (\cite{riechers2010}; \cite{yun2015}), which, when combined with their SED-based properties derived here, enable us to investigate a multitude of their interstellar medium (ISM) and star formation properties. In this paper, we study the key physical properties of a sample of SMGs in the Cosmic Evolution Survey (COSMOS; \cite{scoville2007}) deep field through fitting their panchromatic SEDs. The layout of this paper is as follows. In Sect.~2, we describe our SMG sample, previous studies of their properties, and the employed observational data. The SED analysis and its results are presented in Sect.~3. A comparison with previous literature and discussion of the results are presented in Appendix~C and Sect.~4, respectively (Appendices~A and B contain photometry tables and details of our target sources). The two high-redshift SMGs in our sample that benefit from CO observations are described in more detail in Appendix~D. In Sect.~5, we summarise the results and present our conclusions. The cosmology adopted in the present work corresponds to a spatially flat $\Lambda$CDM (Lambda cold dark matter) universe with the present-day dark energy density parameter $\Omega_{\Lambda}=0.70$, total (dark+luminous baryonic) matter density parameter $\Omega_{\rm m}=0.30$, and a Hubble constant of $H_0=70$~km~s$^{-1}$~Mpc$^{-1}$. A Chabrier (2003) Galactic-disk initial mass function (IMF) is adopted in the analysis. Throughout this paper we define the radio spectral index, $\alpha$, as $S_{\nu}\propto \nu^{\alpha}$, where $S_{\nu}$ is the flux density at frequency $\nu$. | We have studied the physical properties of a flux-limited sample of SMGs in the COSMOS field. The target SMGs were originally uncovered in a 1.1~mm continuum survey carried out with the AzTEC bolometer, and followed up with higher-resolution interferometric (sub)millimetre continuum observations. Our main results are summarised as follows: \begin{enumerate} \item We have used the new version of the {\tt MAGPHYS} code of da Cunha et al. (2008, 2015) to interpret the observed panchromatic SEDs of a sample of 16 of our SMGs, which lie at redshifts of $z \simeq 1.6-5.3$. Based on this analysis, we derived the following median values and 16th and 84th percentiles for the stellar mass, total ($8-1\,000~\mu$m) IR luminosity, SFR, sSFR, dust temperature, and dust mass: $\log(M_{\star}/{\rm M}_{\sun})= 10.96^{+0.34}_{-0.19}$, $\log(L_{\rm IR}/{\rm L}_{\sun})= 12.93^{+0.09}_{-0.19}$, ${\rm SFR}= 856^{+191}_{-310}$~${\rm M}_{\sun}~{\rm yr}^{-1}$, ${\rm sSFR}=9.9^{+21.4}_{-8.1}$~${\rm Gyr}^{-1}$, $T_{\rm dust}=40.6^{+7.5}_{-8.1}$~K, and $\log(M_{\rm dust}/{\rm M}_{\sun})=9.17^{+0.03}_{-0.33}$, respectively. Our stellar masses and dust temperatures are similar to those of the 870~$\mu$m-selected ALESS SMGs that are equally bright to our AzTEC SMGs (\cite{dacunha2015}), while the other parameter values for our SMGs are $\sim1.5-2$ times higher on average. However, given the spread of the values (the 16th--84th percentile ranges), the latter discrepancies are not statistically signifcant. Nevertheless, part of this discrepancy is potentially caused by the different observed wavelengths of the two SMG samples (i.e. $\lambda_{\rm obs}=1.1$~mm versus $\lambda_{\rm obs}=870$~$\mu$m). \item When compared with the galaxy main-sequence as defined by Speagle et al. (2014), our SMGs lie by a factor of $ 0.3^{+0.1}_{-0.2}$ to $13.0^{+0.0}_{-0.6}$ above the main sequence. The median ${\rm SFR}/{\rm SFR}_{\rm MS}$ ratio is found to be $4.6^{+4.0}_{-3.5}$, and most ($63\%$) of the target SMGs can be considered starbursts. \item The 3~GHz radio sizes of our SMGs measured in Paper~II were used in conjunction with the present stellar mass values to examine their possible stellar mass-size relationship. In particular, the radio sizes of the $z>3$ SMGs appear fairly consistent with the $z\sim2$ cQGs' mass--size relation, supporting a scenario where the high-redshift SMGs experience a cQG phase at $z\sim2$ (\cite{toft2014}). \item We used 325~MHz GMRT data in conjuction with the 1.4~GHz and 3~GHz VLA data to investigate the radio SED properties of our SMGs. A radio SED could be constructed for 19 SMGs in total, where each source was detected at least in one of the aforementioned radio bands. The median radio spectral index measured between the observed frame 325~MHz and 3~GHz was found to be $ -0.77^{+0.28}_{-0.42}$, which is consistent with the canonical radio synchrotron value ($\alpha \simeq -0.8 \ldots-0.7 $). \item We found evidence of both spectral flattening and steepening in the radio SEDs of our SMGs, which are indicative of different cosmic-ray energy gain and loss mechanisms taking place in these sources. In the case of the $z_{\rm phot}\simeq 1.8$ SMG AzTEC4, which shows the flattest radio spectral index derived here ($\alpha > -0.18$), the flattening could be due to a non-negligible contribution of thermal free-free emission, which is estimated to be at least one-third of the observed-frame 3~GHz flux density for this source. \item We found an indication for an anti-correlation between distance from the galaxy main sequence and 3~GHz radio size. This suggests that starburst SMGs are more compact, and hence more susceptible to free-free absorption. \item The present data allowed us to study the IR-radio correlation among our SMGs. This was quantified by calculating the total-IR $q$ parameter, and its median value was determined to be $q=2.27^{+0.27}_{-0.13}$. This is in very good agreement with the flux-limited (i.e. equally bright) ALESS SMGs' median $q$ parameter of $2.29\pm0.09$ (recalculated from \cite{thomson2014}). We found a statistically insignificant hint of negative correlation between the $q$ parameter and the source redshift in the binned average data. The weakness of this $q$ evolution might be partially caused by the selection effect of our SMGs being essentially IR-selected, but not necessarily detected at the rest-frame 1.4~GHz used to calculate $q$. This can bias the $q$ parameter towards higher values, and flatten the $q(z)$ distribution. Some of the observed low and high $q$ values compared to the local median value could be linked to the source evolutionary phase. \item The two high redshift SMGs in our sample that benefit from previous CO line data, AzTEC1 and AzTEC3, were analysed in further details (see Appendix~D). These SMGs are found to form stars near or at the Eddington limit, where the process of star formation can exhaust the gas reservoir in only $86^{+15}_{-14}$ and $19^{+1}_{-0}$~Myr, respectively. The current stellar and gas mass estimates for AzTEC1 and 3 suggest they can both evolve to have a final stellar mass of $>10^{11}$~${\rm M}_{\sun}$. Overall, the results of our study support the general view of high-$z$ ($z \gtrsim3$) SMGs being the progenitors of the present-day giant, gas-poor ellipticals, mostly sitting in the cores of galaxy clusters. \end{enumerate} | 16 | 9 | 1609.01157 |
1609 | 1609.07547_arXiv.txt | We perform smoothed particle hydrodynamics (SPH) simulations of an isolated galaxy with a new treatment for dust formation and destruction. To this aim, we treat dust and metal production self-consistently with star formation and supernova (SN) feedback. For dust, we consider a simplified model of grain size distribution by representing the entire range of grain sizes with large and small grains. We include dust production in stellar ejecta, dust destruction by SN shocks, grain growth by accretion and coagulation, and grain disruption by shattering. We find that the assumption of fixed dust-to-metal mass ratio becomes no longer valid when the galaxy is older than 0.2\,Gyr, at which point the grain growth by accretion starts to contribute to the nonlinear rise of dust-to-gas ratio. As expected in our previous one-zone model, shattering triggers grain growth by accretion since it increases the total surface area of grains. Coagulation becomes significant when the galaxy age is greater than $\sim$\,1\,Gyr: at this epoch the abundance of small grains becomes high enough to raise the coagulation rate of small grains. We further compare the radial profiles of dust-to-gas ratio $(\mathcal{D})$ and dust-to-metal ratio $(\mathcal{D}/Z)$ (i.e., depletion) at various ages with observational data. We find that our simulations broadly reproduce the radial gradients of dust-to-gas ratio and depletion. In the early epoch ($\lesssim 0.3$\,Gyr), the radial gradient of $\mathcal{D}$ follows the metallicity gradient with $\mathcal{D}/Z$ determined by the dust condensation efficiency in stellar ejecta, while the $\mathcal{D}$ gradient is steeper than the $Z$ gradient at the later epochs because of grain growth by accretion. The framework developed in this paper is applicable to any SPH-based galaxy evolution simulations including cosmological ones. | The importance of cosmic dust in astrophysical processes has been recognized in recent decades. Dust acts as an efficient catalyst of molecular hydrogen (H$_2$) formation in the interstellar medium \citep[ISM; e.g.][]{1963ApJ...138..393G,2004ApJ...604..222C,2009A&A...496..365C}. In addition, the typical mass of the final fragments in star-forming clouds is also regulated by dust cooling \citep[][]{1998MNRAS.299..554W,2005MNRAS.359..211L,2005ApJ...626..627O,2006MNRAS.369.1437S}. In protoplanetary discs, dust growth eventually leads to planet formation \citep[e.g.,][]{2009ApJ...707.1247O,2014A&A...568A..42K}. Dust grains also play an important role in radiative processes in the ISM by absorbing stellar light and reemitting it in the far-infrared, and change the spectral energy distributions of galaxies \citep[][]{2000ApJ...533..682C,2002A&A...383..801B,2012ApJ...755..144T}. For the dust properties in galaxies, the size distribution of dust grains is of fundamental importance \citep[e.g.,][]{1977ApJ...217..425M,2013ApJ...770...27N}. In particular, the extinction curve (i.e., the wavelength dependence of absorption and scattering cross-section) is shaped by the grain size distribution, given the grain materials \citep[][]{1983Natur.306..625B}. Precise estimates of star formation rate (SFR) in galaxies also require correction for dust extinction \citep[e.g.,][]{1999ApJ...519....1S,2010A&A...514A...4T,2012ARA&A..50..531K}. In addition, the total dust surface area which depends on the grain size distribution, governs the formation rate of molecular hydrogen \citep[e.g.,][]{1976ApJ...207..131B,2011ApJ...735...44Y}. Dust interacts with gas, metals and dust itself in the ISM. It is not only destroyed by supernova (SN) shocks, but also disrupted or shattered by grain--grain collisions in the diffuse ISM \citep[][]{2004ApJ...616..895Y}. In dense environments such as molecular clouds, it grows by accretion and coagulation \citep[][]{2014MNRAS.437.1636H,2014MNRAS.445..301V}. All these processes play important roles in the evolution of dust abundance and grain size distribution. \cite{2013MNRAS.432..637A} have established a full framework for treating the evolution of grain size distribution consistently with the chemical enrichment in a galaxy. Their work revealed that the collisional effects of dust grains such as coagulation, shattering, and accretion are necessary for a comprehensive understanding of the observed dust-to-gas mass ratio and extinction curves in nearby galaxies. However, \cite{2013MNRAS.432..637A} treated a galaxy as a single zone without taking into account the spatial distribution of gas with different density structures. Since the efficiencies of various dust processing mechanisms depend on the density and temperature of the ISM, hydrodynamical evolution of the ISM should also be considered simultaneously with dust evolution. Hydrodynamical simulations have indeed been a powerful tool to clarify galaxy formation and evolution. Many cosmological hydrodynamic simulations have reproduced and predicted the observed galaxy mass and luminosity functions \citep[e.g.,][]{2001ApJ...558..497N,2004MNRAS.350..385N,2012MNRAS.419.1280C,2012MNRAS.427..403J,2013ApJ...766...94J,2014MNRAS.440..731S,2014ApJ...780..145T,2014MNRAS.444.1518V,2015arXiv150900800S,2015MNRAS.446..521S}. In order to compute luminosity functions from simulated galaxies and compare them with observed data, a precise estimate of dust extinction effect is required. For example, \cite{2015MNRAS.451..418Y} calculated the galaxy UV luminosity function at high redshifts $(6 \le z \le 12)$ using cosmological zoom-in hydrodynamical simulations with constrained initial conditions. In their work, chemistry and cooling of hydrogen, helium and metals were computed as in \cite{2009MNRAS.393.1595C}, however, the dust-to-metal ratio was fixed. \cite{2015MNRAS.449.1625B} treated dust as a new particle species in addition to gas, dark matter, and star particles. They included not only the formation and destruction of dust, but also dust-dependent star formation and stellar feedback \citep[][]{2013MNRAS.432.2298B}. Furthermore, in a more recent work, \cite{2016MNRAS.457.3775M} regarded dust as an additional component in gas, and performed cosmological zoom-in simulations. They revealed the importance of dust growth by the accretion of gas-phase metals, and pointed out the necessity of a more realistic treatment of dust destruction and feedback by SNe. In addition, \citet[][]{2016arXiv160602714M} ran cosmological simulations and compared the dust mass function and radial profile of dust with corresponding observational data. They found that their simulation broadly reproduced the observation in the present-day Universe, although it tended to underestimate the dust abundance in high-redshift galaxies. \textcolor{black}{We also note that a similar approach on dust models can be taken with a semi-analytic model of galaxy formation. For example, \citet[][]{2016arXiv160908622P} treated dust growth in dense ISM, destruction by SN shocks and chemical evolution, and estimated the dust abundance and dust mass function of galaxies at various redshifts using a semi-analytic model. } In all of these simulations mentioned above, dust processing by grain-grain collisions such as coagulation and shattering, both of which are important for the grain size distribution, has not been included yet \citep[but see][who implemented part of these processes by postprocessing a hydrodynamic simulation of an isolated galaxy with a particular focus on temperature-dependent sticking coefficient]{2016arXiv160804781Z}. Implementation of dust size distributions in smoothed particle hydrodynamics (SPH) simulations has not been successful, mainly because of the high computational cost. Calculating the grain size distribution in a fully self-consistent manner is computationally expensive even in one-zone calculation as shown by \citet[][]{2013MNRAS.432..637A}. However, because of the aforementioned effects of grain size distribution, implementation of grain size distribution in hydrodynamic simulations is essential in understanding the role of dust in galaxy evolution. In this paper, we perform $N$-body/SPH simulations of isolated galaxies with a model of dust formation and destruction. For the purpose of treating the evolution of grain size distribution within a reasonable computational time, we adopt the two-size approximation formulated by \cite{2015MNRAS.447.2937H}, in which the entire grain size range is represented by two sizes divided at around $a\simeq 0.03~\mu$m, where $a$ is the grain radius. \cite{2015MNRAS.447.2937H} has confirmed that the two-size approximation gives the same evolutionary behaviour of grain sizes and extinction curves as calculated by the full treatment of \cite{2013MNRAS.432..637A,2014MNRAS.440..134A}. Thus, implementing the two-size model, which is computationally light, in hydrodynamic simulations provides a feasible way to compute the grain size evolution in the ISM. Consequently, not only can we compute the spatial variations in dust properties, but also examine the grain size distribution as a function of time and metallicity. This is a significant advantage over the simple one-zone calculations, which generally need to introduce some strong assumptions such as instantaneous mixing and homogeneity. Although our ultimate goal is to understand dust evolution in cosmological structure formation, the target of this paper is an isolated galaxy for the purpose of the first implementation of dust evolution. Using an isolated galaxy enables us to compare our results with previous one-zone calculations and to test our implementation. Since the spatial resolution is higher than typical cosmological simulations, we will be able to predict spatially resolved properties of dust evolution in detail. This paper is organized as follows. In Section 2, we introduce our dust evolution model and calculation method. We present the simulation results in Section 3. We discuss the parameter dependence in Section 4 and compare the simulation results with observational data in Section 5. We conclude in Section 6. Throughout this paper, we adopt $Z_{\odot}=0.02$ for solar metallicity following \cite{2015MNRAS.447.2937H}. \begin{table} \caption{Initial physical parameters of our isolated galaxy. In this paper, we adopt the low-resolution model of the {\sf AGORA} project \citep{2014ApJS..210...14K}. The disc and bulge components are pre-existing stellar components treated by collisionless star particles dynamically, but those particles are not destroyed nor created during the simulation. $^\dagger$The gravitational softening length is taken to be 80 pc, and we allow the baryons to collapse to 10\% of this value. However, in practice, we find that the variable gas smoothing length reached a minimum value of only $\sim$\,22 pc with our models of gas cooling, star formation, and feedback. } \begin{center} \begin{tabular}{lcc}\hline Parameter & Value & \\ \hline Gas mass & $8.59 \times 10^{9} \Msun$ \\ % Dark matter mass & $1.25 \times 10^{12} \Msun$ \\% \hline Disc mass & $4.30 \times 10^{9} \Msun$ \\% \hline Bulge mass & $3.44 \times 10^{10} \Msun$ \\ \hline Total mass & $1.3 \times 10^{12} \Msun$ \\ \hline Number of gas particle & $1.00\times 10^{5}$ \\% \hline Number of dark matter & $1.00\times 10^{5}$ \\% \hline Number of disc particle & $1.00\times 10^{5}$ \\% \hline Number of bulge particle & $1.25\times 10^{4}$ \\ \hline % Gas particle mass & $8.59 \times 10^{4} \Msun$ \\% \hline Dark matter particle mass & $1.25 \times 10^{7} \Msun$ \\% \hline Disc particle mass & $3.44 \times 10^{5} \Msun$ \\% \hline Bulge particle mass & $3.44 \times 10^{5} \Msun$ \\ \hline % Grav. softening length & $80$ pc $^\dagger$\\ \hline \end{tabular} \label{table:params} \end{center} \end{table} | In this paper, we investigate the time evolution and spatial distribution of dust in an isolated galaxy with a modified version of \texttt{GADGET-3} SPH code. To represent the grain size distribution, we calculate the abundances of small and large grains separately based on the one-zone model by \citet[][]{2015MNRAS.447.2937H}. Dust production by stars and destruction by SNe are implemented consistently with star formation. In order to overcome the mass resolution of the simulation, we develop subgrid models for accretion and coagulation, since these processes occur in dense clouds whose sizes are below the spatial resolution of the simulation. We find that the assumption of fixed dust-to-metal mass ratio becomes no longer valid when the galaxy age is $\gtrsim 0.2$ Gyr, because the grain growth by accretion produces a nonlinear dependence of dust-to-gas ratio on the metallicity. Small grain production by shattering triggers accretion, because small grains are more efficient in accreting the gas-phase metals. In addition, coagulation becomes also significant at ages $\ga $1 Gyr after a large amount of small grains are produced by accretion. The age-dependent contributions of those processes are all important in driving the evolution of dust-to-gas ratio and grain size distribution at various epochs, and thus should be included in any calculation of dust evolution in galaxies. Finally, we made a first attempt of comparing our simulation results with spatially resolved observational data of nearby galaxies. To extract the typical age in a simple way, we use the sSFR as an indicator, and compared the observed radial profiles of dust-to-gas ratio and dust-to-metal ratio (i.e., depletion) with the simulation snapshots at various ages. We find that the radial profiles calculated in our models are broadly consistent with observations. The negative radial gradient of dust-to-gas ratio is explained by the tight relation between dust-to-gas ratio and metallicity. The radial profile of depletion is flat at early epochs ($t \lesssim 0.3$ Gyr), because the dust-to-metal ratio is simply determined by the dust condensation efficiency in stellar ejecta. At later stages, the radial gradient of depletion is negative, which represents the fact that the dust-to-gas ratio is a nonlinear (strong) function of metallicity due to accretion. We also reproduce the observational trend that the radial gradient of depletion becomes flatter as the galaxy is aged, which indicates that the regions with efficient grain growth by accretion extend from inside to outwards. | 16 | 9 | 1609.07547 |
1609 | 1609.09070_arXiv.txt | Hydrogen and helium demix when sufficiently cool, and this bears on the evolution of all giant planets at large separations at or below roughly a Jupiter mass. We model the thermal evolution of Jupiter, including its evolving helium distribution following results of ab initio simulations for helium immiscibility in metallic hydrogen. After 4 Gyr of homogeneous evolution, differentiation establishes a thin helium gradient below 1 Mbar that dynamically stabilizes the fluid to convection. The region undergoes overstable double-diffusive convection (ODDC), whose weak heat transport maintains a superadiabatic temperature gradient. With a generic parameterization for the ODDC efficiency, the models can reconcile Jupiter's intrinsix flux, atmospheric helium content, and radius at the age of the solar system if the Lorenzen et al. H-He phase diagram is translated to lower temperatures. We cast the evolutionary models in an MCMC framework to explore tens of thousands of evolutionary sequences, retrieving probability distributions for the total heavy element mass, the superadiabaticity of the temperature gradient due to ODDC, and the phase diagram perturbation. The adopted \scvhi equation of state favors inefficient ODDC such that a thermal boundary layer is formed, allowing the molecular envelope to cool rapidly while the deeper interior actually heats up over time. If the overall cooling time is modulated with an additional free parameter to imitate the effect of a colder or warmer EOS, the models favor those that are colder than \scvhi. In this case the superadiabaticity is modest and a warming or cooling deep interior are equally likely. | Cool giant planets are relics of the protoplanetary systems from which they formed in the sense that they do not fuse protons, and they are well-bound enough that even hydrogen does not escape appreciably over tens of billions of years. Their thermal evolution is thus relatively simple, and understanding it empowers us to use the present states of giant planets to learn about their history and formation. The open questions about planet formation thus motivate a comprehensive theory of giant planet evolution, which will continue to be driven heavily by our own, well-studied giant planets, Jupiter and Saturn. A Henyey-type stellar evolution calculation for a Jupiter-mass object was first performed by \cite{graboske1975}, who showed that a convective, homogeneous sphere of fluid hydrogen and helium could cool to Jupiter's observed luminosity over roughly the right timescale, and noted that among all model inputs, the equation of state (EOS) and superadiabaticity of the temperature gradient have the strongest influence on the overall cooling time. These two fundamental physical inputs are closely related. The EOS (paired with a hydrostatic model) is necessary to translate the planet's tangible properties (surface temperature and composition; external gravity field, size and shape) into an interior density distribution. Knowledge of the thermodynamic state of matter in these regimes includes understanding any phase transitions that can operate in a Jovian-mass planet's interior, the two most important of which are (i) the transition from molecular hydrogen to its denser, pressure-ionized ``liquid metallic'' phase, and (ii) the limited solubility of neutral helium in that liquid metallic hydrogen once it cools below a critical temperature \citep{1975PhRvB..12.3999S}. The latter of these two effects has observable ramifications because the helium-rich phase tends to sink, releasing gravitational energy (constituting a power source beyond mere contraction) and depleting the outer envelope in helium \citep{1973ApJ...181L..83S,ss77b}. Ultimately a robust theory of giant planet evolution must reconcile the atmospheric helium mass fraction $\yatm$ with the helium content of the protosolar nebula, and this demand constrains the plausible EOS and H-He phase diagram. Since the critical temperature for H-He phase separation increases with pressure more slowly than the temperature along a planetary adiabat, the equilibrium helium abundance increases toward the center the planet. Thus in the limit that the hydrogen-helium mixing ratio is equal to its equilibrium value throughout the liquid metallic hydrogen part of the mantle, there exists a stabilizing helium gradient that acts to mitigate the convectively unstable temperature gradient. In this case the dynamics of the fluid (and the degree of macroscopic vertical heat transport that ensues) are dictated by the competing microscopic diffusion of heat and solute; the fluid is in the double-diffusive regime. In such a region the temperature gradient can be significantly larger than the adiabatic gradient, leading to potentially dramatic modifications to the planet's cooling time. For example, double-diffusive convection has been invoked in recent years to explain Saturn's luminosity excess (\citealt{lc13}; the case of a global heavy-element gradient), the inflation of hot Jupiters \citep{2015ApJ...815...78K}, and Jupiter's late thermal evolution including helium rain \citep{2015MNRAS.447.3422N}, which we are revisiting in this paper. Although differentiation alone contributes additional luminosity, extending the overall cooling time, any superadiabatic temperature structure associated with double-diffusive convection generally cools the surface more quickly. For models undergoing helium rain, cases with adiabatic $P-T$ profiles thus give an upper limit to the cooling time (\citealt{2003Icar..164..228F}, \citealt{2016Icar..267..323P}). The inclusion of double-diffusive convection offers a continuum of shorter cooling times, modulated by the efficiency of the heat transport through the double-diffusive region. \cite{2015MNRAS.447.3422N} sought a solution for Jupiter's evolution to its current state assuming a superadiabatic temperature profile in the framework of layered double-diffusive convection (LDDC; \citealt{2012ApJ...750...61M}, \citealt{2013ApJ...768..157W}) and found that a suitable combination of LDD layer height and modifications to the H-He phase diagram could match Jupiter's observed 1-bar temperature and $\yatm$. However, it is likely that a quasi-stable turbulent state like the layered structures characterized by the direct hydrodynamics simulations of \cite{2013ApJ...768..157W} would look quite different in the presence of a phase transition and rainout of a main component. For example, in the context of helium phase separation, homogeneous layers themselves---finite volumes of $(P,\ T)$ space, at effectively uniform helium abundance---are intrinsically unstable to H-He phase separation, and the influence that droplet formation and rainout has on the merging or bifurcation of convective layers, or the transport of solute between layers, has yet to be assessed from the hydrodynamical perspective. The present work thus relaxes the assumption of layered convection, opting instead to treat the superadiabaticity with a generic parameterization, the only physical content of which is the demand that the temperature gradient lie somewhere between the minimum value for overstable double-diffusion and the upper limit imposed by the Ledoux criterion. This amounts to the criterion that gravity waves be linearly overstable, so that thermal transport is enhanced relative to the purely diffusive case by some degree of turbulence. Despite growing confidence that helium has begun differentiating in Jupiter's recent past (and billions of years ago in the case of Saturn; see \citealt{2003Icar..164..228F} and \citealt{2016Icar..267..323P}), it is not known whether helium rain alone can resolve the gaps in our understanding of giant planet evolution given Jupiter and Saturn's luminosities and the helium content of their molecular envelopes at the present day. Although the thermodynamic conditions for phase separation of helium from liquid metallic hydrogen have been evaluated since the early work of \cite{1975PhRvB..12.3999S} and \cite{1977PhRvB..15.1914S}, quantitative knowledge covering the relevant pressures and H-He mixing ratios has only become available over the past several years as a result of \textit{ab initio} simulations making use of density functional theory molecular dynamics \citep{2009PNAS..106.1324M,2009PhRvL.102k5701L,2011PhRvB..84w5109L,2013PhRvB..87q4105M}. The present work demonstrates that using \textit{ab initio} results for the H-He phase diagram, a differentiating non-adiabatic Jupiter comprised of hydrogen and helium surrounding a dense core of heavy elements explain Jupiter's evolutionary state at the solar age. To assess the viability of the evolution models, we formulate the problem in a Bayesian framework, using Jupiter's observed $\teff$, $\yatm$, and volumetric mean radius $\rvol$ to derive posterior probability distributions for the model parameters using a Markov chain Monte Carlo sampling algorithm. Most importantly, we make a probabilistic determination of the superadiabatic temperature gradient to be expected in the deep interior, and simultaneously estimate the temperature correction that must be applied to the \cite{2011PhRvB..84w5109L} phase diagram to satisfy the \textit{Galileo} entry probe measurement of $Y_{\rm atm}$ \citep{2015MNRAS.447.3422N}. The present work thus extends the basic approach of \cite{2003Icar..164..228F}---using forward thermal evolution models to infer a most likely H-He phase diagram---with the power of a Bayesian parameter estimation method and the treatment of non-adiabatic $P-T$ profiles. In \S\ref{s.models} we describe our modeling approach using Modules for Experiments in Stellar Astrophysics (\mesa; \citealt{2011ApJS..192....3P,2013ApJS..208....4P,2015ApJS..220...15P}), including our atmospheric boundary condition, treatment of helium phase separation, thermal transport, and other modifications that were necessary for our application. We describe the three free parameters in our inhomogeneous, non-adiabatic models, namely the heavy-element core mass $\mc$, the double-diffusive superadiabaticity (or ``density ratio'') $\r$, and the phase diagram temperature offset $\dtdmx$. In \S3 we present results of evolutionary calculations, first validating our models for the case of homogeneous composition, then discussing in detail the late inhomogeneous, non-adiabatic evolution as a result of helium rain. We then repeat these calculations, but treating the planet's equilibrium temperature $\teq$ as a fourth free parameter controlling the overall cooling time, mimicking the influence of a ``colder'' or ``warmer'' EOS than the adopted \cite{1995ApJS...99..713S} EOS. Marginalizing over this parameter allows us in an indirect sense to marginalize over the plausible H-He equations of state and thus obtain the most general estimates for the remaining three parameters. In \S4 we summarize and contextualize our findings. | The framework developed here consists of a Python class for creating instances of \mesa work directories, modifying \mesa inlists, executing the evolution program, and processing its output, all as part of a single likelihood calculation called by an \emcee sampler. The method renders it straightforward to add additional parameters to the model or incorporate new or updated constraints in any quantity output by \mesa directly. It is readily adaptable to a host of different problems, most obviously non-adiabatic thermal evolution models for Saturn, where the same fundamental physics operate. Beyond just the Jovian planets and H-He immiscibility, our technique has broad applicability for deriving properties of objects from giant planets to brown dwarfs and stars, e.g., retrieving the age and composition for an object with measured mass and radius. Performing these retrievals with a code as mature as \mesa means that our knowledge of stellar/planetary evolution is built in, including complexities such as self-consistently determining mixing boundaries, modeling double-diffusive transport processes, or calculating nuclear energy generation rates with state of the art nuclear networks. Thus in the example of retrieving an object's composition and age from its measured mass and radius, meaningful inferences can be made about not just the bulk composition, but the composition profile, and indeed the composition profile's possible origins and evolution. The Bayesian approach automatically provides meaningful error bars for model parameters, and combining it with the open source \mesa package offers more flexibility than traditional grid-based isochrone fitting because new parameters---and indeed new physics---can be added at will. This work builds on that of \cite{2015MNRAS.447.3422N} principally in two ways: first, it makes the weakest possible assumption about the temperature gradient resulting from double-diffusive convection in the deep interior, abandoning the assumption of layered convection following the flux laws derived by \cite{2013ApJ...768..157W} in favor of a generic model wherein any temperature gradient can be attained as long as it is consistent with the criterion for linearly overstable gravity waves. Second, performing the calculations in an MCMC framework allows a probabilistic determination of all model parameters simultaneously, and we find a multitude of models that satisfy the imposed constraints (Table~\ref{t.data}). We demonstrated that \scvhi predicts strongly superadiabatic temperature profiles in Jupiter's helium gradient region, such that the planet's surface cools rapidly as most of the metallic hydrogen interior heats up over time. Repeating the calculations with a variable boundary condition to probe the effects of using a different EOS, we found that more modest superadiabaticities are preferred, although the distribution of allowed values is still broad. We found in all cases that the unperturbed phase diagram of \cite{2011PhRvB..84w5109L} is highly unlikely. That such a diversity of models meeting the imposed constraints were obtained in Figures~\ref{fig.ndim4_tracks} and \ref{fig.ndim4_posteriors} underscores the severe uncertainties that persist in modelling the evolution of giant planets. Admittedly, the present work does not exploit all the available data. Most importantly, our models make no use of of Jupiter's gravitational harmonics or its axial moment of inertia, both of which constrain the interior density profile. As discussed in \S\ref{s.models}, a calculation of oblateness and the associated non-spherical components of the gravity field is beyond our scope because the only EOS currently available for modeling giant planets in \mesa, \scvhi, is limited to hydrogen and helium. All heavy elements are in an inert core rather than partially distributed through the envelope, and as such the density profiles in our models are somewhat unrealistic and are not suited for fitting to $J_2$ or any higher-order moments. Nonetheless, we view these models as complimentary to the detailed static models computing using more realistic equations of state (e.g., \citealt{hubbard2016}) in that we use a forward thermal evolution model to derive estimates for Jupiter's deep superadiabatic temperature stratification and corrections to the H-He phase diagram, both of which should be taken into consideration for improving static models of the Jovian planets. Our findings support the existing body of evidence indicating that a realistic H-He equation of state departs significantly from \scvhi. | 16 | 9 | 1609.09070 |
1609 | 1609.00960_arXiv.txt | {} {We compute, for the first time, self-consistent models of planet growth including the effect of envelope enrichment. The change of envelope metallicity is assumed to be the result of planetesimal disruption or icy pebble sublimation.} {We solve internal structure equations taking into account global energy conservation for the envelope to compute in-situ planetary growth. We consider different opacities and equations of state suited for a wide range of metallicities.} {We find that envelope enrichment speeds up the formation of gas giants. It also explains naturally the formation of low and intermediate mass objects with large fractions of H-He ($\sim$ 20 - 30 \% in mass). High opacity models explain well the metallicity of the giant planets of the solar system, whereas low opacity models are suited for forming small mass objects with thick H-He envelopes and gas giants with sub-solar envelope metallicities. We find good agreement between our models and the estimated water abundance for WASP-43b. For HD 189733b, HD 209458b and WASP-12b we predict fractions of water larger than what is estimated from observations, by at least a factor $\sim 2$.} {Envelope enrichment by icy planetesimals is the natural scenario to explain the formation of a large variety of objects, ranging from mini-Neptunes, to gas giants. We predict that the total and envelope metallicity decrease with planetary mass.} | The core accretion model \citep{PerriCam74, mizuno80, BP86, P96} is the most accepted scenario to explain the formation of a vast diversity of planets \citep[e.g,][]{Alibert05, Mord09, Guilera11}. The central idea of the core accretion model can be summarised as follows. First, a solid core must be formed from the accretion of planetesimals/pebbles. Once this core reaches approximately a lunar mass, the core gravity is strong enough to start to bind some gas from the protoplanetary disk. Thus, from this stage on, the protoplanet keeps growing by accreting both solids (planetesimals/pebbles) and gas (basically H-He). Planet formation models typically assume, for simplification, that solids and gas do not mix: all the solids deposit their mass and energy at the top of the core, and the primordial H-He is collected above, building the atmosphere (or envelope). This is, of course, a very strong and unrealistic simplification: bolides that traverse a gaseous atmosphere undergo thermal ablation and mechanical breakup. Hence, volatile material can vaporise and mix with the primordial H-He, changing the composition of the envelope during the formation of a planet. If planetesimal/pebble disruption did not occur during formation, then the envelope metallicities of planets should be rather sub-stellar, because the gas accreted into the planets should in principle be metal-poor compared to the central star (the metals condense to form planetesimals/pebbles). This is not what is observed in the solar system, where the giant plants show some level of envelope enrichment \citep{Irwin14, galileo_probe, Guillot14}. The alternative hypothesis to planetesimal/pebble dissolution for explaining envelopes enriched in heavy elements, is core erosion \citep{Wilson12}. From an energetic point of view, it is possible to mix part of the core upwards \citep{Guillot04}. In addition, core material is miscible in metallic hydrogen \citep{Wilson12}, which allows for the heavy elements (if they can be lifted up) not to settle to re-form a core. Regarding the mixing of an initial core within the gaseous envelope, \citet{Vazan15} showed that this process is favoured if an initial compositional gradient exists in the interior of the planet. Thus, the mixing of heavy elements on the planetary envelope seems to be more likely if the heavy elements are not initially concentrated in well-defined core. The formation of such a diffuse core requires planetesimal dissolution in the deep envelope during the formation of the planet. Hence, even if core erosion could play a relevant role in mixing heavy elements in the planetary envelope, this process seems to demand as well that the envelope is initially enriched by planetesimal/pebble dissolution. The problem of considering an envelope that is enriched with respect to stellar values during the formation of a giant planet has been raised since the very early studies of planet formation. Already in 1986, \citet{BP86} mentioned, among other two problems that remained to be solved ``the fact that the molecular weight of the envelope is expected to increase with time as some of the icy planetesimals dissolve in it", and added that this problem ``could significantly change the accretion scenario". Indeed, \citet{Stevenson82} showed that the critical core mass (the mass required to trigger rapid accretion of gas) is reduced when the envelope mean molecular weight increases. Moreover, \citet{Wuchterl93} showed a direct dependence of the critical core mass with the adiabatic gradient. The adiabatic gradient is expected to decrease when chemical reactions take place. This necessarily occurs when abundant elements such as H, C, O are present in the envelope. Therefore, the effect of polluting the primordial envelopes reduces the critical core mass not only due to the increase of mean molecular weight but also via a reduction of the adiabatic gradient \citep{HI11}. Another effect that can reduce the adiabatic gradient is the condensation of species. We showed \citep{Venturini15} that if a planet forms in cold regions of the disk, such that the temperatures and pressures are low enough for certain species to condense in the atmosphere of the protoplanet, then this effect leads to an even larger reduction of the critical core mass. Despite its expected importance for the formation of giant planets, the effect of envelope enrichment has so far never been implemented in a self-consistent way in any evolutionary calculation of planet formation. This is of course a consequence of the difficulty in modelling all the processes involved, which include: planetesimal thermal ablation and dynamical breakup, mass and energy deposition in different envelope layers, and the inclusion of a self-consistent change in the envelope's microphysics (opacities and equation of state) as the envelope metallicity evolves. The magnitude of the enrichment depends on the accretion rate of solids, and on their size and strength properties. The smaller and more porous the bolide, the easier it is to disrupt it and mix it with the envelope gas when crossing the atmosphere \citep{Podolak88}. This tells us that the effect of envelope enrichment is more relevant for smaller bolides. Hence, when growing planets from cm-m size particles \citep[the so-called \textit{pebbles},][]{Lambrechts12, Lambrechts14}, including this effect is necessary. In this work we compute, for the first time, the in-situ growth of a planet taking into account envelope enrichment by icy planetesimals/pebbles. Given the uncertainties in the initial size distribution of planetesimals, we test the effect of envelope enrichment corresponding to a wide range of particle sizes. We solve internal structure equations using global energy conservation arguments, and taking into account the changes of envelope metallicity in the opacities and equation of state. In Sect. \ref{numerics} we explain the numerical method, Sect. \ref{assumptions} is devoted to discussing our assumptions, in Sect. \ref{resultados} and \ref{P96_section} we show and analyse our results, in Sect. \ref{implications} and \ref{predictions} we discuss our main results and predictions. We summarise our conclusions in Sect. \ref{conclusions}. | We have performed the first self-consistent calculation of the growth of a planet including the effect of envelope enrichment due to the dissolution of icy planetesimals/pebbles. We have implemented suited equations of state and opacities taking into account different metallicities. Moreover, we have considered two different sets of opacities in order to test the impact on our results, which can be summarised as: \begin{itemize} \item Envelope enrichment accelerates notably the formation of gas giants. This is mainly a consequence of the increase of the mean molecular weight of the envelope. The thinner the envelope (i.e, the smaller the planetesimal), the sooner envelope enrichment sets in and the shorter the timescale to form a giant planet. \item When envelope enrichment is taken into account, low and intermediate mass planets (namely mini-Neptunes to Neptunes) can be formed, with total mass fractions of H-He up to $30 \%$, this number being independent of the choice of opacities. \item Low-opacities allow for the formation of mini-Neptunes, whereas high-opacities lead to the formation of Neptunes. \item High-opacities are preferable for explaining the total mass and metallicity of the giant planets of the solar system. \item We were able to quantify the amount of volatile material remaining in the primordial atmospheres as a result of formation. These allowed us to compare our results with water abundances inferred from the transmission spectra of transiting exoplanets. We find good agreement for WASP-43b, whereas for the other three cases, the measured water abundance is lower than what is predicted by our models. \item We predict that envelope metallicity and total metallicity should decrease with planetary mass. \end{itemize} \paragraph{\textit | 16 | 9 | 1609.00960 |
1609 | 1609.09300_arXiv.txt | We report a simultaneous ground and space-based photometric study of the $\beta$~Cephei star $\nu$~Eridani. Half a year of observations have been obtained by four of the five satellites constituting BRITE-Constellation, supplemented with ground-based photoelectric photometry. We show that carefully combining the two data sets virtually eliminates the aliasing problem that often hampers time-series analyses. We detect 40 periodic signals intrinsic to the star in the light curves. Despite a lower detection limit we do not recover all the pressure and mixed modes previously reported in the literature, but we newly detect six additional gravity modes. This behaviour is a consequence of temporal changes in the pulsation amplitudes that we also detected for some of the p modes. We point out that the dependence of theoretically predicted pulsation amplitude on wavelength is steeper in visual passbands than those observationally measured, to the extent that the three dominant pulsation modes of $\nu$ Eridani would be incorrectly identified using data in optical filters only. We discuss possible reasons for this discrepancy. | } $\nu$~Eridani (HD 29248, $V=3.92$, B2 III, henceforth $\nu$~Eri) is arguably the asteroseismically best studied $\beta$~Cephei star (for more information on this group of massive pulsating variable stars see Stankov \& Handler 2005). After an immense ground-based observational effort involving both multisite photometry and high-resolution spectroscopy (Handler et al. 2004, Aerts et al. 2004, De Ridder et al. 2004, Jerzykiewicz et al. 2005, hereinafter JHS), tight constraints on the overall chemical composition and convective core overshooting of this star were obtained, in combination with a detection of differential internal rotation (Pamyatnykh, Handler \& Dziembowski 2004). The latter study as well as alternative models to explain the star's pulsation spectrum (Ausseloos et al. 2004) additionally pointed towards a necessity for an increase of the iron-peak element opacities. This success was possible because the star's pulsation spectrum happened to be very suitable for asteroseismic studies. The pulsations contain a dominant radial mode that immediately constrains the stellar mean density. Furthermore, a triplet of dipole modes was identified observationally, two more $l=1$ multiplets were found, and a single quadrupole mode was detected. Fitting this observed pulsation spectrum with theoretical models (Pamyatnykh et al. 2004, Ausseloos et al. 2004) revealed that the two lowest-frequency $l=1$ multiplets correspond to mixed modes, with different contributions from the gravity and pressure mode cavities, which makes the seismic information from them largely independent and complementary. In addition, low-frequency oscillations likely due to stellar gravity modes were detected (Handler et al. 2004, Aerts et al. 2004, JHS). However, finding excitation of the latter in corresponding stellar models proved to be impossible and would require additional modification to the opacities used for the stellar models (Dziembowski \& Pamyatnykh 2008). Finally, Daszy{\'n}ska-Daszkiewicz \& Walczak (2010) applied their method of complex asteroseismology to $\nu$ Eri and showed that neither with OPAL nor with OP opacities alone the observed complex amplitude of the bolometric flux variation can be reproduced for both its p and g modes at the same time. After these studies, the asteroseismic information on the star appeared to be made full use of, at least as far as studies hinged on ground-based data are concerned: the above-mentioned campaigns yielded some 1130 h of time-resolved photometry and 430~h of time-series spectroscopy. Therefore, a return to $\nu$~Eri only appeared sensible once new data sets, extensive enough to resolve the pulsation spectrum, and of a quality allowing to decrease the noise level significantly would become accessible. Such data sets are available nowadays. BRITE-Constellation (Weiss et al. 2014) is a set of five nearly identical nanosatellites with high-quality pointing stability, each hosting a telescope with 30~mm aperture and an uncooled 11 Megapixel CCD, which allows one to acquire time-series photometry of $V \simlt 4.5$ targets in a 24 degree field of view. Two broadband filters are available, a blue filter with a central wavelength of about 420 nm and a red filter centred at 620 nm. Although these filters do not have the standard Johnson-Cousins bandpasses, their effective wavelengths are similar to those of Johnson $B$ and Cousins $R_c$, and we therefore name them simply $B$ and $R$ in the remainder of this work. The satellites are in low-Earth orbits, meaning that they can observe the target fields for up to six months a year and for about 20 minutes per 101-minute orbit, depending on their position with respect to the Sun and the Earth. $\nu$~Eri was observed during the second BRITE-Constellation campaign directed towards the field of Orion. In anticipation of these measurements, ground-based photometric observations were organized to coincide temporally. In the following, we report the results of both ground and space-based monitoring. \vspace{4mm} | We have reported the first combined analysis of simultaneous BRITE-Constellation and ground-based photometry. The measurements were acquired for the well-studied $\beta$~Cep star $\nu$~Eri, with a combined duration of 173.5~d. This exemplary data set was used to show the power of joining these two types of observations, because they complement each other well in terms of suppressing aliasing problems in the data; aliasing is practically non-existent if the data can be carefully analysed together. Performing such a frequency analysis, we detected 40 signals in the light curves. Among these are six newly discovered gravity-mode frequencies. Their detection is a consequence of the combination of, firstly, the lower noise level in the BRITE data, which amounts to 72\% between $0-1$\,\cd and 80\% between $5-9$\,\cd of that in the combined $2002 - 2004$ ground-based multisite photometry (JHS). The second factor is the evolution of the stellar pulsation amplitudes. Such changes in the stellar mode spectrum make frequency analyses more challenging, but are also an asset as repeated observations may reveal more seismic information. Unfortunately, the data set reported here cannot be analysed together with those from the multisite campaigns carried out more than a decade ago (JHS) as the temporal gap between the two observational campaigns is too large, and just because the amplitude variations have occurred. However, at least some of the BRITE satellites will continue to observe $\nu$~Eri, and eventually this gap can be bridged. We showed that the observed pulsational amplitude ratios for the strongest modes are consistent with their previous identifications. However, the amplitude-wavelength relation in visual passbands is flatter than that predicted from theory. Although we cannot offer a good explanation for this discrepancy at this point, we suggest that mode identification of $\beta$~Cep stars should not be done in the optical alone; a UV band or radial velocities are necessary. The pulsation amplitude-wavelength relation observed for $\nu$~Eri requires theoretical explanation to derive reliable mode identifications from BRITE data alone. Furthermore, the additional gravity modes detected in the present work call for explanation, as current pulsation models have difficulties to excite them. An upcoming theoretical study by Daszy{\'n}ska-Daszkiewicz et al. (2016) will address these questions. | 16 | 9 | 1609.09300 |
1609 | 1609.00003_arXiv.txt | We present radio observations of 18 MIPSGAL bubbles performed at $5\um{GHz}$ ($6\um{cm}$) with the Karl G. Jansky Very Large Array in configuration B and BnA. The observations were aimed at understanding what kind of information high-resolution and high-sensitivity radio maps can supply on the circumstellar envelopes of different kinds of evolved stars and what their comparison with infrared images with similar resolution can tell us. We found that the 18 bubbles can be grouped into five categories according to their radio morphology. The three bubbles presenting a central point source in the radio images all correspond to luminous blue variable star candidates. Eleven bubbles show an elliptical shape and the total lack of a central object in the radio, and are likely associated with planetary nebulae. Under this assumption we derive their distance, their ionized mass and their distribution on the Galactic plane. We discuss the possibility that the MIPSGAL bubbles catalogue (428 objects) may contain a large fraction of all Galactic planetary nebulae located at a distance between $1.4\um{kpc}$ and $6.9\um{kpc}$ and lying in the MIPSGAL field of view. Among the remaining bubbles we identify also a H \textsc{ii} region and a proto-planetary nebula candidate. | The \textit{Spitzer Space Telescope} is permitting a great improvement of the knowledge on the celestial objects populating our Galaxy. Different surveys and targeted observations have allowed astronomers to observe through the Galactic dust, which prevents observations at shorter wavelengths, and many unknown sources have been unveiled. Thanks to the MIPSGAL Legacy Survey\footnote{http://mipsgal.ipac.caltech.edu/} \citep{Carey2009}, conducted with MIPS \citep[The Multiband Imaging Photometer for \textit{Spitzer};][]{Rieke2004}, \citet{Mizuno2010} identified at $24\mic{m}$ 428 roundish objects presenting diffuse emission. These small ($\lesssim1'$) rings, disks or shells (hereafter denoted as `bubbles') are pervasive throughout the entire Galactic plane in the mid-infrared (IR). The main hypothesis about the nature of the bubbles is that they are different types of evolved stars. In fact, follow up studies have found among them planetary nebulae (PNe), supernova remnants, Wolf--Rayet (WR) stars, luminous blue-variable (LBV) stars, asymptotic giant branch (AGB) stars, and so on (see \citealt{Nowak2014} for a review). However, currently, only about 30 per cent of the bubbles are classified. The discovery potential and the implications on the Galactic physics are huge both for high- and low-mass evolved stars. Massive stars play a pivotal role in the evolution of their host galaxies. They are among the major contributors to the interstellar ultraviolet radiation and, via their strong stellar winds and final explosion, provide enrichment of processed material (gas and dust) and mechanical energy to the interstellar medium, strongly influencing subsequent local star formation. The details of post-main sequence (MS) evolution of massive stars are still poorly understood. Increasing the sample of these stars is fundamental to better constrain evolutionary model parameters. On the other hand the bubbles catalogue is the right place where to find new PNe. Currently only about 15 per cent of the expected Galactic PNe have been observed \citep{Sabin2014}. This difference is usually explained in terms of strong interstellar extinction in the Galactic plane. In general, many kinds of evolved stars are known to be radio emitters. In the last phases of their life the stars undergo several periods of enhanced mass-loss, with their external layers ejected to form a circumstellar envelope (CSE). The now-exposed hot inner part of the star can ionize the CSE and continuum radio emission originates from it. The radio emission is therefore a helpful probe to complement IR observations in classifying the bubbles and deriving their physical properties, being a powerful tool to investigate circumstellar ionized material. Between 2010 and 2012 we carried out radio continuum observations with the Karl G.~Jansky Very Large Array (VLA) at $5\um{GHz}$ (configuration D) and at $1.4\um{GHz}$ (configuration C and CnB) of a subset of 55 bubbles (\citealt{Ingallinera2014a}; `Paper I' hereafter). We were able to calculate the radio spectral index ($\alpha$ defined as $S\propto\nu^\alpha$, where $S$ is the flux density and $\nu$ the frequency) for 18 of them and to determine an upper limit for 13. We found that at least 70 per cent of them have spectral indices compatible with a thermal emission. Since one of the main goal of Paper I was to accurately calculate the radio flux densities, we chose VLA compact configurations to avoid issues from the lack of short-spacing information. The drawback was a poorer resolution with respect to IR images, and morphological comparisons proved impossible. To overcome this problem, in this paper we present new VLA observations at $5\um{GHz}$ of 18 bubbles, using the more extended B and BnA configurations. The main goal of this work is to show how high-resolution and high-sensitivity radio images are an extremely powerful tool to discriminate low- and high-mass evolved stars, derive physical properties of PNe, disclose the mutual interaction of massive star ejecta and, in synergy with 8-$\umu$m images, immediately recognize possible H \textsc{ii} regions among the bubbles. In Section \ref{sec:obs} we supply technical details of observations and data reduction, grouping the observed bubbles by their radio morphology. In Sections \ref{sec:bub_cs}, \ref{sec:ell}, \ref{sec:fill} and \ref{sec:others} we discuss each morphological category separately. In Section \ref{sec:PNe} we comment the result obtained on PNe. Summary and conclusions are reported in Section \ref{sec:sumcon}. | \label{sec:sumcon} In this paper we reported radio observations at $5\um{GHz}$ of 18 MIPSGAL bubbles, performed with the VLA in configuration B and BnA. The images show that the bubbles can be grouped in five different categories according to their radio morphology. Three bubbles show a clear evidence of a central point-like object; seven are characterized by an elliptical ring shape and the total lack of a compact central object or diffuse emission toward their centre; for four bubbles the radio morphology is intermediate between the two previous categories, with diffuse emission toward the centre but without a clear central object; one has a bipolar appearance; the remaining three bubbles have a peculiar shape. The bubbles with a central object in radio images (MGE 027.3839-00.3031, MGE 030.1503+00.1237, MGE 042.0787+00.5084) were associated with massive evolved stars, in particular LBVs. This classification is compatible with the spectroscopic identification of the central star of two of them as B/B[e]/LBV stars. The radio emission from the central object is likely due to stellar winds. The CSE of MGE 042.0787+00.5084 shows relevant variations of spectral index, on the contrary the CSE of MGE 030.1503+00.1237 has a more homogeneous spectral index. The 24-$\umu$m images of these bubbles show a morphological similarity with radio only in two cases, while at IRAC wavelengths only the central object is detected. The elliptical bubbles were associated with PNe. One of them is already classified as PN in literature. For the others morphological considerations suggest that can be all proposed as PN candidates. If this hypothesis holds, we derive for them the distance, the diameter, the mean electron density and the ionized mass. We found that the elliptical bubbles are very similar also from the physical point of view. We ascribe this similarity to the selection bias of the bubbles catalogue. Four bubbles presented a morphology intermediate between the first two, with the lack of a central object but with diffuse emission toward their centre. On average they appear fainter at $8\mic{m}$ with respect to elliptical bubbles. Nevertheless the radio and the 24-$\umu$m morphology suggest that they can also be proposed as PN candidates. The remaining bubbles show different radio morphologies. One of them, MGE 356.7168-01.7246, has a clear bipolar shape. The 8-$\umu$m emission of MGE 031.7290+00.6993 is located outside the radio nebula and is proposed as an H \textsc{ii} region. MGE 032.4982+00.1615 is only barely resolved in our radio images. Its flux density probably has varied with respect to 2010 data and its radio spectral index suggests that its radio emission is non-thermal. We propose that it could be a proto-PN. Finally MGE 028.7440+00.7076 is a very peculiar object with the radio emission placed outside the $24\mic{m}$. As discussed in Section \ref{sec:compl} the knowledge achieved so far in the discovery of PNe among the MIPSGAL bubbles allows us to outline some general assertions about Galactic PNe. The number of known Galactic PNe is about the 15 per cent of what expected. The explanation is that, lying in proximity of the Galactic disk, many of them are heavily obscured in visible light. IR surveys, like MIPSGAL, are able to observe through the Galactic clouds and potentially discover a large quantity of previously unknown PNe. In this sense, preliminary results indicated that the bubbles catalogue could harbour many PNe. Given the typical diameter of a PN, the field of view and the resolution of MIPSGAL, we infer that the bubbles catalogue may contain about half of the Galactic PNe that would be resolved in MIPSGAL. It is likely that the most evolved PNe are not detected in MIPSGAL since as the central star becomes white dwarf, the nebular excitation decreases and consequently their flux at $24\mic{m}$. If this hypothesis will be confirmed, beside the discovery of 250 unknown PNe, it will pose an important constraint on the actual total number of Galactic PNe, being a significant statistical search on a relevant portion of our Galaxy. Furthermore it will give the precise indication that the 24-$\umu$m is the best band where to search for the remaining Galactic PNe when next-generation IR telescopes will provide better resolution and sensitivity than \textit{Spitzer}. The main goal of this work was to show the great potential of high-resolution high-sensitivity radio images. We showed that different kinds of evolved stars have strikingly different radio morphologies. We showed also how to use radio images to infer several physical properties of these Galactic objects. Even for the bubbles that we were not able to classify the discovery of their peculiar radio morphology could lead to further investigations and to the discovery a new shape prototypes. We want to remark that the imaging performance achieved in these targeted observations are about to be achieved also by several ongoing Galactic surveys used as pathfinders for next generation radio telescopes (e.g. \citealt{Bihr2016} with VLA or \citealt{Umana2015} with the ATCA\footnote{Australia Telescope Compact Array} and ASKAP\footnote{Australian SKA Pathfinder}). This work shows therefore what kind of information we can expect to derive on Galactic sources from future radio observations. Recalling the fundamental help of comparing radio maps with IR images, we highlight also the importance of the synergy with future IR telescopes, above all the \textit{James Webb Space Telescope}, that will provide us with images of unprecedented sensitivity and angular resolution comparable to radio interferometers. | 16 | 9 | 1609.00003 |
1609 | 1609.02006_arXiv.txt | { Astrophysical images issued from different instruments and/or spectral bands often require to be processed together, either for fitting or comparison purposes. However each image is affected by an instrumental response, also known as PSF, that depends on the characteristics of the instrument as well as the wavelength and the observing strategy. Given the knowledge of the PSF in each band, a straightforward way of processing images is to homogenise them all to a target PSF using convolution kernels, so that they appear as if they had been acquired by the same instrument. We propose an algorithm that generates such PSF-matching kernels, based on Wiener filtering with a tunable regularisation parameter. This method ensures all anisotropic features in the PSFs to be taken into account. We compare our method to existing procedures using measured \textit{Herschel}/PACS and SPIRE PSFs and simulated \textit{JWST}/MIRI PSFs. Significant gains up to two orders of magnitude are obtained with respect to the use of kernels computed assuming Gaussian or circularised PSFs. A software to compute these kernels is available at \url{https://github.com/aboucaud/pypher}. } | \label{sec:intro} The point-spread function (PSF), also known as \textsl{beam}, is one of the main characteristics of any astronomical imager. It is a model of the diffraction pattern resulting from the interaction between the electromagnetic radiation and the instrument optics and detectors at every wavelength. Since most instruments operate on a single or a series of bandpasses (through e.g. filters), the resulting effective PSF is an integral of the monochromatic PSFs over the wavelength range, weighted by the instrumental throughput and the source energy distribution of a given astronomical object. A more accurate model can even include convolutional effects such as guiding errors, trailing effects from a scanning mode, smearing by the detector response or even non-convolutional effects like the brighter-fatter effect. Once imaged, these model PSFs exhibit a complex shape, including anisotropy, wings and spikes that extend far from the center. Another classic feature of the PSF derived from the laws of optics is the radially oscillating pattern of the response, (especially in the monochromatic case) creating a series of peaks and valleys. These secondary peaks can account for a non negligible amount of the total power of the PSF. For ground-based astronomy though, the atmospheric turbulence creates a smearing that redistributes the power of these peaks and valleys and enables the PSF to be modeled by simple analytic profiles like 2D Gaussians. On the contrary, space telescopes can benefit \change{from} a much higher resolution at the expense of a full complexity of the PSF. To cite a few examples, the effective PSF of \textit{IRAS} maps was elliptical due to the scanning strategy, so the angular resolution was strongly anisotropic, with ratios up to 1:6 \citep[\textit{e.g.} 0.75' $\times$ 4.6' at 25\,$\mu$m, from][]{wheelock1994iras}. More recently, the effective PSFs of the \textit{Planck}/HFI\footnote{\url{http://planck.esac.esa.int}} maps appeared to have an ellipticity in a range 1.04 to 1.4, depending on the spectral band \citep{ade2011planck}, and the PSF of the PACS\footnote{\url{http://herschel.esac.esa.int}} photometer \citep{2010A&A...518L...2P} onboard the \textit{Herschel} satellite, characterised by \citet{lutz2012pacs}, showed a narrow core, a tri-lobe pattern and Knotty structured diffraction rings. As we push both optical performances and detector capabilities of the future missions towards the boundaries, the optical design highly increases in complexity. Hence, for upcoming space surveys (Euclid\footnote{\url{http://www.euclid-ec.org/}}, WFIRST\footnote{\url{http://wfirst.gsfc.nasa.gov/}}) or observatories (Athena\footnote{\url{http://www.the-athena-x-ray-observatory.eu/}} or JWST\footnote{\url{http://http://www.jwst.nasa.gov/}}), the characterisation and processing of elaborated PSFs become a crucial task.\\ Most of astrophysical studies necessitate multi-wavelength observations, either from multiple bands/filters within an instrument or from various instruments and telescopes. The different maps are affected by a particular PSF and the pixel-based data comparison cannot be straightforward. However, a technique widely used in multi-band photometry is to perform the measurements on PSF homogenised data, that is to select a dataset as reference (usually the one with the worst resolution, or wider PSF) and transform the other datasets so they are PSF-matched with the reference PSF, a technique called PSF homogenisation or PSF matching \citep[see e.g.][]{bertin2002terapix,gordon2008,darnell2009dark, hildebrandt2012cfhtlens}. PSF homogenisation is usually achieved by convolving the image with a kernel that is generated from the PSF corresponding to the image and the reference PSF. In the literature, one can distinguish between parametric kernels which use a fit of an analytic model to each PSF (Moffat, multiple Gaussians, etc.) or their decomposition on a proper basis (e.g. Gauss-Hermite polynomials, or shapelets), and results in an analytic expression for the kernel \citep[e.g.][]{kuijken2008gaap,hildebrandt2012cfhtlens} ; and non parametric methods that use pixel information from the image \citep[e.g.][]{alard2000} or adopt effective PSF images \citep[e.g.][]{gordon2008,aniano2011} to compute the kernels.\\ With the purpose of taking into account the full complexity and angular extension of space instruments' PSFs, we address the creation of PSF-matching kernels for multi-wavelength studies. We then present two usecases for these kernels, one based on the \textit{Herschel} satellite data, and a second on simulations for the MIRI instrument of \textit{JWST}. We also deliver a program called \texttt{pypher} that computes the kernels given two PSF images (see Appendix~\ref{sub:pypher}). This code has initially been developed in preparation for the Euclid mission \citep{laureijs2010euclid}. In Section~\ref{sec:method}, we describe the algorithm for the generation of convolution kernels used to match the resolution of images. In Section~\ref{sec:herschel}, we assess the improvement brought by these kernels on the multi-wavelength study of dust properties with the \textit{Herschel} satellite, and show in Section~\ref{sec:jwst} the reconstruction power of such kernels on PSF simulations of the future \textit{JWST} satellite, before summarising this work in Section~\ref{sec:conclusion}. | \label{sec:conclusion} In this paper, we propose a new method for the generation of static PSF homogenisation kernels which is applicable for instruments presenting complex PSFs such as recent or future space-born telescopes. \change{The PSF on such optical systems is hardly ever static over the field-of-view, but we restricted the purpose of this paper to the production of homogenization kernels for the study of regions of interest on the image, where the PSF can be considered non-variable. The treatment of the PSF varying over the whole field-of-view of modern instruments cannot be linearized as in this work and requires a very different approach. It will be the subject of a following paper.} The application on \textit{Herschel}/PACS and SPIRE and \textit{JWST}/MIRI instruments demonstrates the performance of the proposed algorithm in terms of low residuals (better than $10^{-2}-10^{-3}$ and $10^{-5}-10^{-6}$ for observed and simulated PSFs, respectively). To assess the improvement brought by our algorithm for multi-wavelength studies, we address the estimation of dust temperature and spectral index $\beta$ of astronomical objects using multi-band images taken in the submillimeter spectral range by \textit{Herschel}. This estimation is made via pixel-by-pixel measurements across these images which have different intrinsic angular resolutions. Homogenisation kernels are thus traditionally used to bring all the images to the same angular resolution. Most of the analysis performed so far use either Gaussian kernels, or the circularised kernels produced by \citet{aniano2011}. However, effective PSFs of space imagers are anisotropic, so these methods are not accurate enough therefore introducing systematic anti-correlation on $\beta$ and temperature measurements with an amplitude which can be larger than the statistical noise. We have checked that using \texttt{pypher} kernels, systematic errors are in any case negligible compared to statistical noise. Finally, we provide the \texttt{pypher} software \citep{alexandre_boucaud_2016_61392} to compute homogenisation kernels to be used for current and future instruments. | 16 | 9 | 1609.02006 |
1609 | 1609.02376_arXiv.txt | We plan to measure the angular diameters of a sample of Penn State-Torun Planet Search (PTPS) giant exoplanet host star candidates using the Navy Precision Optical Interferometer. The radii of evolved giant stars obtained using spectroscopy are usually ill-defined because of the method's indirect nature and evolutionary model dependency. The star's radius is a critical parameter used to calculate luminosity and mass, which are often not well known for giant stars. Therefore, this problem also affects the orbital period, mass, and surface temperature of the planet. Our interferometric observations will significantly decrease the errors for these parameters. We present preliminary results from NPOI observations of six stars in the PTPS sample. | \hskip15pt One of the challenging topics of modern astronomy is the search for exoplanets. Many exoplanets known today are gas giants, close to their central star and detected using the radial velocity (RV) and photometric transit techniques. The orbital properties of these planets and their minimum masses are calculated using the mass ($M$) of the central star. $M$ relies on evolutionary tracks and is calculated from the luminosity ($L$) of the star, which is proportional to the radius ($R$) squared. Because $R$ is usually not well known for giant stars, this parameter should be measured directly when possible. This can be accomplished using interferometric observations, which measure the star's angular diameter.\cite{2001ARAandA..39..353Q} That value, when combined with distance measurements from parallax studies, then produces a physical radius for the star. Our observing list is a subset of the Penn State-Torun Planet Search (PTPS) survey\cite{2008IAUS..249...43N} of giant stars with RV planet candidates. The survey consists of 744 evolved stars, 455 of which have a complete spectroscopic analysis. Niedsielski et al.\cite{2016AandA...589C...1N} used measured spectroscopic properties, such as surface gravity, effective temperature, and metallicity, combined with a distance measurement to derive $R$ and $L$. Then they estimated $M$ and age using the evolutionary tracks and isochrones. Unfortunately this method is uncertain due to difficulties in accurate placement of a single star on red giant clump, which is a very complex region on H-R diagram. We plan to improve this by direct measurements of stellar sizes. Moreover, together with a high-precision interferometric radii determinations and rotational velocities obtained from high resolution spectra, we can analyze stellar surface inhomogeneities such as spots using RV variations. The precise rotation period is needed to rule out stellar atmospheric activity as the source of such variations. Hence, a detailed knowledge of stellar fundamental parameters is very important for interpretation of the giant stars' characteristics in the context of exoplanet searches. Based on the interferometric measurements, we will obtain better estimates of $M$. If we can determine the angular diameter with a precision of 2$\%$, $R$ can be determined with a precision of better than 5$\%$. The largest error source is in the parallax,\footnote{This is the case until the GAIA mission\cite{2001AandA...369..339P} starts releasing improved parallax measurements. Then the errors on stellar radii will be correspondingly more precise. Having an existing archive of interferometrically measured angular diameters will be useful to quickly produce radii using the GAIA parallaxes when they become available.} so, after taking into account a 10$\%$ precision, the error on $M$ will then be approximately 0.1 $M_{\odot}$. This is significantly better when compared to previous estimations based on moderate quality photometry and evolutionary models. For the PTPS targets, we predicted mass values from 1 to 3 $M_{\odot}$ and, even after critical assessment, an uncertainty of 30$\%$ remains possible. Hence, the interferometric data will improve the precision of $M$ sufficiently for the subsequent analysis. The NPOI is capable of observing 25 of the PTPS sample stars after culling the list based on estimated angular diameters (0.8 mas or larger) and brightness ($V$ magnitude of 5.5 or brighter). We have so far obtained data on six of those stars, and present the preliminary findings here. Section 2 describes the interferometer and observing sequence, and Section 3 discusses how we determine angular diameters, radii, bolometric flux, temperatures, and masses from the combination of interferometric data and photometric values from the literature, and Section 4 summarizes our results. | \hskip15pt We observed six stars from the PTPS giant exoplanet host star candidate sample with the NPOI in order to measure their angular diameters. Those new values led to physical radii when combined with \emph{Hipparcos} parallaxes and led to bolometric fluxes when combined with photometric values from the literature and an SED fit. We then calculated the stars' luminosities and temperatures, and used the latter to provide a first estimate of the stars' masses. We will continue to observe the 25 stars available to the NPOI in order to improve their mass determinations. This will ultimately help us pin down which stellar evolution models are the most accurate by comparing the models' predictions with our measurements, and those models can be applied to stars too faint or small to be observed interferometrically. The updated masses will also improve our knowledge of the orbital properties, surface temperature, and minimum masses of the planets. \begin{figure}[h] \begin{center} \includegraphics[width=1.0\textwidth]{visvsb.eps} \end{center} \caption{$\theta_{\rm LD}$ fits for the six stars. The solid lines represent the visibility curve for the best fit $\theta_{\rm LD}$, the points are the calibrated visibilities, and the vertical lines are the measurement uncertainties.} \label{viscurves} \end{figure} \begin{center} Table 3. Measured and Calculated Stellar Properties \\ \vspace{0.01in} \begin{longtable}{cccccccc} \hline\hline \label{example} \vspace{0.01in} & $\theta_{\rm UD}$ & & $\theta_{\rm LD}$ & $R$ & $M$ & $L$ & $T_{\rm eff}$ \\ HD & (mas) & $\mu_\lambda$ & (mas) & ($R_\odot$) & ($M_\odot$) & ($L_\odot$) & (K) \\ \hline \endfirsthead \caption[]{\emph{continued}} \\ \hline & $\theta_{\rm UD}$ & & $\theta_{\rm LD}$ & Radius & $M$ & $L$ \\ HD & (mas) & $\mu_\lambda$ & (mas) & ($R_\odot$) & ($M_\odot$) & ($L_\odot$) \\ \hline \multicolumn{8}{r}{\emph{continued on the next page}} \endfoot \hline \endlastfoot \hline 90537 & 2.51$\pm$0.01 & 0.65 & 2.618$\pm$0.044 & 13.28$\pm$0.38 & 1.04$\pm$0.03 & 47.2$\pm$2.5 & 4149$\pm$41 \\ 113226 & 3.18$\pm$0.01 & 0.65 & 3.321$\pm$0.023 & 11.99$\pm$0.10 & 2.57$\pm$0.01 & 82.3$\pm$1.5 & 5018$\pm$26 \\ 161797 & 1.85$\pm$0.01 & 0.60 & 1.952$\pm$0.012 & 1.74$\pm$0.01 & 1.08$\pm$0.01 & 2.2$\pm$0.1 & 5324$\pm$17 \\ 181276 & 2.03$\pm$0.01 & 0.69 & 2.172$\pm$0.005 & 8.89$\pm$0.04 & 2.10$\pm$0.08 & 45.3$\pm$0.8 & 5022$\pm$22 \\ 188512 & 2.04$\pm$0.01 & 0.66 & 2.166$\pm$0.009 & 3.19$\pm$0.02 & 1.33$\pm$0.04 & 5.7$\pm$0.1 & 4992$\pm$11 \\ 219615 & 2.35$\pm$0.01 & 0.65 & 2.481$\pm$0.011 & 11.28$\pm$0.10 & 2.11$\pm$0.16 & 62.7$\pm$1.5 & 4834$\pm$24 \\ \hline \end{longtable} \end{center} | 16 | 9 | 1609.02376 |
1609 | 1609.09252_arXiv.txt | We investigate the feasibility of measuring the effects of peculiar velocities in large-scale structure using the dipole of the redshift-space cross-correlation function. We combine number counts of galaxies with brightness-temperature fluctuations from 21\,cm intensity mapping, demonstrating that the dipole may be measured at modest significance ($\lesssim 2\sigma$) by combining the upcoming radio survey CHIME with the future redshift surveys of DESI and Euclid. More significant measurements ($\lesssim~10\sigma$) will be possible by combining intensity maps from the SKA with these of DESI or Euclid, and an even higher significance measurement ($\lesssim 100\sigma$) may be made by combining observables completely internally to the SKA. We account for effects such as contamination by wide-angle terms, interferometer noise and beams in the intensity maps, non-linear enhancements to the power spectrum, stacking multiple populations, sensitivity to the magnification slope, and the possibility that number counts and intensity maps probe the same tracers. We also derive a new expression for the covariance matrix of multi-tracer redshift-space correlation function estimators with arbitrary orientation weights, which may be useful for upcoming surveys aiming at measuring redshift-space clustering with multiple tracers. | \label{sec:intro} Large-scale peculiar velocities have long been a rich source of information on the physics of structure formation in the Universe~\citep[e.g.][]{Peebles, 1987MNRAS.227....1K, 1988lsmu.book.....R, 1999ApJ...515L...1F}. However, the direct measurement of peculiar velocity is rendered challenging by the necessity of obtaining an independent measure of the distance to a galaxy, such that the uniform Hubble flow may be subtracted from the measured redshift. This is usually achieved by using empirical relationships such as the Fundamental Plane to measure proxies for the intrinsic luminosity, and hence derive velocities via a luminosity distance~\citep[e.g.][]{2014MNRAS.445.2677S}. With these in hand, constraints may be placed on the standard cosmological model and its extensions~\citep[e.g.][]{2014MNRAS.444.3926J}. However, such measurements require high-resolution spectra in order to measure velocity dispersions, and are hence constrained to fairly low redshifts. An alternative approach to measuring peculiar velocities is provided by their impact on the clustering statistics of galaxies. In~\citep{1987MNRAS.227....1K,1989MNRAS.236..851L,1992ApJ...385L...5H} it was shown that velocities contribute to the observed clustering of matter via the transformation between real and redshift space. These redshift-space distortions, which modify the observed volume of the pixels in which the observer counts galaxies, can be comparable in magnitude to the real-space clustering caused by the large-scale dark matter density field, especially if accurate redshift information for the tracers is available~\citep{1998ASSL..231..185H}. This effect has been measured with high significance in two-point statistics of the galaxy overdensity field~\citep{2001Natur.410..169P,2014MNRAS.443.1065B}. As well as the redshift-space distortion effect, there are signatures of peculiar velocities in the observed galaxy overdensity from the Doppler effect. The reason for this is that when peculiar velocities are present, a galaxy observed at a given redshift will have a different conformal distance from the observer to the FRW expectation corresponding to that redshift. A galaxy with positive peculiar velocity will actually be closer to us (in terms of conformal distance) than an FRW calculation would suggest. Since the background matter density is decaying with time due to expansion, this galaxy resides in a patch of spacetime having lower mean density than the sky-average. Since the peculiar velocity varies over the sky, this results in a contribution to the observed inhomogeneity in the matter distribution from peculiar velocities~\citep{1987MNRAS.227....1K,2008MNRAS.389..292P}. Moreover, since observations are made on our past light-cone, a wrong estimation of the conformal distance to the galaxy results in a wrong estimation of the comoving time at which the observed photons have been emitted. Since both the Hubble flow and the peculiar velocities evolve with time, this results in additional distortions to the observed galaxy overdensity~\citep{Yoo:2010ni,Yoo:2009au,2011PhRvD..84d3516C, 2011PhRvD..84f3505B}. Unfortunately, these beyond-standard Doppler terms are generally much smaller than the density and redshift-space distortion terms, making their detection very challenging. Recently, a potential method for isolating the effects of peculiar velocities has been proposed~\citep{2014PhRvD..89h3535B}. This method uses the fact that peculiar velocities are among the few contributions to the observed number counts that source an \emph{antisymmetric} part to the two-point correlation function of matter tracers, i.e. odd with respect to a flip in sign of the pair-separation vector. Additional sources of an antisymmetric correlation function come from the effect of gravitational redshift~\citep{2011Natur.477..567W,2013MNRAS.434.3008C}, although these may subsumed into velocity terms with use of the Euler equation~\citep{2014CQGra..31w4002B}. The antisymmetric correlation function thus represents a promising route to measuring large-scale motions in the galaxy distribution. As is evident from symmetry considerations, the effect is only non-zero when distinct populations of tracers having different biases or magnification slopes are cross-correlated. This technique is thus a `multi-tracer' method - such methods have been shown to be very promising avenues for beating down cosmic variance~\citep{2009JCAP...10..007M}. Cross-correlations have the further advantage of being unbiased to many of the systematics that affect the auto-correlation, such as foregrounds and Poisson noise. We thus require two distinct populations to be isolated from a galaxy survey, such as red/blue galaxies or bright/faint galaxies. A measurement has already been attempted in~\citep{2015arXiv151203918G}. Alternatively, we may combine galaxy number counts with a distinct tracer from a different survey. In this work, we combine redshift surveys with another tracer of large-scale structure, the 21\,cm brightness temperature fluctuation measured with intensity mapping. This technique has the advantage of having very precisely measured redshifts covering large cosmic volumes~\citep{2009astro2010S.234P}. Additionally, at the low redshifts we consider in this work, 21\,cm emitters are expected to trace the linear matter density on large scales, with relatively small contributions from ionization-fraction perturbations and non-Gaussianity~\citep{2009MNRAS.397.1926W}. We will investigate to what extent the cross-correlation dipole may be measured with combinations of galaxy number counts and 21\,cm intensity mapping from current and future surveys. It may be shown that antisymmetry in the cross-correlation function corresponds to \emph{imaginary} terms in the power spectrum~\citep{2009JCAP...11..026M,Yoo:2012se}. The relative merits of correlation functions over power spectra have been discussed at length in the literature~\citep[e.g.][]{1994ApJ...426...23F, 2014JCAP...06..008T} so we will not belabour the subject here, merely noting that the cross-power spectrum provides an alternative method for measuring the effects discussed in this paper. The structure of this paper is as follows. In Section~\ref{sec:sig} we write down an expression for the signal and discuss potential contaminants. In Section~\ref{sec:var} we write down an estimator for this signal and derive an expression for its covariance matrix. In Section~\ref{sec:surveys} we describe the surveys we consider in our forecasts, which are presented in Section~\ref{sec:forecasts} and tabulated in Appendix~\ref{app:sn}. We conclude in Section~\ref{sec:concs}. We will set the speed of light to unity throughout this work, and assume a fiducial flat $\Lambda$CDM cosmology given by $(\Omega_b h^2, \Omega_c h^2, h, 10^9 A_s,n_s) = (0.0223,0.1056,0.73,1.8,1.0)$. | \label{sec:concs} In this work we have investigated the feasibility of measuring a relatively unexplored observable of large-scale structure, the dipole of the multi-tracer redshift-space correlation function. This quantity is sensitive to contributions to the observed number density that cannot be probed with the standard even multipoles, and provides complementary information on large-scale bulk motion to that provided by redshift-space distortions. This information is however contaminated by wide-angle effects, which dominate current measurements of the dipole~\citep{2015arXiv151203918G}, and must be removed to isolate the desired Doppler terms. We have derived a new expression for the covariance matrix of multi-tracer redshift-space correlation functions in the Gaussian limit, which should be useful for future surveys aiming at conducting a multi-tracer analysis such as eBOSS or DESI. In an upcoming work we will test the robustness of our expression on available data from BOSS~\citep{inprep}. We also account for the extra variance incurred by removing the wide-angle term, finding it to be negligible in most cases due to a partial cancellation of cross and auto terms. Using measured and expected values for biases, magnification slopes, number densities and other survey parameters, we have forecast $S/N$ values for the amplitude of the dipole as a function of redshift. The most significant detection is likely to come from the SKA using its number counts survey combined with its 21\,cm intensity mapping survey, with $S/N \lesssim 100$ possible at low redshift. The significance is enhanced when these two tracers are identified due to a significant suppression of the Poisson noise, although there is a redshift ($z\approx0.4$) where the $S/N$ drops to zero for the SKA, due to the sign of the signal changing. Detections are also possible with SKA combined with the future galaxy surveys DESI and Euclid ($S/N \lesssim 10$), and potentially with the near-term radio survey CHIME when combined with DESI and Euclid ($S/N \lesssim 2$). The significance of the dipole may be enhanced by stacking multiple populations. We have not attempted to derive optimal weights, but even for Poisson-optimal weights the significance may be boosted over the single-population case. For the SKA we expect the dipole to be measured with $S/N \approx 10$ when combined with DESI. We have tested the robustness of our results to the uncertain magnification slope, finding a strong dependence at moderate redshift to high redshift ($z \gtrsim 0.5$), and a fairly weak dependence at lower redshifts. Our results are also insensitive to non-linear corrections to the power spectrum, although we have not included non-linear corrections to the covariance matrix, which would enhance our error bars. Finally, we have seen that the inclusion of 21\,cm intensity maps genuinely adds something to the measurement of the dipole. The large volume accessible with radio surveys combined with the expected high number density of tracers and fundamentally different magnification slopes imply that combining the 21\,cm brightness temperature with number counts from galaxy surveys can be an excellent way to measure the dipole. Potential caveats to this include the removal of the unknown sky-average brightness temperature, which will require the inclusion of the 21\,cm auto-correlation. This will add some variance to our estimator which will need to be accounted for. We have also neglected foregrounds in this work - although these do not bias the estimator they will contribute to the variance. We have assumed that intensity maps have been cleaned of foregrounds, which should be possible in principle due to their distinct frequency dependence~\citep[e.g.][]{2009MNRAS.398..401L}. In conclusion, a detection of the dipole as a function of redshift is seemingly within reach in the next decade. Such a measurement will provide a very interesting consistency check on the $\Lambda$CDM model and will also provide complementary constraints on the equivalence principle and scale-dependent growth, allowing for tests of novel extensions to the standard model, such as a modified theory of gravity. Information from 21\,cm intensity mapping surveys will be invaluable in this endeavour. | 16 | 9 | 1609.09252 |
1609 | 1609.05882.txt | { In this paper we derive constraints on the emission of a massive (pseudo)scalar {$S$} from annihilation of neutrinos in the core of supernovae through the dimension-4 coupling $\nu\nu S$, as well as the effective dimension-5 operator $\frac{1}{\Lambda}(\nu\nu)(SS)$. While most of earlier studies have focused on massless {or ultralight} scalars, our analysis involves scalar with masses of order $\mathrm{eV- GeV}$ which can be copiously produced during {the explosion of supernovae, whose core temperature is} generally of order $T\sim \mathcal{O}(10)$ MeV. From the luminosity and deleptonization arguments regarding the observation of SN1987A, we exclude a large range of couplings $ 10^{-12} \lesssim {|g_{\alpha\beta}|}\lesssim 10^{-5}$ for the dimension-4 case, depending on the neutrino flavours involved and the scalar mass. In the case of dimension-5 operator, for a scalar mass from MeV to 100 MeV the coupling $h_{\alpha\beta}$ get constrained from $10^{-6}$ to $10^{-2}$, with the cutoff scale explicitly set $\Lambda = 1$ TeV. We finally show that if the neutrino burst {of} a nearby supernova explosion {is} detected by Super-Kamiokande and IceCube, the constraints {will} be largely reinforced. } | Among other problems, the standard model (SM) of particle physics suffers from lots of mysteries concerning the neutrino sector. As a matter of fact, the three neutrino flavours have been established to oscillate as they propagate in vacuum or matter and hence be split in mass. A large variety of current experiments aim to detect neutrinos produced in the Sun, atmosphere, reactors, nuclei decay or astrophysical sources. The next generation neutrino experiments, as well as collider studies, may help us pin down some of the fundamental mass and mixing parameters, resolve the mystery of Majorana versus Dirac nature of neutrinos, and reveal hints about the neutrino mass generation mechanisms. As a peculiar source of astrophysical neutrinos, supernovae provide an alternative environment to study neutrinos and their interplay to nuclear physics and possibly new, feeble, secret interactions. Indeed, such interactions could drastically alter the evolution of astrophysical objects, and in particular the dynamics of supernova explosions, and be possibly measured by neutrino detectors on earth. There has been an extensive study regarding the SM together with hypothetical beyond SM particles in the evolution of supernovae, including {both} active and sterile neutrinos~\cite{Shi:1993ee,Pastor:1994nx,Kolb:1996pa,Nunokawa:1997ct,Caldwell:1999zk, Fetter:2002xx,Keranen:2004rg,Beun:2006ka,Choubey:2007ga,Hidaka:2007se,Keranen:2007ga, Fuller:2009zz,Raffelt:2011nc,Tamborra:2011is,Wu:2013gxa,Esmaili:2014gya,Warren:2014qza, Zhou:2015jha,Arguelles:2016uwb,Minakata:1989mk,Hidaka:2006sg,Warren:2016slz,Mathews:2016xba}, (very) light pseudoscalars (e.g. axion~\cite{Turner:1987by,Brinkmann:1988vi, Mayle:1987as,Burrows:1988ah,Mayle:1989yx, Turner:1988bt,Kolb:1988pe,Raffelt:1991pw,Janka:1995ir,Keil:1996ju,Raffelt:2006cw, Giannotti:2010ty,Fischer:2016cyd} and Majoron~\cite{Gelmini:1982rr,Kolb:1987qy, Choi:1987sd,Berezhiani:1989za,Choi:1989hi,Chang:1993yp,Kachelriess:2000qc, Tomas:2001dh,Lindner:2001th,Hannestad:2002ff,Farzan:2002wx,Fogli:2004gy, Das:2011yh}) as well as vector bosons (dark photon~\cite{Kolb:1996pa,Dent:2012mx,Dreiner:2013mua,Kazanas:2014mca}), or even dark matter (DM) particles~\cite{Minakata:1989mk,Hidaka:2006sg,Warren:2016slz,Mathews:2016xba, Fayet:2006sa,Zhang:2014wra,Blackadder:2014wpa,Graham:2015apa,Bramante:2015cua, Guha:2015kka,Brdar:2016ifs}. In this paper we aim to focus on the supernova constraints in the neutrino sector, in the presence of a massive scalar $S$ or pseudoscalar $J$ coupled to the SM neutrinos. A well motivated example of such {particles} is the Majoron~\cite{Chikashige:1980qk,Chikashige:1980ui,Aulakh:1982yn,Gelmini:1980re,Schechter:1981cv}, the Goldstone boson generated from global lepton number symmetry breakdown. This particle is intimately related to neutrino mass generation via the so called seesaw mechanisms~\cite{type1a,type1b,type1c,type1d,type1e, type2a,type2b,type2c,type2d,type3} and the lepton number breaking scale. However, the Majoron does not have to be exactly massless~\cite{Akhmedov:1992hi,Rothstein:1992rh} nor a Goldstone boson~\cite{Bamert:1994hb} as in the original models, and could even play the role of DM~\cite{Berezinsky:1993fm,Starkman:1993ik,Dolgov:1995rm,Arai:1998ni, SommerLarsen:1999jx,Kazanas:2004kv,Lattanzi:2007ux,Lattanzi:2008ds,Bazzocchi:2008fh, Aranda:2009yb,Gu:2010ys,Esteves:2010sh,Ghosh:2011qc,Lattanzi:2013uza,Queiroz:2014yna, Boucenna:2014uma,Lattanzi:2014mia,Dudas:2014bca,Dutra:2015vca,Escudero:2016tzx} or dark radiation~\cite{Chang:2013yva,Chang:2014lxa,Chang:2016pya}. Such a light (pseudo)scalar interacting with neutrinos could also emerge in a large range of beyond SM scenarios, such as supersymmetric and extra dimension models~\cite{Bamert:1994hb,Mohapatra:1988fk,Burgess:1992dt,Montero:2000ar, Mohapatra:2000px}, and could also have large couplings to neutrinos in, for instance, modified seesaw models involving large flavour violation \cite{Heurtier:2016iac}. Without intending to dip into any of these specific phenomenological models but rather investigating in a model independent manner how supernovae can constrain the couplings of light scalar bosons to the active neutrinos~\cite{Pasquini:2015fjv}, the dimension-4 and dimension-5 Lagrangians given respectively in Eqs.~(\ref{eqn:coupling4}) and (\ref{eqn:coupling5}) can be viewed as the low energy remnant of UV complete underlying theories. Setups involving peculiar global symmetries under which both leptons and the Majoron field are charged (such as the original Majoron model in type I seesaw) can naturally provide couplings of the (pseudo)scalar to neutrinos at the tree level whereas the coupling to charged leptons arise at the loop level. An example of such model can be found for instance in~\cite{Heurtier:2016iac} where the possibility of a massive scalar coupling to neutrinos is in tension with the prospective bounds we present in this paper. %To keep our results as general as possible, we will consider separately the couplings of $S$ and $J$ to neutrinos, although in some models we have both the two bosons. Until now the literature has mostly focused on massless or very light ($\lesssim\mathrm{eV}$) particles, in the quest for Majorons or Axion-Like Particles, we will here release a complementary study, exploring masses of the eV-GeV range, since as we will see, such a broad region is to be particularly constrained. %due to the energy spectrum of the supernova neutrino bath. In some of the models involving light scalars in the neutrino sector, there exist also the heavy right-handed neutrinos (RHNs), which are used to generate the tiny active neutrino masses via the seesaw mechanism. %The alternative process that is suggested by the referee could indeed be present in an explicit model of seesaw involving relatively light right-handed neutrinos (low scale type I seesaw e.g.). However One should however comment on the fact that in a certain class of seesaw models, our study cannot be applied. For instance in the case of a standard type I seesaw, writing the lagrangian as follows \begin{equation} \mathcal{L}\supset -\lambda \phi \bar N_R^c N_R - y\bar L H N_R -V(H,\,\phi)\,, \end{equation} where $H$ is the SM doublet and $\phi=v_S+(S+iJ)/\sqrt 2$, the masses of the scalar and RHNs are given respectively by \begin{equation} m_S=\sqrt {\lambda_S} v_S\,\text{~~and~~} M_N = \lambda v_S \,, \end{equation} with $\lambda_S$ quartic coupling in the potential $V$. Thus for an $\mathcal O(1)$ parameter $\lambda$ and a small quartic coupling $\lambda_S$ one can easily be in a situation where the RHNs are far heavier than the scalar $S$. In such a situation, if the RHNs are heavier than the GeV scale (or even hundreds of MeV) it can not be produced in the core of the supernovae and hence will not be present in any of the calculations below. On the opposite, the cases containing low mass RHNs would imply that the presence of RHN's would affect the neutrinos thermal distribution as well as the decay length and mean free path of the scalar $S$. Such consideration would strongly rely on the choice of the seesaw model considered and thus be very model dependent and require a proper modelling of the RHNs distribution in the core. We will for now on consider this case as being out of the scope of our paper, and focus on cases where all RHN's are heavier than the GeV scale. One may anyway note that, RHNs participating to leptogenesis have generically to be heavier than 100 MeV not to hit BBN bounds \cite{Canetti:2012kh, Hambye:2016sby}, which make our study rather general unless one tries to explore the possibility of a RHN dark matter. In the presence of massive degrees of freedom such as the scalar $S$, the evolution of supernova neutrino bursts and the subsequent deleptonization phase will be substantially affected, if the couplings to neutrinos are sufficiently large, and thus one can set limits on these couplings from the observation of SN1987A~\cite{Hirata:1987hu,Bionta:1987qt} as well as a future supernova explosion. Two different types of constraints can be obtained if one assumes that the extra scalar boson couples solely to the SM neutrinos: (i) On the one hand, the energy loss due to emission of (pseudo)scalars from the supernova core could significantly reduce the total flux of neutrinos observed in supernova explosions. For SN1987A the neutrino energy depletion is of order $10^{53}$ erg, and it is expected that the energy carried away by exotic particles could not exceed a sizable fraction of it. (ii) On the other hand, the deleptonization effect, e.g. $\nu_e \nu_e \to J$ can dramatically disable the explosion of supernovae. Indeed, supernova simulations reveal that the explosion process is very sensitive to the electron neutrino fraction $Y_{L_e}$ inside the core~\cite{Bruenn:1985,Baron:1987zz}. %An emission of huge number of light scalars will possibly ruin the supernova explosion. Thus by evaluating the number emission rate of the light scalars, we can set limits on the couplings to neutrinos involving the electron flavor, which depends yet largely on the supernova modelling and simulation details. The supernova constraints for a massless pseudoscalar Majoron have been extensively studied in Ref.~\cite{Gelmini:1982rr,Kolb:1987qy, Choi:1987sd,Berezhiani:1989za,Choi:1989hi,Chang:1993yp,Kachelriess:2000qc, Tomas:2001dh,Lindner:2001th,Hannestad:2002ff,Farzan:2002wx,Fogli:2004gy, Das:2011yh} where the Majoron is produced via the lepton number violating processes $\nu + \nu \to J$ and $\nu \to \bar \nu + J$, rendered possible through matter effects. The limits come out to be $g_{\alpha\beta} \lesssim 10^{-5}$, %\begin{eqnarray} %g_{\alpha\beta} \lesssim 10^{-5}\;, %\end{eqnarray} from both the luminosity and deleptonization arguments. In the case of a massive scalar, if the scalar mass is much larger than the matter effects, then the calculation procedure is somewhat similar to the case of heavy axion or dark photon, with the significant difference that the two latters are produced from nucleon collisions. On the other hand, for a supernova core with temperature $T \simeq 10-30$ MeV, the scalars can not be produced abundantly for masses above $\gtrsim$ GeV, which is heavily suppressed by the factor of $e^{- m / T}$. Thus the limits we will present in this paper apply to scalars in the mass range of eV $\lesssim m \lesssim$ GeV. A massless Majoron could also be emitted from neutrinoless double beta decays~\cite{Mohapatra:1988fk,Chang:1993yp,Bamert:1994hb,Burgess:1992dt, Montero:2000ar,Mohapatra:2000px,Berezhiani:1992cd,Burgess:1993xh,Hirsch:1995in} %i.e. at the hadron level $2n \to 2p + 2 e^- + J$, and from the decays of SM mesons and leptons~\cite{Gelmini:1982rr,Barger:1981vd,Britton:1993cj,Lessa:2007up,Pasquini:2015fjv}. %for instance $\pi^+ \to \mu^+ + \nu + J$ and $\tau \to \mu + \nu + \bar\nu + J$. Ref.~\cite{Pasquini:2015fjv} {derived} recently the limits from meson and lepton decays {in} the case of a massive scalar, with mass up to $\sim 100$ MeV, excluding couplings of order $|g_e|^2\sim 10^{-1}-10^{-6}$. The constraints on massless and massive scalars are complementary to each other, and we will see that supernova constraints for the massive case in this paper will push the couplings down by several orders of magnitude. %The latter study is thus complementary to neutrino decay and neutrino oscillations constraints on ultralight pseudoscalar interactions but we will see that our constraints probe values of the coupling smaller by several orders of magnitude. For the sake of completeness we will consider, in addition to the usual dimension-4 couplings of the form $\nu \nu S$, the possibility of having non-renormalizable dimension-5 operators of the form $(\nu \nu) (S S) / \Lambda$, where $\Lambda$ stands for a cutoff scale after the heavy UV complete sector is integrated out, and in this case the scalar $S$ can be considered for instance to be a neutrino-phillic light DM candidate, whose couplings to other SM particles %(in particular the couplings to electrons and nucleons in our case) are vanishing or highly suppressed. %In $R$-parity conserving supersymmetric theories, $S$ can be interpreted as the sneutrino, and the cutoff scale $\Lambda$ is roughly the supersymmetry breaking scale. All other higher order effective operators are less important from the phenomenological point of view in this paper and will be neglected. The paper is organized as follows: The next section is devoted to the production and decay of the massive scalar in supernova core induced by the dimension-4 couplings. The luminosity limits and trapping effect are presented respectively in Section~\ref{sec:lum} and \ref{sec:mfp}, while the deleptonization constraints are considered in Section~\ref{sec:delep}. The analogous constraints on dimension-5 interactions are derived and collected in Section~\ref{sec:dim5}. {Finally, future prospects for possible Super-Kamiokande and IceCube detections are given in Section~\ref{sec:prospects}}, before we summarize and conclude in Section~\ref{sec:conclusion}. Some of the calculation details are listed in the Appendix. %The supernova constraints on scalars in the neutrino sector is complementary to the limits form the terrestrial experiments. %%\footnote{The cosmic microwave background set also limit on the couplings if neutrinos are allowed to decay $\nu \to \nu' + J$, with the values $g_{ii} < 10^{-7}$ and $g_{ij} \lesssim 6.1 \times 10^{-10}$ in the mass basis.} %For a massless Majoron, neutrinoless double beta decay experiment requires that %\begin{eqnarray} %|g_{ee}| < 2 \times 10^{-4} %\end{eqnarray} %at the 90\% C.L. SM meson and lepton decays could also emit a Majoron in the final states, e.g. $\pi^+ \to \mu^+ + \nu + J$ and $\tau \to \mu + \nu + \bar\nu + J$ and the current limits are %\begin{eqnarray} %|g_{e\alpha}| &<& 5.5 \times 10^{-6} \,, \nonumber \\ %|g_{\mu\alpha}| &<& 4.5 \times 10^{-5} \,, \nonumber \\ %|g_{\tau\alpha}| &<& 5.5 \times 10^{-2} %\end{eqnarray} %with the flavor index $\alpha = e,\, \mu,\, \tau$. | \label{sec:conclusion} Core-collapse supernovae provide a unique circumstance to study the beyond SM particles and couplings, and have been {extensively studied} with regard to neutrinos, axion, Majoron etc. In this letter we demonstrate to what extent the couplings of a massive scalar (or pseudoscalar) to SM neutrinos can be constrained from the supernova side. This is well motivated from the large variety of Majoron models, and applies to the most general cases. Two distinct types of couplings are considered, which are respectively dimension-4 and dimension-5, as shown in Eqs.~(\ref{eqn:coupling4}) and (\ref{eqn:coupling5}). We apply two different constraints on both {the} couplings: the first one concerns the energy loss of supernovae due to the (pseudo)scalar emission and the second one is the electron lepton number depletion in the supernova core. The limits from SN1987A on the dimension-4 couplings are collected in Fig.~\ref{fig:lum}, with the relatively dark coloured regions excluded in the parameter space of (pseudo)scalar mass and couplings. The possibility of scattering with neutrinos inside the core, which tends to trap the scalar particles, is also taken into account. The exclusion regions can be summarized as follows \begin{align*} 2.1\times 10^{-9} \, {\rm MeV} &\lesssim {|g_{ee}|}\times{m_S} \lesssim 1.6\times 10^{-6} \, {\rm MeV} \,,\\ 5.5\times 10^{-9} \, {\rm MeV} &\lesssim {|g_{\mu\mu}|}\times{m_S}\lesssim 1.1\times 10^{-6} \, {\rm MeV}\,,\\ 2.3\times 10^{-8} \, {\rm MeV} &\lesssim {|g_{e\mu}|}\times{m_S}\lesssim 6.6\times 10^{-7} \, {\rm MeV} \,, \end{align*} in the region where, roughly, $m_S \in [10,\, 500] \, \mathrm{MeV}$. The deleptonization constraints overlap largely with the corresponding limits from energy loss. In the case of dimension-5 operator, we can constrain the parameter space for a scalar mass from MeV to 100 MeV and couplings $h_{\alpha\beta}$ from $10^{-6}$ to $10^{-2}$, depending on the neutrino flavours and scalar mass. The deleptonization constraints give again similar bounds for coupling involving the electron flavour. For what concerns future observability, we derive also the prospects in the case of a nearby supernova explosion. Given a huge amount of neutrino data collected in future experiments like {Super-Kamiokande} and IceCube, the current limits {can be largely} improved, as shown in Fig.~\ref{fig:lum2} and \ref{fig:prospects2}. A non-deviation {of experimental data} with respect to {supernova} simulations could {exclude} {large} regions of the parameter space. Probing models standing in this region of parameter space may hence be rendered possible by future supernova observations. %in the same mass range for the (pseudo)scalar considered. Our estimations of supernova constraints on the couplings of massive (pseudo)scalars to neutrinos are complementary to terrestrial experiments such as those from meson and lepton decay, which are both, {in some sense,} the counterpart of constraints on couplings of a massless (pseudo)scalar to the SM neutrinos. Finally, more {involved} simulations of supernova explosions, including the emission of massive scalars, would be of great interest for constraining such secret interactions, as done for the case of axions in~\cite{Fischer:2016cyd}. %These Yukawa couplings of neutrinos may also be important when we come to the points of neutrino decay, non-standard neutrino interactions, Higgs invisible decay, or even the evolution of the Universe. %The supernova constraints on scalar/pseudoscalar is somewhat complementary to the axion constriant, %and also other constraints on ALP (light scalars) and in the neutrino sector... | 16 | 9 | 1609.05882 |
1609 | 1609.09855_arXiv.txt | We consider a cosmology in which dark matter and a quintessence scalar field responsible for the acceleration of the Universe are allowed to interact. Allowing for both conformal and disformal couplings, we perform a global analysis of the constraints on our model using Hubble parameter measurements, baryon acoustic oscillation distance measurements, and a Supernovae Type Ia data set. We find that the additional disformal coupling relaxes the conformal coupling constraints. Moreover we show that, at the background level, a disformal interaction within the dark sector is preferred to both $\Lambda$CDM and uncoupled quintessence, hence favouring interacting dark energy. | Multiple high precision cosmological observations broaden our understanding of the dynamics of the Universe when confronted with theoretical models. For instance, inferences from observations of Supernovae Type Ia (SNIa) \cite{Perlmutter:1998np,Riess:1998cb,Garnavich:1998th,Schmidt:1998ys,Perlmutter:1997zf}, baryon acoustic oscillations (BAO) \cite{Eisenstein:2005su,Percival:2007yw,Percival:2009xn}, and the cosmic microwave background (CMB) \cite{Spergel:2003cb,Spergel:2006hy,Reichardt:2008ay,Ade:2015xua} are complementary---among other things they indicate that our Universe has recently entered an accelerating epoch. Analysis from data sets of this kind has led cosmologists to formulate a standard model that postulates a dark sector consisting of dark energy and dark matter, contributing to about $69\%$ and $26\%$ of the total energy density in the Universe respectively \cite{Ade:2015xua}. The focus of much current research in cosmology is to understand the properties and origins of the dark sector, in particular dark energy, for which the cosmological constant is the simplest explanation \cite{Einstein:1917ce}; this standard model is currently in very good agreement with current cosmological observations. Theoretically, however, the coincidence and fine--tuning problems challenge our understanding of gravity and quantum field theory \cite{Weinberg:1988cp,Zlatev:1998tr}. A plethora of alternative dynamical dark energy models have been proposed, such as quintessence \cite{Wetterich:1987fm,Peccei:1987mm,Peebles:1987ek}, k-essence \cite{Chiba:1999ka,ArmendarizPicon:2000dh}, phantom \cite{Caldwell:1999ew}, Chaplygin gas \cite{Bento:2002ps}, Ricci dark energy \cite{Gao:2007ep}, and holographic dark energy and related ideas \cite{Li:2004rb,Cohen:1998zx}. Furthermore, coupled dark energy models have also been extensively studied since, from the field theoretic point of view, dark energy is not prohibited from interacting with cold dark matter \cite{Wetterich:1994bg,Amendola:1999er,Wintergerst:2010ui,Pettorino:2008ez,Mangano:2002gg,Amendola:2003wa,Koivisto:2005nr,Koivisto1,Guo:2007zk,Quercellini:2008vh,Quartin:2008px,Valiviita:2009nu,Jack} or, for example, massive neutrinos \cite{Gu:2003er,Fardon:2003eh,Brookfield:2005bz,Ichiki:2008rh,Wetterich:2007kr}. In this paper we consider the case of a (non--universally) coupled dark energy model in which dark matter particles feel an additional fifth force mediated by the dark energy scalar field. This coupling between the dark sector elements modifies the background evolution of the Universe, as well as the growth of perturbations: in this paper we concentrate on constraints coming from the background only, deferring the perturbed case for future work. As conformally coupled dark matter models have been well studied \cite{Amendola:2003eq,Xia:2009zzb,Pettorino:2012ts,Amendola:2000ub,Bean:2008ac,Pettorino:2013oxa,Xia:2013nua,Ade:2015rim,Amendola:2011ie}, and tight constraints on the model parameters have been established \cite{Pettorino:2013oxa,Xia:2013nua,Ade:2015rim}, the main aim of this paper will be to augment the models of these studies with a disformal coupling and discern its influence in light of the conformal-only constraints. Models that utilise such disformal interactions within the dark sector have been attracting much attention recently \cite{Zuma5,Zumalacarregui:2012us,Jack,Koivisto,Koivisto1,Sakstein:2014isa,Carsten,Sakstein:2014aca,vandeBruck:2015rma,vandeBruck:2016jgg}, so it has become an imperative that they be compared with state-of-the-art cosmological data sets. This paper is structured as follows. In Section \ref{sec:Model} we introduce our coupled dark energy model and present the background evolution equations in a flat, homogeneous, and isotropic Universe. We list in Section \ref{sec:data} the observational data sets we will use here to derive constraints on our model parameters, while in Section \ref{sec:results} we present the obtained constraints for each coupled dark matter model. Finally Section \ref{sec:conclusions} contains our conclusions, and outlines future work. | \label{sec:conclusions} In the present work we have considered an interacting dark sector in which we allowed for two distinct forms of couplings that connect dark matter with dark energy, where the latter is responsible for the cosmological acceleration. Our current state of ignorance regarding the physics of this dark sector still allows for other interactions beyond the purely gravitational ones to exist between its elements. Various dark sector models involving various coupling functions have been extensively studied, together with their astrophysical and cosmological consequences, and it is these studies, that compare such models with state-of-the-art cosmological data, that will allow us to separate the viable candidates from the false. We here considered a specific coupled dark energy model in which dark energy and dark matter are allowed to couple via a conformal coupling and/or a disformal coupling. We first considered the purely conformal and the purely disformal coupling cases, and finally we also discussed the mixed scenario in which both a conformal and a disformal coupling are present. In our analysis we have only used the cosmological background evolution to constrain cosmological model parameters, namely Hubble parameter measurements, baryon acoustic oscillation distance measurements, and the Supernovae Type Ia Union2.1 compilation consisting of 580 data points. In the conformally coupled model, we obtained results consistent with those found in the literature, although weaker constraints were obtained as we use only the background evolution to test the models. Allowing for an additional constant disformal coupling term, we found that the constraints on the conformal coupling are relaxed. This is consistent with the observations made in Ref. \cite{Jack}, in which it was shown that the disformal term suppresses the coupling $Q$ at larger redshifts and therefore has an impact on the evolution of the effective equation of state $w_{\rm eff}$. We also found that, with our choice of data sets, a non-zero disformal coupling between dark matter and dark energy is preferred over the $\Lambda$CDM model. In the purely conformal coupled case, only the analysis including the HST data prefer a non-zero coupling at 1$\sigma$ confidence level. In the case of a purely disformal coupling, a non-zero coupling is preferred in all analyses, as it is the case in the conformally-disformally coupled scenario. We must now go beyond the background evolution and consider the growth of perturbations as well. Using precise measurements of CMB anisotropies and the matter power spectra of large scale structures, we certainly expect to get tighter constraints on our model parameters. We address this in future work. Finally, on a more speculative note, we can compare our findings above with that of Ref. \cite{Salvatelli:2014zta}, wherein Planck, SNIa, and redshift space distortion data are found to favour a late-time interaction between dark sector elements---it is shown in Ref. \cite{Jack} that the disformal coupling of the type we have just considered switches on at late times and is negligible in the past. We merely highlight this curiosity now and return to a comparison between the models in future work. | 16 | 9 | 1609.09855 |
1609 | 1609.04599_arXiv.txt | {} {Knowing the distribution of stellar rotational velocities is essential for the understanding stellar evolution. Because we measure the projected rotational speed $v \sin i$, we need to solve an ill--posed problem given by a Fredholm integral of the first kind to recover the 'true' rotational velocity distribution.} {After discretization of the Fredholm integral, we apply the Tikhonov regularization method to obtain directly the probability distribution function for stellar rotational velocities. We propose a simple and straightforward procedure to determine the Tikhonov parameter. We applied Monte Carlo simulations to prove that Tikhonov method is a consistent estimator and asymptotically unbiased.} {This method is applied to a sample of cluster stars. We obtain confidences intervals using bootsrap method. Our results are in good agreement with the one obtained using the Lucy method, in recovering the probability density distribution of rotational velocities. Furthermore, Lucy estimation lies inside our confidence interval. } {Tikhonov regularization is a very robust method that deconvolve the rotational velocity probability density function from a sample of $v \sin i$ data straightforward without needing any convergence criteria.} | } The understanding about how stars rotate is essential to describe and modelling many aspect of stellar evolution. From spectroscopy observations we can only get the projected velocity, $v \sin i$, where $i$ is the inclination angle with respect to the line of sight. Furthermore, in order to deconvolve (disentangle or unfold) the rotational velocity distribution function, an assumption on the distribution of rotational axes is required. The standard choice is that the distribution of stellar axes is uniformly (randomly) distributed over the sphere. Using this assumption Chandrasekhar \& M\"unch (1950) studied the integral equation that describe the distribution of 'true' ($v$) and apparent ($v \sin i$) rotational velocities, deriving a formal solution, which is proportional to a derivative of an Abel's Integral. Chandrasekhar \& M\"unch (1950) method is not usually applied, because the differentiation of the formal solution can lead to misleading results due to intrinsic numerical problems associated to the derivative of the Abel's integral. Cur\'e et al. (2014) extended the work of Chandrasekhar \& M\"unch (1950), integrating the formal solution and obtained the cumulative distribution function (CDF) for the rotational velocities. This CDF is attained in one step demonstrating the robustness to this method. While the CDF identifies the distribution of the speed of rotation it is sometimes useful to have the probability density function (PDF) for easy handling and to appreciate directly certain properties of the distribution (e.g., the maximum, its symmetry, variability, etc). It is known also that the observed values of the projected rotational velocities are provided with measurement error. The goal of this work is to propose a methodology that provides straightforward the PDF, taking into account the measurement errors and avoiding numerical problems arising from the derivative of the CDF. Regularization methods are a technique widely used to deconvolve inverse problems. Image processing, geophysics and machine learning are some of the areas where they are usually applied (Bouhamidi $2007$, Deng et al. $2013$, Fomel $2007$). Among the regularization methods we find: Truncated Singular Value Decomposition (TSVD), Selective Singular Value Decomposition (SSVD) and Tikhonov Regularization Method (Hansen 2010). In this article we obtain the estimated probability distribution function directly from the Fredholm integral by means of the Tikhonov regularization method. After its introduction by Tikhonov (1943) to solve integral equation problems, this method (known as Ridge Regression in statistics) has been developed and extensively used since then (see, e.g., Tikhonov 1963, Tikhonov and Arsenin 1977, Tikhonov et al. 1995, Eggermont 1993, Hansen 2010). It allows an increase in the numerical stability and dealing with errors of measurement. This article is structured as follows: In section 2 we briefly present the mathematical description of the method and describe a procedure to calculate the Tikhonov factor. In section 3, we perform Monte Carlo simulations to show the robustness of this method. In section 4, a real sample of cluster stars are deconvolved by Tikhonov regularization, confidence intervals are calculated using bootstrap method and a comparison between our PDF results with the one obtained with the Lucy (1974) method and CDF results from the work of Cur\'e et al. (2014) are performed. Last section presents our conclusions and future work. | In this work we have obtained the estimated probability distribution function of 'true' rotational velocities using Tikhonov regularization method. Furthermore, this estimated PDF uses a Tikhonov parameter $\lambda$ obtained by means of an iterative method with a specific stopping criterion in comparison with the widely used iterative method of Lucy (1974).\\ Through Monte Carlo numerical simulations we assess the proposed method in two cases: when the rotational velocity distribution is described by a Maxwell distribution and for a mixture of two Maxwell distributions. For each situation different scenarios were evaluated obtaining good results for all of them except for $n_s=30$, when the velocities are described by a mixture of two Maxwellian distributions.\\ This method retrieve the typical rotational velocities distribution for uni- and bimodal distribution. We showed, empirically, that the studied estimator is asymptotically unbiased and its variance tends to zero. Furthermore, as measure of goodness of fit, the MISE $\lesssim 10^{-4}$ for all sample sizes and tends to zero when $n_s$ tends to infinity.\\ We apply this method to a set of observed data from Tarantula cluster (Ram\'irez-Agudelo et al. 2013). The estimated PDF from Tikhonov regularization method agreed very well with the PDF obtained using Lucy method, as the q-q plot shows, demonstrating a very good performance to deconvolve rotational velocity distribution (PDF).\\ In comparison with the method that delivers the CDF described in Cure et al. (2014), Tikhonov regularization solution gives, by direct integration of the PDF, almost the same non--parametric estimation of the true underlying cumulative distribution function of rotational velocities.\\ Summarizing, in Cur\'e et al. (2014) we developed a method to obtain the CDF of 'true' rotational velocities and in this work we present Tikhonov regularization method to obtain the corresponding PDF directly from Fredhoml integral, both methods calculate in a simple and straightforward way, the PDF or CDF, without any assumptions of the underlying distribution. \\ Future work: We want to develop a general function of the kernel of Fredholm integral, $p(y|x)$, in order to describe an arbitrary orientation of rotational axes. Thus, we can study the distribution of rotational speeds relaxing the standard assumption of uniformity of stellar axes. | 16 | 9 | 1609.04599 |
1609 | 1609.04416_arXiv.txt | {The exoplanet HD\,97658b provides a rare opportunity to probe the atmospheric composition and evolution of moderately irradiated super-Earths. It transits a bright K star at a moderate orbital distance of 0.08\,au. Its low density is compatible with a massive steam envelope that could photodissociate at high altitudes and become observable as escaping neutral hydrogen. Our analysis of three transits with HST/STIS at Lyman-$\alpha$ reveals no such signature, suggesting that the thermosphere of HD\,97658b is not hydrodynamically expanding and is subjected to a low escape of neutral hydrogen ($<$10$^{8}$\,g\,s$^{-1}$ at 3$\sigma$).\\ Using HST/STIS Lyman-$\alpha$ observations and Chandra/ACIS-S \& XMM-Newton/EPIC X-ray observations at different epochs, we find that HD\,97658 is in fact a weak and soft X-ray source with signs of chromospheric variability in the Lyman-$\alpha$ line core. We determine an average reference for the intrinsic Lyman-$\alpha$ line and X-EUV (XUV) spectrum of the star, and show that HD\,97658 b is in mild conditions of irradiation compared to other known evaporating exoplanets with an XUV irradiation about three times lower than the evaporating warm Neptune GJ436 b. This could be the reason why the thermosphere of HD\,97658b is not expanding: the low XUV irradiation prevents an efficient photodissociation of any putative steam envelope. Alternatively, it could be linked to a low hydrogen content or inefficient conversion of the stellar energy input. The HD\,97658 system provides clues for understanding the stability of low-mass planet atmospheres in terms of composition, planetary density, and irradiation. \\ Our study of HD\,97658 b can be seen as a control experiment of our methodology, confirming that it does not bias detections of atmospheric escape and underlining its strength and reliability. Our results show that stellar activity can be efficiently discriminated from absorption signatures by a transiting exospheric cloud. They also highlight the potential of observing the upper atmosphere of small transiting planets to probe their physical and chemical properties.} | A substantial fraction of known exoplanets orbit extremely close to their stars, within a tenth of an astronomical unit. This population displays a wide diversity in nature, from gaseous giants to super-Earths and even disintegrating rocky cores, raising many questions about the formation and evolution of such objects and their possible relations. The intense X-ray and extreme ultraviolet irradiation from the parent star can lead a hydrogen-rich thermosphere to lose its stability, expand hydrodynamically, and evaporate (\citealt{VM2003}).\\ An extended atmosphere produces a much deeper absorption than the lower atmospheric layers when observed in the spectral lines of elements that are abundant at high altitudes and/or associated with strong electronic transitions. Transit observations in the Lyman-$\alpha$ line of their host star first revealed the existence of extended atmospheres of neutral hydrogen around the hot Jupiters HD\,209458b (\citealt{VM2003,VM2004}; \citealt{BJ2007,BJ2008}; \citealt{VM2008}; \citealt{Ehrenreich2008}; \citealt{BJ_Hosseini2010}) and HD\,189733b (\citealt{Lecav2010,Lecav2012}; \citealt{Bourrier2013}). Observations of other lines in the far UV allowed the detection of heavy metals and ions carried to high altitudes by collisions with the hydrogen outflow (e.g., oxygen, carbon, and magnesium; \citealt{VM2004}, \citealt{Linsky2010}, \citealt{VM2013}, \citealt{BJ_ballester2013}, \citealt{Fossati2010}; \citealt{Haswell2012}), confirming that the upper atmosphere of these giant planets is in a state of blow-off.\\ Many questions remain to be answered about the effect of irradiation on the formation and the structure of extended atmospheres. The strong energy input into hot Jupiters is the source for their evaporation (e.g., \citealt{Lammer2003}, \citealt{Lecav2004}; \citealt{Yelle2004,Yelle2006}; \citealt{GarciaMunoz2007}; \citealt{Owen2012}, \citealt{Koskinen2013a,Koskinen2013b}, \citealt{Johnstone2015}), but the detection of a Lyman-$\alpha$ absorption from the partially transiting upper atmosphere of the warm Jupiter 55 Cnc b first hinted that milder conditions of irradiation can lead to atmospheric expansion (\citealt{Ehrenreich2012}). Interestingly, 55 Cnc b is close to the orbital distance limit where the atmosphere of a giant planet is expected to lose its stability (\citealt{Koskinen2007}). The moderate depth of 55 Cnc b absorption signature (\citealt{Ehrenreich2012}), in comparison to HD\,209458b and HD\,189733b, can be explained if its exosphere fills about a third of the Roche lobe, consistent with the lower irradiation of the planet. \\ Recently, transit observations of the warm Neptune GJ\,436 b in the Lyman-$\alpha$ line at three different epochs revealed deep, repeatable exospheric transits reaching up to 60\%, and lasting for much longer than the optical transit (\citealt{Kulow2014}, \citealt{Ehrenreich2015}). ``Radiative braking'' (\citealt{Bourrier2015}) and interactions with the wind of its M dwarf host star (\citealt{Bourrier2016}) were shown to shape the neutral hydrogen exosphere of GJ\,436b into a giant coma that surrounds the planet and trails for millions of kilometers behind it. Counterintuitively, GJ\,436 b observations revealed that much larger atmospheric signals could be retrieved from the upper atmosphere of moderately irradiated, low-mass planets than from more heavily irradiated massive planets. This opens thrilling perspectives for the characterization of the many small planets in the sub-Neptune and super-Earth mass regimes, which have no equivalent in the solar system and whose nature and evolution remain mysterious. Probing the upper extended atmosphere of such planets will be particularly important because their lower atmosphere, less extended and with a heavier composition, will be more difficult to characterize. The non-detection of a neutral hydrogen exosphere around the super-Earth 55 Cnc e (\citealt{Ehrenreich2012}) hinted at the presence of a high-weight atmosphere -- or the absence of an atmosphere -- recently supported by the study of its brightness map in the IR (\citealt{Demory2016}). Studying the atmospheric escape of small planets will not only bring insights into their nature, but will also help understand their formation and evolution. \\ The exoplanet HD\,97658 b ($M_{p}$ = 7.9$\pm$0.7\,M$_\oplus$; $R_{p}$ = 2.39\,R$_\oplus$) was discovered by a radial-velocity survey (\citealt{Howard2011}), and was later detected in transit across its 9.7$\pm$2.8\,Gy old parent star (\citealt{Dragomir2013_HD976}; \citealt{Bonfanti2016}). Measurement of the planetary radius at 4.5\,$\mu$m with Spitzer have allowed the planet bulk density to be refined to $\rho$ = 3.9$\stackrel{+0.7}{_{-0.6}}$\,g\,cm$^{-3}$ (\citealt{Vangrootel2014}). While its exact nature remains to be unveiled, \citet{Vangrootel2014} have predicted that HD\,97658 should have a large rocky core accounting for up to 60\% of the planet mass, an envelope of water and ices accounting for up to 40\% of the planet mass, and less than 2\% of hydrogen and helium. If its composition is indeed water-rich, HD\,97658 orbits close enough to its K1-dwarf star ($P$ = 9.5\,days, T$_{eq}\sim$725\,K; \citealt{Knutson2014}) that its temperature should allow for the formation of a thick envelope of steam. The brightness of HD\,97658 b host star (V=7.7, $d$=21.1\,pc) makes it one of the handful of small planets currently amenable to atmospheric characterization. However, given the shallowness of the planetary transit seen at optical or near-infrared (NIR) wavelengths ($\sim$0.09\%) and the small expected scale height of a steam envelope, its detection would be extremely challenging through infrared absorption. As it is, transmission spectroscopy of HD\,97658b performed in the near IR with WFC3 (\citealt{Knutson2014}) is consistent with flat transmission spectrum models, indicating either a cloudy atmosphere or a cloudless, water-rich atmosphere. Consequently, HD\,97658 b is a very good target for transit observations of its upper atmosphere. Photodissociation of a steam envelope could produce OH and H at high altitudes (\citealt{Wu1993}; \citealt{Jura2004}). Here, we present a search for neutral hydrogen escape through dedicated Lyman-$\alpha$ line observations. These observations are complemented by X-ray measurements to estimate the high-energy stellar irradiation. This study is comparable to the one performed for the hot Jupiter HD\,189733b, which transits a star with the same type as HD\,97658 and was shown to be evaporating (\citealt{Lecav2010,Lecav2012}, \citealt{Bourrier2013}). Differences in the age and coronal activity of the host stars, in addition to the different orbital and bulk properties of their planets, may induce very different evaporation regimes.\\ Lyman-$\alpha$ observations of HD\,97658 at different epochs are analyzed and interpreted in Sect.~\ref{sec:data ana}. They are used in Sect.~\ref{sec:recons} to estimate the intrinsic Lyman-$\alpha$ line of HD\,97658 and the properties of the interstellar medium (ISM) in its direction. We use these measurements, along with that of the stellar X-ray emission, to study the XEUV irradiation of HD\,97658 b in Sect.~\ref{sect:X-EUV}. In Sect.~\ref{sec:EVE_sim} we compare the Lyman-$\alpha$ observations with numerical simulations of the planet transit with the EVaporating Exoplanet (EVE) code to constrain the presence and properties of a putative extended thermosphere and exosphere of neutral hydrogen. We discuss our results and their importance for the nature of HD\,97658b in Sect.~\ref{sec:discuss}. The properties of the system relevant to our study are given in Table~\ref{tab:param_sys}.\\ \begin{table}[tbh] \caption{Physical parameters for the HD\,97658 system.} \begin{tabular}{llcccc} \hline \hline \noalign{\smallskip} Parameters & Symbol & Value \\ \noalign{\smallskip} \hline \noalign{\smallskip} Distance from Earth & $D_{\mathrm{*}}$ & 21.11\,pc \\ \noalign{\smallskip} Star radius & $R_{\mathrm{*}}$ & 0.74$\,R_{\mathrm{\sun}}$ \\ \noalign{\smallskip} Star mass & $M_{\mathrm{*}}$ & 0.77$\,M_{\mathrm{\sun}}$ \\ \noalign{\smallskip} Planet radius & $R_{\mathrm{p}}$ & 2.39$\,R_{\mathrm{Earth}}$ \\\noalign{\smallskip} Planet mass & $M_{\mathrm{p}}$ & 7.55$\,M_{\mathrm{Earth}}$ \\ \noalign{\smallskip} Orbital period & $P_{\mathrm{p}}$ & 9.49$\,days$ \\ \noalign{\smallskip} Transit center & $T_{\mathrm{0}}$ & 2456665.46415$\,BJD$ \\ \noalign{\smallskip} Semi-major axis & $a_{\mathrm{p}}$ & 0.08$\,au$ \\ \noalign{\smallskip} Eccentricity & $e$ & 0.078 \\ \noalign{\smallskip} Argument of periastron & $\omega$ & 71$^{\circ}$ \\ \noalign{\smallskip} Inclination & $i_{\mathrm{p}}$ & 89.14$^{\circ}$ \\ \noalign{\smallskip} \hline \hline \multicolumn{6}{l}{Note: All parameters come from \citealt{Vangrootel2014}}\\ \multicolumn{6}{l}{except for $T_{\mathrm{0}}$, $P_{\mathrm{p}}$, and $R_{\mathrm{p}}$ from \citealt{Knutson2014}}\\ \end{tabular} \label{tab:param_sys} \end{table} | \label{sec:discuss} Despite appearing quiet in the optical and NIR (\citealt{Vangrootel2014}), HD\,97658 has detectable high-energy emission. It is a weak and soft X-ray source with a variable upper chromosphere and corona. Our HST and XMM-Newton/Chandra observations of HD\,97658 at five different epochs reveal signs of both short-term and long-term variability in the Lyman-$\alpha$ and X-ray emission of this star. We were nonetheless able to determine a stable, average reference for the intrinsic Lyman-$\alpha$ line and XUV spectrum of the star, refining the properties derived by \citet{Youngblood2016}. These estimates will be useful in determining the impact of the incident high-energy radiation on the atmospheric heating and chemistry for this super-Earth, and more generally in understanding the conditions that lead to evaporation. The HD\,97658 system might be crucial in understanding the stability of the atmospheres of small planets in terms of atmospheric composition, planetary density, and irradiation. Indeed, HD\,9758b is a super-Earth more than twice as dense (3.9\,g\,cm$^{-3}$) as the evaporating warm Neptune GJ\,436 b (1.6\,g\,cm$^{-3}$). Furthermore, HD\,97658 b orbits at 0.08\,au from its K dwarf host star and we measure an XUV energy input of 835$\pm$160\,erg\,s$^{-1}$\,cm$^{-2}$ (Sect.~\ref{sec:XUV_irr}), which is about three times lower than the irradiation of GJ\,436 b (at 0.027\,au from its M dwarf host; \citealt{Ehrenreich2015}, \citealt{Bourrier2016}). The upper atmosphere of HD\,97658b is also subjected to a photoionization rate of 4.8$\stackrel{+1.6}{_{-1.4}}\times$10$^{-5}$\,s$^{-1}$, which is more than six times lower than for the evaporating hot Jupiter HD\,189733 b (at 0.031\,au from its K dwarf host; \citealt{Bourrier_lecav2013}).\\ Our analysis of three Lyman-$\alpha$ transits of the super-Earth HD\,97658b at independent epochs yields no signature arising from an extended atmosphere of neutral hydrogen. This suggests that the thermosphere of HD\,97658b is not hydrodynamically expanding, and in any case that the escape of neutral hydrogen is below 10$^{8}$\,g\,s$^{-1}$ at 3$\sigma$. This might be linked to the low XUV stellar irradiation, to an inefficient conversion of the stellar energy input, and/or to a low hydrogen content in the upper atmosphere (possibly linked to a helium enrichment, \citealt{Hu2015}, or to an enhanced mass loss from the irradiation and stellar wind of the young host star). A more exotic possibility would be that HD\,97658b is in a saturation regime with the wind from its host star, as defined by \citet{Bourrier_lecav2013}, where the stellar wind is so dense that it interacts with all neutral hydrogen atoms escaping the upper atmosphere. Provided that the stellar wind protons move faster than about 300\,km\,s$^{-1}$, all hydrogen atoms escaping HD\,97658b would then be ionized through charge-exchange, while the high-velocity neutralized protons would contribute to Lyman-$\alpha$ absorption too far from the line core to be detectable (\citealt{Bourrier2016}).\\ The methodology used in this study is the same as led to the non-detection of Lyman-$\alpha$ signatures around the super-Earth 55\,Cnc e and to the detection of hydrogen exospheres around the giant planets HD\,209458 b (\citealt{VM2003}), HD\,189733 b (\citealt{Lecav2010}; \citealt{Lecav2012}), 55\,Cnc b (\citealt{Ehrenreich2012}), and GJ\,436b (\citealt{Ehrenreich2015}). There is a clear distinction between the stellar activity of HD\,97658 b, revealed as short- and long-term variations in the core of the Lyman-$\alpha$ line, and the transit of a neutral hydrogen exosphere. The latter occurs around and after the time of the optical transit, with the depth and spectral range of the absorption evolving coherently over time. Confirmed signatures of hydrogen escape have been detected within specific wavelength ranges in the blue wing of the Lyman-$\alpha$ line, which can be explained well by the physical mechanisms acting on the upper planetary atmosphere. In this frame our study of HD\,97658 b can be seen as a control experiment; the results we obtained confirm that detections of atmospheric escape are not biased by our methodology, and underline its strength and reliability. Future observations of this system in other FUV lines will be needed to search for escape signatures of heavier species than hydrogen and to further constrain the nature of this super-Earth.\\ | 16 | 9 | 1609.04416 |
1609 | 1609.01719_arXiv.txt | We present zoom-in, AMR, high-resolution ($\simeq 30\, {\rm pc}$) simulations of high-redshift ($z \simeq 6$) galaxies with the aim of characterizing their internal properties and interstellar medium. Among other features, we adopt a star formation model based on a physically-sound molecular hydrogen prescription, and introduce a novel scheme for supernova feedback, stellar winds and dust-mediated radiation pressure. In the zoom-in simulation the target halo hosts \quotes{Dahlia}, a galaxy with a stellar mass $M_{\star}=1.6\times 10^{10}\msun$, representative of a typical $z\sim 6$ Lyman Break Galaxy. {Dahlia} has a total \HH~mass of $10^{8.5}\msun$, that is mainly concentrated in a disk-like structure of effective radius $\simeq 0.6$ kpc and scale height $\simeq 200$ pc. Frequent mergers drive fresh gas towards the centre of the disk, sustaining a star formation rate per unit area of $\simeq 15\,\msun\,{\rm yr}^{-1}\,{\rm kpc}^{-2}$. The disk is composed by dense ($n \gsim 25\,\cc$), metal-rich ($Z \simeq 0.5\,\zsun$) gas, that is pressure-supported by radiation. We compute the $158\mu$m \CII~emission arising from {Dahlia}, and find that $\simeq 95\%$ of the total \CII~luminosity ($L_{\rm [CII]}\simeq10^{7.5}\lsun$) arises from the \HH~disk. Although $30\%$ of the \CIIion~mass is transported out of the disk by outflows, such gas negligibly contributes to \CII~emission, due to its low density ($n \lsim 10\,\cc$) and metallicity ($Z\lsim 10^{-1}\zsun$). {Dahlia} is under-luminous with respect to the local \CII-$SFR$ relation; however, its luminosity is consistent with upper limits derived for most $z\sim6$ galaxies. | The discovery and characterization of primeval galaxies constitute some of the biggest challenges in current observational and theoretical cosmology\footnote{In the following we assume cosmological parameters compatible with \emph{Planck} results, i.e. a $\Lambda$CDM model with total matter, vacuum and baryonic densities in units of the critical density $\Omega_{\Lambda}= 0.692$, $\Omega_{m}= 0.308$, $\Omega_{b}= 0.0481$, Hubble constant $\rm H_0=100\,{\rm h}\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ with ${\rm h}=0.678$, spectral index $n=0.967$, $\sigma_{8}=0.826$ \citep[][]{planck:2013_xvi_parameters}.}. Deep optical/near infrared (IR) surveys \citep{Dunlop13,Madau14,Bouwens:2015} have made impressive progresses in identifying galaxies well within the Epoch of Reionization ($z\simeq6$). Such surveys yield key information about the star formation (SF) of hundreds of galaxies in the early Universe. They also allow to statistically characterize galaxies in terms of their UltraViolet (UV) luminosity up to $z\sim10$ \citep{Bouwens:2015}. However -- using these surveys broad band alone -- little can be learned about other properties as their gas and dust content, metallicity, interactions with the surrounding environment \citep[e.g.][]{Barnes:2014PASP}, feedback \citep[e.g.][]{Dayal14}, and outflows \citep{gallerani:2016outflow}. To obtain a full picture of these systems, optical/IR surveys must be complemented with additional probes. Information on the metal content and energetics of the interstellar medium (ISM) can be obtained with observations of Far IR (FIR) fine structure lines, and in particular the \CII~{\small$\left(^{2}P_{3/2} \rightarrow\,^{2}P_{1/2}\right)$} line at 157.74~$\mu$m. The \CII~line is the dominant coolant of the ISM being excited in different ISM phases, as the diffuse cold neutral medium (CNM), warm neutral medium (WNM), high density photodissociation regions (PDRs), and -- to a lower extent -- ionized gas \citep[][]{Tielens:1985ApJ,Wolfire:1995ApJ,Abel:2006MNRAS,Vallini:2013MNRAS}. As \CII~emission can be enhanced by shocks, it has been suggested as a good outflow tracer\\ (e.g. \citealt{maiolino:2012,kreckel:2014apj,cicone:2015aa,janssen:2016arxiv}), and can thus in general be used to study feedback processes in galaxies. Observationally, the \CII~line is a promising probe as it is often the brightest among FIR emission lines, accounting for up to $\sim1\%$ of the total IR luminosity of galaxies \citep[e.g.][]{Crawford:1985ApJ,Madden:1997ApJ}. It has been successfully used to probe the low-$z$ ISM \citep[e.g.][]{delooze:2014aa}. The unprecedented sensitivity of the Atacama Large Millimeter/Submillmeter Array (ALMA) makes it possible for the first time to use \CII~emission to characterize high-$z$ galaxies. Before the ALMA advent, in fact, detections were limited to a handful of QSO host galaxies, and rare galaxies with extreme SF rates \citep[$SFR\simeq10^3\msun\,{\rm yr}^{-1}$, e.g.][]{maiolino:2005AA,debreuck:2011,Carilli:2013ARA&A,gallerani:2012aa,cicone:2015aa}. However, for \quotes{normal} star forming galaxies ($\lsim10^{2}\msun\,{\rm yr}^{-1}$) at $z\sim 6-7$ early ALMA searches for \CII~lines have mostly yielded upper limits (e.g. \citealt{ouchi2013} \citealt{kanekar2013}; \citealt{ota:2014apj,schaerer:2015}). The situation has changed recently with a number of robust \CII~detections (e.g. \citealt{maiolino:2015arxiv,capak:2015arxiv}; \citealt{Willott:2015arXiv15,knudsen:2016arxiv}). In many cases the high-$z$ \CII~line luminosity is fainter than expected from the \CII-$SFR$ relation found in local galaxies \citep{delooze:2014aa}. To explain such \CII-$SFR$~\emph{deficit}, some efforts have been devoted to model the \CII~emission from high-$z$ galaxies \citep{nagamine:2006ApJ,Vallini:2013MNRAS,munoz:2014MNRAS,vallini:2015,olsen:2015apj}. In brief, these theoretical works show that the \CII-$SFR$~deficit can be ascribed to different effects: \begin{itemize} \item[(a)] Lower metallicity of high-$z$ galaxies \citep{Vallini:2013MNRAS,munoz:2014MNRAS,vallini:2015}, in particular supported by observations of lensed galaxies \citep{knudsen:2016arxiv}. \item[(b)] Suppression of \CII~line around star forming regions \citet{Vallini:2013MNRAS}, typically observed as a displacement of the \CII~ with respect to the UV emitting region, as seen e.g. in BDF3299 \citep{maiolino:2015arxiv} and in some of the \citet{capak:2015arxiv} galaxies. This would be a signature of stellar feedback heating/ionizing the putative \CII-emitting gas. \item[(c)] Suppression of \CII~line by the increased CMB temperature in the WNM/CNM component \citep[][]{pallottini:2015_cmb,vallini:2015}, similarly to what observed for dust emission \citep{dacunha:2013apj}. \end{itemize} Simulating the ISM of early galaxies at sufficient resolution and including feedback effects might shed light on these questions. Feedback prescriptions are particularly important as such process regulates the amount of (dense) gas likely to radiate most of the power detected with FIR lines. Several studies have explored optimal strategies to include feedback in galaxy simulations. For some works, the interest is in the comparison between different kind of stellar feedback prescription, as modelled via thermal and/or kinetic energy deposition in the gas from supernovae (SN), winds \citep[][]{agertz:2012arxiv,fire:2014mnras,barai:2015mnras,agertz:2015apj}, and radiation pressure \citep[][]{wise:2012radpres,ceverino:2014}; other analyses focus on implementing complex chemical networks in simulations \citep{tomassetti:2015MNRAS,maio:2015,bovino:2015arxiv,richings:2016,grassi_dust:2016}, radiative transfer effect \citep{petkova:2012mnras,roskar:2014,rosdahl:2015mnras,maio:2016mnras}, or aim at removing tensions between different coding approaches \citep[][]{agora:2013arxiv}. Thus, we can improve galaxy simulations by providing theoretical expectations for \CII~that should be compared with state-of-the-art data. Such a synergy between theory and observations, in turn, can guide the interpretation of upcoming ALMA data and drive future experiments of large scale \CII~mapping \citep{Gong:2012ApJ,silva:2015apj,bin:2015mapping, pallottini:2015_cmb}, which would led to a statistical characterization of the high-$z$ galaxy population. In the present work we simulate a $z\sim6$ galaxy typically detected in \CII~with ALMA current observations. The paper is structured as follows. In Sec. \ref{sec_numerical} we detail the numerical model used to set-up the zoom-in simulation, and describe the adopted \HH~star formation prescription (Sec. \ref{sec_model_sf}), mass and energy inputs from the stellar populations (Sec. \ref{sec_stellar_inputs}) and feedback (including SN, winds and radiation pressure Sec. \ref{sezione_blast} -- see also App. \ref{app_rad_press} and App. \ref{app_blastwave}). The results are discussed in Sec. \ref{sec_result}, where we analyze star formation history and feedback effects in relation to ISM thermodynamics (Sec. \ref{sec_sfr_result}) and its structural properties. The expected \CII~emission and other observational properties of high-$z$ galaxies are discussed in Sec. \ref{sec_final_results}. Conclusions are given in Sec. \ref{sec_conclusioni}. | \label{sec_conclusioni} With the aim of characterizing the internal properties of high-$z$ galaxies, we have performed an AMR zoom-in simulation of \quotes{Dahlia}, a $z\simeq6$ galaxy with a stellar mass of $M_{\star}=1.6\times10^{10}\msun$, therefore representative of LBGs at that epoch. We follow the zoom-in region with a gas mass resolution of $10^{4}\msun$ and a spatial resolution of $30\,{\rm pc}$. The simulation contains a rich set of physical processes. We use a star formation prescription based on a \HH~dependent Schmidt-Kennicutt relation. The \HH~abundance is computed from the \citetalias{krumholz:2009apj} model (Fig. \ref{fig_kmt_test}). Using stellar evolutionary models \citep{padova:1994,starburst99:1999}, we include chemical, radiative and mechanical energy inputs, accounting for their time evolution and metallicity dependence on the stellar population properties (Fig. \ref{fig_gamete_tables}). We include feedback from SN, winds and radiation pressure with a novel, physically motivated coupling scheme between gas and stars. We also compute \CIIion~abundance and the $158\mu$m \CII~emission, by post-processing the outputs with \textlcsc{cloudy} \citep{cloudy:2013}, and a FIR~emission model drawn from radiative transfer numerical simulations \citep{Vallini:2013MNRAS,vallini:2015}. The main results can be summarized as follows: \begin{itemize} \item[\bf 1.] {Dahlia} sits at the centre of a cosmic web knot, and accretes mass from the intergalactic medium mainly via 3 filaments of length $\simeq 100\,{\rm kpc}$ (Fig. \ref{fig_mappe_hydro}). Dahlia has $\sim 6$ major satellites ($M_{\star}\lsim 10^{9}\msun$) and is surrounded by $\sim 10$ minor ones ($M_{\star}\sim 10^{5}\msun$). The latter represent molecular cloud (MC) complexes caught in the act of condensing as the gas streams through the circumgalactic medium (Fig. \ref{fig_sph_profile}). {Dahlia} dominates both the stellar mass ($M_{\star}\sim 10^{10}\msun$) and the SFR of the galaxy ensemble ($SFR\simeq 100\,\msun\,{\rm yr}^{-1}$, Fig. \ref{fig_sfr_smf_energy}). \item[\bf 2.] Only a small fraction of the available energy produced by stars couples to the gas, as energy is mostly dissipated within MCs where the stars reside. Radiation dominates the feedback energy budget by a factor $> 100$ (Fig. \ref{fig_feedback_vs_time}). \item[\bf 3.] By $z=6$ {Dahlia} forms a \HH~disk of mass of $M_{\rm H2}= 3.6\times 10^{8}\msun$, effective radius $0.6\,{\rm kpc}$, and scale height $200\,{\rm pc}$ (Fig. \ref{fig_mappe_tutte}). The disk is dense ($n\gsim 25\,\cc$), enriched ($Z\simeq 0.5\,\zsun$), and it is fed by frequent mergers driving fresh gas to the centre, and supports a star formation rate per unit area of $\simeq 15\,\msun\,{\rm yr}^{-1}\,{\rm kpc}^{-2}$. \item[\bf 4.] The disk is mostly unaffected by SN shocks, and it is pressure-supported by radiation. SN/winds drive hot metal outflows (Fig. \ref{fig_eos_1}), that are either preferentially aligned with the galaxy rotation axis, or start at the edge of the disk. \item[\bf 5.] The total \CII~luminosity of {Dahlia} is $10^{7.55}\lsun$, and $\simeq 95\%$ of the emission is co-located with the \HH~disk (Fig. \ref{fig_mappe_results_profili}). The diffuse, enriched material surrounding {Dahlia} contains $30\%$ of the \CIIion~mass, but it negligibly contributes to the \CII~emission (Fig. \ref{fig_mappe_tutte}) due to its low density ($n\simeq 10\,\cc$) and metallicity ($Z\simeq10^{-1}\zsun$). {Dahlia} is under-luminous with respect to the local \CII-$SFR$ relation; however, its luminosity is consistent with upper limits derived for most $z\sim6$ galaxies. \end{itemize} We find clear indications that the SF subgrid prescription might considerably affect the \CII-$SFR$ relation and the ISM structure, as noted also by \citep{hopkins:2013arxiv}. This is because stars form in gas of different densities depending on the chosen prescription. In our simulation gas is converted into stars with an efficiency $\zeta_{\rm sf}\,f_{\rm H2}$, where the \HH~fraction is computed from the \citetalias{krumholz:2009apj} model and we set $\zeta_{\rm sf}=0.1$. In \citetalias{semenov:2015} the SF follows a \textit{total} (i.e. not molecular) density Schmidt-Kennicutt relation. Further the SF efficiency depends on the free-fall time and the turbulent eddy turnover time. The SF relation is derived from an empirical fit to MC simulations \citep{padoan:2012}, with no notion of the local metallicity. Interestingly, although the approaches are considerably different, the resulting efficiencies are compatible: in \citetalias{semenov:2015} the bulk of the star forming gas has $n\sim 10^{1.5}\cc$, as in {Dahlia} (Fig. \ref{fig_cfr_semenov}). However, with respect to \citetalias{semenov:2015}, Dahlia misses part of the very dense, star forming gas, and its corresponding contribution to \CII~from $Z\sim\zsun$ MCs with $n\sim10^{3}\cc$. These MC are expected to have high \CII~fluxes (see eq. \ref{eq_stima_luminosita}), but their abundance might be low \citep{padoan:2012}. Further investigation is needed before we draw any solid conclusion. To this aim, we plan to upgrade our simulations to a more sophisticated non-equilibrium \HH~evolution model. This is because the chemical equilibrium assumed in \citetalias{krumholz:2009apj} does not hold in low-metallicity regimes. Another important caveat is that we have assumed a uniform UV background. Instead, discrete sources (stellar clusters) might have a strong impact on star formation. For example, Lyman-Werner photons might locally dissociate the \HH~by generating pockets of \HI~in the gas distribution. Thus, unshielded (low dust column density) gas in the disk would contribute only marginally to the SFR. Furthermore, a uniform UVB assumption likely leads to inaccurate computation of the ISM thermodynamic state. We find that $Z\simeq 10^{-3}\zsun$ gas with $n\gsim 10^{2}\,\cc$ has $T\simeq 10^{4}$ (Fig. \ref{fig_eos_1}), with the temperature been set by the UVB heating. However, such gas should be likely able to self-shield from the impinging UVB, whereas internal radiation sources could still play a role \citep[e.g.][]{gnedin:2010}. Finally, local FUV flux variations can change the \CII~emission from individual regions of the galaxy. Also, very high FUV fluxes can photoevaporate MC on short time scales ($\lsim t_{\rm ff}$ for gas with $Z\sim 10^{-2}\zsun$, \citealt[][]{vallini:2016a}). This effect are particularly important, as it might be responsible for the displacement between the \CII~and the UV emitting region observed in BDF3299 \citep{maiolino:2015arxiv}, and in some of the \citet{capak:2015arxiv} galaxies. To solve these problems, a multi-frequency radiative transfer computation must be coupled to the present simulations. This work is ongoing and will be presented elsewhere. | 16 | 9 | 1609.01719 |
1609 | 1609.08638_arXiv.txt | We analyse a sample of 21 active galactic nuclei (AGN) using data from the Swift satellite to study the variability properties of the population in the X-ray, UV and optical band. We find that the variable part of the UV-optical emission has a spectrum consistent with a powerlaw, with an average index of $-2.21\pm0.13$, as would be expected from central illumination of a thin disc (index of $-7/3$). We also calculate the slope of a powerlaw from UV to X-ray variable emission, $\alpha_{\rm OX,Var}$; the average for this sample is $\alpha_{\rm OX,Var}=-1.06\pm0.04$. The anticorrelation of $\alpha_{\rm OX}$ with the UV luminosity, $L_{\rm UV}$, previously found in the average emission is also present in the variable part: $\alpha_{\rm OX,Var} = (-0.177\pm0.083)\log (L_{\nu,\rm Var}(2500\,\text{\AA})) + (3.88\pm2.33)$. Correlated variability between the emission in X-rays and UV is detected significantly for 9 of the 21 sources. All these cases are consistent with the UV lagging the X-rays, as would be seen if the correlated UV variations were produced by the reprocessing of X-ray emission. The observed UV lags are tentatively longer than expected for a standard thin disc. | The structure of AGN is difficult to determine in part because their small size means they cannot be resolved by current instruments. Fortunately, this small size implies a short light-crossing time and hence AGN emission can vary on observable time-scales. Observations of variations in the emission from AGN have shown that they do indeed vary on all time-scales and at all wavelengths probed. The nature of these variations may be used to infer properties of the structure of AGN. Our fundamental picture of this structure is that the central regions of AGN comprise an accretion disc principally emitting thermally in UV \citep{pringleagndisc} and a central hot corona which Compton upscatters some of these photons to X-rays \citep{haardtagnxrays}. A fraction of the X-rays are then emitted back towards the disc, which heats it, increasing its UV emission \citep{lightman88}. In these two ways, the X-ray and UV emission is linked and studying the details of the interaction can retrieve information about the nature of the UV and X-ray emitting regions. The variability of the emission is strongest and occurs over the shortest time-scales at high energies \citep{mushotzkyvar}, indicating that the hard X-rays are produced on the smallest scales. X-ray variability studies have become a field of their own, mapping the innermost regions around the black hole \citep[e.g.][]{fabianlag,vaughan11,mchardy13,uttley14,alston14,karaglobal}. UV and optical measurements over longer time-scales form the basis for studies at longer wavelengths \citep[e.g.][]{cackettopticallags,cameronlags}, allowing a larger region of the accretion flow to be probed. The relation of the two bands is also studied \citep[e.g. review by][]{gaskell03}. While variability studies do their part in enhancing our understanding of the innermost regions of AGN, studying the time-averaged emission in great detail also provides crucial information. The time-averaged UV spectra of AGN \citep[e.g.][]{shull12,telfer02,vandenberk01,francis91,schneider91} have been measured for many different samples and wavelength ranges. When the continuum is fit with a powerlaw, $F_{\lambda}\propto\lambda^{\alpha}$, the quasars of SDSS have $\alpha=-1.56$ over $1300-5000$\,\AA\ \citep{vandenberk01}. This is softer than the spectrum of a thin accretion disc ($\alpha=-7/3$, \citet{shaksun73}), although the variable part of the spectrum of NGC~7469 has been found to be consistent with that value \citep{collier99}. The difference from the theoretical value may be influenced by the strength of absorption in the UV band \citep[e.g.][]{melendez11}, the presence of strong emission lines \citep[e.g.][]{krolikkallman88} and host starlight \citep[e.g.][]{bentz06,bentz09}. \citet{cackettopticallags} study optical AGN spectra and derive the reddening values necessary for the difference spectra to match a thin disc spectrum. Their reddening values match those from the flux-flux or Balmer decrement method, indicating that the variable spectrum is indeed shaped like that of a thin disc. Softer spectra are found at shorter wavelengths: $\alpha$ is $-1.32\pm0.14$ over $1200-1750$\,\AA\ and $-0.59\pm0.21$ over $550-1000$\,\AA\ \citep[both][]{shull12}, suggesting the presence of a turn over at wavelengths probing the highest temperatures in the disc. The high-energy cut-off in the coolest sources may also redden the average spectral index at longer wavelengths. When the mean UV emission is compared with that of the X-rays, the power is found to be tightly correlated: the X-ray luminosity scales as $L_{\rm X}\propto L_{\rm UV}^k$ with $k=0.5-0.8$ \citep[e.g.][]{lusso16,steffen06,vignali03sdss} which results in the UV (2500\,\AA) to X-ray (2\,keV) slope, $\alpha_{\rm OX}$, being anticorrelated with luminosity: $\alpha_{\rm OX}=a\log L_{\rm UV}+{\rm const}$, $-0.2\lesssim a\lesssim-0.1$ \citep{vagnetti10,just07,strateva05}. This relation suggests that the processes producing the UV and X-ray radiation are closely related, as would be expected for an accretion disc--corona system. The link between the X-ray and different UV bands can also be studied by comparing their correlation for a given source across time. Lags between changes in each band are interpreted as being due to the light travel time between the regions responsible for the emission in the different bands and hence the distances between them can be inferred. Such lags have been sought in various sources \citep[e.g.][]{shemmer01,maoz00} and compared to the predictions for a steady state accretion disc \citep{shaksun73}. Where lags are found, they often disagree with thin disc theory, usually showing a longer lag than expected. Before precision cosmology provided a largely unquestioned value of $H_0\simeq70$\,km\,s$^{-1}$\,Mpc$^{-1}$, the luminosity of a standard disc was used to provide a distance modulus and hence $H_0$ \citep{collier99}. However, the disc sizes from the measured lags implied $H_0=42\pm9$\,km\,s$^{-1}$\,Mpc$^{-1}$ \citep{collier99} or $H_0=44\pm5$\,km\,s$^{-1}$\,Mpc$^{-1}$ \citep{cackettopticallags}, so the disc is not as bright as is expected for its size. Other studies also find deviations from a standard disc. For example, studies of NGC~5548 by \citet{STORM2} and \citet{fausnaugh16} describe the disc as larger than expected for its mass and accretion rate. Similarly, \citet{troyer16} and \citet{mcg6lira} find the best fitting accretion rate, $\dot{M}$, is unreasonably high for a standard disc model in NGC~6814 and MCG-6-30-15 respectively. The longer lags being associated with a larger disc than expected is corroborated by quasar microlensing observations, which find emitting regions a factor of a few ($2-3$, \citet{chartas16}; $\sim4$, \citet{morgan10}) larger than predicted. However, a larger emitting region may not be the whole answer, as longer lags are not always found: \citet{mchardy16} study the low mass AGN NGC~4395 ($3.6\times10^{5}M_{\odot}$) and find lags which are not markedly different from standard thin disc theory. Despite the lags often being longer than expected, the lag-wavelength relation found by these studies in the UV to IR bands is usually consistent with the predicted $\tau\propto\lambda^{4/3}$ for a standard accretion disc. Lags have also been sought in the short time-scale variability within an X-ray observation with simultaneous UV monitoring. \citet{smith07} analyse \textit{XMM} observations of 8 sources but find no significant correlations. \citet{mcg6arevalo05} find the UV emission leading the X-rays by $\sim160$\,ksec (1.9\,days) in a 430\,ksec observation, although this lag is a large fraction of the observation length. These studies of lags in individual sources have shown that, at least for some sources, the reprocessing of X-ray radiation does not behave as expected for a centrally illuminated thin disc. A study of many sources has the potential to show what proportion of sources has a longer lag and whether this correlates with other AGN properties. The \textit{Swift} satellite \citep{Gehrels2004}, principally designed for the detection of GRBs, is ideal for such broadband variability analysis: it has detectors for X-rays \citep{XRT} and ultraviolet/optical emission from 1700--6000\,\AA\ \citep{UVOT}. Since it has been operating for more than a decade, many AGN lightcurves covering time-scales of several years are available. Here, the amount of variability in the UV and X-rays and the time differences between them are analysed for a sample of AGN to determine properties of AGN as a population. Emission from the \textit{V}-band to X-rays is included to consider a large extent of the accretion disc. The choice of sources and observations and the reduction of data is described in Section~\ref{sec:odr}. The methods and results of the analysis are described in Section~\ref{sec:res}. In particular, the UV variability is considered in Section~\ref{sub:UVvar} and the X-ray in Section~\ref{sub:xrayvar}. The bands are compared in terms of power in Section~\ref{sub:power} and time lags are explored in Section~\ref{sec:lags}. These results are interpreted in Section~\ref{sec:discussion}. Comments on individual sources are given in Section~\ref{indsources}. | We have presented a variability analysis of archival \textit{Swift} data from AGN monitoring. We find that essentially all bands vary and that the variable part of the UV emission has a spectrum consistent with that of the thermal emission from dissipation in an accretion disc or central illumination of a flat disc. The time-scales of variability and lags of UV relative to X-ray variability show that the latter is principally responsible. The variable power in sources with heavier black holes is higher. The variable UV power increases faster than the variable X-ray power, as is the case for the average emission. The X-ray and UV variations are significantly correlated in 9 sources; the data for the remaining sources are not sufficient to detect a correlation. All measurements of correlated X-ray/UV variability are consistent with the UV lagging the X-rays. We associate this with the reprocessing of X-rays on the accretion disc. | 16 | 9 | 1609.08638 |
1609 | 1609.09228_arXiv.txt | s{In this talk, based on the work~\cite{iac}, we show an analysis on the gauge-independent observables associated with two stationary configurations of the Standard Model (SM) potential (extrapolated to high energy at Next-to-Next-to-Leading-Order (NNLO)): i) the value of the top mass ensuring stability of the SM electroweak vacuum and ii) the value of the Higgs potential at a rising inflection point. We examine in detail and reappraise the experimental and theoretical uncertainties which plague their determination, keeping alive the possibility for the SM of being stable and studying applications of such configuration to models of primordial inflation.} | Assuming the SM valid up to the Planck scale, we find that stability of the SM is compatible with the present data at the level of $1.5\sigma$. Stability of the SM Higgs potential is thus, in our opinion, still a viable possibility. In order to robustly discriminate between stability and metastability, higher precision measurements of the top quark pole mass, $\alpha_{s}^{(5)}$ and of the matching procedure would be needed. As concerns the inflection point configuration, we find that, despite the large theoretical error on the Higgs potential at the inflection point, application of such configuration to models of primordial inflation based on a shallow false minimum displays a $3\sigma$ tension with the recent bounds on the tensor-to-scalar ratio of cosmological perturbations: modifications due to new physics will be necessarily introduced~\cite{esp}. | 16 | 9 | 1609.09228 |
|
1609 | 1609.02760_arXiv.txt | {We present fully covered phased light curves for 56 Jovian Trojan asteroids as acquired by the K2 mission of the \textit{Kepler} space telescope. This set of objects has been monitored during Campaign 6 and represents a nearly unbiased subsample of the population of small Solar System bodies. We derived precise periods and amplitudes for all Trojans, and found their distributions to be compatible with the previous statistics. We point out, however, that ground-based rotation periods are often unreliable above 20\,h, and we find an overabundance of rotation periods above 60\,h compared with other minor planet populations. From amplitude analysis we derive a rate of binarity of 20$\pm$5\%. Our spin rate distribution confirms the previously obtained spin barrier of $\sim$5\,h and the corresponding $\sim$0.5\,g\,cm$^{-3}$ cometary-like density limit, also suggesting a high internal porosity for Jovian Trojans. One of our targets, asteroid 65227 exhibits a double rotation period, which can either be due to binarity or the outcome of a recent collision.} | \label{sec:introduction} Trojan asteroids are located at a heliocentric distance of $\sim5.2\,{\rm AU}$ in the L4 and L5 Lagrange points of the Sun-Jupiter system ($1:1$ mean-motion resonance). Trojans were traditionally thought to be formed near to their present location, but recently, different scenarios were proposed for their origin. As indicated by the surface composition, they may have formed in the proto-Kuiper belt, and scattered inward and captured (the Nice model, e.g. Morbidelli et al. 2005, Tsiganis et al. 2005, Gomes et al. 2005, Levison et al. 2011) as a result of resonant interactions with the giant planets (e.g. Grav et al. 2011, Emery 2016). The ``jump'' scenario assumes the collisional scattering of Jupiter only, due to close interactions with an ice giant (Nesvorn\'y{} et al. 2013). Due to their stable resonance locking, collisional frequencies are the lowest within these groups in the inner solar system \citep{dahlgren1998,delloro2001}. While dynamical arguments support the capture of Trojans from the outer Solar System via collisional scattering, there are significant differences between the Trojans and the Centaurs or trans-Neptunian objects, indicating a possible surface modification due to the inward migration. The photometric and spectroscopic data revealed the presence of two main taxonomical groups in the Trojan swarms, recognized as D and P in the Tholen (1984) classification. Both types exhibit featureless spectra, while D type has a redder slope and includes the majority of the Trojans. Unlike the Main Belt, the Trojan taxonomical types are not separated in the orbital elements space, but there is an inclination-color gradient present at least in the L4 swarm (e.g. Szab\'o et al. 2007), which represents taxonomical subgroups (Roig et al., 2008). Bimodality of Jovian Trojan asteroids was also identified in their magnitude distribution (especially at the faint-end), in near-infrared spectra, infrared albedo, and also in colours, suggesting the existence of two distinct groups among Jovian Trojans (Wong et al. 2014, and references therein). Since this bimodality extends to several parameters, the presence of ``red'' and ``less red'' {\it populations} are suggested, with different origin and different evolution, instead of simply different taxonomical {\it types} which were mixed together (Wong et al. 2014, 2015). However, objects in these populations are still significantly bluer than the typical ``red'' objects in the Centaur and trans-Neptunian populations (Peixinho et al., 2012; Lacerda et al., 2014). A common, outer Solar system origin of Jovian Trojans and trans-Neptunian objects was recently proposed by Wong \& Brown (2016), also suggesting that the retention or loss of H$_2$S in the early Solar system was the likely reason behind the colour differences we observe today. In addition to the photometric characteristics discussed above, light curves available for Jovian Trojans can provide shape and rotational frequency distributions, and also information on the binary fraction. These statistics can be compared with the prediction of various formation and evolution models. In this sense, binary or multiple systems especially important, as their observations provide reliable masses and densities, a key to composition and internal structure. There are several formation mechanisms proposed for multiple systems (see e.g. Merline et al., 2002; Noll et al., 2008), therefore their properties give an important clue on accretional, collisional and radiative processes as well, and may lead to identify differences between the red and the less red groups in the case of Jovian Trojans. A WISE survey found that 20\% of Jovian Trojan asteroids are either extremely elongated objects, or are binaries (Sonnett et al., 2015). In the K2 mission of the Kepler space telescope (Howell et al. 2014) 56 Jovian Trojan asteroids have been observed in Campaign 6, and long, uninterrupted light curves have been taken that are free from aliases, giving a more comprehensive description of these populations then the sparsely sampled WISE or ground based data. In this paper we present the light curves and photometric properties of these 56 Jovian Trojan asteroids, all orbiting at the L4 Lagrange point of the Sun-Jupiter system. In Sec.~\ref{sec:observations} we summarize the observations and the data reduction schemes used to obtain the light curves of these Trojan asteroids. In Sec.~\ref{sec:results} we present the statistical properties of this sample. Our results are summarized in Sec.~\ref{sec:summary}. Tabulated data and the light curves of individual Trojans are shown in the Appendix. A similar study about Main Belt asteroids with K2 will be published in a related paper (Szab\'o et al., 2016). \begin{figure} \includegraphics[width=234pt]{fig1.eps} \caption{Upper panel: The upper view of Field 6 Trojans (large black dots) superimposed to the SDSS MOC3 Trojans in the L4 swarm (smaller grey dots) projected to the Jupiter's orbital plane. Earth is in origin. Note that Campaign~6 pointed exactly into the core of the L4 swarm. Lower panel: The field-of-view of K2 Campaign 6 superimposed with the apparent trajectories of the 56 Jupiter Trojans discussed in this paper. On each trajectory, the dots show the motion in 5-days long steps.} \label{fig:field} \end{figure} \begin{figure} \begin{center} \noindent \resizebox{27mm}{!}{\includegraphics{fits-r-2633}}\hspace*{1mm}% \resizebox{27mm}{!}{\includegraphics{fits-r-2635}}\hspace*{1mm}% \resizebox{27mm}{!}{\includegraphics{fits-r-2637}} \vspace{5mm} \noindent \resizebox{27mm}{!}{\includegraphics{diff-r-2633}}\hspace*{1mm}% \resizebox{27mm}{!}{\includegraphics{diff-r-2635}}\hspace*{1mm}% \resizebox{27mm}{!}{\includegraphics{diff-r-2637}} \end{center}\vspace*{-4mm} \caption{Typical stamps taken from the image series related to (12974) Halitherses, which was the object with the fastest apparent speed (exceeding 2\,pixels per long-cadence frame). The upper row of image stamps shows the original frames between the cadences \#2633 and\#2637 while the lower row show the registered and differential stamps corresponding to their respective upper counterparts. The elongated aperture (bounded by the thick yellow curve) and the elongated annuli (bounded by the red curves) are used for the photometry and for the estimation of the background level, respectively. These stamps show a region of $20\times 40$ pixels, i.e. an area of $1.33^\prime\times 2.66^\prime$ on the sky.} \label{fig:trailstamps} \end{figure} \begin{figure*} \begin{center} \resizebox{60mm}{!}{\includegraphics{stat-trail-length}} \resizebox{60mm}{!}{\includegraphics{stat-coverage}} \resizebox{60mm}{!}{\includegraphics{stat-lcpoints}} \end{center}\vspace*{-4mm} \caption{Statistics related to the light curve acquisition characteristics and the photometric data coverage. See text for further explanation.} \label{fig:stat} \end{figure*} | \begin{itemize} \item{}The K2 sample shows a significant fraction ($\approx 20\%{}$) of very slow ($P>50$~h) rotation periods. The K2 sample is still unbiased in this period range, therefore this observation reflects the actual occurrence of very slow rotators. \item{}The K2 sample shows a significant overabundance of large amplitude asteroids. 3 of 56 asteroids exceeded the 0\fm9 amplitude, and 5 ($\approx 10\%{}$) Trojans exceed 0\fm714, belonging to $a/c>2$ asphericity. \item{}In the case of $(65227)~2002~ES_{\rm 46}$ we detected double periodicity, 49.7 and 3.53 hours and 0\fm3 and 0\fm4 amplitude, respectively. This is by far the largest asteroid known with double period. \item{}The excess of large amplitude asteroids, the very slow rotators among Trojans, and the presence of double periods can all be explained by a high rate of binary asteroids in the L4 cloud. We estimated the occurrence of binarity between 20-25\%{}, in agreement with previous estimates. \item{}Red and less red populations were found to be identical for light variation properties. The similarity applies for both amplitude and period distributions, and also, the presence of very slow rotators and high amplitude asteroids. \item{}We detected a notable lack of fast rotators among Trojans. We interpreted it as the effect of a density barrier, and estimated the upper limit of the density of 0.5~g/cm$^3$ in the K2 sample, in agreement with previous estimates. \item{}We derived the amplitude distribution of K2 Trojan asteroids and debiased assuming random spin orientation. Both the observed and unbiased distribution differ from the results of Binzel \& Sauter (2011) since K2 observed significantly more asteroids in the high amplitude wing of the distribution. How the collisional history or other evolutionary effects led to the excess of elongated bodies in the Trojan cloud still needs further investigations. \end{itemize} | 16 | 9 | 1609.02760 |
1609 | 1609.02283_arXiv.txt | The mean alpha-to-iron abundance ratio (\afe) of galaxies is sensitive to the chemical evolution processes at early time, and it is an indicator of star formation timescale (\tSF). Although the physical reason remains ambiguous, there is a tight relation between \afe\ and stellar velocity dispersion (\sgm) among massive early-type galaxies (ETGs). However, no work has shown convincing results as to how this relation behaves at low masses. We assemble 15 data sets from the literature and build a large sample that includes 192 nearby low-mass ($18<\sigma<80$~\kms) ETGs. We find that the \afe-\sgm\ relation generally holds for low-mass ETGs, except in extreme environments. Specifically, in normal galaxy cluster environments, the \afe-\sgm\ relation and its intrinsic scatter are, within uncertainties, similar for low-mass and high-mass ETGs. However, in the most massive relaxed galaxy cluster in our sample, the zero point of the relation is higher and the intrinsic scatter is significantly larger. By contrast, in galaxy groups the zero point of the relation offsets in the opposite direction, again with substantial intrinsic scatter. The elevated \afe\ of low-mass ETGs in the densest environments suggests that their star formation was quenched earlier than in high-mass ETGs. For the low-mass ETGs in the lowest density environments, we suggest that their more extended star formation histories suppressed their average \afe. The large scatter in \afe\ may reflect stochasticity in the chemical evolution of low-mass galaxies. | Most early-type galaxies (ETGs) stopped forming stars long ago. They provide a fossil record of the star formation histories (SFHs), quenching scenarios, and mass assembly in the early Universe. A powerful tracer of these early processes is the alpha-to-iron abundance ratio (\afe), which is an indicator of star formation timescale (\tSF). In the first $\sim$0.1~Gyr after star formation begins, enrichment of the interstellar medium is dominated by Type ~II supernovae (SNe~II), which return ejecta with a relatively high \afe\ to the interstellar medium. Afterwards, Type~Ia supernovae (SNe~Ia) begin to contribute Fe-rich ejecta, and the \afe\ of the entire stellar system quickly decreases as stars continue to form from this Fe-enriched gas. Over time, the system reaches an equilibrium value close to the the solar value, \afe $\approx 0$ (Haywood et al. 2013). Galaxies with shorter \tSF\ should reach higher \afe; \afe\ is sensitive to \tSF\ when \tSF\ is relatively short. Massive ETGs ($\sigma\gtrsim80$~\kms) obey a tight empirical relation between \afe\ and central stellar velocity dispersion (\sgm), such that galaxies with larger \sgm\ have higher \afe. The slope and zero point of the \afe-\sgm\ relation do not vary much with environment (e.g., Thomas et al. 2005; McDermid et al. 2015). This relation indicates that more massive ETGs have shorter \tSF\ and, on average, quenched earlier. One possible explanation is feedback from active galactic nuclei (AGNs), as more massive ETGs host more massive central black holes (Kormendy \& Ho 2013). The expected strong quenching by AGN feedback processes (e.g., King 2003) can affect the \afe-\sgm\ relation, according to the cosmological simulations of Segers et al. (2016). Alternatively, the variation of the initial stellar mass function (IMF), fraction of SN~Ia binaries, the delay time distribution of SN~Ia, and stellar yields can also account for the positive correlation between \sgm\ and \afe\ (e.g., Arrigoni et al. 2010; Yates et al. 2013). However, the effects of these parameters on the \afe-\sgm\ relation are highly degenerate, and there is no consensus as to which dominates. It is also possible that some massive ETGs are remnants of wet major mergers, and that their high \afe\ was set by the most recent starburst. However, the frequency of major mergers is not high (e.g., Lotz et al. 2011), and this scenario probably cannot fully account for the \afe-\sgm\ relation. If quenching processes determine the \afe-\sgm\ relation of massive ETGs, then how this relation behaves at low mass is interesting. While the quenching mechanisms of massive galaxies are mass-dependent, low-mass galaxies are mostly quenched by environmental processes (Peng et al. 2010), such as the ram pressure stripping (Gunn \& Gott 1972), harassment (Moore et al. 1996), tidal stirring (Mayer et al. 2001), and starvation (Peng et al. 2015). Even if low-mass galaxies are not quenched by environment, feedback from SN explosions and stellar winds are still distinct from the quenching mechanisms of massive galaxies (e.g., Hopkins et al. 2011; Forbes et al. 2016). Besides quenching, the chemical evolution histories of galaxies also depend on their mass. Peng \& Maiolino (2014) pointed out that for star-forming galaxies, the key parameter that controls galactic evolution is the timescale required to reach equilibrium. While most massive galaxies reach equilibrium in their lifetime, low-mass ($M_*\lesssim10^9~M_\odot$), gas-rich galaxies may not within a Hubble time. As a consequence of their non-equilibrium states, stochastic processes in low-mass galaxies, including inflow, outflow, and star formation, may be imprinted in their stellar population when they are quenched. For instance, Lee et al. (2009) found a systematically lower H$\alpha$/FUV flux ratio with declining luminosity among low-mass, star-forming galaxies, which might be due to the stochastic appearance of high-mass stars at low star formation rates (SFRs; e.g., Fumagalli et al. 2011). Therefore, it is important to investigate the \afe-\sgm\ relation of low-mass ETGs. Unfortunately, no work has studied it using a sample of significant size, possibly due to their low surface brightness. Previous studies all had relatively large uncertainties. Sansom \& Northeast (2008), Smith et al. (2009), and Annibali et al. (2011) obtained different slopes for this relation. Using a sample of low-mass ETGs from the Virgo Cluster, Liu et al. (2016) found a \afe-\sgm\ relation with larger scatter and, based on a correlation between \afe\ and distance from the cluster center, concluded that low-mass ETGs are more governed by environment instead of mass. However, Vargas et al. (2014), from a sample of Local Group dwarf spheroidal galaxies (dSphs), claimed a large scatter without any environmental dependence. To study the early baryonic processes in low-mass galaxies, we collect literature data for a relatively large sample to systematically study the \afe-\sgm\ relation of low-mass ETGs. We are interested in not only the form of the relation, but also its intrinsic scatter, which provides information about the early SFHs of low-mass galaxies. \\ | \label{discuss} \subsection{The Origin of \afe-\sgm\ Relation} \label{D_aMR} The mean \afe\ of galaxies arises from a complex interplay of many factors, including \tSF, IMF, stellar yields, SN~Ia explosion rate and delay time distribution, and gas inflow and outflow. The departure of the standard \afe-\sgm\ relation toward low masses, at least for ETGs residing in high- and low-density environments, implies that some of the physical drivers underlying this empirical scaling relation evidently change under these circumstances. While it is difficult to assess the relative importance of the various potential factors, here we highlight the possible role of \tSF\ and SFH. Two often-discussed candidate quenching mechanisms for massive ETGs are AGN feedback (e.g., Croton et al. 2006) and halo quenching (e.g., Dekel \& Birnboim 2006). These quenching mechanisms appear to be mass-dependent, and more massive ETGs have shorter \tSF. However, low-mass ETGs are quenched by different mechanisms. Some of them were satellite galaxies and were quenched by environmental processes, such as ram pressure stripping and strangulation, when they fell into the dark matter halos of nearby host galaxies (Gunn \& Gott 1972; Peng et al. 2015). Their \tSF\ might be more driven by environment than mass. Moreover, galaxies with shallower potential wells are expected to experience even stronger environmental effects, which may result in shorter \tSF\ and higher \afe. The effect of environment should be especially acute given that most low-mass ETGs sample reside in galaxy clusters. Under these circumstances, we naively expect low-mass ETGs to exhibit a \afe-\sgm\ correlation with negative slope, opposite to that actually observed. A positive \afe-\sgm\ correlation also contradicts the simplest expectations from internal quenching mechanisms such as radiative and energetic feedback from SNe and high-mass stars, which should operate more effectively and stop star formation earlier (thus boosting \afe) in lower mass galaxies. The \afe-\sgm\ relation may also be a consequence of SFH. From cosmological semi-analytical simulations, De Lucia et al. (2006) showed that more massive ETGs had more peaked SFR distributions, which reached their peak at higher redshifts. However, they only studied massive galaxies with stellar masses larger than $4\times10^9\,M_\odot$. Moreover, other studies have not been able to reproduce the positive correlation between \afe\ and \sgm\ for massive ETGs without including special recipes (e.g., Arrigoni et al. 2010; Yates et al. 2013; Segers et al. 2016). Segers et al. (2016) extended their simulations to galaxies of lower masses and reproduced a positive \afe-\sgm\ correlation for stellar masses between $10^8\,M_\odot$ and $10^{10}\,M_\odot$. It is unclear, however, whether these simulations apply to the situation at hand. Segers et al. only considered central galaxies that are still forming stars at $z \approx 0$. \\ \subsection{The Role of Environment} \label{D_env} We find that low-mass ETGs from the densest environments are, on average, offset toward larger \afe. A plausible implication of this finding is that high environmental density induces short \tSF. As discussed in Section~\ref{D_aMR}, low-mass galaxies in high-density regions might experience environmental quenching earlier, which would systematically elevate their \afe. At the same time, environmental density also influences early star formation processes in low-mass galaxies. Santos et al. (2015) found that star-forming galaxies in the central regions of high-redshift clusters have higher SFRs. This suggests that present-day low-mass ETGs residing in denser environments may have experienced more intense star formation at early times, resulting in their higher observed \afe. By contrast, the average \afe\ of low-mass ETGs is lower in galaxy groups, indicating more extended SFHs of low-mass galaxies in low-density environments. This is consistent with the findings of Geha et al. (2012). All the isolated low-mass galaxies without H$\alpha$ emission in their sample showed evidence of recent starbursts, implying bursty SFHs over an extended period. In both of the extreme (high- and low-density) environments highlighted in this work, the large scatter of \afe\ at low-mass can be explained by stochastic chemical evolution processes in non-equilibrium systems. According to the main sequence of star-forming galaxies (e.g., Wuyts et al. 2011), low-mass galaxies have low SFRs. Under such conditions, massive stars and SNe~II appear stochastically because the number of forming stars is not large enough to sample the IMF completely (e.g., Lee et al. 2009; Fumagalli et al. 2011). Furthermore, some SNe in the early universe may produce special abundance patterns, such as both low \afe\ and low [Fe/H] (Kobayashi et al. 2014; Simon et al. 2015). The dispersion in \afe\ also reflects the details of the gas evolution after the appearance of the first generation of stars. For example, star formation may cease in hot bubbles after the surrounding neutral gas is ionized, but it may restart in colder regions afterwards (e.g., Sobral et al. 2015). Outflows with high \afe\ ejected by these stars, if still bound to the halo, might fall back and contribute to subsequent star formation. Both scenarios would temporally increase the mean galactic \afe. Yet, it is curious that the large scatter in \afe\ is not seen in all low-mass ETGs, but rather only in the subset residing in extremely high- or low-density environments. After all, the intrinsic scatter of the \afe-\sgm\ relation over the same low-mass range in normal galaxy clusters is as tight as in high-mass ETGs. We have no explanation for this. | 16 | 9 | 1609.02283 |
1609 | 1609.05376_arXiv.txt | We present kinematic analyses of the 12 galaxies in the ``Survey of \HI{} in Extremely Low-mass Dwarfs'' (SHIELD). We use multi-configuration interferometric observations of the \HI{} 21cm emission line from the Karl G. Jansky Very Large Array (VLA)\footnote{The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.} to produce image cubes at a variety of spatial and spectral resolutions. Both two- and three-dimensional fitting techniques are employed in an attempt to derive inclination-corrected rotation curves for each galaxy. In most cases, the comparable magnitudes of velocity dispersion and projected rotation result in degeneracies that prohibit unambiguous circular velocity solutions. We thus make spatially resolved position-velocity cuts, corrected for inclination using the stellar components, to estimate the circular rotation velocities. We find v$_{\rm circ}$ $\leq$ 30 \kms\ for the entire survey population. Baryonic masses are calculated using single-dish \HI{} fluxes from Arecibo and stellar masses derived from HST and Spitzer imaging. Comparison is made with total dynamical masses estimated from the position-velocity analysis. The SHIELD galaxies are then placed on the baryonic Tully-Fisher relation. There exists an empirical threshold rotational velocity, V$_{\rm rot}$ $<$ 15 \kms, below which current observations cannot differentiate coherent rotation from pressure support. The SHIELD galaxies are representative of an important population of galaxies whose properties cannot be described by current models of rotationally-dominated galaxy dynamics. | \label{S1} One of the most fundamental correlations in astrophysics is that rotation velocity is proportional to luminosity. The Tully-Fisher relation \citep{tullyfisher77} has been refined over the years (e.g., using only the mass of baryons via the ``baryonic Tully-Fisher relation'', or BTFR; {McGaugh \etal\ 2000}\nocite{mcgaugh00}), and many investigators have independently verified the remarkably tight relationship across many orders of magnitude in galaxian mass (see the recent works by {Lelli \etal\ 2016}\nocite{lelli16}, {Papastergis \etal\ 2016}\nocite{papastergis16}, and the references therein). For massive systems with well-organized and easily-modeled rotation, the BTFR is well-populated and statistically robust. How the lowest-mass, gas-rich galaxies populate the BTFR is not yet well understood. As the dynamical mass falls, the ratio of bulk rotation velocity to the magnitude of turbulent motion becomes of order unity, and current observations become unable to differentiate between pressure-supported and rotation-dominated galaxies (see, e.g., {Tamburro \etal\ 2009}\nocite{tamburro09} and {Stilp \etal\ 2013}\nocite{stilp13}). Empirically, this transition has been found to occur near a circular velocity of $\sim$20 \kms; for example, the sample presented in \citet{mcgaugh12} contains no such galaxies with rotation velocities significantly below this value. \citet{ezbc14} estimate that the extremely low-mass and metal-poor galaxy Leo\,P is rotating at 15\,$\pm$\,5 \kms. For the slowest-rotating galaxies, the signatures of rotation become indistinguishable from the random statistical motion of the gaseous component. Systems that populate the low end of the BTFR are uniquely important to our understanding of galaxy evolution. However, by definition, these sources are intrinsically faint, physically small, and technically challenging to study in detail at any significant distance. The total number of such galaxies detected to date remains a significant issue for the $\Lambda$CDM cosmological model, and discrepancies between simulations and observations still persist (the ``missing satellite problem'' and the ``too-big-to-fail'' problem; {Kauffmann \etal\ 1993}\nocite{kauffmann93}, {Klypin \etal\ 1999}\nocite{klypin99}, {Moore \etal\ 1999}\nocite{moore99}, {Boylan-Kolchin \etal\ 2011}\nocite{boylan11}, {Klypin \etal\ 2015}\nocite{klypin15}, {Papastergis \etal\ 2015}\nocite{papastergis15}). Increasing the statistics in this critical mass range offers an opportunity to better understand the physical properties of these galaxies via detailed observational study. To this end, the ALFALFA survey \citep{giovanelli05} has extended the faint end of the \HI{} mass function into the 10$^6$ \msun\ $\lsim$ M$_{\rm HI}$ $\lsim$ 10$^7$ \msun\ regime for the first time. As discussed in the companion paper by Teich \etal\ (hereafter referred to as Paper~I), the SHIELD program was designed to identify those systems from the full ALFALFA catalog with log(M$_{\rm HI}$) $<$ 7.2 and with narrow \HI{} line widths (v$_{\rm 50}$ $<$ 65 \kms, thus removing massive but \HI{}-deficient galaxies). In Paper~I and the present work, 12 of these sources are analyzed extensively in an effort to understand their physical properties and to contextualize them among the general population of low-redshift galaxies. Analysis continues on the other low-mass galaxies discovered in ALFALFA via the same criteria. In this paper, we focus on the dynamical properties of the SHIELD galaxies to extend the BTFR to the lowest-mass gas-rich galaxies. We refer the reader to Paper~I for physical characteristics of the SHIELD galaxies, for details about the \HI{} data reduction, for details about the supporting observations used in both works, and for results specific to the properties of star formation in the SHIELD galaxies (see also {McQuinn \etal\ 2015a}\nocite{mcquinnsfh}). Here we only include discussion of relevant \HI{}-specific data handling. This is followed by formal analysis of the data in an effort to determine the rotation velocities of the SHIELD galaxies. | \label{S4} The study of the SHIELD galaxies represents a significant legacy of the ALFALFA survey: those sources that populate the faint end of the \HI{} mass function and which also harbor an easily-detectable stellar component. In this work, we have presented a detailed examination of the neutral gas dynamics of 12 systems. The discussion in previous sections tells a clear story: the contributions from rotational and pressure support are effectively equal in the SHIELD galaxies. Using Figure~\ref{btfr} as an interpretive guide, we see that the primary contribution of the SHIELD program to our understanding of the dynamics of low-mass galaxies comes in the form of improved statistics in the lowest mass bins. This sample of low-HI mass galaxies effectively doubles the number of points (with v$_{\rm c}$ $\lsim$ 30 \kms\ ) that can be placed on the BTFR. The gas-rich SHIELD galaxies have higher baryon fractions and are less dark matter dominated than dSph galaxies with similar rotational velocities. All of the SHIELD galaxies agree within 3 $\sigma$ model uncertainty to the BTFR presented in Figure~\ref{btfr}. The most massive dSph systems can be considered to be rough analogs of the SHIELD galaxies with stripped \HI{} components. dSphs with v$_{\rm c}$ $\gsim$ 20 \kms\ can be made to lie on the BTFR if an amount of gas which would be appropriate to bring the dSph to a typical M$_{\rm HI}$/M$_{\star}$ ($\sim$10$^7$ \msun\ for systems in this range of circular velocities) were added to their baryonic mass budgets. However, the less massive dSph galaxies are fundamentally different; they are less massive in total, likely a result of significant tidal stripping that has affected both their baryonic and dark matter components. This gain in low-mass systems on the BTFR comes with a significant caveat: for most SHIELD galaxies, the rotational velocities are estimated from methods without the benefit of close constraints on the gas inclination. In comparison with studies of larger dwarfs using similar observational strategies, the rotational dynamics in the SHIELD galaxies are not resolved at high spatial resolution. For example, the recent dynamical modeling of the LITTLE THINGS galaxies by \citet{oh15} performs a full radial mass decomposition for most of these marginally closer, brighter, and more massive sources. There are two empirical limitations that preclude such detailed analysis in the SHIELD galaxies. The first is the simple and perhaps predictable issue of the distance of the sources: the nearest SHIELD galaxy, AGC\,111164, lies at D $=$ 5.11\,$\pm$\,0.07 Mpc; the most distant systems lie beyond 10 Mpc (AGC\,174605, AGC\,731457, AGC\,749237). At these distances, even B configuration resolution VLA data presents a beam smearing of hundreds of parsecs. The second limitation is that the SHIELD galaxies have small total \HI{} flux integrals. These limitations are in agreement with those found in similar studies of low-mass galaxies \citep[e.g., ][]{mcgaugh12}. By way of comparison, the \citet{oh15} sample contains multiple systems with \HI{} masses in the same range as those of the SHIELD galaxies, and in fact some that are less massive still. However, importantly, all three of the \citet{oh15} systems whose rotational velocities are lower than 20 \kms\ are in or just outside the Local Group (DDO\,210, DDO\,216, IC\,1613). The gain in angular resolution and in \HI{} flux from these sources facilitates a depth of analysis that is simply unavailable with current observational capabilities outside of the Local Group. Note that the observational strategies used in this work are very similar to those used in \citet{oh15}. An interesting comparison can be found in Leo\,P, a nearby (D$=$1.62\,$\pm$0.15 Mpc; {McQuinn \etal\ 2015}\nocite{mcquinnleop}), extremely low-mass (log(M$_{\rm HI}$) $=$ 8.1\,$\times$\,10$^{5}$ \msun) galaxy that was discovered by ALFALFA \citep{giovanelli13,rhode13}. In a detailed \HI{} study by \citet{ezbc14}, the authors examine deep VLA \HI{} 21\,cm data that are very similar to the data presented here for the SHIELD galaxies. The conclusion is the same as that in the present work: extracting a meaningful and non-degenerate model of the gas kinematics is extremely challenging at rotation velocities lower than 20 \kms and without well constrained gas inclination. Based on the multiple lines of evidence outlined above, we conclude that there exists an empirical lower threshold rotational velocity, below which current observations cannot differentiate coherent rotation from pressure support. Using the SHIELD galaxies, and the systems from the aforementioned studies, this threshold appears below V$_{\rm rot}$ $\sim$15 \kms. Our observations demand models which can reproduce the kinematics of low-mass galaxies whose gas is dominated by both pressure and rotational dynamics. It is interesting to note that that the ALFALFA survey has discovered many candidate objects whose \HI{} properties are galaxy-like, but that lack an obvious stellar population in survey-depth optical data products. These systems can broadly be categorized as ``ultra compact high velocity clouds'' (UCHVCs; {Adams \etal\ 2013}\nocite{adams13}) and ``Almost Dark'' galaxy candidates \citep{cannon15,janowiecki15}. Further comparisons of all of the SHIELD-class galaxies with members of these ALFALFA sub-samples promise to populate the continuum of sources at the lowest and most extreme masses. \clearpage | 16 | 9 | 1609.05376 |
1609 | 1609.06623.txt | The interaction between the dark/mirror sector and the ordinary sector is considered, where the two sectors interact with each other by sharing the same QCD axion field. This feature makes the mixing between ordinary and dark/mirror photons in ordinary and dark electromagnetic fields possible. Perturbative solutions of the equations of motion describing the evolution of fields in ordinary and dark external magnetic fields are found. User-friendly quantities such as transition probability rates and Stokes parameters are derived. Possible astrophysical and cosmological applications of this model are suggested. | \label{sec:1} One main problem in quantum chromodynamics (QCD) is that it preserves the charge-parity (CP) symmetry which is observed to be broken in weak interactions. In general, if we are not concerned with the violation of the CP symmetry or time (T) symmetry, in any gauge theory we can introduce in the Lagrangian density a term of the type $\mathcal L\propto \theta_{\alpha\beta}\,\epsilon^{\mu\nu\rho\sigma}F_{\mu\nu}^\alpha F_{\rho\sigma}^\beta$, where $\theta_{\alpha\beta}$ is a constant matrix and $F_{\mu\nu}^{\alpha}$ is a gauge field tensor. In the case of QCD, the P, T, and CP violating term in the Lagrangian density is $\mathcal L_\theta\propto \bar\theta\, G_{\mu\nu, a}\tilde G^{a, \mu\nu}$ where $\bar\theta$ is the effective angle of the theory and $G_{a, \mu\nu}$ is the gluon field tensor. However, one problem is that the CP violating term induces electric dipole moments in baryons, where for example in the case of the neutron, theoretical estimates give for the dipole moment $d_n(\bar\theta)\simeq 10^{-16}\bar\theta\, e$ cm \cite{Baluni:1978rf} while experimentally is found $d_n<2.9\times 10^{-26} e$ cm \cite{Baker:2006ts}. Such a small experimental value for $d_n$ implies a small effective angle of the order $\bar\theta \lesssim10^{-10}$, namely the so called strong CP problem. One possible solution for the strong CP problem, is based on the Peccei-Quinn (PQ) mechanism \cite{Peccei:1977hh} where the existence of a new particle, the axion, is proposed. In the PQ mechanism, $\bar\theta$ becomes a dynamical field with an effective potential $V(a)$ for the axion field $a$ induced by non-perturbative QCD effects. The vacuum expectation value (VEV) of the axion field $\langle a\rangle =-\bar\theta f$ is minimum for the effective potential and the CP violating term in the effective Lagrangian is dynamically cancelled. Usually, the axion scale parameter $f$ is a free one and is model dependent. Originally, $f$ was taken to coincide with the electroweak scale \cite{WW} but the non observation of axions in experiments would suggest that its scale could in principle be much larger than the electroweak scale. This fact has been implemented in the so called invisible axion models, namely the KSVZ axion model \cite{Shifman:1979if} and DFSZ axion model \cite{Dine:1981za}. A more complicated possibility that solves the strong CP problem is based on the mirror symmetry, namely M-symmetry\footnote{The first proposed solution for the strong CP problem based on M-symmetry, was considered in Ref. \cite{Rubakov:1997vp} in the context of complex grand unification theories, namely non supersymmetric GUT based on the gauge group $SU(5)\times SU^\prime(5)$.} see Ref. \cite{Berezhiani:2000gh}. This possible solution of the strong CP problem is still based on the PQ mechanism but the particle content group is duplicated with respect to the standard model (SM), namely one adds an additional sector of particles, the mirror sector. In this context the strong CP problem is solved simultaneously in both sectors through the PQ mechanism where the two sectors are supposed to weakly interact with each other, primarily through the gravitational force. The general idea of the M-symmetry is based on the assumption that there exist a parallel sector of mirror or dark particles which has the same group and coupling constants analogous to the SM sector \cite{Foot:1991bp}. In this model the SM Lagrangian is invariant under M-symmetry. More precisely, the gauge group of the theory is $G\times G^\prime$ where $G$ is the ordinary group of the SM of particles $G=SU(3)\times SU(2)\times U(1)$ with fermion fields $\Psi_i= q_i, l_i, \bar u_i, \bar d_i, \bar e_i$ and Higgs doublets $H_1, H_2$ and $G^\prime=SU(3)^\prime\times SU(2)^\prime\times U(1)^\prime$ is the mirror gauge group\footnote{In this paper the sign $(^\prime)$ denotes quantities of the mirror sector if not otherwise specified. } with analogous particle content $\Psi_i^\prime= q_i^\prime, l_i^\prime, \bar u_i^{\prime}, \bar d_i^{\prime}, \bar e_i^{\prime}$ and Higgs doublets $H_1^\prime, H_2^\prime$. Here, $q_i, i=1, 2, 3$ is the left handed quark doublet, $l_i$ is the left handed lepton doublet, $\bar u_i$ is the right handed quark singlet ($u, c, t$), $\bar d_i$ is the right handed quark singlet ($d, s, b$) and $\bar e_i$ is the right handed anti-lepton singlet. Here fermions are represented as Weyl spinors. In the case when M-parity is an exact symmetry, the particle physics must be the same in both sectors. For example, for the Yukawa theory, we would see that ordinary and mirror sectors have the same pattern $\mathcal L_\textrm{Yuk}=Y_{U}^{ij}\bar u_iq_jH_2+Y_D^{ij}\bar d_iq_jH_1+Y_E^{ij}\bar e_il_jH_1+h.c.,\, \mathcal L_\textrm{Yuk}^\prime=Y_{U}^{\prime ij}\bar u_i^{\prime}q_j^\prime H_2^\prime+Y_D^{\prime ij}\bar d_i^{\prime}q_j^\prime H_1^\prime+Y_E^{\prime ij}\bar e_i^{\prime}l_j^\prime H_1^\prime+h.c.,\nonumber$ where $Y_l^{ij}=Y_l^{\prime ij}$ with $l=\{U, D, E\}$ are the Yukawa couplings ($3\times 3$ complex matrices) and are equal in both sectors. Since the Yukawa couplings are the same, this would imply that quark and lepton mass matrices have the same form, namely $\mathcal M_U=G_U\langle H_2\rangle$, $\mathcal M_U^\prime=G_U\langle H_2^\prime\rangle$, $\mathcal M_D=G_D\langle H_1\rangle$, $\mathcal M_D^\prime=G_D\langle H_1^\prime\rangle$ etc. On the other hand, the total renormalizable Higgs potential in this model has the form $ \mathcal V_\text{tot}=\mathcal V+\mathcal V^\prime+\mathcal V_\text{mix}$, where $\mathcal V$ is the standard model Higgs potential and $\mathcal V^\prime$ is the mirror/dark sector Higgs potential with the same pattern as its standard model counterpart. The mixing potential comes out due to gauge symmetry of the theory and has a quartic interaction term of the form $\mathcal V_\text{mix}=-\kappa (H_1H_2) (H_1^\prime H_2^\prime)^\dagger+h.c.,$ where the coupling constant $\kappa$ is real due to M-symmetry. %Its worth to stress that the mixing term $\mathcal V_\text{mix}$ would bring the two sectors in equilibrium in the early universe due to the decay $H_{1, 2}^\dagger H_{1, 2}\rightarrow H_{1, 2}^{\prime\dagger} H_{1, 2}^\prime$ unless $\kappa<10^{-8}$ \cite{Berezhiani:1995am}. The M-parity can be spontaneously broken with the introduction of a real scalar singlet $\eta$ with odd parity, namely under the M-parity it changes the sign $\eta\rightarrow -\eta$. If $\eta$ has a non-zero VEV, namely $\langle\eta\rangle=\mu$, it would induce differences in mass-squared of ordinary and mirror Higgses. This difference would imply that VEVs, $v_{1, 2}$ are different from $v_{1, 2}^\prime$ and consequently we would have different weak interaction scales $v\neq v^\prime$ where $v=(v_1^2+v_2^2)^{1/2}\simeq 247$ GeV and $v^\prime=(v_1^{\prime 2}+v_2^{\prime 2})^{1/2}$. In the M-symmetry solution of the strong CP problem, the axion field is identified as a linear combination of the Higgs doublets phases $\phi$ and $\phi^\prime$ with $a=f_a^{-1}(f\phi+f^\prime\phi^\prime)$ where $f_a$ gets contribution from both ordinary and dark sectors, $f_a=\sqrt{f^2+f^{\prime 2}}$, with $f^\prime=v_1^\prime v_2^\prime/v^\prime$ being the axion decay constant in the dark sector and $f=v_1 v_2/v$ being the axion decay constant in the ordinary sector; see Ref. \cite{Berezhiani:2000gh} for details. Consequently, the axion mass $m_a$ gets contribution from ordinary and dark sectors \begin{equation}\label{ax-mass} m_a^2=\frac{N^2}{f_a^2}\left(\frac{VK}{V+K\,\text{Tr} \mathcal M^{-1}}+\frac{V^\prime K^\prime}{V^\prime+K^\prime\,\text{Tr} \mathcal M^{\prime-1}}\right), \end{equation} where $N$ is the color anomaly of $U(1)_\text{PQ}$ current, $K$ and $K^\prime$ are, respectively, the gluon condensates of ordinary and dark sectors which are, respectively, related to the ordinary and dark QCD scales $\Lambda, \Lambda^\prime$ through $K\sim \Lambda^3, K^\prime\sim \Lambda^{\prime 3}$ and $V, V^\prime$ are, respectively, the quark condensates of ordinary and dark sectors with $V\sim \Lambda^3$ and $V^\prime\sim \Lambda^{\prime 3}$. Here $\mathcal M$ and $\mathcal M^\prime$ are, respectively, the mass matrices of light quarks of ordinary and dark sectors where $\mathcal M=\text{diag} (m_u, m_d)$ and $\mathcal M^\prime=\text{diag}(m_u^\prime, m_d^\prime)$. One characteristic of this model is that in the case when $f^\prime\gg f$ or $\Lambda^\prime\gg \Lambda$, the axion field $a$ couples to ordinary sector as DFSZ-like axion while it couples to the dark sector as the original axion or Weinberg-Wilczek (WW) axion \cite{WW}. In this case while the axion behaves as DFSZ-like axion with respect to the ordinary sector its mass given in \eqref{ax-mass} gets contribution from a small term coming from the ordinary sector and a much larger term coming from the dark sector. In addition, the axion field couples to photons\footnote{In this work we call the photon of the mirror sector simply dark photon. In the literature also the name hidden photon for the dark/mirror photon is used.} with two different coupling constants $g_{a\gamma}$ and $g_{a\gamma}^\prime$, which are, respectively, given by \begin{equation}\label{coup-cons} g_{a\gamma}\simeq \frac{\alpha_S}{\pi}\frac{Nz}{f_a(1+z)}, \quad g_{a\gamma}^\prime\simeq \frac{\alpha_S}{\pi}\frac{Nz^\prime}{f_a(1+z^\prime)}, \end{equation} where $z=m_u/m_d$, $z^\prime=m_u^\prime/m_d^\prime$ and $\alpha_S$ is the fine structure constant. In itself, the introduction of the mirror sector can have several consequences in cosmology \cite{Blinnikov:1982eh} and consequently there exist several constraints on the main parameters of the model, and for a detailed review see Ref. \cite{Berezhiani:2003xm}. The application of the M-symmetry does not necessarily means that the abundances of mirror sector particles are the same as those of the ordinary sector. On the contrary, the abundances of elements of ordinary and mirror sectors must be different, not necessarily for all elements, in order to avoid any conflict with well known constraints on extra degrees of freedom such as those imposed by big bang nucleosynthesis (BBN) etc. Indeed, the BBN constraint on the number of extra degrees of freedom, which usually is expressed in terms of the effective neutrino species, constraints the mirror sector equilibrium temperature $T^\prime$ to be $T^\prime<0.64\, \Delta N_\nu^{1/4} T$ where $\Delta N_\nu$ is the effective number of neutrino species and $T$ is the equilibrium temperature of the ordinary sector. The fact that $T^\prime<T$, means that the mirror and ordinary sectors do not come in thermal equilibrium and therefore they evolve almost separately, a condition which is easily achieved if the two sectors communicate through the gravity force. Another constraint imposed on the parameters of the model comes from the mixing term $\mathcal V_\text{mix}$ of the ordinary and mirror sector Higgs doublets. The presence of such term in the Lagrangian density, would make possible the decay $H_{1, 2}^\dagger H_{1, 2}\rightarrow H_{1, 2}^{\prime\dagger} H_{1, 2}^\prime$, which in principle would bring the two sectors in equilibrium in the early universe unless $\kappa$ is very small, namely $\kappa<10^{-8}$ \cite{Berezhiani:1995am}. Another important consequence with the introduction of the mirror sector is that it may provide the right abundance of elements in order to explain the origin of dark matter in a rather natural way. Indeed, as shown in Refs. \cite{Berezhiani:2000gw}-\cite{Bento:2001rc}, it is possible that the baryon asymmetry in the early universe for the mirror sector could be larger than that of the ordinary sector and consequently the number density of mirror baryons would be larger than that of the ordinary sector, namely $n_B^\prime\geq n_B$. In the case when $n_B^\prime/n_B\simeq 5$, we would see that the mirror particles would be plausible candidates for the dark matter; see Ref. \cite{Berezhiani:2003xm} for details. The solution of the strong CP problem through the PQ mechanism in both sectors and the introduction of the axion field which communicates simultaneously with the ordinary and dark sectors, give a unique possibility to explore the vast implications of the model. As I will show in this work, an important consequence of the model proposed in Ref. \cite{Berezhiani:2000gh} is that ordinary photons can mix with dark photons by sharing the same axion field. Such process is very important especially in those situations where do exist both ordinary and dark external magnetic fields. In this case is possible for dark photons to transform into ordinary photons and vice-versa in external magnetic fields. Such mixing/oscillation is very important in the early universe where in the presence of ordinary and dark large-scale magnetic fields, the dark CMB photons would mix/oscillate into ordinary CMB photons and vice versa. This situation could in principle be realized in the early universe since there are enough left ordinary and mirror baryons that can contribute to the generation of large-scale magnetic fields. In addition, the photon-axion-dark photon mixing/oscillation would be important also in those situations where dark objects emit dark photons into intergalactic space where both ordinary and dark large-scale magnetic fields might coexist. In this work, I present a model in which the two sectors interact only via the same axion field in the case when ordinary and dark external magnetic fields coexist in the same place and at the same time. Here I assume the large-scale dark magnetic field to be generated in an analogous way as the ordinary large-scale magnetic field. In addition, I consider the axion mass given in expression \eqref{ax-mass} to be a free parameter of the model without any a priory assumption if the biggest contribution to $m_a$ comes either from the ordinary sector or from the dark sector. This work is organized as follows: in Sect. \ref{sec:2}, I introduce the model of photon-axion-dark photon mixing and derive the field equations of motion in external magnetic fields. In Sect. \ref{sec:3}, I calculate the transitions probabilities for different transition channels and calculate the Stokes parameters which describe the polarization state of the light. In Sect. \ref{sec:4}, I suggest some possible applications of the proposed model and in Sect. \ref{sec:5}, I conclude. In this work I adopt the metric with signature $\eta_{\mu\nu}=\text{diag}({1, -1, -1, -1})$ and work with the natural (rationalized) Lorentz-Heaviside units ($k_B=\hbar=c=\varepsilon_0=\mu_0=1$) with $e^2=4\pi \alpha$. | \label{sec:5} In this work we proposed and studied the effect of the photo-axion-dark photon mixing in external ordinary and dark magnetic fields. As a consequence of this mixing, dark photons can interact with the ordinary photons via the same axion field. Then we solved equations of motion for time depended mixing matrix where perturbative solutions for the photon, dark photon and axion fields have been found. The derived results can be applied in the cases when ordinary and dark photons propagate through time dependent magnetized media such as those present in cosmological situations. With the introduction of the dark photon in the mixing problem, the usual expressions for the photon-axion transition probability rates, Stokes parameters etc., get modified. This fact could have a significant impact in those situations where an external dark magnetic field is present and one needs to know the magnitude of these quantities in order to compare them with experimentally measurable quantities. Our results have been derived by neglecting the weak gravitational interaction between the two sectors and considered their interaction only through the same axion field. In our model ordinary and dark photons interact solely through the axion field. In principle, one could also include in the interaction Lagrangian density a kinetic mixing between photons and dark photons, namely $\mathcal L_I\propto \epsilon F_{\mu\nu}F^{\prime\mu\nu}$, which is not forbidden by the M-symmetry. The inclusion of such term is only optional and can easily be accommodated in our formalism. In order for the photon-axion-dark photon mixing to work there must coexist in the same place and time both ordinary and dark magnetic fields. The only possibility to apply this mixing, happens to be in astrophysical and cosmological situations. In this work we applied our mechanisms in the context of CMB physics and showed as a matter of example that the photon-axion-dark photon mixing would generates a CMB temperature anisotropy at the ordinary post decoupling epoch. The same effect would also generates polarization of the CMB as is evident from the expressions of the Stokes parameters in \eqref{ph-int}. In an astrophysical situation, our model could be used in order to calculate the generated flux of photons in ordinary and dark magnetic fields by dark stars and other dark objects which emit dark photons, where the generated flux might contributes to well know galactic and/or extragalactic backgrounds. With respect to the case of photon-axion mixing, our model has additional free parameters. Indeed, by a close inspection of the expression \eqref{coup-cons} we may observe that the coupling constants are related with each other through $f_a$, namely the coupling constants are proportional to each other. The proportionality term is a combination of $z$ and $z^\prime$ where the former is usually known while the latter is less known. If both $z, z^\prime$ are known, the number of independent parameters is either $m_a$ or $g_{a\gamma}$ or $g_{a\gamma}^\prime$ similarly as in the case of the photon-axion mixing. Additional implicit parameters of our model essentially do appear in the index of refraction of dark photons which usually contains the plasma frequency which is related to the number density of the free dark electrons and to the amplitude of the dark magnetic field. In the context of the CMB physics, our model can be applied to constrain the parameter space of axions which are essentially either the coupling constant to photons and dark photons or its mass. Indeed, the expression \eqref{temp-int} can be used to limit/constrain the axion parameter space and/or the magnetic field amplitudes based on the known value of the amplitude of the CMB temperature anisotropy. On the other hand, if one knows the values of the parameters which enter in \eqref{temp-int}, one can estimates which is the contribution of photon-axion-dark photon mixing to the CMB temperature anisotropy. The presence of the ordinary large-scale magnetic field generates a CMB temperature anisotropy by itself, so, the result \eqref{temp-int} gives only the contribution of the photon-axion-dark photon mixing to the total CMB temperature anisotropy. On the other hand, even though we studied for simplicity only the effects of the photon-axion-dark photon mixing on the CMB temperature anisotropy, additional limits/constraints can be inferred from the present limits on the CMB polarization. Indeed, our model generates also birefringence and dichroism effects on the CMB, namely it generates an elliptic polarization with non zero Stokes parameters $Q(t), U(t)$ and $V(t)$, as one can observe from the expression \eqref{ph-int}. \vspace{1cm} \hrulefill {\bf{AKNOWLEDGMENTS}}: I would like to thank Zurab Berezhiani for very interesting discussions and for letting me know about his work on mirror world. This work is supported by the Russian Science Foundation Grant no. 16-12-10037. I also would like to thank LNGS for the support received through the fellowship POR 2007-2013 `Sapere e Crescita' where part of this research was conducted. \hrulefill \vspace{1cm} \appendix | 16 | 9 | 1609.06623 |
1609 | 1609.02556_arXiv.txt | \label{sec:intro} The latest observations of the Cosmic Microwave Background indicate that a good theoretical model for the very early universe should predict a nearly scale-invariant power spectrum of curvature perturbations with a small red tilt\ \cite{Ade:2015xua}, a small tensor-to-scalar ratio\ \cite{Array:2015xqh}, and small non-Gaussianities\ \cite{Ade:2015ava}. Inflationary cosmology\ \cite{Guth:1980zm,Mukhanov:1981xt,Linde:1981mu,Bardeen:1983qw} currently stands up as the best candidate for explaining these observations\ \cite{Ade:2015lrj}. Yet, it is still an incomplete theory conceptually\ \cite{Brandenberger:2010dk,Brandenberger:2011gk,Brandenberger:2012uj}, because, for example, it suffers from a singularity at the time of the Big Bang\ \cite{Borde:1993xh,Borde:2001nh}. Thus, in addition to trying to resolve the issues of inflation, it is helpful to study competitive or complementary ideas that could enlighten our understanding of the very early universe. One such idea is bouncing cosmology: one assumes that the universe existed forever before the Big Bang in a contracting phase, after which it transitioned into the expending universe that we observe today. In addition to solving the usual flatness and horizon problems of standard Big Bang cosmology, assuming that quantum cosmological perturbations exit the Hubble horizon in a matter-dominated contracting phase leads to a scale-invariant power spectrum of curvature perturbations\ \cite{Wands:1998yp,Finelli:2001sr}. Furthermore, there exist many models that can avoid reaching a singularity at the time of the Big Bang, hence leading to nonsingular bouncing cosmologies (see\ \cite{Novello:2008ra,Brandenberger:2012zb,Cai:2014bea} and references therein). Yet, it is still hard to construct models that can agree with all observational constraints (see, e.g.,\ \cite{Quintin:2015rta} and also\ \cite{Battefeld:2014uga,Brandenberger:2016vhg} for reviews). An additional difficulty with bouncing cosmology comes from the fact that it appears less robust against certain instabilities as many unwanted features tend to grow in a contracting universe. One example is anisotropies: as $a\rightarrow 0$, anisotropies grow as $\rho\propto a^{-6}$, whereas the background matter and radiation evolve according to $\rho\propto a^{-3}$ and $\rho\propto a^{-4}$, respectively. This is known as the Belinsky-Khalatnikov-Lifshitz (BKL) instability\ \cite{Belinsky:1970ew}. This can be resolved if the background before the bounce can satisfy $\rho\propto a^{-q}$ with $q\gg 6$\ \cite{Erickson:2003zm,Cai:2013vm}, which naturally occurs within the Ekpyrotic model\ \cite{Khoury:2001wf,Khoury:2001zk} (see also\ \cite{Lehners:2008vx} and references therein). There is another type of instability, always in a contracting universe, that has not been explored in as much detail, namely the growth of inhomogeneities. This type of instability was already known from the 1960s\ \cite{Lifshitz&Khalatnikov63}, but it is only in the 2000s that the work was extended\ \cite{Banks:2002fe}, and it suggested that the growth of inhomogeneities in a contracting universe could lead to the formation of black holes. The goal of this paper is thus to revisit the analysis of the growth of inhomogeneities in a contracting universe, and more specifically, characterize the formation of black holes. On one hand, we want to determine in which cases a contracting universe is robust or not against the formation of large inhomogeneities and black holes. This will determine in which cases it is justified to ignore the growth of inhomogeneities and allow us to claim which corresponding models remain healthy or not. On the other hand, we want to determine in which cases a contracting universe inevitably leads to the formation of black holes. These cases could be relevant in light of other alternative theories of the very early universe in which black holes could be the seeds of the current universe. The outline of this paper is as follows. First, in section\ \ref{sec:gravpot}, we begin by setting the general framework in which we work, and we solve for the evolution of the gravitational potential in a contracting universe, aiming for generality. In section\ \ref{sec:densityJeansP}, we move on to find the density contrast in a generic contracting universe, and we comment on its evolution over the different length scales of interest. We also determine the power spectrum of the perturbations over the different scales of interest. In section\ \ref{sec:ICs}, we explore two types of possible initial conditions for the fluctuations, quantum vacuum initial conditions and thermal initial conditions, and we find the power spectra in each cases. We also determine when the perturbations become non-linear. Then, in section\ \ref{sec:BHformation}, we derive the condition for black hole collapse, and we use the Press-Schechter formalism to determine which cases lead to the formation of black holes. We also describe the black holes that form. Finally, in section\ \ref{sec:discussion}, we summarize our results regarding the models that are robust (and those that are not) against the formation of black holes. We end by suggesting possible alternative theories that could take advantage of the formation of black holes. Throughout this paper, we adopt the mostly minus convention for the metric, and we define the reduced Planck mass by $M_\mathrm{Pl}\equiv(8\pi G_{\mathrm{N}})^{-1/2}$ where $G_{\mathrm{N}}$ is Newton's gravitational constant. | \label{sec:discussion} In this paper, we studied the adiabatic cosmological perturbations of a hydrodynamical fluid with constant EoS parameter and constant sound speed in a flat\footnote{Although we did not include the possible effects of spatial curvature in our analysis, we believe that our results would not be greatly affected by those effects since the contribution of spatial curvature decreases in a contracting universe.} contracting universe. We found the general evolution of the density contrast over the different regimes of interest: sub-Jeans scales, super-Jeans/sub-Hubble scales, and super-Hubble scales. The key results that are independent of the initial conditions can be summarized as follows: \begin{itemize} \item for a radiation-dominated contracting universe, the amplitude of the density contrast on sub-Jeans scales is constant in time; \item for a matter-dominated contracting universe, the amplitude of the density contrast on super-Jeans/sub-Hubble scales grows with time as one approaches a possible bounce. \end{itemize} We then considered two sets of initial conditions: quantum vacuum initial conditions and thermal initial conditions. This allowed us to find the general form of the power spectrum, and the main results are given below. \begin{itemize} \item By setting quantum vacuum initial conditions at Jeans crossing, the density contrast power spectrum in a matter-dominated contracting universe on super-Jeans/sub-Hubble scales is scale invariant, grows as $H^2(t)/M_\mathrm{Pl}^2$, and is enhanced by the smallness of the sound speed ($\mathcal{P}_\delta\sim c_\mathrm{s}^{-5}$). In addition, we find that non-linearity is reached well before the Planck scale when the sound speed is small. \item By setting thermal initial conditions at a fixed time on sub-Jeans scales, the density contrast power spectrum in a radiation-dominated contracting universe (on sub-Jeans scales) is blue ($\mathcal{P}_\delta\sim k^3$), and, in a matter-dominated contracting universe (on super-Jeans/sub-Hubble scales), it is red ($\mathcal{P}_\delta\sim k^{-1}$). Accordingly, for radiation, non-linearity occurs first on smaller length scales (Planck scale), whereas for matter, non-linearity occurs first on larger length scales (Hubble scale). \end{itemize} Then, under the assumption that the hoop conjecture is valid, we derived a general requirement for black hole collapse. By smoothing out the density contrast power spectrum and using the Press-Schechter formalism to describe the probability of black hole formation, we arrived at the following final results. \begin{itemize} \item For a matter-dominated contracting universe with quantum vacuum initial conditions, Hubble-size black holes, i.e.~black holes with Schwarzschild radius $R=|H|^{-1}$, form first when the Hubble parameter reaches $|H|\sim c_\mathrm{s}^{5/2}M_\mathrm{Pl}$, a small fraction of the Planck scale for $c_\mathrm{s}\ll 1$. \item We find the same results when we take thermal initial conditions instead of a quantum state, except that the critical energy scale for black hole formation goes as $|H|\sim c_\mathrm{s}^{18/5}(M_\mathrm{Pl}/H_\mathrm{ini})^{1/5}M_\mathrm{Pl}$, which depends on the value of the Hubble parameter at the time that the initial conditions are taken. Yet, in most cases, this is still a small fraction of the Planck scale. \item For a radiation-dominated contracting universe with thermal initial conditions, no black hole can form before the Hubble parameter reaches $|H|\simeq [9\pi^2/(2\gamma_\mathrm{f}^4)]^{1/3}M_\mathrm{Pl}\sim M_\mathrm{Pl}$, i.e.~order the Planck scale. \end{itemize} In light of these results, we showed in this paper that nonsingular bouncing cosmology is robust against the formation of black holes if the sound speed is large enough. In particular, for a radiation-dominated contracting universe with $c_\mathrm{s}^2=1/3$, we found that no black hole could form before reaching a Planck time before the bounce. Equivalently, we expect this result to hold for even stiffer equations of state. In particular, this goes in line with the results of\ \cite{Neves:2015ria} according to which no black hole can form in an Ekpyrotic contracting phase where $w\gg 1$. However, one needs to be slightly careful in applying our results to a model where the background is driven by a scalar field\footnote{We conjecture that an oscillating scalar field with $c_\mathrm{s}^2=1$ would not lead to the formation of black holes. Accordingly, the original matter bounce scenario would be stable against this type of instability. The situation is less obvious for a scalar field with a non-canonical kinetic term in its action (e.g.,~a $k$-essence scalar field), which could result in $c_\mathrm{s}^2\ll 1$. In this case, the result might be closer to that of hydrodynamical pressureless matter where black holes are produced.} since it may have $w\neq c_\mathrm{s}^2$, or equivalently, $w$ may be time dependent. As we mentioned in the text, there remains to show that models of nonsingular bouncing cosmology which could have a mixture of matter and radiation (e.g., the $\Lambda$CDM bounce and its extensions\ \cite{Cai:2014jla,Cai:2015vzv}) can still agree with observations. To avoid the formation of black holes, radiation needs to dominate early enough, and in turn, this will affect the perturbation modes that are of observational interest today and that acquire a nearly scale-invariant power spectrum of curvature perturbations in the matter-dominated contracting phase. In fact, it is known that the transition from matter domination to radiation domination would produce a break in the power spectrum from scale invariance to a very blue spectrum. Such a break is highly constrained from observations, and it implies that the radiation-dominated contracting phase must be shorter than in our expanding universe\ \cite{Li:2009cu}. Yet, it appears to be still possible for these models to satisfy the observational constraints on the power spectrum and avoid the formation of black holes in the contracting phase. In this paper, we also showed that bouncing cosmologies that are solely driven by matter with $w=c_\mathrm{s}^2\ll 1$ (or for which the matter-dominated contracting phase lasts long enough before radiation dominates) are not robust against the formation of black holes. Since we find that these black holes form well before reaching the Planck scale, the corresponding nonsingular bouncing cosmologies cannot ignore the formation of these black holes. This agrees with the results of\ \cite{Banks:2002fe} which find an unstable growth of inhomogeneities and the formation of black holes, hence the name ``black crunch'' that they gave to describe this scenario. Finally, we showed that when the conditions for black hole formation are satisfied, the first black holes that form are of Hubble size (the Schwarzschild radius is equal to the Hubble radius). Once these Hubble-size black holes form, our perturbative analysis breaks down, hence we did not present the subsequent evolution of the universe. Still, we can comment on a number of possible outcomes. It is argued in\ \cite{Banks:2002fe} that such Hubble-size black holes behave as a $w=1$ fluid. This leads to an alternative scenario to inflationary cosmology, named holographic cosmology\ \cite{Banks:2001px,Banks:2003ta,Banks:2004vg,Banks:2004eb}, in which the so-called dense $p=\rho$ ``black hole gas'' serves as the seed to the observed large scale structure of our universe. Also, in line with our motivation coming from bouncing cosmology, it is suggested in\ \cite{Veneziano:2003sz} that such a dense black hole gas could lead to a model for the ``big bounce''. The idea is that, in string theory, the black holes would evolve to become a dense gas of ``string holes'', string states that lie along the correspondence curve between black holes and strings, as the string coupling evolves. Furthermore, it is believed that the Hubble-size string holes saturate the conjectured cosmological entropy bound (see, e.g., \cite{Fischler:1998st,Veneziano:1999ts,Bousso:1999xy}, the review\ \cite{Bousso:2002ju} and references therein), and thus, the entropy associated with the Hubble radius would be proportional to the area. Since this is the same holographic scaling of the entropy and of the specific heat that is found in string gas cosmology, one may hope to have a successful structure formation scenario just as in string gas cosmology (see\ \cite{Brandenberger:1988aj,Nayeri:2005ck,Brandenberger:2006xi,Brandenberger:2006vv,Brandenberger:2006pr,Brandenberger:2014faa} and also\ \cite{Brandenberger:2008nx,Brandenberger:2011et,Brandenberger:2015kga} for reviews). Alternatively,\ \cite{Oshita:2016btk} proposes the idea that a black hole could serve as a nucleation cite of a false vacuum bubble that could tunnel, under some conditions and assumptions, to an inflationary universe, and thus, the black holes that naturally form in a matter-dominated contracting universe could undergo such a tunneling and lead to inflationary universes. At last, it could be that the black holes that are produced in the contracting universe simply ``pass through'' any given model of nonsingular bounce and form primordial black holes when they re-enter the Hubble radius, as suggested by\ \cite{Carr:2011hv,Carr:2014eya}. These would leave specific imprints in today's universe, in the form of, e.g., dark matter or gravitational waves (see, e.g.,\ \cite{Clesse:2015wea,Clesse:2016vqa,Bird:2016dcv}), which could allow us to constrain the given model. In summary, although the formation of black holes in a contracting universe is an undesired feature in typical bouncing cosmologies, it seems to be of particular interest in many alternative scenarios of the very early universe and may allow us to probe new physics and lead to the emergence of new ideas. Consequently, we plan to expand upon the possible outcomes outlined above in more detail in a follow-up paper\ \cite{Quintin:2016}. \paragraph*{Note added:} While this paper was under preparation, we were informed that a similar study had been undertaken by an independent group. This study reaches similar conclusions to ours with a slightly different approach\ \cite{Chen:2016kjx}. | 16 | 9 | 1609.02556 |
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1609 | 1609.06143_arXiv.txt | The majority of cataclysmic variable (CV) stars contain a stochastic noise component in their light curves, commonly referred to as flickering. This can significantly affect the morphology of CV eclipses and increases the difficulty in obtaining accurate system parameters with reliable errors through eclipse modelling. Here we introduce a new approach to eclipse modelling, which models CV flickering with the help of Gaussian processes (GPs). A parameterised eclipse model - with an additional GP component - is simultaneously fit to 8 eclipses of the dwarf nova ASASSN-14ag and system parameters determined. We obtain a mass ratio $q$\,=\,0.149\,$\pm$\,0.016 and inclination $i$\,=\,83.4\,$^{+0.9}_{-0.6}$\,$^{\circ}$. The white dwarf and donor masses were found to be $M_{w}$\,=\,0.63\,$\pm$\,0.04\,$M_{\odot}$ and $M_{d}$\,=\,0.093\,$^{+0.015}_{-0.012}$\,$M_{\odot}$, respectively. A white dwarf temperature $T_{w}$\,=\,14000\,$^{+2200}_{-2000}$\,K and distance $d$\,=\,146\,$^{+24}_{-20}$\,pc were determined through multicolour photometry. We find GPs to be an effective way of modelling flickering in CV light curves and plan to use this new eclipse modelling approach going forward. | \label{sec:introduction} Cataclysmic variable stars (CVs) are interacting binary systems that contain a white dwarf primary and a low mass secondary. Material from the secondary star is transferred to the white dwarf due to the secondary filling its Roche lobe. If the white dwarf has a low magnetic field, this transferred mass does not immediately accrete onto the white dwarf. Instead, in order to conserve angular momentum, the transferred mass forms an accretion disc around the white dwarf. A bright spot is formed at the point on the accretion disc where the gas stream from the donor makes contact. For a general review of CVs, see \cite{hellier01}. At high enough inclinations to our line of sight (\textgreater\,80$^{\circ}$), the donor star can eclipse all other components within the system. As this includes the white dwarf, accretion disc and bright spot, CV eclipses can appear complex in shape. All of these components are eclipsed in quick succession, therefore high-time resolution photometry is required to reveal all the individual eclipse features. Measuring the timings of the white dwarf and bright spot eclipse features allow the system parameters to be accurately determined (e.g. \citealt{wood86}). For some systems, the timing of these features (especially those associated with the bright spot) cannot be accurately measured, even with high-time resolution. This can be due to such systems containing a high amount of flickering, seen as random variability in CV light curves with amplitudes reaching the same order of magnitude as the bright spot eclipse features. Flickering in CVs is found to originate in both the bright spot and the inner accretion disc, and is due to the turbulent nature of the transferred material within the system \citep{bruch00,bruch15,baptistabortoletto04,scaringi12,scaringi14}. Previous photometric studies of eclipsing CVs have used the averaging of multiple eclipses as a way of overcoming flickering and strengthening the bright spot eclipse features, before fitting an eclipse model to obtain system parameters (e.g. \citealt{savoury11,littlefair14,mcallister15}). \cite{mcallister15} also attempted to estimate the effect of flickering on the parameter uncertainties. An additional four $g'$-band eclipses were created -- each containing a different combination of three out of the four original eclipses used for the $g'$-band average -- and fit separately. The spread in system parameters from these average eclipses gave an indication of the error due to flickering, approximately five times the size of the purely statistical error. A downside to the eclipse averaging approach concerns the inconsistent bright spot ingress/egress positions due to changes in the accretion disc radius, which are observed in a significant number of systems. Averaging such light curves can lead to inaccurate bright spot eclipse timings and therefore incorrect system parameters. Eclipse light curves from systems with disc radius changes have to be fit individually, requiring another method to combat flickering. Here we introduce a new approach, involving the modelling of flickering in individual eclipses with the help of Gaussian processes (GPs). GPs have been used for many years in the machine learning community (see textbooks: \citealt{rasmussenwilliams06,bishop06}), and have recently started seeing use in many areas of astrophysics. Some examples include photometric redshift prediction \citep{waysrivastava06,way09}, modelling instrumental systematics in transmission spectroscopy \citep{gibson12,evans15} and modelling stellar activity signals in radial velocity studies \citep{rajpaul15}. See section~\ref{sec:gps} for further discussion of GPs. The modelling of flickering is just one of a number of modifications we have made to the fitting approach. The model now has the ability to fit multiple eclipses simultaneously, whilst sharing parameters intrinsic to a particular system, e.g mass ratio ($q$), white dwarf eclipse phase full-width at half-depth ($\Delta\phi$) and white dwarf radius ($R_{w}$) between all eclipses. More details on the modifications to the model can be found in section~\ref{subsec:modifications}. ASASSN-14ag was the chosen system to test the new modelling approach, due to the combination of a high level of flickering and clear bright spot features in its eclipse light curves. ASASSN-14ag was discovered in outburst (reaching $V$=13.5) by the All-Sky Automated Search for Supernovae (ASAS-SN; \citealt{shappee14}) on 14th March 2014. A look through existing light curve data on this system from the Catalina Real-Time Survey (CRTS; \citealt{drake09}) showed signs of eclipses, with an orbital period below the period gap (vsnet-alert 17036). Follow up photometry made in the days following the initial ASAS-SN discovery confirmed the eclipsing nature of the CV (vsnet-alert 17041). The discovery of superhumps also showed this to be a superoutburst, identifying ASASSN-14ag as a SU UMa-type dwarf nova (vsnet-alert 17042; \citealt{kato15}). | \label{sec:conclusions} We have introduced a new approach to modelling CV eclipses that enables multiple eclipses to be fit simultaneously, with the option to model any inherent flickering with GPs. This no longer requires eclipses to be averaged together in order to overcome the presence of flickering, a technique employed in previous studies and subject to issues caused by disc radius changes. This new approach has been tested using 8 eclipses of the eclipsing CV ASASSN-14ag. These eclipses -- all including flickering -- were fit simultaneously with and without GPs. Although both fits return a similar solution, the errors associated with the GP fit are much more representative given the large amount of flickering present. We have shown GPs to be an effective way of modelling flickering, and plan to use this new eclipse modelling approach on many more eclipsing CV systems going forward. | 16 | 9 | 1609.06143 |
1609 | 1609.03882_arXiv.txt | The Sardinia Radio Telescope (SRT, www.srt.inaf.it) is a new 64-m single-dish antenna operated by INAF (Istituto Nazionale di Astrofisica; Italy). The advanced technology, in particular the active surface, will allow us to observe frequencies from 300 MHz up to 115 GHz. We proposed innovative observing and mapping techniques during the Astronomical Validation phase, with the development of the Single Dish Imager (SDI; Pellizzoni et al. in prep.). This software is dedicated to the production of calibrated maps of extended sources, such as SNRs and pulsar wind nebulae. \newline We present the imaging of the Galactic SNR IC443 at 7.24 GHz obtained with SRT during the Astronomical Validation phase. We compared our results with high-resolution maps of this source obtained with the VLA and Arecibo at 1.4 GHz (Lee et al. 2008). | The first maps of IC443 obtained with SRT at 7.24 GHz are very promising, giving the possibility to study more in details complex sources. The data analysis was performed using the Single Dish Imager (SDI) software, a new tool that demonstrates the capabilities of SRT in performing single-dish images in C-band. SDI will be made available to SRT users in future AO/"Call for Proposals". The resulting maps provide a detailed structure of the remnants, comparable to interferometric observations carried out with the VLA at lower frequencies (Lee et al. 2008; Castelletti et al. 2011). This testifies the excellent capabilities of SRT in making maps of extended sources using OTF observations. This is of great interest to infer the flux in different resolved regions of sources. Further results related to the observations of SNRs IC443 and W44 at 1.4 GHz and 7 GHz are presented in Egron et al. in prep. \newline \newline \small % \textit{This work is based on commissioning observations with SRT operated by INAF. For observations at SRT, we also credit the Astrophysical Validation Team http://www.srt.inaf.it/astronomers/astrophysical-validation-team/}. | 16 | 9 | 1609.03882 |
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1609 | 1609.03599_arXiv.txt | \vspace{0.3cm} We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and a Sorkin-Schutz action for the matter one. Then, we work out the proper viability conditions to guarantee in the scalar sector the absence of ghosts, gradient and tachyonic instabilities. The absence of ghosts can be achieved by demanding a positive kinetic matrix, while the lack of a gradient instability is ensured by imposing a positive speed of propagation for all the scalar modes. In case of tachyonic instability, the mass eigenvalues have been studied and we work out the appropriate expressions. For the latter, an instability occurs only when the negative mass eigenvalue is much larger, in absolute value, than the Hubble parameter. We discuss the results for the minimally coupled quintessence model showing for a particular set of parameters two typical behaviours which in turn lead to a stable and an unstable configuration. Moreover, we find that the speeds of propagation of the scalar modes strongly depend on matter densities, for the beyond Horndeski theories. Our findings can be directly employed when testing modified gravity theories as they allow to identify the correct viability space. | Since its discovery, the late-time cosmic acceleration phenomenon has been the most challenging problem for cosmologists. Usually referred to as the Dark Energy (DE) problem, at first it was explained with the presence of a cosmological constant ($\Lambda$) in General Relativity (GR). The resulting standard cosmological model ($\Lambda$CDM) offers an exquisite fit to cosmological data~\cite{Ade:2015xua}, however it suffers from some major theoretical issues which are still unresolved (see ref.~\cite{Bull:2015stt} and references therein). This has paved the way to new theories of gravity to be considered as valid alternative to GR~\cite{Sotiriou:2008rp,Silvestri:2009hh,DeFelice:2010aj,Clifton:2011jh,Tsujikawa:2013fta,Deffayet:2013lga,Joyce:2014kja,Koyama:2015vza,Bull:2015stt}. Such theories include mechanisms able to give rise to the observed acceleration at large scales and late time, while being hidden at solar system scale~\cite{Joyce:2014kja} where GR is well tested. A common aspect present in most of these modified gravity (MG) theories is to revise GR by including an additional scalar degree of freedom (DoF), whose dynamics can explain the current observations. Irrespectively of the resulting MG model, one has to ensure that the evolution of the modes associated to the extra DoF does not lead to pathological instabilities, such as ghost, gradient and tachyonic instabilities (for a review see ref.~\cite{Sbisa:2014pzo}). In particular, when studying cosmological perturbations the additional DoF is coupled to one or more DoFs representing the matter fields dynamics, then these couplings imply that a consistent and complete study of the stability of the whole system can not be done without considering the interaction with the matter sector. In fact, the stability conditions might be altered by the presence of the additional matter fields, thus changing the viability space of the theory~\cite{Scherrer:2004au,Bertacca:2007ux,Bertacca:2007cv,Gergely:2014rna,Kase:2014cwa,Gleyzes:2014qga}. Identifying the correct viability requirements is important when testing MG theories with cosmological data by using statistical tools~\cite{Zhao:2008bn,Hu:2013twa,Raveri:2014cka,Zumalacarregui:2016pph}, as they can reduce the viability space one needs to explore. Additionally they can even dominate over the constraining power of observational data as recently shown in the case of designer f(R)-theory on $w$CDM background~\cite{Raveri:2014cka}. With the aim to obtain general results, we will employ the Effective Field Theory of Dark Energy and Modified Gravity (hereafter EFT) presented in refs.~\cite{Gubitosi:2012hu,Bloomfield:2012ff}. Inspired by the EFT of Inflation~\cite{Creminelli:2006xe,Cheung:2007st,Weinberg:2008hq,Creminelli:2008wc} and large scale structures~\cite{Park:2010cw,Jimenez:2011nn,Carrasco:2012cv,Hertzberg:2012qn,Carrasco:2013mua,Porto:2013qua,Senatore:2014vja}, it was widely studied in refs.~\cite{Gleyzes:2013ooa,Bloomfield:2013efa,Piazza:2013coa,Frusciante:2013zop,Gleyzes:2014rba,Perenon:2015sla,Kase:2014cwa,Frusciante:2016xoj}. The EFT approach provides a model independent framework to study linear order cosmological perturbations in theories of gravity which exhibit an additional scalar DoF, while at the same time it parametrizes in an efficient way existing models, since most of them can be directly mapped into this language~\cite{Gubitosi:2012hu,Bloomfield:2012ff,Gleyzes:2013ooa,Kase:2014cwa,Frusciante:2016xoj}. Subsequently, the EFT approach has been implemented into the Einstein Boltzmann solver, CAMB/CosmoMC~\cite{CAMB,Lewis:1999bs,Lewis:2002ah}, creating EFTCAMB/EFTCosmoMC~\cite{Hu:2013twa,Raveri:2014cka,Hu:2014sea,Hu:2014oga,Frusciante:2015maa,Hu:2016zrh} (\url{http://www.eftcamb.org/}), providing a perfect tool to test gravity models through comparison with observational data. EFTCAMB comes with a built-in module to explore the viability space of the underlying theory of gravity, which then can be used as \textit{priors}. The results of the present work have a direct application as they can be employed to improve the current EFTCAMB viability requirements but not limited to it as they can be easily mapped to other parametrizations~\cite{Hu:2014oga}. The matter sector is described by the Sorkin-Schutz action, which allows to treat general matter fluids~\cite{Sorkin:1977,Brown:1993}. Among many models used to describe matter Lagrangians and which have been extensively used and investigated in the past years~\cite{Scherrer:2004au,Bertacca:2007ux,Bertacca:2007cv,Gergely:2014rna,Kase:2014cwa,Gleyzes:2014qga}, we choose to follow the recent arguments in ref.~\cite{DeFelice:2015moy}. Indeed, it has been shown that such an action, along with an appropriate choice for the matter field, describes the dynamics of all matter fluids avoiding some problems which might arise when including pressure-less matter fluids, like dust or cold dark matter (CDM), which instead need to be considered as they are relevant in the evolution of the Universe. Recently, a stability analysis has appeared in the context of EFT~\cite{Kase:2014cwa}. However, in our work we present also the conditions which allow to avoid tachyonic instabilities and we analyse, more in detail, in addition to the generic theories, all possible sub-cases concerning the stability conditions. Furthermore, another difference comes with the choice of the matter Lagrangian, indeed in our analysis a pressure-less fluid can be safely considered. With this machinery, we proceed to derive the viability constraints one needs to impose on the free parameters of the theory by focusing on three sources of possible instabilities, ghost, gradient and tachyonic instabilities. We will proceed while retaining the full generality of the EFT approach, i.e.\ without limiting to specific models. However, where relevant, we will make connections to specific theories, such as low-energy Ho\v rava gravity~\cite{Horava:2008ih,Horava:2009uw,Mukohyama:2010xz} and beyond Horndeski models~\cite{Gleyzes:2014dya} and we will analyse the results within the context of these models. The present manuscript is organized as follows. In section~\ref{Sec:EFT}, we briefly recap the EFT formalism we use to parametrize the DE/MG models with one extra scalar DoF. In section~\ref{Sec:matter}, we introduce the Sorkin-Schutz action to describe the dynamics of matter fluids and we discuss the advantage of using this action with respect to previous approaches. We also work out the corresponding continuity equation and second order perturbed action. In section~\ref{Sec:stability}, we work out the action for both gravity and matter fields up to second order in perturbations. Then, we calculate and discuss the stability requirements to avoid ghost instabilities (section~\ref{Sec:ghost}), to guarantee positive speeds of propagation (section~\ref{Sec:speed}) and to prevent tachyonic instabilities (section~\ref{Sec:Mass}). Finally, we conclude in section~\ref{Sec:conclusion}. | \label{Sec:conclusion} In this paper we have presented a thorough analysis of the viability conditions which guarantee the stability of the scalar DoFs in the presence of matter fields. As usual, this includes the avoidance of ghosts and tachyonic instabilities, supplemented with a positive speed of propagation. The study of the viability of specific gravity theories in vacuum or in the presence of matter fields has already yielded an extensive literature. However, our results are more general and directly applicable to most of the well known models which are of cosmological interest. For the gravity sector, we employed the general EFT approach for DE/MG, which has the advantage of being a model independent parametrization of gravity theories with one extra scalar DoF while at the same time preserving a direct link with a wide class of theoretical models which can be explicitly mapped into this formalism. In order to describe the standard perfect fluids we chose the Sorkin-Schutz action which has been shown to be well behaved in contrast to other choices made in the past, such as $P(\mathcal{X})$. In detail, we specialised to the case where the matter fluids are dust (or CDM) and radiation. From these starting blocks we constructed the Lagrangian and then we proceeded to derive the action up to second order in scalar perturbations accompanied by the background equations. Finally, we moved to the study of the viability requirements which we will summarise and discuss in the following. After constructing the Lagrangian for the perturbations one can straightforwardly guarantee the absence of ghosts by imposing the positivity of the kinetic term, or matrix in case more than one field is considered as in the present paper. In deriving such conditions we have considered only the Lagrangian in the high-$k$ regime, following the recent results in ref.~\cite{Gumrukcuoglu:2016jbh}. Indeed, it has been shown that only the high energy terms can turn out in catastrophic instabilities while the sub-leading terms can be recast in mass-like terms through appropriate field redefinitions. Because the EFT approach encompasses a variety of DE/MG models, which in some cases show different and non trivial k-dependence, it is not possible to obtain one general result applicable to all possible theories. Therefore, we have identified five relevant sub-cases for which we have worked out the corresponding no-ghost conditions. In particular, two of the aforementioned sub-cases correspond to well known theoretical models, i.e.\ low-energy Ho\v rava gravity and beyond Horndeski, while the remaining three do not correspond to any specific class of theories but can be useful in a model independent study. In general, we found three no-ghost conditions for each of the sub-cases, two of them contain only matter functions and thus resulting to be trivially satisfied, while the other is more involved as it is a combination of EFT functions. Finally, we have also identified conditions which lead to strong coupling regimes, thus excluding these theories from an effective description. The next step was to study the speeds of propagation of the three DoFs, in the high-$k$ limit, for the sub-cases mentioned before which we demanded to be positive. Depending on the sub-case the results change drastically because the momentum dependence of various terms differs in each sub-case. In general, the gravity speed of propagation does not depend on fluid variables once one consider theories with higher (than second) order spatial derivatives. In particular, for the sub-case to which low-energy Ho\v rava gravity belongs, we find that at high-$k$ the DoFs are completely decoupled and the speeds of propagation of dust and radiation components are unaffected by the coupling to gravity, leading to the standard results. While, in the sub-case corresponding to beyond Horndeski only the dust speed of propagation stays unaltered, while both the radiation and gravity speeds are strongly altered due to their interaction. Moreover, when specifying the beyond Horndeski sub-case to the Horndeski one the three DoFs decouple and both dust and radiation show the standard results for speed while the speed of propagation associated to the gravity mode still manifest modification due to the matter components. The three remaining sub-cases exhibit unaltered matter speeds and the gravity one is not influenced by the matter sector. A surprising result is the sub-case corresponding to $F_4=0, m_2^2\neq0$, for which the gravitational sector has a vanishing speed of sound. In the last part of the work, we have considered the instabilities that show up in case the Hamiltonian is unbounded from below at low energy. This instability is tightly related with the appearance of a tachyonic mass in the Lagrangian. Only for this case we have simplified the approach by assuming only one matter fluid, which we chose to be dust. Consequently, we have identified the two eigenvalues ($\mu_i$) of the system which need to be constrained in the limit $k\rightarrow 0$ in order to guarantee the boundedness of the Hamiltonian. A stringent condition is to demand both the eigenvalues to be positive definite. On the other hand, it is well known that at early times the dust fluid exhibits a Jeans instability, which is necessary in order to allow structures formation. Therefore, it is more realistic to assume that the eigenvalues are of the same order of $H^2$, and in case $\mu_i<0$ impose that their evolution is such that $|\mu_i|\ll H^2$. Due to the complexity of these results, we have chosen to exemplify our findings by studying the minimally coupled quintessence case. We have parametrized the gravity modification in terms of the equation of state for DE, i.e.\ $w_{\rm DE}(a)$ and then through the appropriate mapping, we were able to write $\mu_i(w_{\rm DE})$. Finally, as illustrative example we chose the CPL parametrization for the DE fluid and two sets of values for the DE parameters. In figure~\ref{Fig.CPL}, we showed two typical situations, i.e.\ the case in which the tachyonic instability shows up and the theory becomes pathological and a stable case exhibiting a Jeans instability for the dust sector. Before concluding, we would like to stress that, although in literature the conditions for no-ghost and a positive speed of propagation are usually considered and deeply studied in specific class of theories, in the present work we showed general results for any theory of gravity with one extra scalar DoF in presence of matter fields. This has been done with the EFT of DE/MG approach and an appropriate choice of the matter DoFs (see section \ref{Sec:matter}). Our choice for the matter DoF allowed us to construct the no-ghost conditions when considering a dust fluid, a result which was not present in the literature before. Moreover, we have also presented the tachyonic conditions which are usually not considered and provide an additional way to explore the parameter space of scalar tensor theories. In some cases, when we specialize the EFT functions to specific sub-cases, we found our results to be compatible with other results already present in literature. In those cases the main improvement coming from our approach is the fact we work directly with the density perturbation as the fluid variable, hence avoiding issues with the definition of the matter Lagrangian and, subsequently, any need to take limits in order to include pressureless fluids. The lack of such ambiguities solidifies the pre-existing results and guarantees their accuracy. As a final remark, we would like to stress that, due to the generality of the approach we used, one can safely apply our results to most of the well known cosmological models {when any matter species is present, once the mapping between the chosen model and the EFT functions is known. Therefore, they can be employed by cosmological tools, such as EFTCAMB, in order to reduce the viability space and ensure that the model under consideration is free of any pathological instabilities. | 16 | 9 | 1609.03599 |
1609 | 1609.01280_arXiv.txt | {} {We present an analysis of the region IRAS\,08589$-$4714 with the aim of characterizing the molecular environment.} {We observed the $^{12}$CO($3-$2), $^{13}$CO($3-$2), C$^{18}$O($3-$2), HCO$^{+}$($3-$2), and HCN($3-$2) molecular lines in a region of 150$''$ $\times$ 150$''$, centered on the IRAS source, to analyze the distribution and characteristics of the molecular gas linked to the IRAS source. } {The molecular gas distribution reveals a molecular clump that is coincident with IRAS\,08589$-$4714 and with a dust clump detected at 1.2 mm. The molecular clump is 0.45 pc in radius and its mass and H$_2$ volume density are 310 $M_{\sun}$ and 1.2$\times 10^{4}$ cm$^{-3}$, respectively. Two overdensities were identified within the clump in \hcn\ and \hco\ lines. A comparison of the LTE and virial masses suggests that the clump is collapsing in regions that harbor young stellar objects. An analysis of the molecular lines suggests that they are driving molecular outflows. } {} | IRAS\,08589$-$4714 (\radec\ = 09:00:40.5, --47:25:55) { can be} classified as an ultracompact \hii\ region (UCHII) according to the criteria by Wood and Churchwell (1989). {This source coincides with a massive dust clump detected in the IR continuum at 1.2 mm by \cite{Beltran_2006}. They estimated a luminosity of 1.8$\times$10$^{3}$ $L_{\sun}$ and a mass of 40 $M_{\sun}$ for this object.} \cite{Wouterloot_1989} detected emission in the $^{12}$CO(1$-$0) molecular line (angular resolution: 43\arcsec) toward the IRAS source at $V_{LSR} =$ +5.2 km\,s$^{-1}$. The molecular line shows an asymmetry in the blueshifted peak that is likely produced by noncentral self-absorption and a wing extended toward the red, which is a tracer of a potential outflow. \cite{Bronfman_1996} observed the source in the CS(2-1) molecular line at $V_{LSR} =$ +4.3 km\,s $^{-1}$, and \cite{Urquhart_2014} detected emission from the high density ammonium molecular tracer. The central velocity coincides with that of the CS line. With velocities in the range 4-5 \kms, the circular galactic rotation model by \cite{Brand_1993} predicts a kinematical distance of 2.0 kpc. An uncertainty of 0.5 kpc is assumed, adopting a velocity dispersion of 2.5 km\,s$^{-1} $ for the interstellar molecular gas. We report molecular line observations of the IRAS source using tracers of low and high density regions with the aim of studying the molecular gas content of the source, identifying dense gas clumps, finding massive YSOs linked to the clumps, and identifying possible outflows. | \label{Conclusions} IRAS 08589$-$4714 was observed in five molecular lines with the APEX telescope to characterize the molecular environment. An area of $\sim$\,150$''$ $\times$ 150$''$, centered on the IRAS source position, was covered in the (3$-$2) transition of $^{12}$CO, $^{13}$CO, C$^{18}$O, HCO$^{+}$, and HCN lines. A search for candidate YSOs in the WISE database allowed us to identify three IR point sources with characteristics of Class I/II objects according to the criteria by \cite{Koenig_2012} within the surveyed region. The molecular line profiles of $^{12}$CO, $^{13}$CO, and C$^{18}$O, show multiple velocity components and strong broadening effects toward sources 1 and 3. The spatial distribution of the CO emission shows the presence of a molecular clump of 0.45 pc in radius with mass and H$_2$ volume density of 310 $M_{\sun}$ and 1.4$\times 10^{4}$ cm$^{-3}$, respectively. The comparison between the LTE and virial mass indicates that the clump is collapsing. The HCO$^+$ and HCN spectra reveal molecular overdensities that are coincident with sources 1 and 3. Finally, we detect two possible outflows associated with each source. | 16 | 9 | 1609.01280 |
1609 | 1609.06719_arXiv.txt | {We present the first study of the isotropy of the all-sky distribution of morphological types of galaxies in the Local Universe out to around 200 Mpc using more than 60,000 galaxies from the HyperLeda database. We use a hemispherical comparison method in which by dividing the sky into two opposite hemispheres, the abundance distribution of the morphological types, $T$, are compared using the Kolmogorov-Smirnov (KS) test and by pointing the axis of symmetry of the hemisphere pairs to different directions in the sky, the KS statistic as a function of sky coordinates is obtained. For three samples of galaxies within around 100, 150, and 200 Mpc, we find a significant hemispherical asymmetry with a vanishingly small chance of occurring in an isotropic distribution. Astonishingly, regardless of this extreme significance, the observed hemispherical asymmetry for the three distance ranges is aligned with the Celestial Equator at the $97.1\%-99.8\%$ and with the Ecliptic at the $94.6\%-97.6\%$ confidence levels, estimated using a Monte Carlo analysis. Shifting $T$ values randomly within their uncertainties has a negligible effect on this result. When a magnitude limit of $B\leq 15$ mag is applied to the above mentioned samples, the galaxies within 100 Mpc show no significant anisotropy after randomization of $T$. However, the direction of the asymmetry in the samples within 150 and 200 Mpc and the same magnitude limit is found to be within an angular separation of 32 degrees from $(l,b)=(123.7, 24.6)$ with 97.2\% and 99.9\% confidence levels, respectively. This direction is only 2.6 degrees away from the Celestial North Pole. Unless the Local Universe has a significant anisotropic distribution of galaxy morphologies aligned with the orientation or the orbit of the Earth (which would be a challenge for the Cosmological Principle), our results show that there seems to be a systematic bias in the classification of galaxy morphological types between the data from the Northern and the Southern Equatorial sky. Further studies are absolutely needed to find out the exact source of this anisotropy.} | Galaxies appear in various shapes and are observed to have a range of different properties and one of the main ways of studying their evolution is to classify them based on those observed features. The most widely known classification of galaxies, which is famous as the ``Hubble's tuning fork''\footnote{Based on a classification originally published in \citet{reynolds} and later by \citet{hubble26}, and on the tuning fork of \citet{jeans}. Its famous form was later presented in \citet{hubble}. See \citet{block} for a historical note.}, categorizes the (mostly nearby) galaxies into a range of morphological types based on bulge/disk domination. This classification was later revised by \citet{devauc59} who added a numerical value to each Hubble type and also to the intermediate stages. The morphology of galaxies is closely linked to their physical properties and those of their environments \citep{sandage75,kormendy82,bergh98,abraham98,calvi12} and is one of the important tools for studying galaxy formation and evolution. Bulge formation scenarios depend on galaxy formation models \citep{hopkins2010,kroupa15,corredoira16,combes16}, distinct galaxy types are observed to have very different stellar populations and star formation rates \citep{grebel11} and different spectral properties \citep{sanchez}, and their inner structure like bar and bulge types is connected with their observed kinematics \citep{molaeinezhad}. For a study on the evolution of the Hubble sequence see \citet{serrano} and for a recent review on galaxy morphology see \citet{buta13}. Though the majority of the bright nearby galaxies fit in the Hubble's tuning fork, the high redshift galaxies detected by deep surveys and the low surface brightness dwarf galaxies whose number is increasing with various surveys inside and outside the Local Group (e.g. by \citeauthor{des} \citeyear{des} and \citeauthor{javanmardi16} \citeyear{javanmardi16}, respectively), are hard to be classified using the standard morphological classification system \citep{naim97,abraham01}. One of the most widely used classification schemes is that of \citeauthor{devauc59} compiled in the Third Reference Catalogue of Bright Galaxies (RC3) \citep{devauc91} from which many other catalogs extract the morphological types of different galaxies. As pointed out by \citet{makarov14}, visual inspection has been the main method of classification in RC3.\\ The need for automated morphology classification has been known since decades \citep{naim95} and has been exercised in recent years (see e.g. the recent studies by \citeauthor{company} \citeyear{company} and \citeauthor{kuminski16} \citeyear{kuminski16}, and references there in). \citet{nair10} and \citet{baillard11} used the data from the Sloan Digital Sky Survey (SDSS) and attempted to improve the visual classification of galaxy morphologies with the aim of paving the way for automated galaxy classification by providing training sets and calibration samples \citep[for other catalogs of galaxy morphologies see][and \citeauthor{psychogyios} \citeyear{psychogyios}]{fukugita07,shibuya,herrera,krywult, poudel}. In general, the goal is to achieve a catalog of the morphological types of the observed galaxies as complete and systematic-free as possible and to have a well-defined classification method applicable to future large galaxy surveys. Such a catalog is obviously crucial for studies of galaxy formation and evolution.\\ In this work, and for the first time, we search for possible deviations from isotropy in the all-sky distribution of the morphological types of galaxies within around 200 Mpc using the HyperLeda database. Based on the Cosmological Principle (generally understood to be confirmed by most of the observations so far), on sufficiently large scales the properties of the Universe, including the distribution of galaxy types, should be statistically isotropic. Therefore, deviations from isotropy can be a hint of systematic issues in the morphological classification of galaxies or in the homogenization of catalogs. \\ On the other hand, it is vital to re-inspect the assumption of isotropy with various observations \citep{maartens11} and this is one of the motivations of our study. If a significant deviation from cosmic isotropy is detected and confirmed by various data sets, cosmology will face a major paradigm change. During the last decade, probing isotropy in all-sky extragalactic data has become a vibrant research topic and continues to deliver interesting results. \cite{tegmark}, \citet{eriksen} and \citet{hansen04} reported some large scale anisotropies (hemispherical asymmetry and quadrupole-octopole alignment) in the Cosmic Microwave Background (CMB) radiation data from the \textit{WMAP} satellite. These CMB ``anomalies'' were recently confirmed by the \citet{planck} suggesting that they are not artifacts caused by the detectors or data-reduction procedures \citep[see also][and \citeauthor{mukherjee} \citeyear{mukherjee}]{akrami,rassat,copi15}. \citet{javanmardi15} found an anisotropy in the magnitude-redshift relation of high redshift Type Ia Supernovae (SNe Ia) that is significantly aligned with the direction of the CMB dipole and very close to the CMB quadrupole-octopole alignment \citep[for similar studies see][and references there in]{carvalho15,bengaly16,migkas,lin}. Also an inconsistency between the amplitude of the observed dipole in the distribution of radio galaxies and the value expected from the CMB dipole was reported in \citet{singal}, \citet{rubart} and \citet{tiwari}. For a recent review on various isotropy studies see \citet{zhao}. \\ The isotropy of the spatial distribution of galaxies has been probed by various authors \citep{gibelyou,yoon,appleby,alonso,bengaly16b}. These studies have found some mild anisotropies with different directions but none of them reported a significant deviation. In our analysis, we consider three distance ranges separately; galaxies with radial velocity less than 7,000, 10,000 and 14,000 km/s (equivalent to around 100, 150 and 200 Mpc from us, respectively\footnote{Assuming the Hubble constant value of $H_0=70.0$ km s$^{-1}$ Mpc$^{-1}$.}). Based on the standard model of cosmology, at such distance scales and specially beyond $\approx$150 Mpc \citep{marinoni12}, the distribution of galaxies should be statistically isotropic. For each distance range, we separate the galaxies by dividing the sky into two opposite hemispheres and compare their morphological type distribution using the Kolmogorov-Smirnov test. By pointing the axis of symmetry of our hemispheric cut towards different directions on the sky and repeating the test, we find the pair of hemispheres with the largest difference in the distribution of morphological types and quantify the significance of the difference.\\ The rest of this paper is organized as follows. In Section \ref{sec:data} we describe our sample from the HyperLeda database. Our method of analysis is explained in Section \ref{sec:method}. We present the results in Section \ref{sec:results}, discuss them critically in Section \ref{sec:dis} and finally we summarize and conclude in Section \ref{sec:conc}. | \label{sec:conc} We presented the first probe of isotropy of the distribution of morphological types of galaxies in the Local Universe. Using the de Vaucouleurs morphological types of more than 60,000 galaxies with radial velocity $V_{CMB}<$14,000 km/s (corresponding to within a distance of $\approx$200 Mpc) from the HyperLeda database, we searched for any directional difference in the distribution of morphological types. We used a hemispherical comparison method and by dividing the sky into two opposite hemisphere pairs, compared the frequency of morphological types, $T$, using a Kolmogorov-Smirnov test. The KS test was applied to hemisphere pairs with the axis of symmetry pointing at the centers of the pixels of a HEALPix grid. This gave us all-sky maps of the KS statistics, $D$. We performed this analysis for three radial velocity ranges, i.e. for galaxies with $V_{CMB}<$7,000, 10,000 and 14,000 km/s (corresponding to distances of about 100, 150 and 200 Mpc).\\ The directions $\hat{r}_{max}$ corresponding to the hemisphere pairs with the largest difference, $D_{max}$, were found to be similar for the three distance ranges. These directions are very far from the directions with the largest difference in the number of galaxies. Under the assumption that the galaxy morphologies should be statistically isotropic in the distance ranges under consideration, the probability of obtaining the observed difference or larger from the KS distribution, $p(D_{max})$, was obtained to be $\leq 10^{-133}$. In addition, using a Monte Carlo analysis and by creating 1000 isotropic realizations, the number of realizations with equal or larger $D_{max}$ was found to be zero and the largest values of $D_{max}$ obtained from the 1000 realizations were found to be an order of magnitude smaller than the observed values.\\ Interestingly, the hemispherical asymmetry that we found in the distribution of the morphological types of galaxies is aligned with both the Ecliptic and the Celestial Equator planes. The direction $\hat{r}_{max}$ for the sample with $V_{CMB}<$7,000 km/s is only $12^{\circ}.3$ and $14^{\circ}.7$ away from the Celestial and the Ecliptic North poles, respectively. Using our Monte Carlo analysis with 1000 isotropic realizations, we quantified the significance of the alignment with the Ecliptic to be at the 97.6\% confidence level, and that of the alignment with the Celestial Equator to be at the 97.1\% (both regardless of the extreme significance obtained from the KS test). It may be interesting for the reader to note that the hemispherical asymmetry in the CMB power spectrum discovered in the \textit{WMAP} data and confirmed by the \textit{Planck} satellite is also aligned with the plane of the Ecliptic \citep{planck}.\\ For the other two samples with $V_{CMB}<$10,000 and 14,000 km/s, the observed anisotropy is aligned with the Celestial Equator at the 99.8\% confidence level, with an angular separation of only $5^{\circ}.1$. In general, when looking at the sky distribution of morphological types of the whole sample ($V_{CMB}<14,000$ km/s), the northern sky is more populated by late type galaxies whereas early type galaxies are the dominant type in the southern sky. In particular, the largest difference in the abundance of morphological types is observed to be related to the galaxies with $9\leq T \leq 10$ (i.e. Sm and Im types) whose number is twice larger towards the Northern sky, and the galaxies with $-1\leq T < 0$ (i.e. S0$^+$ types) whose number is more than twice larger in the Southern sky. Excluding galaxies with large uncertainty on $T$ (i.e. $\sigma_T \geq 3.0$) does not affect the direction of the asymmetry. Also, repeating the analysis on the independent subsamples of galaxies with 7,000$<V_{CMB}$ (km/s)$<$10,000 and 10,000$<V_{CMB}$ (km/s)$<$14,000, yields similar direction for the largest difference in the distribution of $T$.\\ To increase the completeness of our sample, we applied a conservative magnitude limit and included only the galaxies with $B\leq 15.0$ mag in our analysis. This resulted in a decrease in the values of $D_{max}$, though still with a small probability of consistency with the null hypothesis of isotropy of $p(D_{max})\leq 10^{-21}$ for all the three distance ranges. For the sample with $V_{CMB}<$7,000 km/s, the direction of $\hat{r}_{max}$ remained unchanged with respect to the sample without the magnitude limit, however, for the samples with $V_{CMB}<$10,000 and 14,000 km/s and $B\leq 15.0$ mag the direction of $\hat{r}_{max}$ was found to be closer to the Celestial North Pole with only $2^{\circ}.6$ angular separation, i.e. the hemispherical asymmetry is even more aligned to the Celestial Equator than in the samples with the same distance ranges but without the magnitude limit.\\ Using a separate 1000 Monte Carlo realizations in each of which the $T$ values are shifted randomly within their uncertainties, we quantified the effect of random errors on the anisotropy in the distance limited samples to be negligible. However, for the $V_{CMB}<$7,000 km/s and $B\leq 15.0$ mag sample, shuffling $T$ within $\sigma_T$ can change the direction of anisotropy towards various directions in each realization, meaning that the anisotropy in this sample is not significant. On the other hand, in 97.2\% and 99.9\% of the realizations for $V_{CMB}<$10,000 and 14,000 km/s and $B\leq 15.0$ mag, the direction $\hat{r}_{max}$ is within $32^{\circ}.0$ of the observed direction showing that the anisotropy in these samples (especially in the latter one) is robust against the effect of random errors. For these two sample, the number of galaxies with $-5\leq T < -4$ and with $3\leq T < 4$ is respectively around 50\% and 40\% larger, and the number of galaxies with $-3\leq T < -2$ and $5\leq T < 6$ is respectively around 40\% and 34\% smaller, in the Northern sky. A simple shift (e.g. +1 or -1) in the $T$ values of one hemisphere does not decrease the value of $D_{max}$ (it actually increases it in most cases). Various combinations of shifts in $T$ around $-5\leq T < -2$ and around $3\leq T < 6$ can only partially alleviate the tension in the number of morphological types between north and south.\\ If this significant deviation from isotropy is real and not due to issues with the catalog and the classifications, it could mean that the galaxies in these two opposite directions have had different evolution and/or formation history which would be a major challenge for the Cosmological Principle. However, the fact that the asymmetry has an Equatorial North-South alignment indicates that most probably its source is a systematic bias in the classification of morphological types between the data of the northern and the southern sky possibly due to the fact that different telescopes (with different systematics) were used for observing these galaxies. \\ The morphological types cataloged in RC3 and HyperLeda database have been used for many studies and also some other cataloges and online databases extract the morphological information from them. Our results indicate that some of the studies based on this morphological information may need to be reconsidered. In addition, we should not forget that these classifications have been mostly done visually and it is necessary to put even more effort on making well-defined quantitative and automated approaches for morphological classifications. Further investigations though are indispensable to uncover the exact reason for the anisotropy we found in this study. \begin{figure} \begin{center} \includegraphics[scale=0.22]{t_allsky_equ_7000_btc-le-15.pdf} \includegraphics[scale=0.22]{t_allsky_equ_10000_btc-le-15.pdf} \includegraphics[scale=0.22]{t_allsky_equ_14000_btc-le-15.pdf} \caption{The Equatorial coordinate system distribution of all the galaxies in the HyperLeda database with $B\leq 15.0$ mag and measured $T$ and M$_B$, from top to bottom corresponding to $V_{CMB}<$7,000, 10,000 and 14,000 km/s, respectively. The color code is $T$, the empty parts are the region around the disk of the Milky Way, the plane of the Ecliptic is shown with a dotted line and the pair of hemispheres with the largest difference in the distribution of morphologies are divided by a red solid line. Though the sharp contrast seen in Figure \ref{fig:sky_dist_t} is not visible any longer, the hemispherical asymmetry obtained from the KS test is even more aligned with the Celestial Equator for galaxies with $V_{CMB}<$ 10,000 and 14,000 km/s. \label{fig:sky_dist_t_maglim}} \end{center} \end{figure} | 16 | 9 | 1609.06719 |
1609 | 1609.01503_arXiv.txt | We construct gravitational modifications that go beyond Horndeski, namely theories with extended nonminimal derivative couplings, in which the coefficient functions depend not only on the scalar field but also on its kinetic energy. Such theories prove to be ghost-free in a cosmological background. We investigate the early-time cosmology and show that a de Sitter inflationary phase can be realized as a pure result of the novel gravitational couplings. Additionally, we study the late-time evolution, where we obtain an effective dark energy sector which arises from the scalar field and its extended couplings to gravity. We extract various cosmological observables and analyse their behavior at small redshifts for three choices of potentials, namely, for the exponential, the power-law, and the Higgs potential. We show that the Universe passes from deceleration to acceleration in the recent cosmological past, while the effective dark-energy equation-of-state parameter tends to the cosmological-constant value at present. Finally, the effective dark energy can be phantom-like, although the scalar field is canonical, which is an advantage of the model. | Horndeski's theory \cite{Horndeski:1974wa} is the most general single-scalar tensor theory that has second-order field equations, both for the metric and the scalar field in four dimensions. It was originally discovered in 1974, then rediscovered independently \cite{Deffayet:2011gz}, and recently been brought back to attention \cite{fab4,Charmousis:2011bf,Kobayashi:2011nu} (for a review see \cite{Charmousis:2014mia}). The generality of the theory is reminiscent of Lovelock's theorem \cite{Lovelock:1971yv} and it comes as no surprise that many of its terms, especially those that involve derivative couplings of the scalar with curvature terms, come from a dimensional reduction of higher dimensional Lovelock theories \cite{VanAcoleyen:2011mj}. Note that having second-order field equations is crucial, in order to avoid Ostrogradski instabilities \cite{ostro,Woodard:2006nt,Woodard:2015zca}. The advantage of Horndeski cosmological models is that they are able to screen the vacuum energy coming from any field theory, assuming that after this screening the space should be in a de Sitter vacuum \cite{Martin-Moruno:2015bda,Martin-Moruno:2015eqa}. These models allow us to understand the current accelerated expansion of the Universe as the result of a dynamical evolution towards a de Sitter attractor \cite{Martin-Moruno:2015lha}. Thus, it was shown that Horndeski models with a de Sitter critical point for any kind of material content may provide a mechanism to alleviate the cosmological constant problem \cite{Martin-Moruno:2015kaa}. The cosmological scenario that results when considering the radiation and matter content was also studied, and it was concluded that their background dynamics is compatible with the latest observational data. Despite the huge interest in these theories, extensions of Horndeski's theory have also been recently discussed. In \cite{Gleyzes:2014dya} a new class of scalar-tensor theories was introduced, going beyond Horndeski's theory, where despite the fact that the equations of motion contain higher derivatives, they can be cast in a way that they contain only second-order ones \cite{Zumalacarregui:2013pma}. Additionally, these generalized theories were shown to be free of ghost instabilities in the unitary gauge \cite{Gleyzes:2014qga}, and later on this was also verified using the Hamiltonian formalism \cite{Domenech:2015tca,Langlois:2015cwa,Deffayet:2015qwa,Langlois:2015skt, Crisostomi:2016tcp}, due to the existence of a primary constraint which prevents the propagation of extra degrees of freedom \cite{Crisostomi:2016tcp} (see also \cite{Gao:2014soa} and \cite{Crisostomi:2016czh,Ezquiaga:2016nqo,BenAchour:2016fzp} for additional descriptions). We mention that these extended theories can also address the cosmological constant problem \cite{Babichev:2015qma} via a self-tunning mechanism, similarly to the analysis done in the original Horndeski theory for the so-called \textit{Fab Four} theory \cite{fab4,Charmousis:2011bf} (the cosmological aspects of the Fab-Four have been explored in \cite{Copeland:2012qf}). A detailed analysis of the cosmological self-tunning and local solutions in the context of beyond Horndeski theories has also been explored in \cite{Babichev:2016kdt}. Recently, it was shown that the two additional Lagrangian pieces, appearing in theories beyond Horndeski, could be re-expressed in a very elegant and compact way, by allowing the potentials to also depend on the kinetic term of the scalar field \cite{Babichev:2015qma}. One interesting subclass of Horndeski theory, which has been given much attention recently, includes the nonminimal (kinetic) coupling of matter to gravity by inserting derivative couplings between the geometry and the kinetic part of the scalar field \cite{Amendola:1993uh}, which leads to interesting new dynamical cosmological phenomena \cite{Sushkov:2009hk,Saridakis:2010mf}, including the existence of an effective cosmological constant \cite{Capozziello:1999uwa,Capozziello:1999xt}. The nonminimal derivative coupling leads to cosmological models with rich phenomenology, such as solutions containing a Big Bang, expanding Universes with no beginning, cosmological bounces, eternally contracting Universes, a Big Crunch, and a Big Rip avoidance \cite{Saridakis:2010mf,Granda:2010ex,Granda:2010hb,Sadjadi:2010bz, Sami:2012uh,Banijamali:2012kq,Bruneton:2012zk,Sheikhahmadi:2016wyz}. In particular, it was shown that one is able to explain in a unique manner both a quasi-de Sitter phase and an exit from it without any fine-tuned potential \cite{Sushkov:2009hk}. Furthermore, one can successfully describe the sequence of cosmological epochs without any fine-tuned potential \cite{Sushkov:2012za}. Using couplings of this type, it was found that in the absence of other matter sources or in the presence of only pressureless matter, the scalar field behaves as pressureless matter and its sound speed is vanishing \cite{Gao:2010vr}. These properties enable the scalar field to be a candidate of cold dark matter. It was also shown that if the kinetic term is coupled to more than one Einstein tensor, then the equation of state is always approximately equal to $-1$, independently from the potential flatness, and hence the scalar may also be considered a candidate for the inflaton. Tachyon models involving nonminimal derivative coupling have also been explored \cite{Shchigolev:2011nma,Banijamali:2011qb}, while Chaplygin gas model in this framework were studied in \cite{Granda:2011zy}. Moreover, the dynamics of entropy perturbations in the two-field assisted dark energy model with mixed kinetic terms was also studied in \cite{Karwan:2010xw}. Recently there has also been an investigation on how the derivative coupling can mimic cold dark matter at cosmological level and also explain the flattening of galactic rotation curves \cite{Rinaldi:2016oqp}. The inflationary context within this theory has been extensively analysed too. In the case of a power-law potential, and using the dynamical system method, all possible asymptotical regimes of the model were analysed \cite{Skugoreva:2013ooa}. It was shown that for sloping potentials there exists a quasi-de Sitter asymptotic corresponding to an early inflationary Universe. In contrast to standard inflationary scenario, the kinetic-coupling inflation does not depend on a scalar field potential and is only determined by the coupling parameter. In addition to this, there is a unique nonminimal derivative coupling of the Standard Model Higgs boson to gravity which propagates no more degrees of freedom than General Relativity sourced by a scalar field, and reproduces a successful inflating background within the Standard Model Higgs parameters and, finally, does not suffer from dangerous quantum corrections \cite{Germani:2010gm}. The slow-roll conditions have been found \cite{Granda:2011zk}, and the reheating temperature was obtained \cite{Sadjadi:2012zp,Sadjadi:2013na} (see also recent analyses in \cite{Gumjudpai:2016ioy} and \cite{Dalianis:2016wpu}). Furthermore, the cosmological perturbations originated at the inflationary stage were studied and the consistency of the results with observational constraints coming from Planck 2013 data were investigated \cite{Sadjadi:2013psa}. Moreover, these scenarios exhibit a gravitationally enhanced friction during inflation, where even steep potentials with theoretically natural model parameters can drive cosmic acceleration \cite{Tsujikawa:2012mk}, while being compatible with the current observational data mainly due to the suppressed tensor-to-scalar ratio. Finally, the gravitational production of heavy $X$-particles of mass of the order of the inflaton mass, produced after the end of inflation, was also studied \cite{Koutsoumbas:2013boa}, where it was found that this production is suppressed as the strength of the coupling is increased. A combined perturbation and observational investigation of the scenario of nonminimal derivative coupling between a scalar field and curvature was performed in \cite{Dent:2013awa}. Using Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB) observations, it was shown that, contrary to its significant effects on inflation, the nonminimal derivative coupling term has a negligible effect on the Universe acceleration, since it is driven solely by the usual scalar-field potential. Therefore, the scenario can provide a unified picture of early and late time cosmology, with the nonminimal derivative coupling term responsible for inflation, and the usual potential responsible for late-time acceleration. Finally, nonminimal derivative couplings to gravity have also been explored in a variety of extended theories of gravity. For instance, one can incorporate an additional coupling to the Gauss Bonnet invariant, obtaining rich cosmological behavior, with both decelerated and accelerated phases \cite{Granda:2011eh,Granda:2012hm}. Additionally, a large class of scalar-tensor models with interactions containing the second derivatives of the scalar field but not leading to additional degrees of freedom have also been extensively investigated \cite{Deffayet:2010qz}. These models exhibit peculiar features, such as an essential mixing of scalar and tensor kinetic terms, named kinetic braiding, and possess a rich cosmological phenomenology, including a late-time asymptotic de Sitter state, and a possible phantom-divide crossing, with neither ghosts nor gradient instabilities. Finally, the nonminimal derivative coupling to gravity has also been investigated in the context of the curvaton model \cite{Feng:2013pba}, or in the framework of $N = 1$ four-dimensional new-minimal supergravity \cite{Farakos:2012je}. In this work we are interested in investigating a theory that goes beyond Horndeski, based on a generalization of nonminimal derivative coupling. In particular, we consider the latter coupling and introduce an additional arbitrary coefficient-function of the field and its derivatives. We mention that this class is not included in Horndeski theory, since only specific combinations of it are allowed \cite{Deffayet:2011gz,Gleyzes:2013ooa,Gleyzes:2014rba}. This paper is outlined in the following manner. In Section \ref{sec1}, we present the action and deduce the gravitational field equations. In Section \ref{sec2}, we apply the developed formalism to a spatially flat Friedmann-Robertson-Walker (FRW) background metric, and present the modified Friedmann equations. The early-time cosmology is briefly analysed in Section \ref{sec3}, and the late-time evolution is considered in Section \ref{sec4}. In the latter, we study the full Friedmann equations and focus on important observables, by considering three well-known scalar potentials, such as the exponential, power-law and the Higgs potential. Finally, in Section \ref{sec5} we discuss our results and conclude. | \label{sec5} In this work we considered gravitational modifications that go beyond Horndeski, namely we presented theories with extended nonminimal derivative coupling, in which the coefficient functions depend not only on the scalar field but on its kinetic energy too. Such theories prove to be ghost-free in a cosmological background, and hence it is interesting to examine their cosmological implications. We first analyzed the cosmology of these novel gravitational modifications at early times, neglecting the matter sector, and we showed that a de Sitter inflation can be realized even in the absence of a potential term or of an explicit cosmological constant, and hence it is a pure result of the extended gravitational couplings. Additionally, we studied the behavior of these cosmological scenarios at late times, where we obtained an effective dark energy sector arisen from the scalar field and its extended couplings to gravity. We extracted various cosmological observables such as the Hubble function, the deceleration parameter, and the dark energy equation-of-state parameter, and we numerically investigated their evolution at small redshifts, for three choices of potentials, namely for the exponential, the power-law, and the Higgs one. As we showed, in all cases the Universe passes from deceleration to acceleration in the recent cosmological past, while the effective dark-energy equation-of-state parameter tends to the cosmological-constant value at present, in agreement with observations. Moreover, we showed that the phantom regime can be accessible too, which is an advantage of the scenarios since it is obtained despite the scalar field is canonical, i.e it results purely from the novel, extended gravitational couplings. The above features indicate that theories with extended nonminimal derivative could be a good candidate for the description of early and late time Universe. Hence one could proceed to more detailed analyses. In particular, one could use observational data from Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB) in order to constrain the coefficient functions, as well as the new coupling parameters. Additionally, one could perform a complete dynamical analysis, in order to by-pass the non-linearities of the equations, and extract the global behavior at asymptotically late times. Moreover, one should analyze the perturbations in a thorough way, in order to extract the values for inflation-related observables such as the spectral index and the tensor-to-scalar ratio. Furthermore, the issue of the influence of the scalar degree of freedom in local gravity is an open problem, however it lies beyond the scope of the present work. It would be interesting to examine whether there are any issues related to the fifth force, as it has been done previously on the original Horndeski theory \cite{DeFelice:2011th,Koyama:2013paa}. Finally, it could be interesting to apply extended nonminimal derivative couplings to bi-scalar theories, such as those proposed recently in \cite{Ohashi:2015fma,Naruko:2015zze,Saridakis:2016ahq,Saridakis:2016mjd}. These investigations lie beyond the scope of the present work, and are left for future projects. | 16 | 9 | 1609.01503 |
1609 | 1609.01818_arXiv.txt | \justify We have analyzed the temperature, velocity and density of H$_{2}$ gas in NGC~7023 with a high-resolution near-infrared spectrum of the northwestern filament of the reflection nebula. By observing NGC~7023 in the $H$ and $K$ bands at $R$ $\simeq$ 45,000 with the Immersion GRating INfrared Spectrograph (IGRINS), we detected 68 H$_{2}$ emission lines within the 1$\arcsec$ $\times$ 15$\arcsec$ slit. The diagnostic ratios of 2-1 S(1)/1-0 S(1) is 0.41$-$0.56. In addition, the estimated ortho-to-para ratios (OPR) is 1.63$-$1.82, indicating that the H$_{2}$ emission transitions in the observed region arises mostly from gas excited by UV fluorescence. Gradients in the temperature, velocity, and OPR within the observed area imply motion of the photodissociation region (PDR) relative to the molecular cloud. In addition, we derive the column density of H$_{2}$ from the observed emission lines and compare these results with PDR models in the literature covering a range of densities and incident UV field intensities. The notable difference between PDR model predictions and the observed data, in high rotational $J$ levels of $\nu$ $=$ 1, is that the predicted formation temperature for newly-formed H$_{2}$ should be lower than that of the model predictions. To investigate the density distribution, we combine pixels in 1$\arcsec$ $\times$ 1$\arcsec$ areas and derive the density distribution at the 0.002 pc scale. The derived gradient of density suggests that NGC~7023 has a clumpy structure, including a high clump density of $\sim$10$^{5}$ cm$^{-3}$ with a size smaller than $\sim$5 $\times$ 10$^{-3}$ pc embedded in lower density regions of 10$^{3}$$-$10$^{4}$ cm$^{-3}$. | \justify Molecular hydrogen H$_{2}$ is a major component of the interstellar medium (ISM). Rovibrational H$_{2}$ emission lines arise either in shock-heated regions or in photodissociation regions (PDRs). In PDRs, the far-UV (FUV) photons illuminate the transition layer between the ionized gas and the surface of the molecular cloud (\citealp{Tielens85a}; \citealp{Tielens85b}; \citealp{Black87}; \citealp{Sternberg89}; \citealp{Burton89}; \citealp{Draine96}; \citealp{Luhman97}; \citealp{Hollenbach99}). Molecular hydrogen emission has been observed in reflection nebulae (e.g., NGC~2023: \citealp{Gatley87}; \citealp{Sellgren86}; \citealp{Hasegawa87}; \citealp{Burton98}; \citealp{Martini99}; \citealp{McCartney99}; \citealp{Habart04,Habart11}; \citealp{Sheffer11}; \citealp{Fleming10}), the Orion nebula (\citealp{Hayashi85}; \citealp{Luhmank96,Luhmank98}; \citealp{Bertoldi99}; \citealp{Rosenthal00}; \citealp{Allers05}; \citealp{Habart04}), M17 (\citealp{Chrysostomou92,Chrysostomou93}; \citealp{Sheffer13}), and in planetary nebulae (e.g., Hubble 12: \citealp{Ramsay93}; \citealp{Hora96}; \citealp{Chrysostomou98}; \citealp{Marquez15}). In general, H$_{2}$ emission lines at $\nu$ = 0 and low rotational $J$ levels are good indicators of the gas temperature in the layer where they arise, while H$_{2}$ lines arising from higher excitation energy states are pumped by UV photons and are sensitive to the radiation field, gas temperature, and gas density. Theoretical PDR models predict the intensities and line ratios of H$_{2}$ in PDRs well (\citealp{Sternberg89}; \citealp{Draine96}; \citealp{Shaw05}; \citealp{Shaw09}). However, observations of rotational H$_{2}$ emission lines by ISO (the Infrared Space Observatory, \citealp{Kessler96}) indicate that the gas temperature derived from first rotational levels of H$_{2}$ is higher than that predicted in the PDR models (\citealp{Timmermann96}; \citealp{Fuente99}; \citealp{Bertoldi99}; \citealp{Draine99}; \citealp{Thi00}). Theoretical models have difficulty in explaining the existence of much warmer H$_{2}$ rotational emission zones. Modification of the heating and cooling processes, or H$_{2}$ formation rates, have been proposed to explain these discrepancies (\citealp{Habart04}; \citealp{Draine99}; \citealp{Allers05}). \citet{Weingartner99} suggest that radiation forces on dust grains can enhance the dust-to-gas ratio, thus increasing the gas heating rate. Discrepancies between the observed intensities of fluorescent H$_{2}$ emission from highly excited energy levels, or high rotational states, and those predicted by PDR models are a source of debate. \citet{Burton98} indicated that the observed intensities of high $\nu$ lines are weaker than model predictions. Yet, \citet{Bertoldi00} pointed out that the observed intensities of H$_{2}$ emission lines at very high energy states ($\nu$ = 9 and 12) were stronger than the values predicted by their PDR model. In addition, H$_{2}$ lines arising from high-$\nu$ or high-$J$ states are sensitive to UV field intensity and gas density. The difference between model results and observations may be explained by the effects of collisional de-excitation of the UV excited H$_{2}$, the formation H$_{2}$, or changing ortho-to-para ratios \citep{Burton98}. \citet{Burton92b} suggested that H$_{2}$ formation has a significant effect on the $\nu$ = 4 level from observations of NGC~2023 but the level distribution of newly-formed H$_{2}$ is unclear (\citealp{Draine96}, \citealp{Bertoldi99}). To date, most of the observations of fluorescently excited H$_{2}$ emission lines have been taken at low spatial and spectral resolution. Those spectra do not have enough resolution to robustly test H$_{2}$ line intensities. At high spatial and spectral resolution, H$_{2}$ emission lines resolve the physical structure of PDRs and test the predictions and assumptions of fluorescent PDR models. The reflection nebula NGC~7023 is illuminated by the Herbig B3Ve$-$B5 star HD~200775 (\citealp{Witt06}; \citealp{Alecian08,Alecian13}), with an effective temperature of 17,000 K \citep{Baschek82}, at a distance of $430_{-90}^{+160}$ pc \citep{van97}. The proximity of this object to us and the known properties of the exciting star make it one of the best objects for studying PDRs. Observations show that this nebula hosts different gas density structures, including dense clumps (n $\sim$ 10$^{6}$ cm$^{-3}$) embedded in lower density gas (n $=$ 10$^{4}$$-$10$^{5}$ cm$^{-3}$) (\citealp{Chokshi88}; \citealp{Sellgren92}; \citealp{Fuente96}; \citealp{Lemaire96}; \citealp{Martini97}; \citealp{Martini99}; \citealp{Fuente00}; \citealp{Takami00}; \citealp{An03}; \citealp{Fleming10}; \citealp{Habart11}; \citealp{Kohler14}; and \citealp{Pilleri12,Pilleri15}). At the wall of the cavity, PDR emission arises $\sim$42$\arcsec$ northwest, $\sim$55$\arcsec$ southwest, and $\sim$155$\arcsec$ east of the central illuminating star where the FUV field intensities of $G$ = 2600, 1500, and 250, respectively, in units of {\it G$_{0}$} $=$ 1.6 $\times$ 10$^{-3}$ erg cm$^{-2}$ s$^{-1}$ \citep{Pilleri12}. NGC~7023 has been observed in the near-infrared (near-IR) by many authors (e.g., \citealp{Sellgren86}; \citealp{Sellgren92}; \citealp{Lemaire96}; \citealp{Lemaire99}; \citealp{Martini97}; \citealp{Martini99}). In particular, low spectral resolution observations of H$_{2}$ emission (\citealp{Martini97,Martini99}) found high density clumps in the PDR regions of NGC~7023. In addition, \citet{Lemaire96} found small scale structure, less than 0.004 pc, based on high spatial resolution images of $\nu$ = 1-0 S(1) and S(2) rovibrational lines. The Immersion Grating Infrared Spectrograph (IGRINS) covers the whole $H$ and $K$ bands ($1.4$$-$$2.5$ $\mu$m) in a single exposure with a resolving power of $R$ $\simeq$ 45,000 (\citealp{Yuk10}; \citealp{Park14}). Since its commissioning in 2014, many interesting results in the ISM have been explored by (\citealp{Lee15}; \citealp{Sterling16}; \citealp{Afsar16}; \citealp{Oh16a}; \citealp{Oh16b}; \citealp{Lee16}; \citealp{Kaplan17}). With our IGRINS observations we can isolate the physical structure and properties in the observed region with high spectral and spatial resolution, and study many H$_{2}$ transitions simultaneously with exact spatial registration of the observations at different wavelengths. In this paper, we present detections of many H$_{2}$ lines from the northwestern (NW) filament of NGC~7023 and derive the distribution of temperature, column density, and ortho-to-para ratio of H$_{2}$ in the observed area. We also test the reliability of PDR models at the \ion{H}{2} and H$_{2}$ interface in NGC~7023. | \label{sum} We analyzed the near-infrared H$_{2}$ emission lines from the 1$\arcsec$ $\times$ 15$\arcsec$ region in the NW filament of the reflection nebula, NGC~7023. The high spatial and spectral resolution of IGRINS provides many H$_{2}$ rovibrational emission lines, which we have used to resolve the physical structure of the PDR, and look into details of the physical excitation mechanisms of the observed regions. With these observations we have determined: The diagnostic ratios of 2-1 S(1)/1-0 S(1) in regions A, B, and C are between 0.41$-$0.56. The ratios indicate that regions B and C are mostly UV excited, while the excitation mechanism in region A is partially collisional excitation or collisional de-excitation. The derived OPR of 1.63$-$1.82 also indicates that the observed H$_{2}$ lines are UV fluorescence. In addition, the distributions of the excitation diagrams confirm that the detected H$_{2}$ emission lines are from PDR. The exhibits of the gradient of kinetic temperature, velocity, and OPR of H$_{2}$ emission lines in the observed areas demonstrate a presence of the dynamic PDR front relative to the molecular cloud. We found the gradient density distribution within the observed regions. We suggest that the area has a clumpy structure, including a high density clump of $\sim$10$^{5}$ cm$^{-3}$ with a size smaller than $\sim$5 $\times$ 10$^{-3}$ pc embedded in lower density regions of 10$^{3}$$-$10$^{4}$ cm$^{-3}$ closer to the Herbig B3Ve$-$B5 star HD~200775. | 16 | 9 | 1609.01818 |
1609 | 1609.08614_arXiv.txt | We present a numerical simulation of the dynamical interaction between the proposed Planet Nine and a debris disk around the Sun for $4{\rm Gyr}$, accounting for the secular perturbation of the four giant planets in two scenarios: (a) an initially thin circular disk around the Sun (b) inclined and eccentric disk. We show, in both scenarios, that Planet Nine governs the dynamics in between $1000{\rm -5000{\rm AU}}$ and forms spherical structure in the inner part ($\sim1000{\rm AU}$) and inclined disk. This structure is the outcome of mean motion resonances and secular interaction with Planet Nine. We compare the morphology of this structure with the outcome from a fly-by encounter of a star with the debris disk and show distinct differences between the two cases. We predict that this structure serves as a source of comets and calculate the resulting comet production rate to be detectable. | \label{sec:Introduction} The structure of the outer solar system is complex and interesting. \citet{Oort1950} explained the isotropic distribution of long-period comets, by conjecturing with the existence of a Sun-centred spherical cloud with inner semi-major axis (sma) of $2\times10^{4}{\rm AU}$ and an outer sma of $2\times10^{5}{\rm AU}$. Later work by \citet{Marsden1978} extended the inner sma to $1\times10^{4}{\rm AU}$. Oort showed that the comet reservoir can easily be perturbed by frequent distant stellar encounter and the Galactic tides. These perturbations can drive the objects in the Oort cloud to the inner-solar system with eccentricities close to unity, yielding the constant rate of Sun grazing comets. \citet{Hills1981} suggested that the inner boundary of the Oort cloud reflects an observational bias, and the actual inner boundary is closer than $2\times10^{4}{\rm AU}$. He found that the critical sma $a_{c}$ that satisfies both the rate of stellar encounters and a typical comet lifetime is $a_{c}=2\times10^{4}{\rm AU}$. In this model, the inner Oort cloud (``Hills cloud'') continues inward of $2\times10^{4}{\rm AU}$ but stellar encounters that on this scale occur on a longer timescale than the typical lifetime of comets. Therefore, on these scales there should be a burst of comet showers after each stellar encounter. \citet{Duncan1987} studied numerically how the Oort and Hills clouds were formed. They focused on scattering by the planets to high sma and the interaction with the Galactic tides and stellar perturbations and found that the inner part of the Hills cloud is $\sim3\times10^{3}{\rm AU}$. Recently \citet{Batygin2016} reported intriguing evidence for the existence of a ninth planet in our solar system \citep{Batygin2016,Trujillo2014}. The proposed Planet Nine has a mass of $m_{9}=10m_{\oplus}$, sma of $a_{9}=700{\rm AU}$, eccentricity $e_{9}=0.6$, inclination to the ecliptic, $i_{9}=30^{\circ}$, and argument of the periapsis, $\omega_{9}=130^{\circ}$. Several other follow up studies supported the existence of Planet Nine by different methods \citep{Fienga2016,Holman2016,Bailey2016,Gomes2017,Lai2016}. Additionally, \citet{Li2016} calculated the survival rates and the interaction cross section of the proposed planet, and \citet{Lawler2016} investigated the impact of Planet Nine of the Kuiper belt objects. \citet{Perets2012a} described a mechanism of a planet captured from a different star system or a rouge planet, and predicted a wide, eccentric and inclined orbit of the captured planet. In this work we explore the interaction of a captured Planet Nine with a debris disk in two scenarios: (a) an initially flat ecliptic disk around the Sun and (b) an initially inclined and eccentric disk. The disk we consider represents the early debris disk, remnant from the Sun's formation era. For a short-term interaction of a planet with a ring of debris around it, see \citet{Lee2016}. We show that Planet Nine, due to its large sma, dominates the evolution of the outer disk between $1000-5000{\rm AU}$. This results in a spheroidal structure at $1100{\rm AU}\lesssim a_{{\rm TAUS}}\lesssim1500{\rm AU}$ where TAUS stands for ``Thousand AU Sphere''. For scenario (a) this structure is surrounded by an inclined disk aligned with Planet Nine's orbital plane and a warped disk towards the ecliptic plane. For scenario (b) the TAUS and inclined disk are created but less visible due to the initial conditions. This structure serves as a new source of Sun grazing comets, penetrating the inner solar system by long term secular evolution and dynamical interaction with Planet Nine. Our paper is organized as follows: in section~\ref{sec:Numerical-experiments} we describe the numerical simulation. In section~\ref{sec:Results} we describe the results of the numerical runs in comparison to the standard Hills cloud formation mechanism, i.e. a fly-by event in the early stages of the solar system. In section~\ref{sec:Implications-and-Discussion} we present the implications of TAUS to the morphology of the outer solar system as well as the rate and orientation of comets originating from this region. Finally, we summarize the results and their implications in section~\ref{sec:Summary}. | \label{sec:Implications-and-Discussion} Assuming that Planet Nine captured in the early stages of the solar system lifetime, it must have interacted with the disk of planetesimal around it. We chose the simplest structure of a debris disk that is initially flat and circular. Our initial conditions are conservative in the sense that disk, that is more inclined or eccentric would have a lower specific angular momentum and therefore would tend to be more influenced by Planet Nine. We have found that a spheroidal structure (TAUS) is created around the Sun at $\sim1200{\rm AU}$ and is surrounded by an inclined disk beyond $\sim1500{\rm AU}$. \subsection{New structure in the solar-system} \label{sub:New-structure-in} The TAUS is a spheroidal structure. It does not represent a perfect sphere because the particles' longitude of the ascending nodes is not uniformly distributed. This implies that some parts of the sphere are populated more than others. The number of particles in the TAUS is not well constrained, as it depends on the initial conditions, number of particles in the disk and their surface density distribution. Scenario (a) and (b) differ in the size of the TAUS; in scenario (a) TAUS end at $\sim1500\rm{AU}$ while in scenario (b) at $\sim3000\rm{AU}$. We assumed the power law index of the density distribution be $\gamma=-1$. Unlike the Oort cloud at $\sim10^{5}{\rm AU}$ or even the Hills cloud at$\sim10^{4}{\rm AU}$ the TAUS is relatively close and perhaps could be detected by a dedicated infrared survey. Figure \ref{fig:Loss Fraction} implies that in the early stage of the solar system evolution, around $300{\rm Myr}$ after formation, there was a spike in the rate of ejected objects from the disk into the inner solar systems, by up to two orders of magnitude relative to the current rate. This implies that there was an epoch during which a large number of objects from the region of $\sim1000{\rm AU}$ crossed the orbits of the inner planets, similarly to the ``heavy bombardment'' epoch described in the Nice model \citep{Levison2008}. \subsection{New origin of comets} \label{sub:New-origin-of} Some TAUS objects are excited to high eccentricities due to resonance and secular interaction with Planet Nine (see section \ref{sub:Ejected-particles}). These objects enter the solar system with eccentricities close to unity and therefore can be considered as comet candidates. Due to the specific orientation of the TAUS, we expect the comets to originate from $1100{\rm AU}\lesssim a_{{\rm comet}}\lesssim1500{\rm AU} (3000\rm{AU})$, and have the distribution of the specific argument of periapsis, longitude of the ascending node and inclination shown in Figures \ref{fig:Orbital-parameter-distribution-ejected} and \ref{fig:Comets_inclined}. This is a prediction of our model that can be tested observationally. For a total number of objects in the TAUS, $N$, one can estimate the rate of these events per year, as \begin{equation} \Gamma_{{\rm comet}}\sim10^{-2}-10^{-1}{\rm yr^{-1}}\left(\frac{N}{10^{12}}\right).\label{eq:comet rate} \end{equation} The Large Synoptic Survey Telescope (LSST) will survey 20,000 square degrees of the sky about 2,000 times over 10 years \citep{LSSTScienceCollaboration2009}. This survey is expected to discover $10,000$ new comets and potentially shed light on the size distribution of long period comets, which is currently unknown. The Starshot Breakthrough Initiatives could also explore the solar system (http://breakthroughinitiatives.org/Concept/3/). The gravitational interaction of the comet candidates with the solar systems planets was not explored here. An extensive study on this interaction and its observational signatures will be studied elsewhere. We calculated the dynamical imprint of Planet Nine on the outer solar system, assuming a flat circular initial debris disk out to a distance of $7000{\rm AU}$. We showed that orbits with $a<3000{\rm AU}$ interacted with Planet Nine over the lifetime of the solar system. Our main conclusions are as follows: \begin{itemize} \item A spheroidal structure, TAUS, forms at $\sim1200{\rm AU}$ due to MMRs with Planet Nine. \item TAUS is not uniformly distributed. \item The interaction of Planet Nine with the disk produces a qualitatively different morphology than a fly-by interaction with a passing star. \item Objects from TAUS that are excited to high eccentricities could become comets. \end{itemize} These predictions can be tested observationally with future surveys such as LSST or the Starshot Breakthrough Initiative. | 16 | 9 | 1609.08614 |
1609 | 1609.04963.txt | %% context heading (optional) {The $\rho$~Ophiuchi molecular complex and in particular the Lynds L1688 dark cloud is unique in its proximity ($\sim$130~pc), in its richness in young stars and protostars, and in its youth (0.5~Myr). It is certainly one of the best targets currently accessible from the ground to study the early phases of star-formation. Proper motion analysis is a very efficient tool for separating members of clusters from field stars, but very few proper motions are available in the $\rho$ Ophiuchi region since most of the young sources are deeply embedded in dust and gas.} % aims heading (mandatory) {We aim at performing a kinematic census of young stellar objects (YSOs) in the $\rho$ Ophiuchi F core and partially in the E core of the L1688 dark cloud.} % methods heading (mandatory) {We run a proper motion program at the ESO New Technology Telescope (NTT) with the Son of ISAAC (SOFI) instrument over nine years in the near-infrared. We complemented these observations with various public image databases to enlarge the time base of observations and the field of investigation to 0.5$\degr \times 0.5\degr$. We derived positions and proper motions for 2213 objects. From these, 607 proper motions were derived from SOFI observations with a $\sim$1.8 mas/yr accuracy while the remaining objects were measured only from auxiliary data with a mean precision of about $\sim$3 mas/yr.} % results heading (mandatory) {We performed a kinematic analysis of the most accurate proper motions derived in this work, which allowed us to separate cluster members from field stars and to derive the mean properties of the cluster. From the kinematic analysis we derived a list of 68 members and 14 candidate members, comprising 26 new objects with a high membership probability. These new members are generally fainter than the known ones. We measured a mean proper motion of ($\mu_{\alpha}\cos\delta$, $\mu_{\delta}$)=(-8.2, -24.3)$\pm$0.8 mas/yr for the L1688 dark cloud. A supervised classification was applied to photometric data of members to allocate a spectral energy distribution (SED) classification to the unclassified members.} % % conclusions heading (optional), leave it empty if necessary {We kinematically confirmed that the 56 members that were known from previous studies of the $\rho$~Ophiuchi F cluster and that were also part of our survey are members of the cluster, and we added 26 new members. We defined the evolutionary status of the unclassified members of the cluster. We showed that a large part (23) of these new members are probably brown dwarfs, which multiplies the number of known substellar objects in the cluster by a factor of 3.3.} | %=========================================================================== Stars are believed to form predominantly in groups that gradually lose their content in gas and disperse. Clusters are groups that remain stable against tidal disruption by the Galaxy or by passing interstellar clouds and that do not loose their members rapidly (evaporation time $> $100 Myr), whereas associations are looser, less stable groups \citep{Lada(2003)}. The youngest clusters and associations keep a fresh record of the physical and kinematic conditions involved in their formation. They are the precursors of the visible open clusters and of the dispersed galactic streams of stars. The youngest of the very young ($< 5$ Myr) clusters are still embedded in their parent cloud. Their properties and scientific interest in them have been reviewed by \cite{Lada(2003)} who listed 76 clusters. Since these clusters are extremely young, they should not have lost any stars yet because of the gravitational well of the embedding interstellar cloud. As in addition substellar objects have their peak luminosity in their first Myr, embedded clusters constitute excellent benchmarks for studies of the initial mass function, especially at the low-mass end. Strong absorption ($A_V \sim$ 10-50) by the remaining interstellar matter prevents studying embedded clusters at visible wavelengths, however. Near-infrared (NIR) observations are required and the NIR range is also best suited to studying the spectral energy distribution (SED) of the low-mass objects. Separating true brown dwarfs from field objects is not simple, however. The confirmed membership of objects to a forming cluster makes their identification as brown dwarfs much more reliable when it is joined to colour-magnitude and colour-colour diagrams because it fixes their distance and age within a narrow range. This method also produces the least biased samples in this mass range \citep{Luhman(2012b)}. Another debated question is the age determination of the youngest clusters and the possible age spread within a given cluster. Here secure membership is also crucial, as interloping field stars, especially at the very faint end of the luminosity distribution, can lead to misinterpretations (e.g. \cite{Soderblom(2014)}. The only membership analysis in clusters that does not depend on a hypothesis is the kinematic analysis which uses the proper motions of objects to separate cluster members from field stars. The main limitations of this method are the accuracy of the proper motions, the limiting magnitude of the observations, and obviously the distance of the cluster. Astrometric surveys of embedded clusters are still rare, however mainly because traditionally astrometry is performed at optical wavelengths and no good astrometric reference catalogue exists in the near IR, especially in K band. Even the astrometric space mission Gaia \citep{Perryman(2001),Mignard(2008),Lindegren(2010)} will not be able to provide proper motions in such obscure regions, and the ground-based astrometric works in the NIR therefore remain very unique. A variety of proper motion studies, including surveys of large regions have been conducted in the NIR (e.g. recently \cite{Dawson(2014)} with UKIDSS, \cite{Vrba(2004), Vrba(2012)} with USNO, \cite{Pena(2015), Pena(2016)}, \cite{Bouy(2013), Bouy(2015)}). The Upper Sco region is part of the Sco OB2 association, is probably physically related to the $\rho$ Ophiuchi region but somewhat older ($\sim 10$ Myr), is no longer embedded in its parent cloud and has low absorption ($A_V \sim$ 1--2). It has recently been the target of proper motion studies in the NIR (\cite{Luhman(2012a)}, \cite{Lodieu(2013)}). Very few studies of high-absorption regions ($A_V\sim$10-50) have been conducted because they require measuring positions in the less absorbed K band (2.2 $\mu$m; $A_K/A_V\sim$0.1). A very special case is the Galactic centre region ($A_V\sim$27; e.g. \cite{Eckart(2013)}, \cite{Fritz(2010),Fritz(2016)}; \cite{Do(2013),Boehle(2016)}), where very high precision astrometry in K band has been conducted, in particular to study stellar orbits around the central black hole. A wide-field study of the Carina region has also been conducted in K band by \cite{Preibisch(2014)} with proper motion accuracy $\sigma_{\mu} \sim$ 9--10 mas/yr. To improve our knowledge of the cluster membership, we decided to run a NIR proper motion program in the $\rho$ Ophiuchi complex. The $\rho$~Ophiuchi IR cluster is unique in its proximity (120-140~pc) \citep{Wilking(2008)}, in its richness in young stars and protostars, and in its youth because it is one of the youngest known clusters at $\sim$0.5~Myr \citep{Bontemps(2001), Andre(2007)}. It is certainly one of the best targets currently accessible for star-formation studies. Many works in the $\rho$~Ophiuchi region tried to assess the membership to the $\rho$~Ophiuchi complex through spectroscopy and photometry. In a pioneer work, \cite{Bontemps(2001)} performed a census of the population of young stars with IR excesses in this region using Infrared Space Observatory (ISO) \citep{Cesarsky(1996)} observations. \cite{Evans(2003)} delivered the c2d Spitzer \citep{Gallagher(2003)} final data release (DR4) providing observations and characterisation of sources from molecular cores to planetary disks in the mid- to far-infrared wavelengths. In a recent series of paper, \cite{Alves(2010), Alves(2012), Alves(2013)} established which objects belong to the low-mass population in the $\rho$ Ophiuchi molecular cloud through photometric observations in the NIR regime. With a spectroscopic follow-up, the authors characterised the brown dwarf population of an exhaustive list of candidates and detected disks around several brown dwarfs. All these works performed a census of the $\rho$ Ophiuchi complex, that relied on photometric data and extinction models. We present here a study of the proper motions in the direction of the sub-cluster $\rho$~Ophiuchi~F of the Lynds L1688 dark cloud that exhibits a clear association of young stars with the Ophiuchi~F molecular dense core. A study recently published by \citep{Wilking(2015)} also addressed proper motions in the $\rho$ Oph cluster (cores B-2,F,C-S,E and A-3, which partly overlaps the region covered here). This study used the same telescope and ASTROCAM as the USNO IR astrometry program (e.g. \cite{Vrba(2004), Vrba(2012)}) and is complementary to our work. By choosing to derive relative proper motions of objects with Ks $<16$, the authors reached a very good precision on proper motions ($\sigma_\mu \sim$ 1 mas/yr) that is well-suited to discussing the internal dynamics of the cluster. Here we attempt to derive positions and proper motions linked to the International Celestial Reference Frame (ICRF, \cite{Ma(1998)}) for objects with Ks $<$ 18-19 by using for the reduction catalogues that are defined in this frame. This is at the price of a degraded precision because there are few reference stars, but it enables us to address the question of cluster membership including substellar objects down to M9 spectral type. This paper is organised as follows. In Sect. 2 we present the observational material used for the proper motion measurements. In Sect. 3 we present the reduction procedure and the resulting proper motion catalogue. In Sect. 4 we present the astrometric validation of the proper motions, in Sect. 5 the kinematic analysis of the $\rho$~Ophiuchi~F/E cores and in Sect. 6 a tentative classification of its content. We discuss the nature of the new members in Sect. 7. Our conclusions are summarised in Sect.8. %**************************************************************************************************************** % Observations %**************************************************************************************************************** | %=========================================================================== With our astrometric observations we have determined the proper motions of 2213 stellar and sub-stellar objects in the $\rho$~Ophiuchi cluster region. We performed a kinematic membership analysis and derived a list of 82 kinematic \textit{members} and \textit{candidate} members, 26 of them are new members. We established in a reliable way the mean kinematic properties of the L1688 dark cloud ($\mu_{\alpha}\cos\delta$, $\mu_{\delta}$)=(-8.2, -24.3)$\pm$0.8 mas/yr and confirm that the velocity of this core is very similar to the one of the Upper Scorpius association. We assigned a SED class to the 53 unclassified kinematic members or candidates using a non-parametric random forests supervised method for classifying objects using any combination of the (J, H, K, w1, w2, w3 and w4) 2MASS and AllWISE colours. Nine objects are defined as class I, 52 as class II, and 21 objects as class III. We discovered 23 new BDs candidates as part of the cluster, potentially multiplying the number of known BDs in $\rho$ Ophiuchi cluster by 3.3. A few of them might be extremely low mass BDs in the 10 M$_{\rm Jup}$ regime. We were able to establish a secondary astrometric reference frame in the NIR in a region where reference stars in the large existing astrometric catalogues can hardly be found. The Gaia catalogue will undoubtedly be a valuable tool for studying associations of young stars, as Hipparcos was in its time. For a clear view of the star-formation processes and to access the youngest clusters (< a few Myr), infrared astrometric catalogues will be the crucial tool, however. The future space infrared astrometric mission Jasmine \citep{Jasmine(2005)} may in this respect be the first to bring insight into embedded star-forming regions. The secondary reference frame established in this work is a first step on this way. %**************************************************************************************************************** % ACKNOWLEDGMENTS %**************************************************************************************************************** | 16 | 9 | 1609.04963 |
1609 | 1609.04260_arXiv.txt | Blazars are high-energy engines providing us natural laboratories to study particle acceleration, relativistic plasma processes, magnetic field dynamics, black hole physics. Key informations are provided by observations at high-energy (in particular by {\it Fermi}/LAT) and very-high energy (by Cherenkov telescopes). I give a short account of the current status of the field, with particular emphasis on the theoretical challenges connected to the observed ultra-fast variability events and to the emission of flat spectrum radio quasars in the very high energy band. | Blazars \cite{UrryPadovani1995} represent a quite small but remarkably interesting fraction of the entire population of active galactic nuclei (AGN). Their defining phenomenology includes the presence of a compact unresolved radio core, with flat or even inverted spectrum, extreme (both in timescale and in amplitude) variability at all frequencies (but generally being more extreme at the highest frequencies), high degree of optical and radio polarization. The most distinctive feature, however, is the intense emission in the $\gamma$-ray band, often dominating the bolometric radiative power output. Indeed, blazars are the most numerous extragalactic $\gamma$-ray sources, both at GeV and TeV energies. The 4-years catalogue of {\it Fermi}-LAT (3FGL, \cite{3FGL}) reports more than 1600 blazars, to be compared with about 30 non-blazar extragalactic sources. Similar is the situation at higher energies. Cherenkov telescopes detected 62 blazars and only 6 non blazar sources (4 radiogalaxies and 2 starburst galaxies). Blazars are further divided in two subgroups, namely BL Lacertae objects, characterized by extremely weak or even absent emission lines in their optical spectra, and Flat Spectrum Radio Quasars (FSRQ), showing broad emission lines typical of quasars. FSRQs are generally more powerful than BL Lacs and their radiative output tend to be more dominated by the high-energy emission. BL Lacs, on the other hand, are characterized, on average, by larger energies of the emitted $\gamma$-ray photons and, in fact, are the large majority of the blazars detected at VHE. The peculiarities of blazars are explained assuming that these sources are AGN hosting a jet of plasma expelled at relativistic speeds (bulk Lorentz factors $\Gamma\approx 10-20$), whose axis points almost toward the Earth \cite{BlandfordRees1978}. In this geometry, the luminosity of the non-thermal continuum produced within the jet appears amplified by 3-4 orders of magnitude because of relativistic beaming effects and it easily outshines any other isotropic emission component associated to the active nucleus (accretion disk, emission lines, dust) or to the host galaxy. In the so-called unified model for radio-loud AGN, BL Lacs and FSRQ are the aligned counterpart of FRI (low power) and FRII (high power) radiogalaxies, respectively \cite{UrryPadovani1995}. The remarkably smooth SED of blazars, extending over the entire electromagnetic spectrum, from the radio band to $\gamma$-ray energies, is characterized by a typical ``double humped'' shape. The low energy component -- peaking, depending on the source, between the IR and the UV-soft X-ray band -- is understood as beamed synchrotron radiation of relativistic electrons (or, more generally, $e^{\pm}$ pairs), while for the origin of the second component -- reaching its maximum in the $\gamma$-ray band -- there is no complete consensus. In leptonic models (see e.g., \cite{Maraschi1992}), the emission is explained as inverse Compton (IC) radiation from the same leptons producing the low-energy component. In hadronic scenarios \cite{Boettcher2013}, instead, $\gamma$ rays are thought to originate from high-energy hadrons (protons) loosing energy through synchrotron emission (if the magnetic field is large enough, \cite{Aharonian2000}) or photo-meson reactions \cite{Mannheim1993}. In the latter case neutrino emission from the decaying charged pions is also foreseen. Despite huge efforts, several crucial aspects of the blazar phenomenology remains unclear and poorly understood. Even the physical process(es) responsible for the acceleration of the emitting relativistic particles is (are) not very clear. While until few years ago it was widely accepted that the main acceleration mechanism is the Fermi I-like process acting at shock fronts in the flow (diffusive shock acceleration), this view is now strongly debated. Another point subject to lively discussions is the location of the regions from which a large fraction of the observed radiation originates. This problem is particularly acute for FSRQ, in which the radiative environment surrounding the jet (influencing the IC process and causing the absorption of the $\gamma$-ray photons) varies with the distance from the central supermassive black hole. All these discussions have been recently triggered or revitalized by important observational results obtained in the past years by space ({\it AGILE}, {\it Fermi}) and ground-based (Cherenkov arrays) $\gamma$-ray detectors, in particular the evidence for ultra-fast ($\approx$ minutes) variability events and the detection of FSRQ at high ($E>10$ GeV) and very-high ($E>100$ GeV) energies. A quite interesting discussion concerns also the nature of the so-called {\it extreme} BL Lacs, showing extremely hard TeV continua and limited (if any) variability at high energy (e.g. \cite{Bonnoli2015} and references therein). It is also important to remind that, besides the astrophysical issues, the intense high-energy photon beams of blazars are ideal probes for the cosmological fields permeating the Universe (the extragalactic background light and the extragalactic magnetic field) or even to search for new particles (axion-like particles) or look for violation of the Lorentz invariance at high energies. For a discussion of these topics see De Angelis (these proceedings). In the following, after a sketch of the general framework, I will review in particular the observational status concerning the ultra-rapid variability and the VHE emission of FSRQ and the impact on our understanding of the functioning of blazars. \subsection{THE GENERAL FRAMEWORK AND ITS EPICYCLES} Blazar jets are hosted by an active nucleus comprising a central supermassive black hole ($M_{\rm BH}=10^8-10^9$ $M_{\odot}$) accreting matter from the surroundings. The phenomenological division between FSRQ and BL Lac objects can be interpreted as reflecting a more fundamental difference in the nature of the accretion flow in the two kind of sources, ultimately regulated by the accretion rate of the infalling material, e.g. \cite{CavaliereD'Elia2002,GMT09}. In FSRQ, which show bright thermal features (optical lines) and, in some cases, a bump at optical-UV frequencies (thought to mark the direct emission from the hot accreting gas), the accretion likely occurs through a radiatively efficient (optically thick) accretion disk. The luminous UV continuum emitted by the disk is responsible for the photoionization of the gas confined in ``clouds" rapidly orbiting the black hole and occupying the so-called broad line region (BLR). Various methods (in particular the reverberation mapping technique) allows us to locate the clouds at $\approx$0.1 parsec (the ``radius" of the BLR), which displays a clear dependence on the luminosity of the disk \cite{Bentz2006}. Farther out (1-10 pc), dust grains -- likely organized in the geometrical shape of a torus -- intercepts a fraction $\xi\approx 0.5$ of the disk continuum, reprocessing it as thermal IR emission (with temperature close to that corresponding to the sublimation of dust, $T\approx 10^3$ K). On the other hand, the lack of strong thermal components in BL Lac optical spectra is generally interpreted as an evidence that the accretion flow present in these sources is radiatively inefficient, as expected for accretion rates much smaller than that of quasars, when the accretion flow assumes the structure of an ADAF/ADIOS \cite{CavaliereD'Elia2002}. This scheme could allows one to explain the difference between the GeV $\gamma$-ray spectra of BL Lacs (generally displaying hard spectra) and those of FSRQ (characterized by soft -- photon index larger than 2 -- spectra), as the effect of the different radiative losses characterizing the high-energy electrons in the two kind of sources \cite{GMT09}. More generally, the interplay between radiative losses of the emitting electrons in the jet and the accretion rate onto the black hole could be at the base of the so-called ``blazar sequence" \cite{Ghisellini1998}, i.e. the trend between the observed luminosity (progressively increasing from BL Lacs to FSRQ) and the synchrotron and high-energy SED peak frequencies (decreasing from BL Lacs to FSRQ) displayed by the blazar population \cite{Fossati1998} -- but see \cite{Giommi2012} for an alternative view. While there is wide consensus about the general picture, there are several fundamental questions still awaiting an answer. The list of the most pressing problems includes the nature of the mechanism powering the jet, its structure, its composition ($ep$ or $e^{\pm}$?), the role of the magnetic field. Although not conclusive, the modelling of the emission from blazars -- especially of the high-energy emission -- is used as an effective tool to start to address several of these questions. The most adopted emission models (``one-zone") assume that a single region of the jet is responsible for the bulk of the observed emission.\footnote{This is strictly true for frequencies above the radio band ($\nu\gtrsim 100$ GHz). At lower frequencies it is expected that the source is opaque due to synchrotron-self absorption. Radio emission must therefore arise from larger, less compact, regions downstream of the blazar region \cite{BlandfordKonigl1979}.} This region could be identified with the shocked portion of the jet resulting from the collision of parts of the jet moving at different speeds (internal shocks), \cite{Spada2001}. One-zone models have the advantage to require a limited number of free parameters. The simplest version of the one-zone leptonic scenario is at the base of the the one-zone synchrotron-self Compton model, which assumes that the IC component is produced through the scattering of the synchrotron radiation produced by the same relativistic electrons. This framework is thought to be especially suitable to model BL Lacs, in which the possible external sources of soft target photons are negligible. The limited number of free physical parameters required by the one-zone SSC model allows us to uniquely determine them in case a well sampled SED is available \cite{BednarekProtheroe1997a, Tavecchio1998}. The application of the one-zone SSC model to the SED of the $\gamma$-ray emitting BL Lac (e.g., \cite{Tavecchio2010}) requires magnetic fields in the range 0.01-1 G, typical radius in the interval $10^{15}-10^{16}$ cm, Doppler factors\footnote{The relativistic Doppler factor $\delta$, determining the apparent amplification of the emission, is defined by $\delta=1/[\Gamma(1-\beta\cos\theta_{\rm v})]$, where $\Gamma$ is the jet bulk Lorentz factor, $\beta$ the jet speed and $\theta_{\rm v}$ the viewing angle.} in the interval $\delta=10-30$ and electron energies (at the SED peak) of the order of 0.1-1 TeV. If the jet is assumed to be conical, with typical aperture angle $\theta_{\rm j}\approx 5^{\rm o}$ the source radius can be translated into a distance from the central engine, $r_{\rm em}\approx 10^{16}-10^{17}$ cm, corresponding to $10^2-10^3$ gravitational radii. The results also suggest that most of BL Lac objects are quite inefficient in emitting the radiation, since the derived cooling time of the electrons is generally much longer then the dynamical timescale and thus most of the energy stored in the relativistic particles is lost \cite{TavecchioGhisellini2016, InoueTanaka2016}. Somewhat paradoxically for source emitting conspicuous VHE radiation, a relatively low efficiency is also found to characterize the acceleration process itself, see \cite{Baring2014}. Another important point is that the emission regions appear to be matter-dominated, the magnetic field providing a negligible contribution to the power carried by the jet (more on this later). For FSRQ the situation is more complex, due to the presence of several sources of external photons potentially involved in the IC emission \cite{GhiselliniTavecchio2009}. The ``canonical" choice is to locate the emission region within the BLR, thus exploiting for the IC emission the dense radiation field produced by the photoionized gas. Representative values of the magnetic field are larger than those of BL Lacs, in the range 1-10 G, but Doppler factors and radius are similar \cite{Ghisellini2010,GhiselliniTavecchio2015}. For FSRQ we have some control on the accretion power through the observed thermal components and it is thus possible to compare the power carried by the jet with that advected by the accreting material. The comparison show that, on average, jets carry a power larger than that associated to the infalling accretion flow, suggesting that the source of the jet power is the BH spin \cite{Ghisellini2010,Ghisellini2014}, as supported by recent GR-MHD simulations \cite{MAD}. Although very attractive, the one-zone model is clearly quite a simplification of the actual, likely complex, structure of the emitting region(s). A minimal approach is to add one or more supplementary emission regions, such as in two-component models, e.g. \cite{BarresdeAlmeida2014, Aleksic2015} A more refined modelling within the shock-in-jet scenario includes a shock front -- at which particles are accelerated -- moving within a ``background" plasma, in which the particles injected by the shock radiatively cool and emit \cite{Kirk1998,Chen2011,Chen2015}. Among all possible extensions of the one-zone framework (see below for other alternatives stemming from the interpretations of the ultra-rapid variability) I would like to mention in particular the {\it structured jet} model \cite{Ghisellini2005}, which envisages a flow with two components, a faster core (the {\it spine}) surrounded by a slower sheath or layer. This kind of structure has been advanced as a possible solution for several issues related to TeV emitting BL Lacs and to unify the BL Lacs and radiogalaxy populations \cite{Chiaberge2000, Meyer2011}. Direct radio VLBI imaging of jets both in low-power radiogalaxies and BL Lac objects (e.g. \cite{Nagai2014,Giroletti2004}), often showing a ``limb brightening" transverse structure, provides a convincing observational support to this idea, further supported by MHD simulations \cite{McKinney2006, Rossi2008}. For this system we expect an increased IC $\gamma$-ray luminosity, based on the fact that for particles carried by the faster (slower) region, the radiation field produced in the layer (spine) is amplified by the relative motion between the two structures \cite{Ghisellini2005, TavecchioGhisellini2008}. The spine-layer structure could be involved in the possible production of high-energy neutrino by BL Lac jets \cite{TGG14}. The structured jet scenario can also accommodate the high-energy emission (extending at VHE) observed in the misaligned jets of radiogalaxies, such as M87 \cite {TavecchioGhisellini2008} and NGC 1275 \cite{TavecchioGhisellini2014}, although the large opacity to $\gamma$ rays caused by the intense layer radiation field could be an issue. | 16 | 9 | 1609.04260 |
|
1609 | 1609.05785_arXiv.txt | {The Sun provides us with the only spatially well-resolved astrophysical example of turbulent thermal convection. While various aspects of solar photospheric turbulence, such as granulation (one-Megameter horizontal scale), are well understood, the questions of the physical origin and dynamical organization of larger-scale flows, such as the 30-Megameters supergranulation and flows deep in the solar convection zone, remain largely open in spite of their importance for solar dynamics and magnetism. Here, we present a new critical global observational characterization of multiscale photospheric flows and subsequently formulate an anisotropic extension of the Bolgiano-Obukhov theory of hydrodynamic stratified turbulence that may explain several of their distinctive dynamical properties. Our combined analysis suggests that photospheric flows in the horizontal range of scales between supergranulation and granulation have a typical vertical correlation scale of 2.5 to 4 Megameters and operate in a strongly anisotropic, self-similar, nonlinear, buoyant dynamical regime. While the theory remains speculative at this stage, it lends itself to quantitative comparisons with future high-resolution acoustic tomography of subsurface layers and advanced numerical models. Such a validation exercise may also lead to new insights into the asymptotic dynamical regimes in which other, unresolved turbulent anisotropic astrophysical fluid systems supporting waves or instabilities operate.} | The solar photosphere is the stage of many spectacular (magneto-)hydrodynamic phenomena and it provides us with a unique observationally well-resolved example of strongly nonlinear thermal convection, one of the most common fluid instabilities and transport processes encountered in nature and astrophysics \citep{kupka07}. While some aspects of solar thermal turbulence, such as granulation, are now well understood \citep{nordlund09}, we still lack definitive answers to many important questions, such as how the turbulence organizes on large scales, and how it interacts with and amplifies magnetic fields or transports quantities such as angular momentum or magnetic flux \citep{miesch05,charbonneau14}. The most direct observational characterization of flows connected to the solar convection zone at scales larger than the granulation has been achieved through measurements of Doppler-projected velocities at the photospheric level. In particular, even a simple visual inspection of Doppler images of the quiet Sun clearly reveals the pattern of supergranulation flow ``cells'', whose trademark signature is a peak around $\ell\sim 120-130$ (35~Megameters, Mm) in the spherical-harmonics energy spectrum of Doppler-projected velocities \citep{hathaway2000,williams14, hathaway15}. The physical origin of this supergranulation is widely debated \citep{rieutord10a}. In particular, while the idea that supergranulation-scale flows may just be a manifestation of some form of thermal convection has a long history, it has often been dismissed due to the seeming lack of photometric intensity contrast at the same scales \citep{langfellner16}. Besides, there is as yet no general consensus on local helioseismic estimates of the amplitude, depth and structure of subsurface flows on this scale \citep{nordlund09,rieutord10a,gizon10,svanda13,degrave14,svanda15} -- or in fact on any scale larger than that \citep[see, e.g.,][]{hanasoge12,gizon12,hanasoge15,greer15,toomre15,greer16}. Numerical simulations of the problem have, until recently, also been quite limited. While their results have not led to clear-cut results and conclusions \citep[see reviews by][]{miesch05,nordlund09,rieutord10a}, many of them suggest that meso- to supergranulation-scale flows have a convective (buoyant) origin \citep[e.g.,][]{rincon05,lord14,cossette16}. In this article, we attempt to make further progress on this problem using the high-quality observations of the solar photosphere provided by the Solar Dynamics Observatory (SDO) and a new theoretical analysis. In Sect.~\ref{obs}, we present a global observational analysis of multiscale photospheric vector flows reconstructed from quasi-full disc Doppler and photometric data from SDO using a tracking technique. This analysis subsequently leads us in Sect.~\ref{theory} to formulate a theory of anisotropic turbulent convection that may explain several distinctive dynamical properties of these flows. As further argued in Sect.~\ref{consistency}, the combined results consistently suggest that photospheric flows in the horizontal range of scales in between supergranulation and granulation operate in a strongly anisotropic, self-similar, buoyant dynamical regime. Connections between these results and earlier work, as well as future perspectives, are discussed in Sect.~\ref{discussion}. The main text of the article is focused on results. The technical details of the data processing and analysis are provided in the two Appendices. | } We have presented a set of consistent arguments suggesting that turbulent flows at scales larger than granulation are a manifestation of statistically self-similar, strongly nonlinear convection in the bulk adiabatic layer below the solar surface. While the classic idea that supergranulation has a convective origin has usually been dismissed due to the seeming lack of photometric intensity contrast at the corresponding scales at the surface \citep{langfellner16}, helioseismology suggests that relative temperature fluctuations of approximately a few percent are present underneath the surface at such scales \citep{duvall97}, in line with our calculation in Sect.~\ref{thestimate}. Besides, all existing large-scale simulations, including those with radiative transfer that do not display any ``meso'' or ``super'' scale intensity contrast at the surface, exhibit a strong buoyancy driving and flows at such scales in the bulk of the convective layer \citep[e.~g.,][see also \cite{rieutord10a}, Fig. 12]{rincon05,nordlund09,bushby14,lord14,cossette16}. Importantly, in these simulations, these scales are significantly larger than those of the most unstable linear modes of the system at rest, and the statistical order at such scales emerges dynamically in the nonlinear regime. If there are indeed significant thermal fluctuations associated with supergranulation-scale convection in the first few Mm below the surface, they may be blanketed by the thinner thermal granulation boundary layer, or could be optically thick due to the extreme dependence of opacities on temperature \citep{nordlund09}. Our theory also suggests that anisotropic supergranulation-scale convection, although it generates strong horizontal flows, does not significantly contribute to the transport of thermal energy due to the weakness of the radial component of the velocity field at such scales. We do not have a quantitative answer as to what determines the spectral supergranulation break, and can only offer directions. Our theory predicts that thermal fluctuations increase with scale as $E_\theta(\ell)\propto \ell^{-9/5}$ in the nonlinear convection regime. However, there is a physical limit to how large such fluctuations can be, which could determine the maximum buoyant scale at which the self-similar scaling should break down. This limit should be related in some way to the maximum entropy fluctuations that can be injected into the adiabatic layer and, therefore, to the details of granulation and of the superadiabatic thermal boundary layer at the surface. This conclusion appears to be in line with the recent numerical simulations of this problem by \cite{cossette16}, which show that the thickness of the boundary layer has a strong effect on the energy-containing scale of the turbulent energy spectra. However, other physical explanations \citep[e.g.,][]{featherstone16} cannot be ruled out at this stage. Based on our experience with this data, the observational analysis and comparison with theory presented above are close to the limit of what is achievable with a combination of surface tracking and direct Doppler measurements given their disparate natures. Future progress will probably come from acoustic tomography \citep{toomre15} and advanced numerical models. While somewhat speculative at this stage, our theory, including \equs{vscaling}{tscaling}, may soon be testable using such tools. An important question in this respect asks to what extent pristine power-law scalings derived from simple dynamical arguments can be realized in systems such as the photospheric transition region, where a variety of physical processes become intertwined. The qualitative implications of such analyses could be wider than the solar context. They may notably provide us with fundamental insight into the structure of anisotropic turbulence in general \citep[e.g.,][]{nazarenko11}, as well as into turbulence in more distant, unresolved astrophysical systems supporting anisotropic waves or instabilities, such as stellar interiors \citep{zahn08,miesch09}, galaxy clusters \citep{zhuravleva14} and accretion discs \citep{walker16}. | 16 | 9 | 1609.05785 |
1609 | 1609.07263_arXiv.txt | {We discuss the potential of a next generation space-borne Cosmic Microwave Background (CMB) experiment for studies of extragalactic sources. Our analysis has particular bearing on the definition of the future space project, \mission\!\!, that has been submitted in response to ESA's call for a Medium-size mission opportunity as the successor of the \textit{Planck} satellite. Even though the effective telescope size will be somewhat smaller than that of \textit{Planck}, \mission will have a considerably better angular resolution at its highest frequencies, since, in contrast with \textit{Planck}, it will be diffraction limited at all frequencies. The improved resolution implies a considerable decrease of the source confusion, i.e.~substantially fainter detection limits. In particular, \mission will detect thousands of strongly lensed high-$z$ galaxies distributed over the full sky. The extreme brightness of these galaxies will make it possible to study them, via follow-up observations, in extraordinary detail. Also, the \mission resolution matches the typical sizes of high-$z$ galaxy proto-clusters much better than the \textit{Planck} resolution, resulting in a much higher detection efficiency; these objects will be caught in an evolutionary phase beyond the reach of surveys in other wavebands. Furthermore, \mission will provide unique information on the evolution of the star formation in virialized groups and clusters of galaxies up to the highest possible redshifts. Finally, thanks to its very high sensitivity, \mission will detect the polarized emission of thousands of radio sources and, for the first time, of dusty galaxies, at mm and sub-mm wavelengths, respectively. } | \label{par:intro} Although not specifically designed for the observation of extragalactic sources, space-borne experiments aimed at investigating the Cosmic Microwave Background (CMB) have the potential to bring breakthroughs also in this field. An investigation of the impact on studies of extragalactic sources of the project named the Cosmic Origins Explorer plus (COrE$+$), submitted in response to ESA's call for the 4th Medium-size mission (M4) opportunity, was carried out by Ref.~\cite{DeZotti2015}. Various options were considered, with effective telescope sizes of $\simeq 1\,$m, $1.5\,$m and 2\,m, and a frequency range from 60 to 1200\,GHz. A proposal for ESA's 5th Medium-size mission (M5) is envisaging an instrument (named \mission\!\!) with a baseline telescope size of 1.2\,m and 19 frequency channels, distributed over the 60--600\,GHz frequency range. A decrease or an increase of the telescope size to 1\,m and to 1.5\,m, respectively, were also considered. These options will be referred to as \mission\!\!100 and \mission\!\!150. For the \mission\!\!150 configuration we will also consider the added value of an extension of the frequency range to 800\,GHz. % Since the analysis by Ref.\cite{DeZotti2015} was completed, considerable relevant new data have become available and more detailed studies have been carried out, motivating an update for the 5th Medium-size mission (M5) proposal. In particular, most analyses of the \textit{Planck} data have now been published, giving much clearer predictions for the capabilities of next generation CMB experiments. The plan of the paper is the following. In Sect.~\ref{sec:counts_intens} we present a new assessment of the expected counts of the various classes of extragalactic sources in total intensity. In Sect.~\ref{sect:protocluster} we highlight the \mission potential for detecting galaxy proto-clusters during their early evolutionary phase when they did not yet possess the hot intergalactic medium allowing detection via their X-ray emission and/or the Sunyaev-Zeldovich (SZ) effect. As shown in Sect.~\ref{sect:cluster}, \mission will also provide unique information on the evolution of the star-formation rate (SFR) in virialized clusters. Section~\ref{sect:CIB} deals with the information provided by \mission surveys on the Cosmic Infrared Background (CIB), while the effect of bright sub-mm lines on the power spectra measured in different frequency intervals and the possibility of counts being estimated in lines are considered in Sect.~\ref{sect:lines}. In Sect.~\ref{sect:counts_pol} we discuss counts in polarized flux density and report the results of new simulations aimed at determining the \mission detection limits in polarization, showing that \mission will provide a real breakthrough in this field. Our main conclusions are summarized in Sect.~\ref{sec:conclusions}. Throughout this paper we adopt the fiducial $\Lambda$CDM cosmology with the best-fit values of the parameters derived from \textit{Planck} CMB power spectra, in combination with lensing reconstruction and external data: $H_0=67.74\,\hbox{km}\,\hbox{s}^{-1}\,\hbox{Mpc}^{-1}$; $\Omega_\Lambda=0.6911$; and $\Omega_{\rm m}=0.3081$ \cite{Planck_parameters2015}. This work is part of a series of papers that present the science achievable by the CORE space mission. The performance requirements and the mission concept are described in \cite{Delabrouille2017}. The instrument is described in \cite{deBernardis2017}. Reference \cite{Ashdown2017} explores systematic effects that may represent a threat to the measurement accuracy. Reference \cite{Remazeilles2017} discusses polarised foregrounds and the $B$-mode component separation. The constraints on cosmological parameters and fundamental physics that can be derived from CORE measurements are discussed in \cite{DiValentino2016} while the constraints on inflationary models are discussed in \cite{Finelli2016}. References \cite{Bartlett2017} and \cite{Melin2017} deal large-scale structure and cluster science, respectively, while \cite{Burigana2017} addresses the effect on the CMB of the observer's peculiar motion. \begin{table} \centering \caption{Estimated $4\,\sigma$ \mission detection limits, $S_{\rm d}$ (mJy), for 4 effective telescope sizes. The values of $S_{\rm d}$ were derived from the simulations described in Ref.~\protect\cite{DeZotti2015} and refer to regions of low Galactic emission. } \vskip12pt \begin{tabular}{rrrrr} \hline \hline \multicolumn{1}{l}{$\nu$\,(GHz)} & \multicolumn{1}{c}{1\,m} & \multicolumn{1}{c}{1.2\,m} & \multicolumn{1}{c}{1.5\,m} & \multicolumn{1}{c}{2\,m} \\ \hline 60 & 197.9 & 147.1 & 94.4 & 55.3 \\ 70 & 200.1 & 149.5 & 94.8 & 55.3 \\ 80 & 197.1 & 148.1 & 92.7 & 53.9 \\ 90 & 190.5 & 144.2 & 89.1 & 51.6 \\ 100 & 182.0 & 138.7 & 84.8 & 49.0 \\ 115 & 169.5 & 130.7 & 78.6 & 45.2 \\ 130 & 156.7 & 122.2 & 72.5 & 41.7 \\ 145 & 144.7 & 114.0 & 66.9 & 38.4 \\ 160 & 131.8 & 105.3 & 61.0 & 35.1 \\ 175 & 119.2 & 96.6& 55.2 & 31.9 \\ 195 & 104.9 & 86.9& 49.0 & 28.8 \\ 220 & 91.6 & 78.1& 43.8 & 26.4 \\ 255 & 80.7 & 70.9& 41.1 & 26.0 \\ 295 & 81.0 & 73.1& 44.1 & 29.1 \\ 340 & 90.5 & 83.2& 51.5 & 34.9 \\ 390 & 104.5 & 97.1& 60.7 & 41.6 \\ 450 & 121.8 & 113.7 & 71.3 & 49.3 \\ 520 & 140.7 & 131.5 & 82.5 & 57.6 \\ 600 & 150.5 & 139.8& 90.4 & 63.5 \\ \hline\hline \end{tabular} \label{tab:detlim} \end{table} | \label{sec:conclusions} In spite of their sensitivities, now approaching fundamental limits, modern space-borne CMB experiments have provided only shallow surveys of extragalactic sources. The key limitation is source confusion, i.e. intensity peaks due to random positive fluctuations of faint sources that mimic real individual sources. The rms confusion noise scales approximately as the square of the {FWHM} (see figure~3 of \cite{DeZotti2015}). Hence the substantially better resolution of the diffraction-limited \mission telescope, compared to \textit{Planck}, especially at the highest frequencies, offers a large advantage in terms of detection limits. The advantage is further boosted in terms of the number of detected sources by the steepness of the source counts. The power of all-sky surveys at mm and sub-mm wavelengths has already been vividly demonstrated by \textit{Planck}, which has detected thousands of dusty galaxies as well as many hundreds of extragalactic radio sources in this spectral range, which is difficult or impossible to explore from the ground and only lightly surveyed by other space missions. \textit{Planck} photometry proved to be crucially important to characterize the synchrotron peak of blazars. Surveys at mm wavelengths are the most effective way to select this class of sources, which, among other things, constitute the overwhelming majority of the identified extragalactic $\gamma$--ray sources detected by the \textit{Fermi}-LAT. \textit{Planck} data have also provided key information on the energy spectrum of relativistic electrons responsible for the synchrotron emission with interesting implications for their acceleration mechanisms. \textit{Planck} detected several of the most extreme, strongly-lensed, high-$z$ galaxies, with estimated gravitational amplifications, $\mu$, of up to 50; \mission will detect thousands of strongly lensed galaxies. Strong lensing offers the opportunity of detailed follow-up studies of high-$z$ galaxies with otherwise unattainable sensitivity: the exposure time to reach a given flux density limit varies as $\mu^{-2}$ and, since lensing conserves surface brightness, it stretches the image, thus effectively increasing the angular resolution by a substantial factor (at least in one dimension). Moreover, \textit{Planck} proved to be a powerful probe of the evolution of the large-scale structure of the Universe in the phase when early-type galaxies, the dominant population in rich clusters and groups of galaxies, were forming the bulk of their stars. Beyond strongly expanding the samples of source populations detected by \textit{Planck}, \mission will open new windows. In particular, it will: (i) provide unbiased, flux limited samples of dense proto-cluster cores of star-forming galaxies, some examples of which were detected by \textit{Herschel}; (ii) allow a detailed investigation, via direct detections complemented with stacking analysis, of the evolution of the star-formation rate in virialized galaxy clusters detected by surveys of the SZ effect (including those carried out by \mission itself) or by X-ray surveys; (iii) provide the spectrum of the CIB dipole anisotropy, which contains important information on the average CIB intensity spectrum; and (iv) provide the first blind high frequency census of the polarization properties of radio sources and of star-forming galaxies. | 16 | 9 | 1609.07263 |
1609 | 1609.09081_arXiv.txt | The XQ-100 survey provides optical and near infrared coverage of 36 blindly selected, intervening damped Lyman $\alpha$ systems (DLAs) at $2<$\zabs{}$<4$, simultaneously covering the Mg\sion{} doublet at $\lambda \lambda$ 2796, 2803 \AA{}, and the Ly$\alpha$ transition. Using the XQ-100 DLA sample, we investigate the completeness of selecting DLA absorbers based on their Mg\sion{} rest-frame equivalent width (\Mgeqw{}) at these redshifts. Of the 29 DLAs with clean Mg\sion{} profiles, we find that six (20\% of DLAs) have \Mgeqw{}$<0.6$ \AA{}. The DLA incidence rate of \Mgeqw{}$<0.6$ \AA{} absorbers is a factor of $\sim5$ higher than what is seen in $z\sim1$ samples, indicating a potential evolution in the Mg\sion{} properties of DLAs with redshift. All of the \Mgeqw{}$<0.6$ \AA{} DLAs have low metallicities ($-2.5<[M/H]<-1.7$), small velocity widths (\vninety$<50$ \kms{}), and tend to have relatively low N(\HI{}). We demonstrate that the exclusion of these low \Mgeqw{} DLAs results in a higher mean N(\HI{}) which in turn leads to a $\sim7$\% increase in the cosmological gas density of \HI{} of DLAs at $2<$\zabs{}$<4$; and that this exclusion has a minimal effect on the \HI{}-weighted mean metallicity. | Quasar (QSO) absorption line systems provide an excellent probe of the evolution of the \HI{} gas content over cosmic time. Of the many classes of QSO absorption line systems, damped Lyman $\alpha$ systems (DLAs) are the highest \HI{} column density absorbers, defined as having log N(\HI{})$\geq 20.3$ \citep{Wolfe86,Wolfe05}. Although fewer in number compared to lower N(\HI{}) counterparts (such as subDLAs; $19.0<$logN(\HI{})$<20.3$), DLAs dominate the \HI{} column density distribution from \zabs{}$\sim5$ to the present epoch and are used to trace the cosmological gas density of \HI{} (\omegaDLA{}), eventually fuelling future generations of star formation \citep[][]{Lanzetta95,Rao00,StorrieLombardi00,Peroux03,Prochaska05DR3,Rao06,Prochaska09, Noterdaeme12,Zafar13,Crighton15, Neeleman16,SanchezRamirez16}. At absorption redshifts where the \HI{} is observed in optical bands (\zabs{}$\gtrsim1.5$), \omegaDLA{} remains relatively constant with redshift \citep[for the most recent results at these redshifts, see][]{Crighton15,SanchezRamirez16}. At $z\sim 0$, \omegaDLA{} is currently best measured from 21 cm emission line surveys of galaxies \citep{Zwaan05,Martin10}. Between these $z\sim 0$ measurements and \omegaDLA{} measured in DLAs at $z \sim 1.5$, the gas content of galaxies has only evolved by a factor of $\sim2$ \citep{Zwaan05, SanchezRamirez16}. Despite well constrained estimates of \omegaDLA\ at $z \sim 0$ and at $z>2$, studying the nature of the \omegaDLA{} evolution between $0.3\lesssim$\zabs{}$\lesssim1.5$ is challenging, as the Ly$\alpha$ transition shifts into the ultraviolet, requiring expensive space-based observations; and 21 cm emission becomes extremely difficult to detect \citep{Rhee16}. In an effort to improve the efficiency of space telescope observations, it has become common practice to pre-select candidate DLAs based on the rest-frame equivalent widths (EWs) of the associated Mg\sion{} $\lambda \lambda$ 2796, 2803 \AA{} absorption observed in the optical \citep[][hereafter referred to as R00 and R06, respectively]{Rao00,Rao06}. With the inclusion of absorbers satisfying a Mg\sion{} 2796 \AA{} EW cut of \Mgeqw{}$\geq0.3$ \AA{} (R00), the final statistical sample compiled in R06 contains \emph{no} DLAs at \zabs{}$\sim1$ with \Mgeqw{}$<0.6$ \AA{}\footnote{ Although some DLAs with \Mgeqw{}$<0.6$ \AA{} have been previously identified \citep[e.g.][R06]{Peroux04}.}. \omegaDLA{} derived from \zabs{}$\sim1$ DLA samples pre-selected from Mg\sion{} (\omegaDLA{}$\sim7.5\times10^{-3}$) are consistent with the \zabs{}$\gtrsim 2$ value, implying strong evolution at the lowest redshifts (R06). However, a recent `blind' archival survey of DLAs at $z\sim1$ derived a value of \omegaDLA{} a factor of 3 lower than R06 ($\sim2.5\times10^{-3}$), and consistent with 21 cm results at $z\sim0$ \citep{Neeleman16}. This tension in \omegaDLA{} has led to suggestions that Mg\sion{} DLA pre-selection may be biased, possibly leading to high \omegaDLA{} \citep[][]{Peroux04,Zavadsky09,Neeleman16}. In this Letter, we investigate the nature of Mg\sion{} selection of 36 DLAs at $2<$\zabs{}$<4$ from the XQ-100 Legacy Survey (P.I. S. Lopez). The blind nature of the XQ-100 DLA sample combined with simultaneous observations of Ly$\alpha$ and Mg\sion{} $\lambda$ 2796 \AA{} provide an excellent test of the effectiveness of the Mg\sion{} selection technique for comparison with low redshift statistics. | The vast majority of DLAs identified at \zabs{}$\sim1$ have \Mgeqw{}$\geq0.6$ \AA{} (R00, R06). For example, in a recent compilation of 369 Mg\sion{} systems (Rao et al. in prep), there are 70 Mg\sion{} absorbers with $0.3\leq$\Mgeqw{}$< 0.6$ \AA{}, but only one of these is a DLA (S. Rao private communication). As a result, many works have typically used \Mgeqw{}$\geq0.6$ \AA{} to pre-select potential DLA systems (R00, R06). Moreover, R06 used the EW of Fe\sion{} 2600 \AA{} (\Feeqw{}) to aid in identifying DLAs, and found that their DLA sample is confined to \fracMgFe{}$<2$, whereas their subDLAs span a larger range of \fracMgFe{}. Figure \ref{fig:MgSelection} shows how the XQ-100 measurements of \Mgeqw{} (left panel), the ratio \fracMgFe{} (middle panel), and $D$-index (right panel) vary with logN(\HI{}). Starting with the left panel of Figure \ref{fig:MgSelection}, we find that six\footnote{Two of these six DLAs with \Mgeqw{}$<0.6$ \AA{} have previously been observed in the literature (DLAs towards J1108+1209 and J0134+0400), but previous observations have not covered the Mg\sion{} absorption. We also note that one of the excluded proximate DLAs (J0034+1639 at \zabs{}$=4.25$) does not satisfy the \Mgeqw{}$\geq0.6$ \AA{} cut. This DLA is metal-poor ([M/H]$=-2.40$) and has an equivalent width \Mgeqw{}$=0.344\pm 0.013$ \AA{}.} (20\% of the sample) of the XQ-100 DLAs with measured \Mgeqw{} have \Mgeqw{}$<0.6$ \AA{} (dashed line). However, \emph{all DLAs pass the \Mgeqw{}$\geq0.3$ \AA{} cut}. The middle panel of Figure \ref{fig:MgSelection} shows the \fracMgFe{} ratio for the XQ-100 and R06 samples, and demonstrates that 30\% of the XQ-100 DLAs with Fe\sion{} 2600 \AA{} measurements have \fracMgFe{}$>2.0$ (DLAs above dashed line). Only one DLA (J0034+1639, \zabs{}$=3.69$) does not satisfy both \Mgeqw{}$\geq0.6$ \AA{} and \fracMgFe{}$<2$ restrictions. Lastly, the right panel of Figure \ref{fig:MgSelection} shows the $D$-index \citep[i.e. \Mgeqw{} normalized by the velocity width of the line ${\rm \Delta V}$; from][]{Ellison06} for the XQ-100 DLAs as a function of logN(\HI{}). The minimum $D$-index cuts required for absorbers to be DLA candidates are derived from \citet[their Table 2]{Ellison06}, and are tabulated in Table \ref{tab:EWs}. The $D$-index cuts are based on the resolution of the X-Shooter spectrum at each Mg\sion{} line (assuming a FWHM resolution of R$=5300$). We note that the $D$-index of the XQ-100 DLAs does recover all the DLAs (i.e. points are above the grey band in the right panel of Figure \ref{fig:MgSelection}). \begin{figure*} \begin{center} \includegraphics[width=\textwidth]{tb_EWs.pdf} \caption{ \emph{Left Panel}: The rest-frame \Mgeqw{} as a function of logN(\HI{}) for the XQ-100 DLAs (large circles; colours indicate metallicity) and R06 data (black squares). For reference, the \Mgeqw{} cuts (\Mgeqw{}$\geq0.3$ \AA{} and \Mgeqw{}$\geq0.6$ \AA{}) are shown as horizontal lines (dotted and dashed; respectively). Six of the \ndla{} XQ-100 DLAs show \Mgeqw{}$<0.6$ \AA{}. \emph{Middle Panel}: The ratio \fracMgFe{} as a function of logN(\HI{}) for the XQ-100 sample and R06 data. The region below the dashed line at \fracMgFe{}$\leq2.0$ characterizes the Mg\sion{}-selected DLAs in the R06 sample, while the dotted line divides subDLAs from DLAs. 30\% of the XQ-100 DLAs do not exhibit \fracMgFe{}$<$2. \emph{Right Panel}: The $D$-index (\Mgeqw{}/${\rm \Delta V}$) as a function of logN(\HI{}) for the XQ-100 DLA sample. The grey horizontal band represents the range of possible $D$-index cuts for the XQ-100 data. All XQ-100 DLAs pass their respective $D$-index cuts.} \label{fig:MgSelection} \end{center} \end{figure*} \emph{Are the properties of \Mgeqw{}$<0.6$ \AA{} DLAs different to the higher EW systems?}\quad The colour bar in Figure \ref{fig:MgSelection} indicates the metallicity of each DLA in the XQ-100 sample \citep{Berg16}. Interestingly, the DLAs whose \Mgeqw{}$<0.6$ \AA{} all have low metallicities, below [M/H]$<-1.7$. The mean metallicity of the XQ-100 DLAs subsample with \Mgeqw{}$\geq0.6$ \AA{} is [M/H]$=-1.42\pm0.03$\footnote{All errors for mean quantities are derived using a bootstrap technique with one million iterations. The errors on individual measurements were assumed to be Gaussian.}, whereas the entire sample has a mean metallicity of [M/H]$=-1.60\pm0.02$. However, the \HI{}-weighted metallicity that is generally used to trace the evolution of DLA metallicity with cosmic time \citep[e.g.][]{Pettini99,Rafelski12} is negligibly affected, increasing from [M/H]$=-1.47\pm0.03$ for the full sample to [M/H]$=-1.43\pm0.03$ when \Mgeqw{}$<0.6$ \AA{} absorbers are excluded. In addition to the metallicity, we checked for other DLA properties dependent on \Mgeqw{}$\geq0.6$ \AA{} selection. Figure \ref{fig:dists} shows the distributions of [M/H], \vninety{} \citep[which has been suggested as a proxy for mass, e.g.][]{Prochaska97,Haehnelt98}, \zabs{}, and logN(\HI{}) for the XQ-100 DLAs for a selection cut of \Mgeqw{}$\geq0.6$ \AA{}. DLAs passing the equivalent width selection cut are shown as the shaded region, whilst DLAs that fail the selection cut are shown as the red line. DLAs with \Mgeqw{}$<0.6$ \AA{} tend to show low metallicities, low logN(\HI{}), and low \vninety{} widths with respect to DLAs with \Mgeqw{}$\geq0.6$ \AA{}. These properties are consistent with a `mass-metallicity' relationship seen in DLAs \citep{Ledoux06,Jorgenson10,Moller13,Neeleman13, Christensen14}, where narrower metal lines are typically found in lower metallicity systems. The dependence of \Mgeqw{} on velocity width has been previously identified in other works \citep[][R06]{Nestor03,Ellison06,Murphy07}. The $D$-index defined in \cite{Ellison06} potentially corrects for this bias towards low \vninety{}, as the EW is normalized by the velocity width of the line. As demonstrated by the right panel of Figure \ref{fig:MgSelection}, the $D$-index provides a more complete DLA sample relative to a fixed Mg\sion{} EW cut by including those absorbers with low metallicity and \vninety{}. \begin{figure*} \begin{center} \includegraphics[width=\textwidth]{tb_dists.pdf} \caption{XQ-100 DLA distribution of metallicity ([M/H]), \vninety{}, \zabs{}, and logN(\HI{}) (from left to right). Different histograms are shown for DLAs that pass (shaded grey region) or fail (red line) the equivalent width cut \Mgeqw{}$\geq0.6$ \AA{}. The simple \Mgeqw{}$\geq0.6$ \AA{} cut clearly misses low metallicity systems, with small logN(\HI{}) and \vninety{}. For reference, the \HI{} distribution of the R06 DLAs is shown as the dashed line. For visual purposes the R06 distribution is scaled down by a factor of $\sim1.8$ to match the number of DLAs in the shaded region.} \label{fig:dists} \end{center} \end{figure*} \emph{What are the implications for the cosmological context of DLAs at $2\leq$\zabs{}$\leq4$?}\quad The typical approach to calculating \omegaDLA{} at high redshifts is to sum the total N(\HI{}) observed over the total redshift path (X) for all QSOs observed, i.e. \begin{equation} \label{eq:sum} \Omega_{\rm HI} = \frac{H_{0} \mu m_{H}}{c \rho_{crit}} \frac{\sum N(\HI{})}{\sum \rm{X}}. \end{equation} If DLAs are missed from a Mg\sion{}-selected sample, the computed \omegaDLA{} from Eq. \ref{eq:sum} would be underestimated, as the sum of N(\HI{}) would exclude the low Mg\sion{} EW DLAs while $\sum \rm{X}$ remains unaffected. For the entire XQ-100 DLA sample, \omegaDLA{} would be \emph{underestimated} by $\sim5$\% if \Mgeqw{}$<0.6$ \AA{} DLAs were excluded. However, R06 used a different approach to compute \omegaDLA{}, that combines the number density of DLAs ($n_{\rm DLA}$; observed along Mg\sion{} absorber sightlines in R06) and the average N(\HI{}) of DLAs ($\langle {\rm N(\HI{})} \rangle$), \begin{equation} \label{eq:Mg} \Omega_{\rm HI}(z) = \frac{H_{0} \mu m_{H}}{c \rho_{crit}} \frac{E(z)}{(1+z)^{2}} n_{\rm DLA}(z) \langle N(\HI{}) \rangle. \end{equation} With the R06 formalism, the calculation of \omegaDLA{} depends on two measured variables: the frequency of absorbers and their mean N(\HI{}). As shown in Fig. \ref{fig:dists}, in the XQ-100 sample, DLAs with \Mgeqw{}$<0.6$ \AA{} tend to have lower N(\HI{}) than higher EW absorbers. If the low EW systems were not included in the XQ-100 sample statistics then $\langle$N(\HI{})$\rangle$ and thus \omegaDLA{} would be overestimated. However, this effect in our sample is minimal: the mean log($\langle$ N(\HI{}){}$\rangle$) of the XQ-100 sample increases minimally from $20.98\pm0.03$ to $21.01\pm0.03$ ($\sim7$\%) upon exclusion of the DLAs with \Mgeqw{}$<0.6$ \AA. Therefore, for a constant $n_{\rm DLA}$, \omegaDLA{} would be \emph{overestimated} by $\sim7$\% when low EW systems are excluded. \emph{Comparison with the properties of Mg\sion{} in DLAs at \zabs{}$\leq1.5$.}\quad In the latest compilation of 369 \zabs{}$\sim1$ Mg\sion{} absorbers (Rao et al.~in prep) only 1 out of 70 (1.4$_{-1.2}^{+3.3}$\%\footnote{The subscript and superscript represent the Poisson 1$\sigma$ confidence limits derived from Tables 1 and 2 in \cite{Gehrels86}.}) systems with $0.3\leq$\Mgeqw{}$<0.6$ \AA{} is confirmed to be a DLA (S. Rao, private communication). In contrast, $\sim7_{-2}^{+4}$\% of $0.3\leq$\Mgeqw{}$<0.6$ \AA{} systems are DLAs\footnote{We note that the DLA incidence rate for \Mgeqw{}$>0.6$ \AA{} absorbers in the XQ-100 sample is $\sim14_{-3}^{+4}$\% (compared to the $\sim22$\% seen at \zabs{}$\sim1$; R06).} (Lopez et al.~in prep). The DLA incidence for the low \Mgeqw{} regime is a factor of $\sim 5$ higher at \zabs{}$\sim 3$ than at \zabs{}$\sim 1$. These incidence rates indicate a potential evolution in the Mg\sion{} properties of DLAs as a function of redshift. Whereas DLAs at low \zabs{} are almost uniquely associated with \Mgeqw{} $\geq0.6$ \AA{}, at high redshift a significant fraction of DLAs (20\% in our sample) can have lower values. The known relationship between \Mgeqw{} and velocity spread \citep[e.g.][]{Ellison06}, as well as the relatively low values of measured \vninety{} and low metallicity of the \Mgeqw{}$<0.6$ \AA\ DLAs in the XQ-100 sample indicate that low \Mgeqw{} absorbers may preferentially be probing low mass galaxies, which are less prevalent at low redshift. This is consistent with the lack of low metallicity DLAs at low redshift \citep{Rafelski14, Berg15II}. What is currently unknown is whether, despite their rarity, low Mg\sion{} EW DLAs at low \zabs{} show the same distribution of properties (metallicities, \vninety{}, N(\HI{})) as high \zabs{} DLAs of the same \Mgeqw{}. Based on our high \zabs{} results, we caution that DLAs that have been selected based on a high Mg\sion{} EW cut have the potential to be biased against low metallicity systems. Indeed, \cite{Kulkarni07} have argued that Mg\sion{} pre-selection could select against DLAs with [M/H]$<-2.5$. Nonetheless, the low frequency of such systems at low redshifts (and their tendency towards lower N(\HI{})) means that \omegaDLA{} and the \HI{}-weighted metallicity is unlikely to be significantly affected. | 16 | 9 | 1609.09081 |
1609 | 1609.00733_arXiv.txt | Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin ({\it Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy} {\bf 31}, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular. | \noindent There is a general interest in constructing magnetohydrostatic models of the solar atmosphere. These models describe large-scale, long-lived, magnetic structures like sunspots ({\it e.g.} \citealp{1958IAUS....6..263S}), prominences ({\it e.g.} \citealp{1957ZA.....43...36K}), coronal loops ({\it e.g.} \citealp{1982SoPh...76..261Z}), the coronal magnetic field on global scales ({\it e.g.} \citealp{1986ApJ...306..271B,2008A&A...481..827R}), and low-lying magnetic structures in the upper photosphere and lower chromosphere ({\it e.g.} \citealp{2015ApJ...815...10W}). Unfortunately, the equations of the model --- the magnetohydrostatic equations --- are a set of nonlinear partial differential equations that defy general analytic solution. Only a handful of idealized analytic solutions are known, and existing numerical methods are typically limited to two dimensions. Solution methods for the general three-dimensional equations are lacking, which limits the scope of the modeling. In this article, we present a new numerical scheme for treating the general three-dimensional problem. Our method is an extension of the Grad-Rubin method \citep{24756} to include a finite gravity force.\\ \noindent The magnetohydrostatic equations describe a magnetized plasma in which magnetic, pressure, and external forces are in mechanical equilibrium. In the solar context, the external force is usually gravity, implying that the condition for mechanical equilibrium is \begin{equation} \mathbfit J \times \mathbfit B - \nabla p + \rho \mathbfit g = \mathbfit 0 \end{equation} \citep{9559}, where $\mathbfit J$ is the electric current density, $\mathbfit B$ is the magnetic field, $p$ is the gas pressure, $\rho$ is the gas density, and $\mathbfit g$ is the local acceleration due to gravity. The special case with $\mathbfit g = \mathbfit 0$ is of interest to modeling fusion plasmas ({\it e.g.} \citealp{4317418,CHODURA198168,greenpaper}), but in this article we consider only the case with a finite gravity force, which is more relevant to modeling the Sun. Since $\mathbfit J$ is the curl of $\mathbfit B$ in accordance with Amp{\'e}re's law, the force-balance equation is nonlinear through the Lorentz force term. It is this nonlinearity that makes the magnetohydrostatic equations difficult to solve.\\ \noindent Magnetohydrostatic models find various applications in solar physics ({\it e.g.} \citealp{1958IAUS....6..263S,1957ZA.....43...36K,1982SoPh...76..261Z, 1986ApJ...306..271B,2008A&A...481..827R,1986A&A...170..126S, 1971SoPh...18..258P}). One area where they are becoming increasingly relevant is local helioseismology, where magnetohydrostatic sunspot models are used as the background atmosphere to magnetohydrodynamic wave propagation simulations ({\it e.g.} \citealp{2006ApJ...653..739K,2008SoPh..251..589K, 2009ApJ...690L..72M,2011SoPh..268..293C}). The present modeling is based on axisymmetric magnetohydrostatic solutions (see \citealp{2010SoPh..267....1M} for a full list of models) and so is limited to monopolar sunspots. To construct atmospheres for more complex sunspot groups requires more general solution methods. \\ \noindent Data-driven modeling of the coronal magnetic field is another area where three-dimensional magnetohydrostatic models have potential applications. The coronal magnetic field is often ``extrapolated'' from vector-magnetogram data based on a nonlinear force-free model ({\it e.g.} \citealp{2002A&A...392.1119R,2008A&A...488L..71T, 2012SoPh..276..133G,2012SoPh..278...73V}). However, it is known that the magnetogram data represent the magnetic field at a height in the atmosphere where pressure and gravity forces, which the force-free model excludes, are significant \citep{1995ApJ...439..474M, 2001SoPh..203...71G,2005ApJ...631L.167S}. This inconsistency is a potential source of problems for the modeling (\citealp{2009ApJ...696.1780D},\citeyear{2015ApJ...811..107D}), and a self-consistent approach based on a magnetohydrostatic model has been suggested as a solution but never applied to actual data \citep{2003SoPh..214..287W,2009ApJ...696.1780D}. To the best of our knowledge, the only magnetohydrostatic extrapolations performed to date have been based on a special class of ``linear'' magnetohydrostatic solution that assumes a particular functional form for the current density \citep{1992ApJ...399..300L,2000A&A...356..735P}. These solutions have been used to extrapolate the coronal magnetic field from magnetogram data for several studies ({\it e.g.} \citealp{1998SoPh..183..369A,1999A&A...342..867A,2000PhDT.........2P,2015ApJ...815...10W})\\ \noindent The nonlinearity of the magnetohydrostatic equations complicates their solution, and no method is known for constructing general analytic solutions. Particular analytic solutions, however, can be derived by simplifying the equations at the expense of generality. One strategy is to reduce the dimensionality of the problem by assuming self-similarity \citep{1958IAUS....6..263S,1980SoPh...67...57L}, translational symmetry \citep{1982SoPh...76..261Z}, or rotational symmetry \citep{1981JApA....2..405U}. Another approach, which produces three-dimensional solutions, is to impose a special form on either the current density \citep{1985ApJ...293...31L, 1997A&A...325..847N,2000A&A...356..735P} or the magnetic tension \citep{1984ApJ...277..415L}. All these solutions are special cases --- the general three-dimensional magnetohydrostatic problem remains unsolved.\\ \noindent A numerical approach can in principle address the shortcomings of the analytic methods. With this goal, a number of numerical methods have been developed, although a majority have only been implemented in two dimensions. These methods include magnetohydrodynamic relaxation methods ({\it e.g.} \citealp{1984A&A...139..426D}), fixed-point iteration methods ({\it e.g.} \citealp{1986ApJ...302..785P,1990ApJ...365..764P}), and nonlinear multigrid methods applied to the magnetohydrostatic equations formulated in inverse coordinates ({\it e.g.} \citealp{1990JCoPh..89..490C}). This list is not exhaustive: \citet{2001SoPh..201..289H} provide a more complete list of references.\\ \noindent Less work has been done on numerical methods for the three-dimensional problem. \citet{2001SoPh..201..289H} develop a three-dimensional inverse coordinate nonlinear multigrid method. Their method also solves the free-surface problem for a flux rope bounded by a current sheet. The optimization method that was originally introduced by \citet{2000ApJ...540.1150W} for solving the nonlinear force-free equations has been extended to treat the magnetohydrostatic equations in Cartesian \citep{2003SoPh..214..287W} and spherical coordinates \citep{2007A&A...475..701W}. \\ \noindent In this article we develop a fixed-point method for solving the general three-dimensional magnetohydrostatic equations in a Cartesian box. In particular, we extend the method of \citet{24756} to model a gravity force. The original Grad-Rubin method solves the magnetohydrostatic equations without gravity by replacing the nonlinear equations by a system of linear equations for each unknown variable, which are solved interactively. The linearization is achieved by constructing nonlinear terms using variables from previous iterations. For example, the Lorentz force is constructed as \begin{equation} \nabla \times \mathbfit B^{[k+1]} \times \mathbfit B^{[k]}, \end{equation} which is linear in $\mathbfit B^{[k+1]}$, since $\mathbfit B^{[k]}$ is known from a previous iteration (the superscript denotes the iteration number). This makes it possible to define a system of linear ``update equations'' that relate each variable at the current iteration to those known from previous iterations. The update equations are solved successively, and a solution to the complete nonlinear system is obtained when and if the iteration converges to a fixed point. This method has been previously used to solve the magnetohydrostatic equations with $\mathbfit g = 0$ \citep{greenpaper,doi:10.1137/070700942,2013SoPh..282..283G}. It has also been used to solve the nonlinear force-free equations \citep{1981SoPh...69..343S,1999A&A...350.1051A,2004SoPh..222..247W, 2007SoPh..245..251W}, which is the special case of the magnetohydrostatic equations defined by the condition $\mathbfit J \times \mathbfit B = 0$. In this article we extend the method to solve the magnetohydrostatic equations with $\mathbfit g \ne 0$. \\ \noindent Constructing solutions using a fixed-point method has several potential advantages over the methods of \citet{2001SoPh..201..289H} and \citet{2003SoPh..214..287W}. Firstly, unlike methods formulated in inverse coordinates, our method does not fix the toplogy of the magnetic field {\it a priori}. Secondly, the method does not overspecify the boundary-value problem like the optimization method.\\ | \noindent We present a new fixed-point iteration method for solving the magnetohydrostatic equations in a three-dimensional Cartesian box and its implementation in code. We apply the code to a known analytic solution to verify that it works as expected. We perform the calculation at four different numerical resolutions to determine how this affects the convergence and numerical accuracy of the method as well as the calculation time.\\ \noindent We find that the fixed-point iteration converges in the sense that the change in the magnetic field between iterations, as measured by the metric $\Delta B_{\rm max}$ (Equation (\ref{eq_con_metric})), decreases by approximately six orders of magnitude over 20 iterations. The decrease in $\Delta B_{\rm max}$ appears to be exponential with a rate that does not depend strongly on the number of grid points. Although the method converged for all the cases presented, we found that if the resolution was made very low, by either using a small $N$ or a large domain, then the method would not reach a fixed point. In this limit, we expect that the solution was dominated by the numerical truncation error.\\ \noindent We also measure the numerical truncation error of the method by comparing the known analytic solution to the numerical solution. We do this for calculations at four different resolutions in order to establish a scaling law for the truncation error. We find that for the metric $u_{\rm max}$, which is sensitive to the maximum truncation error, the power-law index is \iumax, as determined by a fit to the data. For the metric $u_{\rm avg}$, which is sensitive to the average truncation error, we find the power-law index of the fit is \iuavg. The theoretical maximum truncation error in the field-line tracing solution to the hyperbolic equations is expected to have $\sim 1/N$ scaling (see the discussion in \citealp{2013SoPh..282..283G}), while the maximum truncation error for the second-order finite-difference solution to the elliptic equations is expected to have $\sim 1/N^2$ scaling. These represent worst-case error estimates and in practice we would expect to find a power-law index for the truncation error somewhere in between one and two, which is what we find. We note some departure from the fit for $u_{\rm max}$ at $N=256$. The value here is approximately half that at $N=128$, so while it does not lie on the fitted line, it is still consistent with the maximum theoretical error scaling of $\sim 1/N$.\\ \noindent We also perform a visual comparison between the field lines of the numerical and analytic solutions. After 20 iterations, the two sets are almost indistinguishable, except for field lines in the lower corners of panels (b) and (d) in Figure 3. We found that the field lines in this region can change significantly with even small changes in the electric current density. The region may have the largest error because the analytic solution in this region departs significantly from the initial potential field. The magnetic field in this region is also very weak compared with the field at the center of the domain. We emphasize that the discrepancy decreases with resolution (as can be seen in Figure \ref{fig_lines}), and would not appear to be due to the local failure of the method. \\ \noindent We also establish a scaling law for the total execution time of the code. We find that for a grid with $N$ grid points in each dimension, the total run time has $\sim N^4$ scaling. This scaling is consistent with force-free codes based on the Grad-Rubin method \citep{2006SoPh..238...29W}. As in the case of the force-free codes, the time-consuming step is the field line tracing. We note that although the scaling is similar, the magnetohydrostatic code is significantly slower in absolute terms because a single iteration of the magnetohydrostatic method involves more stages than the force-free Grad-Rubin method.\\ \noindent Our method requires that all field lines connect to the boundary, but no actual constraints on the connectivity are imposed during the iteration to enforce this. In one sense this is an advantage of the method, because it means the method can compute solutions whose topologies differ significantly from the magnetic field used to initiate the calculation. However, in another sense it is a weakness, because there is nothing to prevent closed field lines from forming during the calculation, at which point the calculation cannot proceed. We find that in our tests the appearance of closed field lines is generally in response to the formation of strong electric currents in weak-field regions. Future versions of the method could solve a more general formulation of the boundary-value problem that accounts for closed field lines. Despite this limitation, the method is still applicable to a range of interesting problems.\\ \noindent Finally, we note that the test case used is particularly simple. In particular, because it is untwisted, step iv) of the method is not tested. The numerical methods are similar to those used to solve step \ref{p_update}), and we have tested the method on analytic solutions with a finite $\sigma$ but no gravity, and we have found that the known solution is well reproduced. This gives us confidence that the method would work when applied to a case with both a finite twist and gravity force. We stress that although the test case was axisymmetric, since we work in Cartesian coordinates, our calculation was three-dimensional.\\ \noindent The work presented here has several limitations that could be addressed with future work. The fixed-point method could be generalized to explicitly model the energetics via an energy equation similar to the approach of \citet{1993ApJ...404..788P}. Regarding the code itself, no significant optimization has yet been performed on the current first version, which could be addressed in the future.\\ \noindent In this article we present a new iterative method for solving the magnetohydrostatic equations in a three-dimensional Cartesian domain and the details of an implementation of the method in code. We use our code to reconstruct a known analytic solution and thereby establish the correctness of the code and the viability of the method in general. This work is a step towards the generation of realistic three-dimensional magnetohydrostatic models of the solar atmosphere.\\ \subsection*{Appendix A} \label{sec_stable} \noindent In this appendix we explain why the decomposition of the pressure into a magnetohydrostatic and a hydrostatic components presented in Section \ref{sec_pd_decomp} is necessary for the stability of the fixed-point method. We find that without solving for these components separately, an instability occurs due to the failure to achieve exact hydrostatic force balance in weak-field regions.\\ \noindent In terms of the total pressure, $p$, and density, $\rho$, the update equation for the perpendicular electric current density is \begin{equation} \mathbfit J_{\perp}^{[k+1]} = \frac{ - \nabla p^{[k+1]} \times \mathbfit B^{[k]} + \rho^{[k+1]} \mathbfit g \times \mathbfit B^{[k]} }{ % ||\mathbfit B^{[k]}||^2 }. \label{eq_Jp_norm} \end{equation} Using this equation rather than Equation (\ref{iter_eq3}) results in the formation of spurious electric currents in weak-field regions, where the denominator becomes small but the numerator remains finite due to numerical error. To understand this, let $p$ and $\rho$ be split as in Section \ref{sec_pd_decomp}. Equation (\ref{eq_Jp_norm}) then becomes \begin{equation} \mathbfit J_{\perp}^{[k+1]} = \frac{ (- \nabla p^{[k+1]}_{\rm mhs} \times \mathbfit B^{[k]} + \rho^{[k+1]}_{\rm mhs} \mathbfit g \times \mathbfit B^{[k]}) + (- \nabla p^{[k+1]}_{\rm hs} \times \mathbfit B^{[k]} + \rho^{[k+1]}_{\rm hs} \mathbfit g \times \mathbfit B^{[k]}) }{ % ||\mathbfit B^{[k]}||^2 }. \end{equation} In principle, the second term in the numerator is zero, however, in practice this is not achieved numerically, which introduces an error, $\epsilon(\mathbfit r)$, in the numerator. The functional form of $\epsilon(\mathbfit r)$ depends on the details of the numerical implementation, but, in general, its magnitude varies with position and decreases with resolution. In weak-field regions $p_{\rm mhs}$ and $\rho_{\rm mhs}$ are small, and thus the perpendicular current density has scaling $\sim \epsilon/||\mathbfit B^{[k]}||$. The hydrostatic component of the atmosphere is independent of the magnetic field, and so the error $\epsilon$ is not necessarily small in weak-field regions. This results in the formation of strong spurious currents in weak-field regions because the denominator $||\mathbfit B^{[k]}||$ becomes small while the numerator remains finite. These currents can prevent the method from converging.\\ | 16 | 9 | 1609.00733 |
1609 | 1609.00219_arXiv.txt | {% Hydrodynamical, i.e. multi-dimensional and time-dependent, model atmospheres of late-type stars have reached a high level of realism. They are commonly applied in high-fidelity work on stellar abundances but also allow the study of processes that are not modelled in standard, one-dimensional hydrostatic model atmospheres. Here, we discuss two observational aspects that emerge from such processes, the photometric granulation background and the spectroscopic microturbulence. We use CO5BOLD hydrodynamical model atmospheres to characterize the total granular brightness fluctuations and characteristic time scale for FGK stars. Emphasis is put on the diagnostic potential of the granulation background for constraining the fundamental atmospheric parameters. We find a clear metallicity dependence of the granulation background. The comparison between the model predictions and available observational constraints at solar metallicity shows significant differences, that need further clarification. Concerning microturbulence, we report on the derivation of a theoretical calibration based on CO5BOLD models, which shows good correspondence with the measurements for stars in the Hyades. We emphasize the importance of a consistent procedure when determining the microturbulence, and point to limitations of the commonly applied description of microturbulence in hydrostatic model atmospheres.} | The structure of late-type stellar atmospheres is mainly shaped by two processes: radiation and convection. The standard modelling approach of these atmospheres tries to capture the properties of the stellar radiation field in great detail while the gas-dynamical aspects are simplified by assuming one-dimensional (1D), plane-parallel or spherical symmetry. Mixing-length theory is employed to model the energy transport by convection. In contrast, hydrodynamical, 3D model atmospheres put emphasis on the representation of convection, trying to capture the complex geometry and time-dependence of the gas flows. This comes at the expense of a less detailed treatment of the radiation field in comparison to 1D models. Nevertheless, the treatment of radiation is sufficiently accurate to derive the atmospheric structure with a high degree of realism, e.g., demonstrated by the exquisite reproduction of the solar center-to-limb variation of the line-blanketed intensity at different wavelengths \citep[e.g.,][]{Koesterke+al08,Ludwig+al10}. The main application of model atmospheres is the analysis of stellar (electromagnetic) spectra, i.e., the derivation of a star's atmospheric parameters and its chemical composition. To this end the precise knowledge of the thermal structure of the stellar atmosphere is essential. And indeed, differences in the thermal structure between 1D and 3D models cause differences in the derived parameters and composition. Applications of the 3D model atmospheres documented in the literature mainly revolve around abundance issues \citep[see][as recent examples]{Amarsi+al15,Caffau+al15,Dobrovolskas+al15,Scott+al15}, and are commonly rooted in differences between the thermal structure of 1D and 3D models. Besides predicting changes in the thermal properties, 3D models provide information on the flow dynamics taking place in a stellar atmosphere. Knowledge of the velocity field allows one to eliminate the classical free parameters of micro- and macro turbulence in spectral analysis. Moreover, pressure fluctuations associated with the non-stationary flow are believed to be the exciting agent of solar-like oscillations in late-type stars which establishes a link to asteroseismology \citep{Nordlund+Stein01,Samadi+al07b,Samadi+al13a}. In this contribution we intend to discuss ongoing projects in the field of spectroscopy and asteroseismology besides the main application of 3D models in abundance work. They are related to i) the diagnostic potential of the so-called granulation background; and ii) microturbulence calibration with 3D models and related insights concerning the deficiencies of classical 1D model atmospheres. The reader should be aware that both examples are work in progress, so not all issues are fully worked out. | 16 | 9 | 1609.00219 |
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1609 | 1609.07113_arXiv.txt | \sao is a rare example of a star that allows us to witness stellar evolution in real time. Between 1971 and 1990 it changed from a B-type star into the hot central star of the Stingray Nebula. This observed rapid heating has been a mystery for decades, since it is in strong contradiction with the low mass of the star and canonical post-asymptotic giant branch (AGB) evolution. We speculated that \sao might have suffered from a late thermal pulse (LTP) and obtained new observations with HST/COS to follow the evolution of the surface properties of \sao and to verify the LTP hypothesis. Our non-LTE spectral analysis reveals that the star cooled significantly since 2002 and that its envelope is now expanding. Therefore, we conclude that \sao is currently on its way back towards the AGB, which strongly supports the LTP hypothesis. A comparison with state-of-the-art LTP evolutionary calculations shows that these models cannot fully reproduce the evolution of all surface parameters simultaneously, pointing out possible shortcomings of stellar evolution models. Thereby, \sao keeps on challenging stellar evolution theory and we highly encourage further investigations. | Revealing the evolution of stars is a complex task, since their evolutionary history can usually only be reconstructed indirectly due to the long evolutionary times scales. In a few cases, however, the evolution of the surface properties of a star occurs on a time-scale shorter than a human lifetime. Such events allow us to witness stellar evolution in real time and provide a unique way to gain a direct knowledge of stellar evolution.\\ \sao, the ionization source of the Stingray Nebula (\mbox{PN\,G331.3$-$12.1}), is one such rare example of an unusually fast evolving star. Rapid changes of its observable properties were at first noticed by \cite{partha1993, partha1995}. Based on the optical spectrum of \sao obtained in 1971 and its \textit{UBV} coulors, they concluded that \sao was a B-type star with an effective temperature of \Teff\ $\approx 21$\,kK at that time. However, the optical spectra from 1990 and 1992 as well as IUE spectra from 1992 on display many nebular emission lines, which let them conclude that \sao has ionized its surrounding nebula within only two decades. In \citeauthor{Reindletal2014a} (\citeyear{Reindletal2014a}, \pa), we presented first quantitative spectral analyses of all available spectra taken from 1988 to 2006 with various space-based telescopes. We found that the central star had steadily increased its \Teff\ from 38\,kK in 1988 to a peak value of 60\,kK in 2002. During the same time, the star was contracting, as concluded from an increase in surface gravity from $\log$(g\,/\,cm\,s$^{-2}$)\,=\,4.8 to 6.0 and a drop in luminosity. Simultaneously, the mass-loss rate declined from $\log$(\Mdot\,/\,\Msol\,yr$^{-1}$)\,=\,$-9.0$ to $-11.6$ and the terminal wind velocity increased from $v_\infty$ = $1800$ to $2800$\,km\,s$^{-1}$.\\ The existence of the planetary nebula (PN) suggests that \sao is likely a post-AGB star because -- in general -- only such a star is expected to eject a PN. On the other hand, its low mass is in strong contradiction with canonical post-AGB evolution \citep{partha1995, Bobrowsky1998}. A comparison of the position of \sao in the log \Teff\ -- \logg\ plane with latest post-AGB stellar evolutionary calculations \citep{MillerBertolami2016} indicates a mass below $0.53$\,\Msol, while the rapid heating rate (d\Teff\,/\,d$t$) would require a central star mass of $0.7$\,\Msol.\\ Under certain circumstances, however, the classical picture of the evolution of post-AGB stars is altered by the occurrence of a late He-shell flash. These can occur either during the blue-ward excursion of the post-AGB star (late thermal pulse, LTP), or during its early white dwarf cooling phase (very late thermal pulse, VLTP). The release of nuclear energy by the flashing He-shell forces the already very compact star to expand back to giant dimensions -- the so-called born-again scenario. This scenario was first explored in detail by \cite{Schoenberner1979} and by \cite{Iben1983} and is of great importance for the explanation of H-deficient post-AGB stars, which make up about a quarter of the post-AGB stars. The evolutionary time-scales of stars, which are considered to have undergone such a late He-shell flash, are very short (decades) and thus, the detection and the repeated observation of such quickly evolving objects make it possible to record the temporal evolution of their stellar parameters and to establish constraints for stellar evolution theory. Well known examples for ``born-again'' stars are \mbox{V605\,Aql} (e.g., \citealt{Clayton2006}), \mbox{V4334\,Sgr} (Sakurai's object, e.g. \citealt{Hajduk2005}) and FG\,Sge (e.g., \citealt{Jeffery2006}). \mbox{V605\,Aql} and \mbox{V4334\,Sgr} are considered to have undergone a VLTP, which produces an H-free stellar surface already during the flash. FG\,Sge, on the other hand, had a slower cooling rate and turned H-deficient only when it had returned back to the AGB. Therefore FG\,Sge must instead have experienced an LTP (see \citealt{Schoenberner2008} for a review about these objects).\\ In \pa, we speculated that \sao might also have experienced a late He-shell flash shortly after leaving the AGB. This scenario predicts that \sao would eventually become a cool supergiant, i.e., that the star will become cooler and expand. To follow the evolution of the surface properties of \sao and to verify the LTP hypothesis, we performed further observations with the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope (HST). | \label{sect:conclusions} In this work we have shown, that after the initial rapid heating and contraction (\pa), \sao has cooled significantly since 2002 and is now expanding. This can only be explained with a LTP scenario, and indicates that the star is now on its way back to the AGB. We stress that \sao is the only LTP object, that was observed during its blue- and red-wards motion through the Hertzsprung-Russell diagram. The evolutionary speed suggests a central star mass between 0.53 and 0.56\,\Msol. However, none of the current LTP models can fully reproduce the evolution of all surface parameters simultaneously. In particular the problem with the apparently high gravity of the star should be pursued further. A high S/N near-UV spectrum would therefore be highly desirable in order to derive \logg\ more precisely. Refined LTP evolutionary calculations, on the other hand, may not only help to explain the nature of \sao, but could also provide a deeper insight into the evolution of central stars of PNe as well as the formation of H-deficient stars. \vspace*{-5mm} | 16 | 9 | 1609.07113 |
1609 | 1609.05927_arXiv.txt | Dark matter drops out of kinetic equilibrium with standard model particles when the momentum-transfer rate equals the expansion rate. In a radiation-dominated universe, this occurs at essentially the same time as dark matter kinetically decouples from the plasma. Dark matter may also fall out of kinetic equilibrium with standard model particles during an \mbox{early matter-dominated era (EMDE)}, which occurs when the energy content of the Universe is dominated by either a decaying oscillating scalar field or a semistable massive particle before big bang nucleosynthesis. Until now, it has been assumed that kinetic decoupling during an EMDE happens similarly to the way it does in a radiation-dominated era. We show that this is not the case. By studying the evolution of the dark matter temperature, we establish a quasidecoupled state for dark matter in an EMDE, during which the dark matter temperature cools faster than the plasma temperature but slower than it would cool if the dark matter were fully decoupled. The dark matter does not fully decouple until the EMDE ends and the Universe becomes radiation dominated. We also extend the criteria for quasidecoupling to other nonstandard thermal histories and consider how quasidecoupling affects the free-streaming length of dark matter. | \label{sec:Intro} Weakly interacting massive particles (WIMPs) are prime candidates for cold dark matter. WIMPs interact with other standard model (SM) particles solely via the electroweak force, which allows them to fall out of kinetic equilibrium with the relativistic plasma as early as one second after the big bang. This departure from equilibrium occurs when the momentum-transfer rate, $\gamma$, between WIMPs and SM particles equals the Hubble expansion rate, $H$, \begin{equation}\label{Tkd} \gamma(T_{\mathrm{neq}}) \equiv H(T_{\mathrm{neq}}), \end{equation} which defines the nonequilibrium temperature \mbox{$T_{\mathrm{neq}}$ \cite{Hofmann2001}}.\footnote{{The EMDE literature typically uses Eq.~\eqref{Tkd} to define $T_{\mathrm{kd}}$ in a generic nonstandard thermal history, but we are using Eq.~\eqref{Tkd} to define a new temperature $T_\mathrm{neq}$ in order to distinguish it from $T_{\mathrm{kd}}$ defined in Eq.~\eqref{TkdLT}.}} After dark matter (DM) kinetically decouples from the plasma, its temperature $T_{\chi}$ begins to scale as $a^{-2}$, where $a$ is the scale factor. It has been customary to define the kinetic decoupling temperature for DM based on the late-time behavior of $T_{\chi}$ \cite{Bringmann2007, Bringmann2009}, \begin{equation}\label{TkdLT} T_{\mathrm{kd}} \equiv {T_{\chi}}|_{T\rightarrow 0} \, \left(\frac{a}{a_\mathrm{kd}}\right)^{2}, \end{equation} where $T$ is the plasma temperature and $a_\mathrm{kd}$ is the value of the scale factor when $T = T_\mathrm{kd}$. In a radiation-dominated (RD) universe, Eqs.~\eqref{Tkd} and \eqref{TkdLT} imply that $T_\mathrm{kd} = T_\mathrm{neq} / K_n$, where $K_n$ is a numerical factor of order unity that depends on how the velocity-averaged DM scattering cross section scales with temperature ($\langle \sigma v \rangle\, \propto T^{n}$): \mbox{$K_2 \simeq 1.03$} for $p\,$-wave \mbox{scattering \cite{Visinelli2015, WE2017}}. Therefore, in a RD universe, the temperature at which DM falls out of equilibrium with the plasma is essentially the same as the kinetic decoupling temperature. The timing of kinetic decoupling sets the cutoff scale in the matter power spectrum \mbox{\cite{Hofmann2001, Green2004, Green2005, Loeb2005, Bert2006, Bringmann2009, Gondolo2012, Bringmann2007}.} The small-scale cutoff, in turn, fixes the mass of the smallest protohalos that can form at high redshift \mbox{\cite{Hofmann2001, Green2004, Green2005, Loeb2005, Profumo2006, Bert2006, Bringmann2009, Gondolo2012, Bringmann2007}.} Several investigations have explored the possibility that the Universe was not radiation dominated when DM kinetically decoupled from the plasma \cite{Gelmini2008, Arcadi2011, Kane22015, Visinelli2015, Erickcek2011, Barenboim2014, Fan2014, Erickcek2015long, Erickcek2015short}. Big bang nucleosynthesis (BBN) requires the Universe to be radiation dominated at a plasma temperature of \mbox{$T \simeq 3$ MeV} \cite{Kawasaki1999, Kawasaki2000, Hannestad2004, Ichikawa2005}, but the evolution of the Universe at higher temperatures is unknown. Both delayed inflationary reheating and the presence of gravitationally coupled scalar fields support the possibility that the Universe could have been dominated by an oscillating scalar field prior to BBN. Since scalar fields that oscillate around the minimum of a quadratic potential behave like a pressureless fluid, these scenarios include an early matter-dominated era (EMDE) prior to BBN \cite{Coughlan1983, deCarlos1984, Banks1994, Banks1995_1, Banks1995_2, Acharya2008, Acharya2009, Blinov2014}. A recent review \cite{Kane2015} concluded that EMDEs are a generic consequence of gravitationally coupled scalars in string theories. EMDEs have also been explored in the context of models where the inflaton decays to a hidden sector \cite{Tenkanen2016} and where a long-lived light mediator is responsible for interactions between DM and SM particles \cite{Zhang2015}. If DM is produced thermally from interactions with SM particles in the plasma, then an EMDE raises the value of $T_{\mathrm{neq}}$ relative to its value in a RD era, which leads to a smaller free-streaming length \cite{Gelmini2008}. However, if DM is produced nonthermally through energy injection from a decaying scalar field, then an EMDE can lower the value of $T_{\mathrm{neq}}$ and make the transition from fully coupled to fully decoupled less sharp \cite{Arcadi2011}. Most recently, Ref.~\cite{Visinelli2015} derived analytic expressions for how the DM temperature evolves during an EMDE and other nonstandard thermal histories. DM kinetic decoupling in an EMDE has received a great deal of recent attention because it has been shown that an EMDE enhances the small-scale matter power spectrum and boosts the abundance of microhalos if DM stops interacting with the plasma before the onset of radiation domination \cite{Erickcek2011, Barenboim2014, Fan2014, Erickcek2015long}.\footnote{If DM remains kinetically coupled during the EMDE, then the evolution of the matter and radiation perturbations generate isocurvature perturbations that enhance the small-scale matter power spectrum \cite{Choi2015}.} Matter perturbations that enter the horizon during radiation domination grow logarithmically with the scale factor, but they grow linearly during an EMDE.\footnote{The enhanced growth of density perturbations in an EMDE may enable primordial black holes (PBHs) to form on subhorizon scales, but PBHs only constrain EMDE scenarios if the primordial power spectrum is blue tilted \cite{Georg2016}.} The resulting enhancement in the small-scale matter power spectrum significantly increases the abundance of microhalos at high redshift ($z\gtrsim 100$) \cite{Erickcek2011, Erickcek2015long}, which can boost the DM annihilation rate by many orders of magnitude \cite{Erickcek2015long}. Such a boost to the annihilation rate can bring formerly untestable DM candidates within reach of current and future observations \cite{Erickcek2015short}. In this short paper, we reconsider the differential equation governing the evolution of the DM temperature, $T_{\chi}$. All prior analyses of DM kinetic decoupling in an EMDE assume that $T_{\chi}\propto a^{-2}$ when $\gamma < H$, just as it does in a RD universe. We show that this is not the case: at plasma temperatures $T < T_{\mathrm{neq}}$ in an EMDE, $T_{\chi}$ decays faster than $T$, but slower than $a^{-2}$, which implies that DM does not fully decouple in an EMDE. This \mbox{\textit{quasidecoupled}} state for DM implies that the value of $T_\mathrm{neq}$ is much greater than the value of $T_\mathrm{kd}$ in an EMDE and that $T_{\mathrm{kd}}$ is \emph{not} the temperature at which DM starts cooling as $a^{-2}$. We show that $T_\mathrm{kd}$, as defined by Eq.~\eqref{TkdLT}, does not correspond to any physical transition in the evolution of $T_{\chi}$ during an EMDE. Rather, $T_\mathrm{neq}$ marks the moment that DM drops out of equilibrium with the plasma, and the reheat temperature $T_\mathrm{RH}$ marks the end of the EMDE and the onset of full kinetic decoupling, $T_{\chi} \propto a^{-2}$. Finally, we establish the criteria for quasidecoupling in other nonstandard cosmologies. A quasidecoupled state for DM is likely to have profound implications for our understanding of DM behavior in EMDE scenarios, including the growth of density perturbations, the free-streaming length, the abundance of microhalos, and the observational signatures of an EMDE. As a first pass at understanding these ramifications, we calculate the DM free-streaming length with quasidecoupling in an EMDE. While the DM free-streaming length is still smaller than it would be in the absence of an EMDE, it is an order of magnitude greater than it would be if DM fully decoupled during the EMDE. We begin in Sec.~\ref{sec:2} by establishing the cosmological framework that we use throughout this paper. In Sec.~\ref{sec:3}, we solve the evolution equation for the DM temperature in a generic cosmology in the post-equilibrium limit and show how a quasidecoupled state for DM occurs during an EMDE. We then explore the conditions for quasidecoupling in other thermal histories, and we confirm that the general solution to the differential equation for the DM temperature agrees with the solution to the differential equation for the DM temperature in the postequilibrium limit. We also discuss the difference between the nonequilibrium temperature $T_\mathrm{neq}$, as defined by Eq.~\eqref{Tkd}, and the kinetic decoupling temperature $T_\mathrm{kd}$, as defined by Eq.~\eqref{TkdLT}, in an EMDE. In Sec.~\ref{sec:4} we use a piecewise model for the DM velocity to study the effect of quasidecoupling in an EMDE on the free-streaming length of DM. Finally, we summarize our results in Sec.~\ref{sec:5}. The appendix presents a proof of the asymptotic series expansion for the upper incomplete gamma function that enters into the general solution for the DM temperature in a generic cosmology. We use natural units ($\hbar=c=1$) throughout this work. | \label{sec:5} We have established the existence of a quasidecoupled state for DM in thermal histories in which entropy is produced by a decaying scalar field with \mbox{$w < 16 / [3(1+n)]-1$}, where $n$ determines how the DM scattering cross section depends on temperature \mbox{($\langle\sigma v\rangle \propto T^n$)}. The nonequilibrium temperature $T_\mathrm{neq}$ is still higher than it is in a radiation-dominated era, but it marks a transition from tightly coupled to quasidecoupled as opposed to a shift from tightly coupled to fully decoupled. The DM remains quasidecoupled until the onset of radiation domination; the transition from quasidecoupled to fully decoupled does not depend on the interactions between DM and the SM. Therefore, the quasidecoupled phase should be considered as a fundamentally new state of DM. These surprising results force us to reconsider the body of work on kinetic decoupling of DM in nonstandard thermal histories, which, until now, has been built on the assumption that DM fully decouples from the plasma when the momentum-transfer rate falls below the expansion rate. Quasidecoupling calls all previous work on the behavior of DM during an EMDE into question and merits new investigations. We have demonstrated that quasidecoupling increases $\lambda_\mathrm{fs}$ by an order of magnitude compared to the fully decoupled calculation, which has profound implications for the small-scale cutoff in the matter power spectrum, the size of the first microhalos, and the timing of their formation \cite{Erickcek2015long}. In future work, we will explore these ramifications in more detail \cite{WIE2016}. | 16 | 9 | 1609.05927 |
1609 | 1609.07503.txt | Tidal Downsizing is the modern version of the Kuiper (1951) scenario of planet formation. Detailed simulations of self-gravitating discs, gas fragments, dust grain dynamics, and planet evolutionary calculations are summarised here and used to build a predictive planet formation model and population synthesis. A new interpretation of exoplanetary and debris disc data, the Solar System's origins, and the links between planets and brown dwarfs is offered. This interpretation is contrasted with the current observations and the predictions of the Core Accretion theory. Observations that can distinguish the two scenarios are pointed out. In particular, Tidal Downsizing predicts that presence of debris discs, sub-Neptune mass planets, planets more massive than $\sim 5$~Jupiter masses and brown dwarfs should not correlate strongly with the metallicity of the host. For gas giants of $\sim$ Saturn to a few Jupiter mass, a strong host star metallicity correlation is predicted only at separation less than a few AU from the host. Composition of massive cores is predicted to be dominated by rock rather than ices. \SNc{Debris discs made by Tidal Downsizing are distinct from those made by Core Accretion at birth: they have an innermost edge always larger than about 1 au, have smaller total masses and are usually in a dynamically excited state. It is argued that} planet formation in surprisingly young or very dynamic systems such as HL Tau and Kepler-444 \SNc{may be} a signature of Tidal Downsizing. Open questions and potential weaknesses of the hypothesis are pointed out. | A planet is a celestial body moving in an elliptic orbit around a star. Although there does not appear to be a sharp boundary in terms of properties, objects more massive than $\approx 13\mj$ are called brown dwarfs (BDs) since they can fuse deuterium while planets are never sufficiently hot for that \citep{BurrowsEtal01}. Formation of a star begins when a large cloud dominated by molecular hydrogen collapses due to its self-gravity. The first hydrostatic object that forms in the centre of the collapsing cloud is a gaseous sphere of 1 to a few Jupiter masses; it grows rapidly by accretion of more gas from the cloud \citep{Larson69}. Due to an excess angular momentum, material accreting onto the protostar forms a disc of gas and dust. Planets form out of this (protoplanetary) disc, explaining the flat architecture of both the Solar System and the extra-solar planetary systems \citep{FabryckyEtal14,WF14}. The most widely accepted theory of planet formation is the Core Accretion (CA) scenario, pioneered by \cite{Safronov72}. In this scenario, microscopic grains in the protoplanetary disc combine to yield asteroid-sized bodies \citep[e.g.,][]{GoldreichWard73}, which then coalesce to form rocky and/or icy planetary cores \citep{Wetherill90,KL99}. These solid cores accrete gas from the disc when they become sufficiently massive \citep{Mizuno80,Stevenson82,IkomaEtal00,Rafikov06}, becoming gas giant planets \citep{PollackEtal96,AlibertEtal05,MordasiniEtal14}. \cite{Kuiper51b} envisaged that a planet's life begins as that of stars, by gravitational instability, with formation of a few Jupiter mass gas clump in a massive protoplanetary disc. In difference to stars, young planets do not accrete more gas in this picture. They may actually loose most of their primordial gas if tidal forces from the host stars are stronger than self-gravity of the clumps. However, before the clumps are destroyed, solid planetary cores are formed inside them when grains grow and sediment to the centre \citep{McCreaWilliams65}. In this scenario, the inner four planets in the Solar System are the remnant cores of such massive gas condesations. Jupiter, on the other hand, is an example of a gas clump that was not destroyed by the stellar tides because it was sufficiently far from the Sun. The other three giants in the Solar System are partially disrupted due to a strong negative feedback from their massive cores \citep[][and \S \ref{sec:SS_basic}]{HW75}. It was later realised that gas clumps dense and yet cool enough for dust grain growth and sedimentation could not actually exist at the location of the Earth for more than a year, so Kuiper's suggestion lost popularity \citep{DW75}. However, recent simulations show that gas fragments migrate inward rapidly from their birth place at $\sim 100$~AU, potentially all the way into the star \citep[][more references in \S \ref{sec:rapid}]{BoleyEtal10}. Simulations also show that grain sedimentation and core formation can occur inside the clumps while they are at separations of tens of AU, where the stellar tides are weaker. The clumps may eventually migrate to a few AU and could then be tidally disrupted. Kuiper's top-down scenario of planet formation is therefore made plausible by planet migration; it was recently re-invented \citep{BoleyEtal10} and re-branded "Tidal Downsizing" hypothesis \citep{Nayakshin10c}. \SNc{This review presents the main ideas behind the Tidal Downsizing scenario, recent theoretical progress, detailed numerical simulations and a wide comparison to the current observational data. An attempt is made at finding a physically self-consistent set of assumptions within which Tidal Downsizing hypothesis could account for all observational facts relevant to the process of planet formation.} \SNc{Exploration of this extreme scenario is the quickest route to rejecting the Tidal Downsizing hypothesis or constraining its inner workings if it is successful. Further, it is possible that the final planet formation theory will combine elements of both Tidal Downsizing and Core Accretion, e.g., by having them operating at different epochs, scales, or systems. By pushing the Tidal Downsizing scenario to the limit we may locate the potential phase space divide between the two theories sooner.} This review is structured as following. \S \ref{sec:TD_scenario} lists important physical processes underpinning the scenario and points out how they could combine to account for the Solar System's structure. \S\S 4-7 present detailed calculations that constrain these processes, whereas \S \ref{sec:dp_code} overviews a population synthesis approach for making statistical model predictions. \S\S \ref{sec:Z}-\ref{sec:kepler444} are devoted to the comparison of Tidal Downsizing's predictions with those of Core Accretion and the current observations. \S \ref{sec:SS} is a brief summary of the same for the Solar System. The Discussion (\S \ref{sec:discussion}) presents a summary of how Tidal Downsizing might relate to the exoplanetary data, observations that could distinguish between the Tidal Downsizing and the Core Accretion scenarios, open questions, and potential weaknesses of Tidal Downsizing. % % % % % % % % % % % % | \label{sec:discussion} \subsection{Tidal Downsizing, summary of outcomes}\label{sec:exo_basic} \begin{figure*} \includegraphics[width=0.95\textwidth]{Figs/TD_outcomes_sketch5.pdf} \caption{A schematic illustration of how Tidal Downsizing scenario may relate to the observed companions to stars, from planets to low mass stars, as described in \S \ref{sec:exo_basic}.} \label{fig:sketch2} \end{figure*} \SNc{Fig. \ref{fig:sketch2} illustrates as gas clumps born at separations of $\sim 100$~AU from the host star by gravitational disc instability could evolve to produce sub-stellar objects with masses from asteroids and comets to brown dwarfs an host separations from a few stellar radii to tens and even hundreds of AU. The evolutionary paths taken by the objects are shown with arrows on top of the planet mass versus separation diagram from "exoplanets.org" \citep{HanEtal14}.} In the top right corner of the figure, the main object of Tidal Downsizing, a pre-collapse gas clump with an ongoing grain sedimentation and core formation is shown. The two arrows pointing away from the clump show the first important bifurcation in the fate of the clump. If the \SNc{clump accretes gas rapidly (see \S \ref{sec:AorM}), it becomes a brown dwarf or a low stellar mass companion to the host star (path 1, black, pointing down from the clump in the Figure). This evolutionary path is quite analogous to the first--second core evolution of protostars \citep{Larson69}, except it takes place inside a massive protoplanetary disc.} \SNc{ If the clump does not accrete gas, it evolves towards becoming a planet or planetary remnant(s) (grey, to the left from the clump in the figure). Three main outcomes could be distinguished here:} (2A) {\it A gas giant planet} (green arrows in the sketch). If the inward radial migration of the fragment is slower than planet contraction, and if the core feedback is sufficiently weak, the fragment contracts and survives as a gas giant planet. Usually, this requires the core mass to be below a Super Earth mass ($\lesssim 5 \mearth$, \S \ref{sec:feedback}). Planet migration may bring the planet arbitrarily close to the host star, including plunging it into the star. No debris ring of planetesimals is created from this clump since it is not disrupted. (2B){\it A low mass solid core planet}, $M_{\rm p}\lesssim$ a few $\mearth$ (red arrows). Similar to the above, but the fragment is migrating in more rapidly than it can collapse. In this case it fills its Roche lobe somewhat outside the exclusion zone boundary and gets tidally disrupted. This results, simultaneously, in the production of a small rocky planet and an Asteroid belt like debris ring at a few AU distance from the host star. (2C) {\it A high mass solid core planet}. If the fragment is able to make a massive solid core, $M_{\rm core}\gtrsim 5-10\mearth$, its feedback on the fragment may unbind the fragment at separations as large as tens of AU. This process is shown with the blue arrow and leaves behind the massive core, plus a Kuiper-belt like debris ring. All of the planets and even stars so created may continue to migrate in, as shown by the black open arrow on the bottom right of the sketch, until the disc is finally removed. Note that a much more massive disc is needed to move a brown dwarf or a star into the inner disc region as opposed to moving a planet. Because very massive gas discs cannot be very common, this predicts that brown dwarfs and stellar mass companions are more likely to be found at large (tens of AU or more) separations; gas giant planets are more likely to migrate closer in to the host star. \subsection{Observations to test this scenario} Dozens of independent numerical simulations (\S \ref{sec:rapid}) show that Jupiter mass planets migrate from $\sim 100$~AU into the inner $\sim 10$~AU or less in about 10,000 years or even less. Therefore, the popular idea \citep[e.g.,][]{Boley09} of dividing the observed population of planets onto "made by Core Accretion" (inside the inner tens of AU) and "made by Gravitational Instability" (outside this region) is not physically viable. Based on the rapid migration speeds found in the simulations, a giant planet observed at $\sim 0.1$~AU is as likely to have migrated there from a few AU as it is to have migrated there from $100$~AU. Likewise, due to tidal disruptions, Tidal Downsizing produces a numerous supply of core-dominated planets, many of which may end up at same distances as normally reserved for the Core Accretion planets. We thus need to be crystal clear on which observables can be used to differentiate between the two scenarios and which are actually less discriminating than previously thought. \subsubsection{Similarities between the two scenarios} The observed planets naturally divide into two main groups -- those dominated by solid cores, usually below mass of $\sim 20\mearth$, and those dominated by gas, usually more massive than Saturn ($\sim 100 \mearth$). This has been interpreted as evidence for gas accretion runaway \citep[e.g.,][]{MordasiniEtal09b,MayorEtal11} above the critical mass for the core-nucleated instability \citep{Mizuno80,Stevenson82,Rafikov06}. However, a similar bi-modality of planets is found in Tidal Downsizing (Fig. \ref{fig:atmo}). When the parent gas fragment is disrupted, the mass of the gas remaining bound to the core is usually a small fraction of the core mass for reasons quite analogous to those of Core Accretion (\S \ref{sec:atm}). This implies that the observed dichotomy of planets may be driven by the fundamental properties of matter (equation of state and opacities) rather than by how the planets are made. The bulk composition of planets is another example where the predictions of the two theories are not so different. In Core Accretion, the more massive the planet is, the smaller the fraction of the total planet mass made up by the core. This may account for the observed over-abundance of metals decreasing with the planet mass \citep{MillerFortney11}. In Tidal Downsizing, the more massive the gas giant is, the smaller is the "pebble accretion boost" needed for it to collapse, and this may also account for the observations (see Fig. \ref{fig:Zpl} \& \S \ref{sec:Zpl_giants}). The strong preference amongst gas giants to orbit metal rich rather than metal poor hosts is well known \citep[e.g.,][]{Gonzalez99,FischerValenti05,SanterneEtal15}, and is normally attributed to the more rapid assembly of massive cores in metal rich discs \citep{IdaLin04b,MordasiniEtal09b}. However, if gas giants collapse due to "metal loading" \citep{Nayakshin15a} rather than due to the classical radiative collapse \citep{Bodenheimer74}, then the frequency of their survival is also a strong function of the host disc metallicity \citep{Nayakshin15b,NayakshinFletcher15}. These observations cannot be claimed to support one of the two planet formation scenarios. \subsubsection{Observable differences between the theories} %Predictions of the two theories diverge on the number of issues. Tidal Downsizing however predicts that beyond the exclusion zone at $a\sim$ a few AU, there should be no correlation between the gas giant presence and the host star metallicity because the tidal disruption "filter" does not apply or at least applies not as strongly there (\S \ref{sec:cold_giants_Z}). Observations \citep[][]{AdibekyanEtal13} started to probe the few-AU region of the parameter space, and there is a hint that this prediction is supported by the data \citep[][see also Fig. \ref{fig:Vardan}]{AdibekyanEtal15}, but more observations are needed. Similarly, planets more massive than $\sim 5-10\mj$ and brown dwarfs should not correlate with the metallicity of the host in the Tidal Downsizing model (\S \ref{sec:transition}), whatever the separation from the star. Currently, this prediction is clearly supported by observations of brown dwarfs and low mass stellar companions to stars \citep{RaghavanEtal10,TroupEtal16} but the transition region between planets and brown dwarfs is not well studied. Massive gas giant planets do appear to become less sensitive to the host metallicity above the mass of $5\mj$ (\S \ref{sec:massive_giants_Z} and Fig. \ref{fig:Z_massive}), but more data are desirable to improve the statistics. At the lower mass end, there are differences between the models too. In the framework of Tidal Downsizing, planetary debris is only made when the gas clumps -- the future gas giant planets -- are disrupted (see \S \ref{sec:planetesimals} \& \ref{sec:hier}). Since tidal disruption of the clumps anti-correlates with the host metallicity as explained above, no simple correlation between the debris disc presence and host [M/H] is predicted \citep{FletcherNayakshin16a}. Secondary predictions of this picture (see \S \ref{sec:Z_debris}) include a possible correlation of the debris disc presence with that of a sub-Saturn planet (that is, any downsized planet), and an anti-correlation with the presence of gas giant planets. \SNc{Further, post-collapse planets are too hot to permit existence of asteroid or comet like debris inside of them. Pre-collapse planets are disrupted not closer than the exclusion zone, as mentioned above, so that debris belts made by Tidal Downsizing must be never closer than $\sim 1$~AU to the host solar type star. This is different from Core Accretion where planetesimals are postulated to exist as close as $\sim 0.1$~AU from the host star \citep[e.g.,][]{ChiangLaughlin13}. \cite{KenyonEtal16} identifies the very low frequency of observed {\em warm} debris discs ($\sim 2-3$\%) in young debris discs as a significant puzzle for Core Accretion, and offers a solution. Another difference is the likely much smaller mass of the debris rings made by Tidal Downsizing, and their significant birth eccentricities \citep[up to $e\sim 0.1$;][]{NayakshinCha12}.} For cores, the host star metallicity correlation is predicted to depend on the core mass in Tidal Downsizing. Low mass cores, $M_{\rm core} \lesssim$ a few $\mearth$, are most abundant around low metallicity hosts because of the already mentioned tendency of the parent gas clumps to be disrupted more frequently at low metalicites. High mass cores, on the other hand, are mainly made in disruptions of gas clumps made by metal-rich discs \citep[e.g., see the black curve in Fig. 3 in][]{FletcherNayakshin16a}. Therefore cores more massive than $\sim 10-15\mearth$ are likely to correlate with the metallicity of the host. For a broad range of core masses, one gets no strong correlation with [M/H], somewhat as observed \citep{NayakshinFletcher15}. Future observations and modelling of core correlations with metallicity of the host are a sensitive probe of the two planet formation scenarios. While some of the Core Accretion population synthesis models also predict no strong correlation between core-dominated planets and the host star metallicity \citep[e.g.,][]{MordasiniEtal09b}, the degeneracy between the two models may be broken in two areas. Tidal Downsizing predicts that massive core formation is a very rapid process, even at $\sim 100$ AU, requiring less than $\sim 10^5$ years \citep{Nayakshin16a}, whereas Core Accretion takes $\sim 1-3$~ Million years even at distances $a\lesssim 10$~AU. ALMA observations of protoplanetary discs such as HL Tau (\S \ref{sec:HLT}), showing signs of very early planet formation, is key to constrain the timing of massive core growth and is a challenge to the classical version of Core Accretion.\footnote{As an aside, the recently discovered rapid core growth via pebble accretion \citep[e.g.,][]{JohansenEtal14a,JohansenEtal15a,LevisonEtal15} may solve the HL Tau mystery in the context of Core Accretion, but then the classical framework for the metallicity correlations suggested by \cite{IdaLin04b,MordasiniEtal09b} is in doubt because it is based on a long core growth time scale. Therefore, at the present it appears that Core Accretion may account for either the well known gas giant planet -- host star metallicity correlations (\S \ref{sec:giants_Z}) or the HL Tau young cores, but not both.} Another area where the two models differ is the expected core composition. Core Accretion predicts that ices may be the dominant contributor to the mass budget of massive cores \citep{PollackEtal96}. While these cores would form beyond the snow line, many would migrate all the way into the inner tenths of an AU region that is accessible to modern observations \citep[e.g., see Fig. A1 in][]{ColemanNelson16}. Tidal Downsizing predicts that ices and organics are less likely to contribute to making planetary cores than silicates because the ices and organics are too volatile to sediment into the centres of hot pre-collapse fragments \citep[][also \S \ref{sec:composition}]{HS08,HelledEtal08}. Cores that are further away than $\sim 0.1$~AU from their hosts, including the Solar System giants, do not present us with a clean composition test because their mass-radius relation is degenerate due to the unknown H/He mass fraction \citep[e.g., see \S 5.1.2 in][]{HelledEtal13a}. However, moderately massive cores \citep[$M_{\rm core}\lesssim 7\mearth$, see][]{OwenWu13} lose their H/He envelopes due to photo-evaporation at separations less than $\sim 0.1$~AU. It is thus sensible to concentrate on these close-in cores when pitting Tidal Downsizing against Core Accretion. The close-in cores are (so far) observed to have a rocky Earth-like composition (\S \ref{sec:core_comp}), but the current data are still scarce. Observations show a strong roll-over in frequency of planets more massive than $\sim 20 \mearth$ \citep{MayorEtal11} or larger than $\sim 4 R_\oplus$ \citep{HowardEtal12}. Building solid cores via accretion of planetesimals or via giant impacts has no obvious limit at this mass range except for the run away by gas accretion \citep{PollackEtal96,MordasiniEtal09b}. This scenario should however not apply to metal-poor systems: if these are made in gas-free discs \citep{IdaLin04b}, then their cores should be free to grow more massive than $M_{\rm crit}$. Very massive solid cores are however not observed around metal-poor stars. In Tidal Downsizing, the drop above the mass of $\sim 20 \mearth$ may be due to the strong feedback unleashed by the massive cores onto their host gas fragments (\S \ref{sec:feedback} and Fig. \ref{fig:pmf_fb}). This mechanism should affect both metal rich and metal poor systems. Observations of stars more massive than the Sun may be helpful here, as these are expected to have more massive discs \citep{MordasiniEtal12}, and thus their cores should be more massive if made by Core Accretion and not if made by Tidal Downsizing. Finally, planet formation in extreme systems such as binaries is a very tough test for any planet formation scenario. Kepler-444 may be an example of a system where the observed planets could not have been made by Core Accretion, as argued in \S \ref{sec:kepler444}, due to the inner disc being both too hot to make the planets in situ, and yet not long lived enough to move them in place if made further out. However, it remains to be seen if detailed simulations in the framework of Tidal Downsizing could produce such an extreme planetary system. \subsection{Open issues}\label{sec:dis_ass} %\subsubsection{Initial fragment mass and gas accretion} The population synthesis model of \cite{NayakshinFletcher15} assumes, for simplicity, that gas fragments evolve at a constant {\it gas} mass until they are disrupted or they collapse. The disruption is assumed to remove all of the gas envelope except for the dense layers of gas strongly bound to the core, the core atmosphere (\S \ref{sec:atm}). This is based on the fact that a polytropic gas clump with index $n=5/2$ is strongly unstable to the removal of mass as it expands as $R_{\rm p}\propto M_{\rm p}^{-3}$ when the mass is lost. Within these assumptions, the model requires gas clumps with the minimum initial mass min[$M_{\rm in}$]$\sim (0.5-1)\mj$ to account for the observed gas giant planets, many of which have mass around that of Jupiter or less. This is somewhat uncomfortable since most authors \citep[e.g.,][and \S \ref{sec:AorM}]{ForganRice13} find that the minimum initial mass of a gas clump born by gravitational instability of a protoplanetary disc is $M_{\rm in} \sim 3-10\mj$, and that gas clumps may accrete more gas \citep[e.g.,][]{KratterEtal10}. This important disagreement needs to be investigated with 3D numerical simulations of both fragmenting discs and individual gas clumps. Similarly, 3D numerical simulations of gas fragment collapse are needed to ascertain angular momentum evolution of gas clumps, which is of course not resolved in the current 1D population synthesis. This evolution may dictate how much of the clump collapses into the planet proper and how much into the circum-planetary disc \citep{BoleyEtal10,GalvagniEtal12}, and what the spins of the planets and the core are \citep{Nayakshin11a}. Formation of the circum-planetary disc is key to formation of planet satellites. Further, grain sedimentation, core formation and especially planetesimal/debris formation within the fragment are certainly not spherically symmetric (e.g., see Fig. \ref{fig:num3D}), so 3D coupled gas-grain simulations of gas clumps are urgently needed. %Risking some speculation at this point (based on preliminary results, though), it is possible that grain sedimentation modifies the structure of the fragment from the polytrop assumed in the model, steepening the density profile of the clump. If this effect is strong enough then the clump may loose mass gradually rather than abruptly when it fills its Roche lobe. In this case a $1\mj$ gas giant planet may have started as a $3-5\mj$ gas fragment. Another unsolved issue is gas accretion onto gas clumps, which is likely to control the frequency with which planets are made as opposed to brown dwarfs \citep[][see also \S \ref{sec:AorM}]{ZhuEtal12a,NayakshinCha13,Stamatellos15}. \SNc{Preliminary work (\S \ref{sec:desert} shows that efficiency of gas accretion strongly depends on the cooling rate of gas in the Hill sphere of the planet. This suggests that this issue will remain uncertain for some time since dust opacity of the gas is uncertain.} 3D simulations are also needed to address how the presence of multiple gas clumps changes the predictions of population synthesis \citep[][allowed multiple gas fragments in their protoplanetary discs, but it was not possible to track stochastic clump-clump interactions or orbit interchanges]{ForganRice13}. So far, 3D numerical simulations of fragmenting discs did not resolve the internal processes within the fragments, and have also been performed for a relatively small number of test cases \citep[e.g.,][]{BoleyEtal10,ChaNayakshin11a}. Ideally, the strengths of the 1D isolated clump models (grain physics, long term evolution of the clumps and the disc) should be imported into the 3D simulations of global discs with self-consistent fragment formation in order to overcome the shortcomings. Another assumption made in the population synthesis presented here is that dust opacity has not been modified much by grain growth inside the clumps. This is an approximation only. Grain growth clearly occurs in protoplanetary discs and should be included into the models. Numerical experiments of \cite{Nayakshin15c} suggest that grain opacity reduction by a factor of $\sim 3$ can be tolerated, but factors of tens would be too large. Self-consistent models of fragment evolution with grain growth \citep[in the style of][]{HB11} and metal loading are needed to explore these issues better. Tidal Downsizing hypothesis is very young and is so far untested on dozens of specific planet formation issues in the Solar System and beyond, such as formation of short period tightly packed systems \citep[e.g.,][]{HandsEtal14}, the role of ice lines in the model, etc. and etc. \SNc{One may clearly critique the model for failing to address these systems. However, } these issues have not been covered here not because of the author's desire to hide away from the data but rather due to a lack of detailed work on these specific issues. Commenting on these without performing a thorough calculation first would amount to speculation one way or another. The author plans, and invites the community, to examine these additional constraints in the future. | 16 | 9 | 1609.07503 |
1609 | 1609.06735_arXiv.txt | \noindent We examine updated prospects for detecting WIMPs in supersymmetric models via direct and indirect dark matter search experiments. We examine several historical and also still viable scenarios: projections for well-tempered neutralinos (WTN), projections from the MasterCode (MC), BayesFits (BF) and Fittino (FO) collaborations, non-thermal wino dark matter (NThW) and finally mixed axion-higgsino dark matter from SUSY with radiatively-driven naturalness (RNS). The WTN is ruled out by recent limits from XENON and LUX collaborations. The NThW scenario, previously on tenuous ground due to gamma-line searches, appears also ruled out by recent combined Fermi-LAT/MAGIC limits combined with new HESS results from continuum gamma rays. Substantial portions of MC parameter space and 1 TeV higgsino parameter space from BF group are ruled out. The 100-300 GeV higgsino-like WIMP from RNS survives due to its possible depleted local abundance (where the axion may make up the bulk of dark matter). Projections from ton-scale noble liquid detectors should discover or rule out WIMPs from the remaining parameter space of these surviving models. \vspace*{0.8cm} | Supersymmetric models of particle physics have long generated excitement due to their ability to tame the naturalness or hierarchy problem associated with quadratic divergences in the Higgs mass~\cite{wittenkaul}. These models actually receive indirect support from experiment in that 1. the measured values of the gauge couplings from LEP unify to a common value at $m_{\rm GUT}\simeq 2\times 10^{16}$ GeV under Minimal Supersymmetric Standard Model (MSSM) renormalization group (RG) evolution~\cite{gauge}, 2. the measured value of the top quark mass is in the right range to trigger a radiative breakdown of electroweak symmetry~\cite{rewsb} and 3. the measured value of the Higgs boson mass~\cite{lhc_higgs} falls squarely within the narrow allowed window required by the MSSM, namely $m_h \lesssim 135$ GeV~\cite{mhiggs}. In addition, the lightest SUSY particle (LSP) is expected to be absolutely stable under conservation of $R$-parity which is highly motivated both by theoretical unification issues and also by the need to stabilize the proton. In this case, then the LSP -- assumed here to be the lightest neutralino of SUSY, $\tz_1$ -- presents an excellent candidate for cold dark matter. Simple calculations of its relic abundance indicate about the right level of thermal dark matter production in the early universe to gain accord with measured values -- a situation known as the WIMP miracle. Thus, WIMPs (weakly interacting massive particles) from supersymmetric models have long been an important target for dark matter hunters~\cite{hunt}. However, lately this long-dominant paradigm appears to be under considerable siege due to: \begin{itemize} \item lack of SUSY signals at the CERN Large Hadron Collider (LHC)~\cite{lhc_s} and \item the rather high value of $m_h\simeq 125$ GeV requires TeV-scale highly mixed top squarks, a situation in conflict with some early evaluations of SUSY electroweak naturalness~\cite{oldnat,Papucci:2011wy} and \item the lack of any (definitive, verifiable) WIMP signal in either direct or indirect dark matter detection experiments~\cite{Baudis:2015mpa}. \end{itemize} Given the above conflicting currents, it is incumbent upon theorists to take occasional stock of the theory vs. experiment situation with regard to which theoretical models are excluded by data, which (if any) are allowed, how plausible the surviving models are, and what remains to be done to verify or exclude the surviving models. In this paper we present such an evaluation. We focus our attention on several recent evaluations of SUSY model parameter space with regard to direct and indirect dark matter detection. These include: \begin{itemize} \item models of well-tempered neutralinos (WTN)~\cite{ArkaniHamed:2006mb}, \item the MasterCode (MC) evaluation of Constrained Minimal Supersymmetric Standard Model (CMSSM) parameter space~\cite{Buchmueller:2010ai}, \item the BayesFIT (BF) group evaluation of CMSSM parameter space~\cite{Roszkowski:2014wqa}, \item the Fittino (FO) group evaluation of CMSSM parameter space~\cite{Bechtle:2015nua}, \item projections for non-thermal wino-like WIMPs (NThW), \item projections from SUSY models with radiatively-driven naturalness (RNS) and a higgsino-like WIMP\cite{Baer:2011ec,Baer:2013vpa,Bae:2015jea} and \item projections from the 19 free weak scale parameter phenomenological MSSM or pMSSM~\cite{Cahill-Rowley:2014boa}. \end{itemize} The first five of these models generally assume the (thermally and non-thermally produced) relic abundance of SUSY WIMPs saturates the measured dark matter abundance. The fifth model requires naturalness in both the electroweak and QCD sectors of the theory and thus includes two dark matter particles: a higgsino-like WIMP required by electroweak naturalness and an axion which is required in QCD for a natural solution to the strong CP problem. The pMSSM evaluations require the thermally-produced WIMP abundance to lie at or below the measured value $\Omega_{\tz_1}^{\rm TP}h^2\le 0.12$. The above SUSY models are confronted by updated experimental exclusion plots. These include: \begin{itemize} \item updated spin-independent (SI) scattering limits from 447 days of XENON100~\cite{Aprile:2016swn}, PandaX~\cite{Tan:2016zwf} and 332 lives days of exposure from the LUX experiment~\cite{Akerib:2016vxi}, \item improved spin-dependent (SD) scattering limits on dark matter annihilations in the Sun from IceCube~\cite{Aartsen:2016exj}, \item new combined indirect detection (IDD) limits from Fermi-LAT and MAGIC collaborations on gamma rays arising from WIMP annihilations into $W^+W^-$ states in dwarf spheroidal galaxies~\cite{Ahnen:2016qkx} and \item search for WIMP annihilations in the galactic center via ten years of data from the HESS collaboration~\cite{::2016jja}. \end{itemize} Along with the above excluded regions, it is worthwhile to confront the theoretical expectations against projections from future direct and indirect detection searches. The wide variety of new and upgraded WIMP search experiments are aiming towards ever greater sensitivity which promises to either discover SUSY or other WIMP dark matter or else exclude many compelling models. In accord with our goal of an updated assessment of theory vs. experiment on SUSY WIMP dark matter, in Sec. \ref{sec:models} we review some of the major features of the above listed SUSY WIMP models. In Sec. \ref{sec:SI}, we compare current limits for SI direct dark matter detection against projections from the various models. The case of SD WIMP detection is shown in Sec. \ref{sec:SD}. In Sec. \ref{sec:IDD}, we show results from IDD of WIMPs from searches for excesses in continuum gamma ray spectra emanating from galactic WIMP-WIMP annihilation. One useful feature of our results is that projections from the various models can be compared on a single plot. Furthermore, each model is projected onto each different search plot so that the strengths of different search techniques can be compared. In Sec. \ref{sec:conclude} we present a summary and conclusions. | \begin{itemize} \item The well-tempered neutralino is solidly excluded by recent XENON100, PandaX and LUX SI direct detection bounds. \item The non-thermal wino which might comprise all dark matter was previously claimed to be excluded based mainly on gamma ray line searches. It now seems also excluded by gamma ray continuum searches by Fermi-LAT/MAGIC combined with recent HESS results. It will also be probed completely via multi-ton noble liquid detectors via SI scattering. The scenario of wino-like WIMP seems to survive if one postulates that the wino {\it comprises only a fraction} of the dark matter~\cite{Fan:2013faa} with {\it e.g.} axions comprising the remainder~\cite{Bae:2015rra}. \item Predictions from the CMSSM model have been strongly constrained by recent LUX SI DD limits although broad sections of parameter space still survive. These all seem to have $m_{\chi}\gtrsim 350$ GeV. Multi-ton noble liquid detectors will be needed to completely explore the allowed parameter space. This model may already be considered not-so-pausible because the remaining parameter space gives rise to a $\mu$ parameter with $|\mu |\gg m_Z$: this can be interpreted as a poor prediction of $m_Z$ if fine-tuning had not been invoked. \item The RNS models with small $\mu \lesssim 300$ GeV are natural and predict the existence of a higgsino-like LSP that comprises only a fraction of the dark matter. The predicted parameter space, even accounting for a depleted local abundance, is amenable to searches by ton-scale noble liquid detectors such as XENON, LZ, DarkSide, DEAP and DARWIN. If naturalness in the QCD sector is eschewed so that the axion does {\it not} constitute the extra relic abundance, then non-thermal higgsino production must be invoked and the higgsinos would comprise all dark matter with $\xi =1$. This case is already severely constrained by SI DD searches. \item If XENON1T does not see a WIMP signal, the remaining parameter space for the CMSSM model (that saturates the measured dark matter abundance) predicts a heavy gluino mass $m_{\tilde{g}} \gtrsim 8$ TeV which is far above from expectations from a natural SUSY model. This lower limit on gluino mass applies for NUHM2 model with $\sim1$ TeV higgsino-like neutralino as well. RNS models with $m_{\tilde{g}}\lesssim4$ TeV will still survive since the SI detection rate is scaled down by the factor $\xi$. Furthermore, resonance annihilations such as $\chi_1\chi_1\to A/H$ would decrease the local WIMP abundance and push a substantial amount of the RNS region beyond XENON1T reach. Indeed for $m_{A/H} \simeq 2 m_{\tz_1}$, $\Omega_{\chi_1}^{\rm TP}h^2$ decreases by a factor of $\sim30$ but fortunately DarkSide-20K and DEAP-50T will eventually explore such regions. We expect additional contributions to the neutralino abundance from axino decays (which increases $\xi$); then a WIMP detection would be expected sooner. \item If a WIMP signal is seen in the near future, then it will be highly useful to be able to distinguish its properties based on mass and mixing. The case of ascertaining a WIMP mass $m_{\chi}\lesssim 350$ GeV (RNS) from the CMSSM case of $m_{\chi}\gtrsim 350$ GeV may be possible using mass measurement techniques and signals from different target materials~\cite{wimpmass}. \item While many constrained SUSY models are indeed under seige from direct/indirect WIMP search experiments, the pMSSM-- with unconstrained soft parameters-- is typically less under seige. For instance, if the WIMP is nearly pure bino with a diminished relic abundance such that $\Omega h^2(bino)\simeq 0.12$ (due perhaps to co-annihilation or resonance annihilation or entropy dilution) and all other sparticles are heavy and beyond collider reach, then such scenarios yield very low direct/indirect detection rates. Such an unusual scenario might survive most or all search venues. \item Detection of WIMPs or associated particles (in this case superpartners) at collider experiments will provide crucial information for distinguishing amongst the models considered here. \end{itemize} | 16 | 9 | 1609.06735 |
1609 | 1609.08728_arXiv.txt | In this manuscript, we study properties of long-term optical variability of a large sample of 106 SDSS spectroscopically confirmed AGN with double-peaked broad low-ionization emission lines (double-peaked emitters). The long-term optical light curves over 8 years are collected from the Catalina Sky Surveys Data Release 2. And, the Damped Random Walk (DRW) process is applied to describe the long-term variability of the double-peaked emitters. Meanwhile, the same DRW process is applied to long-term optical light curves of more than 7000 spectroscopically confirmed normal quasars in the SDSS Stripe82 Database. Then, we can find that the DRW process determined rest-frame intrinsic variability timescales $\ln(\tau/{\rm days})$ are about 5.8 and about 4.8 for the double-peaked emitters and for the normal quasars, respectively. The statistically longer intrinsic variability timescales can be confirmed in the double-peaked emitters, after considerations of necessary effects, such as the effects from different distributions of redshift, BH mass and accretion rate between the double-peaked emitters and the normal quasars. Moreover, a radial dependence of accretion rate $\dot{m}_{\rm R}~\propto~R^\beta$ with larger values of $\beta$ could be an acceptable interpretation of the longer intrinsic variability timescales in the double-peaked emitters. Therefore, there are different intrinsic properties of emission regions between the double-peaked emitters and the normal quasars. The double-peaked emitters can be well treated as an unique subclass of AGN. | Variability is one of fundamental characteristics of active galactic nuclei (AGN) \citep{um97}. To study AGN variability can provide further clues to properties of emission regions of AGN \citep*{re84, tc00, haw02, hh06, me11}. And commonly, there are three characteristic timescales of around days to hundreds of days through accretion physics \citep*{pe01, kbs09}, the light crossing timescale ($t_{\rm lc}$), the gas orbital timescale ($t_{\rm orb}$) and the accretion disk thermal timescale ($t_{\rm th}$), \begin{equation} \begin{split} &t_{\rm lc}~=~1.1~\times~M_8\times~R_{\rm 2}~{\rm days} \\ &t_{\rm orb}~=~104~\times~M_8\times~R_{\rm 2}^{3/2}~{\rm days}\\ &t_{\rm th}~=~4.6~\times~(0.01/\alpha)~\times~M_8\times~R_{\rm 2}^{3/2}~{\rm years} \end{split} \end{equation}, where $M_8~=~M_{\rm BH}/{\rm 10^8~M_\odot}$ represents black hole (BH) mass, $R_{\rm 2}$ represents distance of emission regions to central engine in unit of ${\rm 100~R_G}$ (${\rm R_G}$ is the Schwarzschild radius), and $\alpha$ means the standard disk viscosity parameter. Therefore, the expected AGN variability timescales strongly connected with accretion physics should sensitively depend on the fundamental parameter of AGN, the BH mass, and on the distance of emission regions to the central black hole. Hence, to study AGN variability could provide further properties of emission regions of AGN. More recently, the Damped Random Walk (DRW) process \citep{bd02} (or AutoRegressive process), with two basic parameters of the intrinsic variability timescale $\tau$ and the intrinsic variability amplitude $\sigma$, has been proved to be a preferred modeling process to describe AGN intrinsic variability. \citet{kbs09} firstly proposed the DRW process to describe the AGN intrinsic variability, and found that the AGN intrinsic variability timescales are consistent with disk orbital or thermal timescales. \citet{koz10} provided an improved robust mathematic method to estimate the DRW process parameters, and found that AGN variability could be well modeled by the DRW process. Then, \citet{zu11} provided a public code of JAVELIN (http://www.astronomy.ohio-state.edu/\~{}yingzu/codes.html\#javelin) (Just Another Vehicle for Estimating Lags In Nuclei) based on the method in \citet{koz10} to describe the AGN variability by the DRW process. Meanwhile, there are many other reported studies on the AGN variability through the DRW process. \citet{mi10} modeled the variability of about 9000 spectroscopically confirmed quasars covered in the SDSS (Sloan Digital Sky Survey) Stripe82 region, and found correlations between the AGN parameters and the DRW process determined parameters. \citet{bj12} proposed an another fully probabilistic method for modeling AGN variability by the DRW process. \citet{ak13} have shown that the DRW process is preferred to model AGN variability, rather than several other stochastic and deterministic models, by fitted results of long-term variability of 6304 quasars. \citet{zu13} have checked that the DRW process provided an adequate description of AGN optical variability across all timescales. Therefore, the DRW process determined parameters from the long-term AGN variability can be well used to check or predict further different properties of different kinds of AGN with probable different intrinsic properties of emission regions. Among broad line AGN, there is one special kind of AGN, the AGN with double-peaked broad low-ionization emission lines (hereafter, double-peaked emitters). Since the first reported double-peaked emitter of 3C390.3\ in 1980s \citep*{ss83}, more and more double-peaked emitters have been reported in \citet*{eh94, st03, sh11}, etc.. And the proposed theoretical model with broad emission lines coming from central accretion disk has been preferred to explain the unique double-peaked broad emission lines \citep*{ch89, el95, fe08}. Long-term variability of a few double-peaked emitters, especially profile variability of the double-peaked broad emission lines, have been reported in \citet*{era97, sh01, sn03, lew10, zh13}, etc., and applied to test the accretion disk origin of the double-peaked broad emission lines. However, there are so far no clear statistic results on the long-term variability properties of double-peaked emitters by the DRW process. As the results in \citet*{mi10, sch10, mh11, sch12, zh14}, etc., the public SDSS Stripe82 Database (hereafter, SDSS S82) \citep{bra08} is the widely used database to study the long-term SDSS AGN variability. However, there are only several double-peaked emitters in the SDSS S82, and it is hard to do statistical research on the long-term variability of a large sample of double-peaked emitters through the SDSS S82. More fortunately, the well-known Catalina Sky Survey (CSS) \citep{dra09} has provided public long-term (over 8 years) light curves of more than 500 million objects from an area of 33000 square degrees. And we can find that hundreds of double-peaked emitters are covered in the CSS. Thus, it is the time to statistically study the long-term variability of a large sample of double-peaked emitters, to check whether are there different properties of emission regions in the double-peaked emitters. The manuscript is organized as follows. In Section 2, we presented our main results and necessary discussions on long-term variability properties determined by the DRW process for a large sample of double-peaked emitters and a large sample of normal quasars. Then, in Section 3, we gave our final conclusions. | Our main results and conclusions are as follows. First and foremost, the long-term light curves from the CSS DR2 have been well analyzed by the DRW process for a large sample of SDSS spectroscopically confirmed double-peaked emitters. Meanwhile, the long-term light curves from the SDSS S82 have been analyzed by the same DRW process for the spectroscopically confirmed normal quasars. Besides, the longer variability timescales can be confirmed in the double-peaked emitters than in the normal quasars, even after considerations of necessary effects, such as effects from different distributions of redshift, BH mass and accretion rate between the normal quasars and the double-peaked emitters. The radial dependence of accretion rate $\dot{m}_{\rm R}~\propto~R^{\beta}$ with larger value of $\beta$ could be an acceptable interpretation of the longer variability timescales in the double-peaked emitters. Last but not the least, the intrinsic difference between the double-peaked emitters and the normal quasars strongly supports that the double-peaked emitters could be well treated as a unique subclass of AGN. | 16 | 9 | 1609.08728 |
1609 | 1609.01862_arXiv.txt | Einstein established the theory of general relativity and the corresponding field equation in 1915 and its vacuum solutions were obtained by Schwarzschild and Kerr for, respectively, static and rotating black holes, in 1916 and 1963, respectively. They are, however, still playing an indispensable role, even after 100 years of their original discovery, to explain high energy astrophysical phenomena. Application of the solutions of Einstein's equation to resolve astrophysical phenomena has formed an important branch, namely relativistic astrophysics. I devote this article to enlightening some of the current astrophysical problems based on general relativity. However, there seem to be some issues with regard to explaining certain astrophysical phenomena based on Einstein's theory alone. I show that Einstein's theory and its modified form, both are necessary to explain modern astrophysical processes, in particular, those related to compact objects. | Within a few months of the celebrated discovery of Einstein's field equation \cite{ein}, Schwarzschild obtained its vacuum solution in spherical symmetry \cite{sch}. However, it took almost another half a century before Kerr obtained its vacuum solution for an axisymmetric spacetime \cite{kerr}, which was a very complicated job at that time. The former solution is very useful to understand the spacetime properties around a static black hole, called Schwarzschild black hole. The latter solution corresponds to the spacetime properties around a rotating black hole, called Kerr black hole, in particular after its generalization by Boyer and Lindquist \cite{bl} to its maximal analytic extension. Both the solutions have enormous applications to relativistic astrophysics; however, as black holes in general possess spin, the Kerr solution is much more important. In the Boyer-Lindquist coordinates, the outer radius of a black hole is defined as $r_+=GM/c^2\left(1+\sqrt{1-a^2}\right)$, when $M$ is the mass of the black hole, $c$ the speed of light, $G$ the Newton's gravitational constant and `$a$' the spin parameter (angular momentum per unit mass) of the black hole. Hence, for $|a|> 1$, the collapsed object will form a naked singularity without an event horizon, rather than a black hole. In addition, $a=0$ corresponds to the Schwarzschild black hole. Hence, predicting `$a$' of black holes from observed data would serve as a natural proof for the existence of the Kerr metric in the universe. In the presence of matter (i.e. nonvanishing energy-momentun tensor of the source field $T_{\mu\nu}$), there are a variety of solutions of Einstein's equations (e.g. \cite{hr,cook,xns}), depending upon the equation of state (EoS). In order to understand the properties of neutron stars, and also white dwarfs, these solutions serve as very important tools. In this context, a very important class of objects is binary pulsars, which are one of the few objects that help to test Einstein's general relativity (GR). Such binary systems have a pulsating star along with a companion, often a white dwarf or a neutron star. PSR~B1913+16 was the first binary pulsar discovered by J. Taylor and R. Hulse which led to them wining the Nobel Prize in Physics in 1993 \cite{hulse}. It has been found that its pulsating rate varies regularly due to the Doppler effect, when it is orbiting another star very closely at a high velocity. PSR~B1913+16 also allowed determining accurately the masses of neutron stars, using relativistic timing effects. When the two components of the binary system are coming closer, the gravitational field appears to be stronger and, hence, creating time delays which furthermore in turn increase pulse period. Binary pulsars, as of now, are perhaps the only tools based on which gravitational waves are being evident. According to GR, two neutron stars in a binary system would emit gravitational waves while orbiting a common center of mass and, hence, carrying away orbital energy. As a result, the two stars come closer together, shortening their orbital period, which we observe. Although the validity of the solutions of Einstein's equation, i.e. GR, has been well tested, particularly in the weak field regime --- such as through laboratory experiments and solar system tests --- question remains, whether GR is the ultimate theory of gravitation or it requires modification in the strong gravity regime. Indeed, scientists have been trying to resolve the astrophysical problems related to the strong field regimes, like expanding universe, massive neutron stars, by introducing modified theories of GR (e.g. \cite{staro,capo,eksi}). Recently, there are observational evidences for massive neutron star binary pulsars PSR~J1614-2230 \cite{nat} and PSR~J0348+0432 \cite{sc} with masses $1.97M_\odot$ and $2.01M_\odot$ respectively, where $M_\odot$ is solar mass. Similarly, there is a lot of interest in exploring massive white dwarfs (see \S4 for details). The possibility of very massive neutron stars has been examined \cite{weissenborn} in the presence of hyperons and the conditions to obtain the same. Note that the likely presence of $\Lambda$-baryons in dense hadronic matter tends to soften EoS such that the above mentioned massive neutron stars are difficult to explain, known as `hyperon problem'. Based on the quark-meson coupling model, it has been shown \cite{whittenbuary} that the maximum mass of neutron stars could be $\approx 2M_\odot$, when nuclear matter is in $\beta$-equilibrium and hyperons must appear. Apart from the EoS based exploration, neutron stars with mass $\gtrsim 2M_\odot$ have been shown to be possible by exploring effects of magnetic fields, with central field $\sim 10^{16}$G \cite{pili}, and modification to GR \cite{capo,eksi,cheon}. Black holes are not visible and neutron stars too are hardly visible, unless the latter possess stronger magnetic fields. Hence, in order to understand their properties, light coming out off the matter infalling towards them (as well as influenced by them), called accretion, plays a very important role. Study of accretion around compact objects is a vast part of relativistic astrophysics. While a simple spherical accretion model in the Newtonian framework was introduced by Bondi in the 50s \cite{bondi}, later its general relativistic version was worked out by Michael \cite{michael} in the Schwarzschild spacetime, which was perhaps the first venture into accretion physics in GR. However, generically, accretion flows possess angular momentum, as inferred from observed data, forming accretion disks around compact objects. Such a (Keplerian) disk model in the general relativistic framework was formulated by Novikov and Thorne \cite{nt73} (whose Newtonian version \cite{ss73} is highly popular as well). Later on, in order to satisfactorily explain observed hard X-rays, the geometrically thick (and sub-Keplerian) disk model was initiated, in the Newtonian (e.g. \cite{sel76,ny94}), pseudo-Newtonian (e.g. \cite{pw80,m02}), as well as general relativistic (e.g. \cite{liang80,c90,gp98,belo07}) frameworks. All of them explicitly reveal the importance of GR in accretion flows. Furthermore, observed jets from black hole sources have been demonstrated to be governed by general relativistic effects in accretion-outflow/jet systems, based on general relativistic magnetohydrodynamic (GRMHD) simulations, with and without the effects of radiation (e.g. \cite{sasha11,jon12,jon14}). It has been demonstrated therein that the spin of black holes plays a crucial role to control the underlying processes. It is also known that accretion flows (directly or indirectly) are intertwined with several other observed relativistic features in modern astrophysics, e.g. quasi-periodic oscillation (QPO) in compact sources, gamma-ray bursts (combined disk-jet systems), supernovae etc. In recent years, many observations reveal that several gamma-ray bursts (which are the extremely energetic explosions that have been observed in distant galaxies) occur in coincidence with core-collapse supernovae, which are related to the formation of black holes and neutron stars. American federal institutions such as NASA, European agencies such as ESO, Japanese institutions etc. have been devoted to conduct numerous satellite experiments (such as HST, Chandra, XMM-Newton, Swift, Fermi, Astro-H, Suzaku etc.) which regularly receive data from galactic and extragalactic (compact) sources, producing all the above mentioned features. Similarly, Indian satellite Astrosat is gathering data from black hole, white dwarf and neutron star sources. All these missions help in understanding relativistic astrophysical sources, their evolution and up-to-date status. They furthermore help to verify theoretical concepts of GR. In the present article, I plan to touch upon some of the specific issues in relativistic astrophysics, the ones which are very {\it hot-topics} at present and I am working on them, in detail. However, before I go into their detailed discussions, in the next section, let me recall some of their basic building blocks. | In the last several decades, relativistic astrophysics has turned out to be a highly important branch in astrophysics. In this branch, many major astrophysical discoveries are still taking place in the contexts of black holes, quasars, neutron stars, white dwarfs, X-ray binaries, gamma-ray bursts, particle acceleration, the cosmic background, dark matter, dark energy etc., even 100 years after Einstein's discovery of GR, which is the basic building block for them. The present article has touched upon some of the underlying latest astrophysical problems and their possible resolutions. It has been revealed that while Einstein's gravity itself is indispensable to uncover modern high energy astrophysical problems, modified Einstein's gravity also appears to be playing an important role behind certain phenomena and, in general, to explain astrophysical processes.\\ \\ \noindent {\large\bf Acknowledgment}\\ \\ \noindent I am thankful to Indrani Banerjee, Mukul Bhattacharya, Upasana Das, Chanda J. Jog, Subroto Mukerjee, A. R. Rao, Prateek Sharma and Sathyawageeswar Subramanian, for continuous discussions on the topics covered in this article. | 16 | 9 | 1609.01862 |
1609 | 1609.08943_arXiv.txt | \label{S-Abstract} We investigated some properties of coronal mass ejections (CMEs), such as speed, acceleration, polar angle, angular width and mass, using data acquired by the {\it Large Angle Spectrometric coronagraph} (LASCO) onboard {\it Solar and Heliospheric Observatory} (SOHO) from 31 July 1997 to 31 March 2014, \ie during the Solar Cycles 23 and 24. We used two CME catalogs: one provided by the {\it Coordinated Data Analysis Workshops} (CDAW) Data Center and one obtained by the {\it Computer Aided CME Tracking software} (CACTus) detection algorithm. For each dataset, we found that the number of CMEs observed during the peak of Cycle 24 was higher or comparable to the one during Cycle 23, although the photospheric activity during Cycle 24 was weaker than during Cycle 23. Using the CMEs detected by CACTus we noted that the number of events $[N$] is of the same order of magnitude during the peaks of the two cycles, but the peak of the CME distribution during Cycle 24 is more extended in time ($N$ $>$ 1500 during 2012 and 2013). We ascribe the discrepancy between CDAW and CACTus results to the observer bias for CME definition in the CDAW catalog. We also used a dataset containing 19,811 flares of C-, M-, and X-class, observed by the {\it Geostationary Operational Environmental Satellite} (GOES) during the same period. Using both datasets, we studied the relationship between the mass ejected by the CMEs and the flux emitted during the corresponding flares: we found 11,441 flares that were temporally correlated with CMEs for CDAW and 9120 for CACTus. Moreover, we found a log--linear relationship between the flux of the flares integrated from the start to end in the 0.1\,--\,0.8 nm range and the CME mass. We also found some differences in the mean CMEs velocity and acceleration between the events associated with flares and those that were not. | \label{S-Introduction} Many studies of eruptive phenomena occurring in the solar atmosphere, such as flares, filament eruptions and coronal mass ejections (CMEs) are aimed at understanding the role the global and local magnetic fields play in their triggering. According to most recent theoretical and observational works, flares, filaments, and CMEs are all manifestations of the same physical phenomenon: magnetic reconnection. However, the temporal and spatial relationships among these events are still unclear. A preliminary aspect in this kind of investigation concerns the properties of CMEs. For instance, \cite{Ivanov2001} studied the semiannual mean CME velocities for the time interval 1979\,--\,1989 and revealed a complex cyclic variation with a peak at the solar-cycle maximum and a secondary peak at the minimum of the cycle. The growth of the mean CME velocity is accompanied by a growth of the mean CME width. Moreover, they concluded that the secondary peak of the semiannual mean CME velocity in 1985\,--\,1986 is due to a significant contribution of fast CMEs with a width of about $100^{\circ}$ at the minimum of the cycle. This peak is supposed to be due to the increasing role of the global large-scale magnetic-field system at the minimum of the solar cycle. \cite{Chen2006} reexamined whether flare-associated CMEs and filament eruption-associated CMEs have distinct velocity distributions and investigated which factors may affect the CME velocities. They divided the CME events observed from 2001\,--\,2003 into three types: the flare-associated type, the filament eruption associated type, and the intermediate type. For the filament eruption associated CMEs, the speeds were found to be strongly correlated with the average magnetic field in the filament channel. \cite{Cremades2007} presented a survey of events observed during the period 1980\,--\,2005 and found that the latitude of a CME matches well with the location of coronal streamers, in agreement with \citet{hun93}. More recently, \cite{Mittal2009a} have analyzed more than 12,900 CMEs observed by the { \it Solar and Heliospheric Observatory} (SOHO)/ { \it Large Angle Spectrometric coronagraph} (LASCO) during the period 1996\,--\,2007. They found that the speeds decrease in the decay phase of Solar Cycle 23. There is an unusual drop in speed in the year 2001 and an abnormal increase in speed in the year 2003. This increase corresponded to the so called Halloween events, \ie the high concentration of CMEs, X-class flares, solar energetic particle (SEP) events and interplanetary shocks observed during the months of October and November of that year. The same dataset showed that about 66\,\% of CMEs have negative acceleration, 25\,\% have positive acceleration and the remaining 9\,\% have very low acceleration \citep{Mittal2009b} in the outer corona. Some difficulties in understanding the relationships between flares and CMEs are due to the different methods of observation that must be used to investigate these phenomena. In fact, the coronagraphs used to observe the outer corona where the CMEs are detected occult the solar disk and do not allow one to observe the source region where the corresponding flares take place. Therefore, many authors have tried to study these relationships from a statistical point of view. For example, \cite{st.cyr91} considered, a dataset of two years, \ie from 1984 to 1986 acquired by the {\it Solar Maximum Mission} (SMM: \inlinecite{ph90}) (see Table \ref{T1}), found that 76\,\% of the CMEs were associated with erupting prominences, 26\,\% with H$\alpha$ flares, and 74\,\% with flares observed in the X-ray range. \cite{gil2000}, analyzing 18 CMEs observed by LASCO-C2 \citep{bec1995} and the ground-based {\it Mark-III K-Coronameter} (MK3) at the {\it Mauna Loa Solar Observatory} (MLSO: \citealp{mcf83}; \citealp{cyr99}) and 54 flares observed in H$\alpha$ during two years of observation, between 1996 and 1998, found that 94\,\% of H$\alpha$ flares were associated with CMEs and that 76\,\% of the CMEs were associated with eruptive prominences. Moreover, analyzing the same period, \cite{subd2001} using LASCO and the \textit{Extreme Ultraviolet Imaging Telescope} (EIT) instrument onboard \soho, \citep{del95}) found that 44\,\% of the CMEs were associated with eruptions of prominences embedded in an active region, while 15\,\% of those with eruptions occurred outside active regions. \cite{zho2003} used data taken by LASCO onboard \soho from 1997 to 2001 and selected 197 front-side halo CMEs. They found that 88\,\% of those CMEs were associated with flares, while 94\,\% were associated with eruptive filaments. For 59\,\% of the CMEs, their initiation seemed to precede the associated flare onset recorded by GOES: \citealp{how74} ; \citealp{ludjon81}), while 41\,\% of the CMEs seemed to follow the flare onset. \begin{table} \caption{Previous results on the correlation between CMEs, flares and eruptive prominences.} \label{T1} \begin{tabular}{lccccc} % Authors & Number & Period & CMEs & CMEs & CMEs \\ & of & & associated with & associated with & associated with \\ & events & & eruptive prominences & H$\alpha$ flares & X-ray flares \\ \hline \cite{st.cyr91} & 73 CMEs & 1984\,--\,1986 & 76\,\% & 26\,\% & 74\,\% \\ \cite{gil2000} & 18 CMEs & 1996\,--\,1998 & 76\,\% & 94\,\% & \\ \cite{subd2001} & 32 CMEs & 1996\,--\,1998 & 59\,\% & & \\ \cite{zho2003} & 197 CMEs & 1997\,--\,2001 & 94\,\% & 88\,\% & \\ \hline \end{tabular} \end{table} Many authors (see, for example,\cite{gop2015} \cite{gop2015b}, \cite{you2012}) investigated possible relationships between the CMEs physical parameters and the flare properties not excluding the narrow CMEs and using only the { \it Coordinated Data Analysis Workshops} (CDAW) dataset, even though the CACTus catalog was developed around 2004. The authors point out that the list is necessarily incomplete because of the nature of identification. In the absence of a perfect automatic CME-detection program, the manual identification is still the best way to identify CMEs \citep{you2012}.\\ Using the LASCO and EIT data taken by the \soho spacecraft, \cite{zha2001a} analyzed four events and found that the impulsive acceleration phase of the selected CMEs coincided well with the rise phase of the associated X-ray flares. Later, \cite{qiu2005} studied 11 events with varying magnetic-field configurations in the source regions and concluded that the CMEs velocities were proportional to the total magnetic-reconnection flux, while their kinetic energy was probably independent of the magnetic configuration of the source regions. An in-depth analysis of the correlation between X-ray flares and CMEs using GOES and LASCO archives from 1996 to 2006 has been performed by \cite{aar2011}. They considered 13,682 CMEs and selected 826 flare--CME pairs. They found that the CME mass increases with the flare flux, following an approximately log--log relationship: log(CME mass) $=$ 0.70 × log(flare flux), while the CME mass appears unrelated to their acceleration. % \cite{aar2011} also noted that CMEs associated with flares have higher average linear speeds ($495 \pm 8$ km\,s$^{-1}$) and negative average acceleration ($−1.8 \pm$ 0.1 m\,s$^{-2}$), while CMEs not associated with flares have lower average linear speed ($422 \pm 3$ km\,s$^{-1}$) and marginally positive average acceleration ($0.07 \pm$ 0.25 m\,s$^{-2}$). Finally, the width of CMEs resulted to be directly correlated with the flare flux: X-class flares are associated with the widest CMEs ($80^{\circ} \pm 10^{\circ}$),while B-class flares are associated with the narrowest CMEs ($42^{\circ}$ $\pm$ $1.4^{\circ} $). In this context, we intend to provide a further contribution to the knowledge of CMEs properties and of the correlation between flares and CMEs. In this article we present results obtained from the analysis of a dataset more extended than that of \cite{aar2011}, including 22,876 CMEs and 19,811 flares of GOES class C, M, and X observed from 31 July 1996 to 31 March 2014. We investigate how some previous mentioned relationships vary with the solar cycle. In the next Section we describe our dataset, in Section 3 we show our results, and in Section 4 we discuss the results and draw our conclusions. \urlstyle{same} | \label{S-conclusions} In this article we used the huge dataset of CMEs observed for nearly all of the operational time,to date, of the LASCO mission onboard \soho to infer some properties of these events over Solar Cycles 23 and 24 and to study their correlation with the flares observed in the X-ray range between 1.0 and 8.0 $\AA$, by GOES. We used two CME catalogs; one based on manual identification of CMEs (CDAW) and one based on their automatic tracking (CACTus). From the analysis that we have performed we conclude that the peak in the number of CMEs in Cycle 24 is higher than the number during Cycle 23. In particular, for the CDAW dataset the number of CMEs at the maximum of Solar Cycle 24 is higher than the number at the maximum of Solar Cycle 23; for CACTus the peaks during the maxima are similar, but the one corresponding to Solar Cycle 24 is more extended in time than the one corresponding to Solar Cycle 23. This result seem to be in contrast with the fact that the magnetic activity during Cycle 24 was weaker than during Cycle 23, as noted in the work of \cite{tjh2015} who analyzed the frequency shifts of the acoustic solar-modes measurement separately for the two cycles and found that the magnetic activity during Solar Cycle 24 was weaker than during Cycle 23.\\ Solar Cycle 24 has been extremely weak as measured by the sunspot number (SSN) and is the smallest since the beginning of the space age. The weak activity has been thought to be due to the weak polar field strength in Cycle 23. Several authors have suggested that the decline in cycle 24 activity might lead to a global minimum. (\citealp{pad2015}; \citealp{zol2014}).\\ From the analysis of the CME average velocity, we found two peaks that reflect the solar-activity cycles and can be interpreted, according to \cite{qiu2005} as an effect of the magnetic flux involved by the events during the solar maxima, but we also observe another peak at the minimum of the cycles, even if only for the CACTus dataset, in the year 2009. This peak agrees with the cyclic variation of the CME velocities in the previous solar-activity cycles, as reported by \cite{Ivanov2001}. From the distribution of the average acceleration of the CMEs, we see a maximum of about 15 m\,s$^{-2}$ $\pm$ 2.71 m\,s$^{-2}$ , corresponding to the minimum of the distribution of the average velocity (see Figure \ref{fig2}, upper and middle panel). We think that this peak may be due to the contribution of the slower CMEs occurring during solar-activity minimum; These CMEs are characterized by higher positive values of acceleration. We found also that the tail of the distribution of the higher velocities of the CMEs observed during the descending part of Solar Cycle 23 (from 2000 to 2006) is no longer present when going from the maximum (2000) to the minimum (2006) of the cycle (see Figure \ref{fig3}). The distribution of the CME angular widths for CDAW shows that on average, the narrower CMEs are slower and the majority of the CMEs are characterized by an angular width lower than $100^{\circ}.$ Only during the maximum of the solar cycle (2000 and 2001) do we observe a significant number of CMEs with an angular width larger than $100 \pm 0.44^{\circ} $ The CDAW and CACTus datasets present a different amplitude of the range spanned by the mean angular width, \ie for the CACTus catalog the mean width varies from $\approx 30^{\circ}$ during solar-activity minimum to $\approx 40^{\circ}$ during the maximum of activity, while for CDAW the mean width varies from $\approx 20^{\circ}$ to $\approx 80^{\circ}$. The latitude distribution of CMEs follows the latitude distribution of the closed-magnetic-field regions of the corona, which is consistent with the fact that CMEs originate in closed-field regions \citep{hun93}. We also note that the distribution of PA changes in time from a broader distribution in 2000 (near the maximum of Solar Cycle 23) to a more peaked distribution in 2006 (near the minimum of solar activity). Using the dataset of CMEs and flares and selecting the event occurring in the same time window of $\pm 2$ hour,$\pm 1$ hour and $\pm 30 $ minutes we identified CMEs and flares that are temporally correlated. Although the number of associated CMEs--flares that are both temporally and spatially correlated might seem low, \cite{aar2011}, studying the correlation between flares flux and CMEs mass, found a similar result with 826 associated CMEs--flares during the time interval 1996\, -- \,2006. \cite{you2012}, studied the correlation between flare flux and CME energy, and found 776 associated CME--flares during the time interval 1996\,--\,2010. Considering the flare start time, we found that the highest number of CMEs and flares detected in the CDAW dataset (59.57\,\%) are characterized by a difference in time between 10 and 80 minutes (see the black line in the top panel of Figure \ref{fig9}), in agreement with \citet{aar2011}. The CME--flare associated events for the CACTus dataset show a wider temporal range. We argue that this difference between the two datasets depends on the different criteria used by the observer for defining a CME in CDAW. A time window of 10--80 minutes is clear evidence that in many cases the flare occurs before the first observation of the CME in the coronagraph and, taking into account that the temporal resolution of LASCO is about 30 minutes, There are a number of cases in which the flare most likely precedes the CME initiation and may be the first manifestation of the initiation process. One should also need to investigate the role of filaments/prominences in the initiation. The shape of the distributions of C-, M-, and X-class flares associated with CMEs varies with the intensity of the flares, (see Figures \ref{fig10} and \ref{fig10b}), but it is similar for both datasets. In particular, we note that the distribution of X-class flares associated with CMEs is quite uniform with respect to the one of C- and M- class flares across the solar cycle. However, when we consider only the flares associated with CMEs in the $\pm 30 $ minutes time window, we find a distribution of the X-class flares more consistent with the solar cycle (see Figure \ref{fig10}, bottom panel). We found that most of the CMEs characterized by higher linear velocities are associated with flares (see-\eg - \cite{gos1976}; \cite{mon2003}). The mean velocities for CMEs associated with flares are higher than the velocities for CMEs not associated with flares in both datasets. Our results are therefore very similar to those found by \cite{aar2011}. Moreover, our analysis shows that the width of the CMEs associated with flares is positively correlated with the flare flux. The mean angular width of the flares associated with CMEs is $68.61 ^{\circ}$, $116.82 ^{\circ} $, $258.49 ^{\circ}$ for C-, M-, and X-class flares, respectively. The distribution of the CME acceleration ( left panel of Figure \ref{fig11d}) shows that the CMEs associated with flares have an average acceleration of -0.32 $\pm$ 0.34 m\,s$^{-2}$ , while the CMEs not associated with flares have an average positive acceleration of 3.44 $\pm$ 0.37 m\,s$^{-2}$ . We suggest that these values are slightly different from those found by \cite{aar2011} due to the diverse sample of events considered in our article. We also used our dataset to further extend the study on the log--linear relationship between the flare flux [$\phi_f$] and the CME mass [$m_{CME}$] performed by \citet{aar2011}. In this case, we considered not only the temporal correlation between flares and CMEs, but also their spatial correlation. As mentioned above, this allows us to be more confident that the CMEs and the flares may be linked, although some events may be neglected. We found that $\log(m_{CME}) \propto 0.23\,\log (\phi_f)$. The differences between the results of \cite{aar2011} and ours may be due to several reasons. First of all we considered a more extended dataset. We also used the flux of the flares integrated from their start to end in the 0.1\,--\,0.8\,nm range. Finally, we used different criteria to determine the association between flares and CMEs. Therefore, we conclude that the log--linear relationship is valid not only when we consider the peak of the flare flux, but also when we consider the energy released during the whole event. It is worth of note that this relationship disappears when we limit the sample of flare--CME pairs to the different phases of the solar cycle. This means that the log--linear relationship is valid only from a statistical point of view, \ie when we consider a large sample of events. We argue that this result is due to different aspects (intensity of magnetic field, magnetic reconnection, configuration of sunspots on the solar surface) that influence the evolution of these phenomena. Further study and analysis must be made on the intensity of the magnetic flux involved in these phenomena and consequently on the capacity to eject the mass into in the interplanetary space. In fact, the magnetic configuration can play an important role in determining the different ways to buildup and release magnetic free energy and the role of magnetic reconnection \begin{ack} The authors wish to thank the anonymous referee for their useful suggestions which allowed to improve the article. This research work has received funding from the European Commission’s Seventh Framework Programme under the Grant Agreements no. 606862 (F-Chroma project) and no. 312495 (SOLARNET project). This research is also supported by the ITA MIUR-PRIN grant on ``The active sun and its effects on space and Earth climate'' and by Space WEather Italian COmmunity (SWICO) Research Program. We are also grateful to the University of Catania for providing the Grant FIR 2014. \end{ack} | 16 | 9 | 1609.08943 |
1609 | 1609.01265_arXiv.txt | The superconducting critical temperature ($T_\mathrm{c} >$ 15 K) of niobium titanium nitride (NbTiN) thin films allows for low-loss circuits up to 1.1 THz, enabling on-chip spectroscopy and multi-pixel imaging with advanced detectors. The drive for large scale detector microchips is demanding NbTiN films with uniform properties over an increasingly larger area. This article provides an experimental comparison between two reactive d.c. sputter systems with different target sizes: a small target ($\diameter$100 mm) and a large target (127 mm $\times$ 444.5 mm). This article focuses on maximizing the $T_\mathrm{c}$ of the films and the accompanying $I$-$V$ characteristics of the sputter plasma, and we find that both systems are capable of depositing films with $T_\mathrm{c} >$ 15 K. The resulting film uniformity is presented in a second manuscript in this volume. We find that these films are deposited within the transition from metallic to compound sputtering, at the point where target nitridation most strongly depends on nitrogen flow. Key in the deposition optimization is to increase the system's pumping speed and gas flows to counteract the hysteretic effects induced by the target size. Using the $I$-$V$ characteristics as a guide proves to be an effective way to optimize a reactive sputter system, for it can show whether the optimal deposition regime is hysteresis-free and accessible. | Reactive sputter deposition is a physical vapour deposition technique, where a metallic target is sputtered by ions of an inert element from a plasma while a flow of reactive gas passes the the whole system, including the target, plasma and substrate \cite{ohring}\cite{deplamahieu}. For the fabrication of niobium titanium nitride (NbTiN), an alloy target of niobium and titanium is used in combination with argon and nitrogen as inert and reactive gasses respectively. Current fabrication of NbTiN thin films at the Kavli Institute of NanoScience in Delft, the Netherlands, is performed using a Nordiko 2000 reactive sputter deposition machine. Yet the new astronomical sub-millimeter detectors A-MKID \cite{baryshev} and DESHIMA \cite{endo} require a uniform thin film over the surface of a complete \diameter100 mm wafer. Uniformity on so large a surface cannot be obtained with the small \diameter100 mm target of the Nordiko 2000, fit with an even smaller \diameter60 mm magnet. As the size of the target and specifically the size of the erosion track is expected to influence the thickness profile of the film, we make a switch to the Evatec LLS801 at SRON Utrecht. This system houses a large 127 mm $\times$ 444.5 mm target on which the erosion track covers almost 70\% of the surface. Although a small target is more easily applicable, for the required gas flows and power are lower, this larger target is expected to result in better deposition uniformity on a large substrate concerning thickness, critical temperature ($T_\mathrm{c}$) and other material quality factors. The aim of this article is to provide an empirical insight in the shift from a small-target reactive sputter machine to a large-target reactive sputter machine, while maintaining a high $T_\mathrm{c}$ of 15 K in the center of the deposited films. This insight is granted by exploring the $I$-$V$ characteristics of both sputter machines. | A reactive sputter deposition machine is a complex physical system, where electrical, geometrical and material parameters together define the plasma behavior, the plasma-target interaction and finally the deposition onto the substrate. We show that by using the shape of $I$-$V$ curves as a guide, we can easily examine the behavior of the system to adapt film properties to our need. The $I$-$V$ curves are a tool to compare various set-ups with different target size, for it provides quantitative feedback depending on every internal parameter and setting. Furthermore, NbTiN thin films with high $T_\mathrm{c}$ can only be sputtered in the transition of a metallic target towards a saturated target. This transition should therefore be accessible and free of hysteresis. The system parameters required for such behaviour are highly dependent on the target size, which primarily defines the nitrogen consumption. Eliminating hysteresis by using an appropriate pumping speed and gas flows, opens up the possibility to fabricate stoichiometric NbTiN with $T_\mathrm{c} >$ 15 K. | 16 | 9 | 1609.01265 |
1609 | 1609.08344_arXiv.txt | Recently, the first lithium detection outside of the Milky Way was made in low-metallicity gas of the Small Magellanic Cloud, which was at the level of the expected primordial value. Part of the observed lithium in any environment has primordial origin, but there is always some post-BBN (Big Bang Nucleosynthesis) contamination, since lithium can also be produced in cosmic-ray interactions with the interstellar medium. Using the fact that processes involving cosmic rays produce lithium, but also gamma rays through neutral pion decay, we use the Small Magellanic Cloud gamma-ray observations by \emph{Fermi}-LAT to make predictions on the amount of lithium in this galaxy that was produced by galactic cosmic rays accelerated in supernova remnants. By including both fusion processes, as well as spallation of heavier nuclei, we find that galactic cosmic rays could produce a very small amount of lithium. In the case of ${}^6\mathrm{Li}$ isotope (which should only be produced by cosmic rays) we can only explain $0.16\%$ of the measured abundance. If these cosmic rays are indeed responsible for such small lithium production, observed abundances could be the result of some other sources, which are discussed in the paper. | \label{introduction} Products of interactions of hadronic cosmic rays (CR) with the interstellar medium (ISM) can be used to probe the history as well as present day cosmic-ray production and interactions. High energy CRs produce gamma rays ($\mathrm{p}+\mathrm{p}\rightarrow \pi^{0}\rightarrow\gamma+\gamma$) through neutral pion decay~\citep{STE70,STE71}. Cosmic-ray collisions with the ISM can also produce light elements (lithium, beryllium and boron). For example, production of lithium can be the result of fusion ($\alpha+\alpha \rightarrow {}^{6,7}\mathrm{Li}$;~\cite{MO77}) and spallation of heavier nuclei ($\mathrm{p},\alpha+\mathrm{C,N,O}\rightarrow{}^{6,7}\mathrm{Li}$;~\cite{RV84}). Since both processes are the result of hadronic CR interactions they can be linked, as was done by Fields \& Prodanovi\'c (2005)~\cite{FP05}, who gave a simple model-independent connection between lithium produced in fusion reactions and pionic gamma rays, produced by some cosmic-ray population. They linked Solar lithium abundances~\citep{AG89} and the isotropic diffuse gamma-ray background (which excludes any resolved sources) - IGRB~\citep{SB98} observed by the EGRET telescope~\citep{FP05, PF05}. This relation can be used to constrain any CR population from two sides. Still, the difference between these two CR products, does exist. Production of lithium is a cumulative process, and the present day abundances of lithium in the gas of any galaxy are the result of CR production over the history of the galaxy (plus some primordial, as well as some pre-galactic production). On the other hand, gamma-ray luminosity of a galaxy at any given moment is the result of the CR interactions at that moment. First measurements of ${}^7\mathrm{Li}$ outside of the Milky Way (MW) were made in the low-metallicity interstellar gas of the Small Magellanic Cloud (SMC), which has one quarter of the Sun's metallicity~\citep{HL12}. Observation of ${}^7\mathrm{Li}$ in low-metallicity interstellar gas is important since these abundances should not be affected by changes in stellar atmospheres that could be present in lithium abundances measured in for example MW halo stars. So, in case of lithium in the interstellar gas it might be easier to distinguish between primordial and CR-produced components of lithium. The measured value $({}^7\mathrm{Li}/\mathrm{H})_\mathrm{SMC,obs}=(4.8\pm1.8)\times10^{-10}$ ~\citep{HL12} is at the level of the expected primordial abundance $({}^7\mathrm{Li}/\mathrm{H})_\mathrm{BBN}=(4.56-5.34)\times10^{-10}$~\citep{CUV14}. Measurements also give the isotopic ratio $({}^6\mathrm{Li}/{}^7\mathrm{Li})_\mathrm{SMC,obs}=0.13\pm0.05$, with the formal limit of $({}^6\mathrm{Li}/{}^7\mathrm{Li})_\mathrm{SMC,obs}<0.28\,(3\sigma)$~\citep{HL12}. This small neighboring galaxy is also interesting since it was detected in gamma rays by \emph{Fermi} telescope with an integrated flux of $F_{\gamma,\mathrm{SMC,obs}}(>100\,\mathrm{MeV})=(3.7\pm0.7)\times10^{-8}\,\mathrm{phot}\,\mathrm{cm}^{-2}\mathrm{s}^{-1}$~\citep{AA10}. Here we will use model-independent gamma-ray--$\mathrm{Li}$ connection~\citep{FP05,PF05} and models for production of GCRs in normal galaxies~\citep{PF01,PF02} to constrain the post-BBN lithium production by GCRs in SMC and check weather GCRs could produce an important part of the observed SMC lithium abundance. | \label{discussion} Using the \emph{Fermi}-LAT gamma-ray detection of the SMC we have estimated the amount of lithium that can be produced by GCRs which we assume to be the cosmic-ray population producing observed gamma-ray flux. Even though, GCRs are expected to be the dominant CR population, our calculation shows that GCR-produced ${}^6\mathrm{Li}$ is less then $1\%$ of the observed abundance. We have included $\alpha\alpha$ interactions, as well as spallation processes. In case of SMCs metallicity and CR spectrum, spallation is a subdominant production channel and most of the CR produced lithium in case of this galaxy is produced via fusion processes. As the most extreme assumption, we can say that the \emph{Fermi}-LAT diffuse gamma-ray background~\citep{AA15} is entirely produced by gamma rays from unresolved SMC-like galaxies. If we go through the same procedure as before, with this extreme assumption, we can explain $55\%$ of the observed ${}^6\mathrm{Li}$ abundance. On the other hand this extreme assumption can produce only $12\%$ of the observed ${}^7\mathrm{Li}$ abundance (and $0.04\%$ without this extreme assumption), which is consistent with the fact that this lithium isotope, is in big part produced in the BBN. Observed abundance of this isotope in the SMC is consistent with the expected primordial abundance, so after removing GCR-produced ${}^7\mathrm{Li}$ that we get, we still won't deviate much from the expected primordial abundance. Also, in~\cite{HL12} it was found that the observed lithium isotopic ratio of $0.13$ implies that CRs in general could have produced $19\%$ of the observed ${}^7\mathrm{Li}$ abundance in the SMC. All of this, leaves room for some additional CR component next to the GCRs. We can also use the observed lithium abundances in the SMC and predict how much can SMC-like galaxies contribute to the observed IGRB if the entire observed lithium in SMC was produce solely by GCRs. If this was the case, the resulting gamma-ray production would be $1.8$ times larger than the observed IGRB in case of the propagated CR spectrum (if we include both fusion and spallation processes). This would also mean that the present day gamma-ray flux of the SMC should be $3$ orders of magnitude larger than the observed value. On the other hand, if an important part of the observed SMC lithium is made by some other process, other than GCR interactions, it would be possible to produce the observed lithium abundances without producing that many gamma-rays. The isotopic ratio of lithium measured in the SMC is consistent with the ratio measured in the MW gas~\citep{KK09}. Since SMC is a lower metallicity system and with a lower CR fluence than in the MW, if GCRs are the dominant CR species one would expect the isotopic ratio ${}^6\mathrm{Li}/{}^7\mathrm{Li}$ to be lower than in the MW. Observed abundance of ${}^6\mathrm{Li}$, which is larger than the one derived from our models, and the observed isotopic ratio work in favor of some other cosmic-ray acceleration mechanism being present in the SMC, which could in turn produce more lithium. For example cosmic rays could be produced by large scale structure formation~\citep{MR00,FL04,FP05,DP14}, high-energy pulsars~\citep{OG69,AA10}, pulsar wind nebulae~\citep{BE07} or binary systems~\citep{RC05,DU13}. If any of these mechanisms is an important contributor to lithium production and accelerates CRs for a long time, it would also enhance the gamma-ray flux of these galaxies. The observed IGRB can constrain any of these mechanism, but since we are dealing with small galaxies (and our GCR produced gamma-ray intensity is much lower than the observed IGRB), there is still room for additional CR populations. Also, SMC might not be a typical small galaxy, corresponding to the CSFR curve we have used. For example SMC might have had periods of much larger star formation than the present one, triggered by close flybys with the MW and their tidal interaction~\citep{PB13,DP15}. This could also lead to the production of additional CR population, only present during galaxy interaction. This CR population would not be present for a long time compared to the life of a galaxy, so their gamma-ray production in all unresolved SMC-like galaxies would not violate the observed IGRB, nor would it affect the present day gamma-ray flux of the SMC. Also, these tidal interactions would impact smaller galaxies more, so more lithium would be produced in the SMC, but not in the MW. In~\cite{PB13} it was shown that tidal interactions could be a very effective mechanism for lithium production in the SMC, and that even a single close fly-by of MW and SMC could produce a non-negligible abundance of lithium. The observed gamma-ray flux and lithium abundances of the SMC imply a more interesting galactic history of this galaxy in order to fully explain both measurements and understand how the CR flux inside the galaxy has changed during the lifetime of the SMC, which is something we will consider in the follow-up work. \bigskip \emph | 16 | 9 | 1609.08344 |
1609 | 1609.04395_arXiv.txt | We use the \emph{Gaia} data release 1 (DR1) to study the proper motion (PM) fields of the Large and Small Magellanic Clouds (LMC, SMC). This uses the \emph{Tycho}-\emph{Gaia} Astrometric Solution (TGAS) PMs for 29 \emph{Hipparcos} stars in the LMC and 8 in the SMC. The LMC PM in the West and North directions is inferred to be $(\mu_W,\mu_N) = (-1.872 \pm 0.045, 0.224 \pm 0.054) \masyr$, and the SMC PM $(\mu_W,\mu_N) = (-0.874 \pm 0.066, -1.229 \pm 0.047) \masyr$. These results have similar accuracy and agree to within the uncertainties with existing Hubble Space Telescope (\emph{HST}) PM measurements. Since TGAS uses different methods with different systematics, this provides an external validation of both data sets and their underlying approaches. Residual DR1 systematics may affect the TGAS results, but the \emph{HST} agreement implies this must be below the random errors. Also in agreement with prior \emph{HST} studies, the TGAS LMC PM field clearly shows the clockwise rotation of the disk, even though it takes the LMC disk in excess of $10^8$ years to complete one revolution. The implied rotation curve amplitude for young LMC stars is consistent with that inferred from line-of-sight (LOS) velocity measurements. Comparison of the PM and LOS rotation curves implies a kinematic LMC distance modulus $m-M = 18.54 \pm 0.39$, consistent but not yet competitive with photometric methods. These first results from \emph{Gaia} on the topic of Local Group dynamics provide an indication of how its future data releases will revolutionize this field. | \label{s:intro} Almost everything that is known about Local Group dynamics, and of galaxy dynamics in general, is based on LOS velocity observations. Such measurements constrain only one component of motion, and interpretation therefore requires that various assumptions be made. PMs in the plane of the sky provide a more complete picture. However, the PMs are generally small and inversely proportional to the distance of the target. The \emph{Hipparcos} satellite provided a detailed understanding of the PMs of stars in the solar neighborhood (ESA 1997), but its accuracy was insufficient for detailed studies of other Local Group objects. Water maser observations yielded the first accurate PMs for other Local Group galaxies (Brunthaler et al.~2005). However, this technique is limited to a few galaxies with high star formation rates. Only with \emph{HST} has it become possible to determine PMs for objects throughout the Local Group. For example, the HSTPROMO collaboration has studied the PM dynamics of globular clusters, stellar streams, and nearby galaxies (van der Marel 2015). The \emph{Gaia} satellite will provide the next step forward through PM measurements for objects across the sky to optical magnitude $\sim$20.7 (Gaia Collaboration 2016a). Initial five-parameter astrometric solutions (including PMs) are expected in late 2017, with a final DR in 2022. By contrast, the \emph{Gaia} DR1 of Sep 14, 2016 (Gaia Collaboration \etal 2016b), includes PMs only for stars in common between \emph{Gaia} and the \emph{Hipparcos} Tycho-2 Catalogue (Hoeg \etal 2000). This Tycho-\emph{Gaia} Astrometric Solution (TGAS) Catalog (Lindegren \etal 2016) is restricted to the same bright stars previously studied by \emph{Hipparcos} and is therefore not well suited for studies of Local Group dynamics. However, we show in this paper that it does yield some first new insights. The LMC and SMC are the most massive satellites of the Milky Way. They have been studied extensively for a wide range of astrophysical subjects. To place these results in a proper context, it is important to understand the dynamics of the Magellanic Clouds and their history in the Local Group. They have therefore been of special interest for \emph{HST} studies. Kallivayalil \etal (2006a,b) presented PMs for 26 fields based on two epochs of \emph{HST} data with a 2-year time baseline. These measurements were refined by Kallivayalil \etal (2013; hereafter K13) using a third epoch for 12 fields, which extended the time baseline to 7 years. The latter provided a median per-coordinate PM uncertainty of only 0.03 mas/yr (7 km/s), 3--4 times better than the two-epoch measurements. \begin{deluxetable*}{rrrrrr} \setlength{\tablewidth}{\hsize} \tablecaption{TGAS Proper Motions of Magellanic Cloud stars\label{t:TGAS}} \tablehead{ \colhead{HIP} & \colhead{\emph{Gaia}} & \colhead{RA} & \colhead{dec} & \colhead{${\rm PM}_W$} & \colhead{${\rm PM}_N$} \\ \colhead{ID} & \colhead{sourceId} & \colhead{(deg)} & \colhead{(deg)} & \colhead{(mas/yr)} & \colhead{(mas/yr)} \\ } % \startdata LMC\ \ \\ \hline 22392 & 4655349652394811136 & 72.3017 & -69.4565 & $-2.012 \pm 0.151$ & $-0.226 \pm 0.151$ \\ 22758 & 4655510043652327552 & 73.4304 & -68.7148 & $-1.772 \pm 0.160$ & $-0.296 \pm 0.171$ \\ 22794 & 4655460771785226880 & 73.5594 & -69.2101 & $-1.895 \pm 0.088$ & $-0.122 \pm 0.088$ \\ 22849 & 4661769941306044416 & 73.7390 & -66.7524 & $-1.756 \pm 0.120$ & $-0.045 \pm 0.130$ \\ 22885 & 4661720532007512320 & 73.8400 & -67.4365 & $-1.766 \pm 0.145$ & $-0.030 \pm 0.147$ \\ 22900 & 4655136518933846784 & 73.8853 & -69.9625 & $-1.951 \pm 0.232$ & $-0.102 \pm 0.221$ \\ 22989 & 4655158131209278464 & 74.1962 & -69.8402 & $-1.869 \pm 0.234$ & $0.015 \pm 0.227$ \\ 23177 & 4662293892954562048 & 74.7878 & -65.6677 & $-1.613 \pm 0.162$ & $0.026 \pm 0.159$ \\ 23428 & 4654621500815442816 & 75.5308 & -71.3370 & $-1.973 \pm 0.146$ & $-0.099 \pm 0.140$ \\ 23527 & 4655036841335115392 & 75.8733 & -70.6998 & $-1.942 \pm 0.240$ & $0.077 \pm 0.230$ \\ 23665 & 4661920986713556352 & 76.3009 & -66.7368 & $-1.675 \pm 0.104$ & $0.005 \pm 0.114$ \\ 23718 & 4661472145451256576 & 76.4813 & -67.8864 & $-1.785 \pm 0.072$ & $0.123 \pm 0.079$ \\ 23820 & 4662061311885050624 & 76.8091 & -66.0551 & $-1.555 \pm 0.212$ & $0.238 \pm 0.216$ \\ 24006 & 4651629489160555392 & 77.4122 & -71.4006 & $-2.236 \pm 0.105$ & $0.065 \pm 0.098$ \\ 24080 & 4658269336800428672 & 77.5950 & -68.7733 & $-1.896 \pm 0.092$ & $0.169 \pm 0.094$ \\ 24347 & 4658204053297963392 & 78.3783 & -69.5399 & $-2.084 \pm 0.196$ & $0.251 \pm 0.177$ \\ 24694 & 4658137739001073280 & 79.4433 & -69.8492 & $-1.882 \pm 0.131$ & $0.182 \pm 0.126$ \\ 24988 & 4660601607121368704 & 80.2571 & -65.8007 & $-1.499 \pm 0.079$ & $0.387 \pm 0.089$ \\ 25097 & 4660444926713007872 & 80.5878 & -66.2603 & $-1.510 \pm 0.173$ & $0.337 \pm 0.191$ \\ 25448 & 4658486455992620416 & 81.6454 & -68.8687 & $-1.710 \pm 0.138$ & $0.587 \pm 0.133$ \\ 25615 & 4660175580731856128 & 82.0847 & -67.4051 & $-1.568 \pm 0.204$ & $0.479 \pm 0.208$ \\ 25892 & 4660124762671796096 & 82.9101 & -67.4699 & $-1.587 \pm 0.182$ & $0.669 \pm 0.186$ \\ 26135 & 4660246224352015232 & 83.5936 & -67.0232 & $-1.633 \pm 0.095$ & $0.429 \pm 0.113$ \\ 26222 & 4657280635327480832 & 83.8193 & -69.6773 & $-1.723 \pm 0.187$ & $0.497 \pm 0.188$ \\ 26338 & 4657700408260606592 & 84.1349 & -68.9005 & $-1.874 \pm 0.185$ & $0.621 \pm 0.200$ \\ 26745 & 4657627943562907520 & 85.2409 & -69.2586 & $-1.779 \pm 0.231$ & $0.518 \pm 0.242$ \\ 27142 & 4657722879521554176 & 86.3193 & -68.9978 & $-1.733 \pm 0.142$ & $0.705 \pm 0.137$ \\ 27819 & 4659188769038018816 & 88.2918 & -68.1186 & $-1.560 \pm 0.153$ & $0.834 \pm 0.106$ \\ 27868 & 4659091084305723392 & 88.4571 & -68.3132 & $-1.661 \pm 0.154$ & $0.843 \pm 0.111$ \\ \hline \multicolumn{2}{l}{straight mean\tablenotemark{[1]}} & & & $-1.776 \pm 0.033$ & $ 0.246 \pm 0.059$ \\ \multicolumn{2}{l}{weighted mean\tablenotemark{[2]}} & & & $-1.779 \pm 0.024$ & $ 0.241 \pm 0.024$ \\ \hline\\ SMC\ \ \\ \hline 3934 & 4685876046561549184 & 12.6316 & -73.4785 & $-0.541 \pm 0.177$ & $-1.304 \pm 0.177$ \\ 3945 & 4685876046561548800 & 12.6600 & -73.4717 & $-0.668 \pm 0.154$ & $-1.160 \pm 0.148$ \\ 4004 & 4689033534707612800 & 12.8525 & -72.3829 & $-0.670 \pm 0.148$ & $-1.165 \pm 0.143$ \\ 4126 & 4685940436697751168 & 13.2135 & -73.1149 & $-0.667 \pm 0.132$ & $-1.291 \pm 0.116$ \\ 4153 & 4688967357860689024 & 13.2704 & -72.6334 & $-0.821 \pm 0.131$ & $-1.231 \pm 0.130$ \\ 4768 & 4690499767820637312 & 15.3208 & -72.2920 & $-1.144 \pm 0.151$ & $-1.239 \pm 0.143$ \\ 5267 & 4687436700227349888 & 16.8259 & -72.4677 & $-0.849 \pm 0.152$ & $-1.262 \pm 0.144$ \\ 5714 & 4687159863816994816 & 18.3771 & -73.3362 & $-0.992 \pm 0.091$ & $-1.182 \pm 0.082$ \\ \hline \multicolumn{2}{l}{straight mean\tablenotemark{[1]}} & & & $-0.794 \pm 0.066$ & $ -1.229 \pm 0.018$ \\ \multicolumn{2}{l}{weighted mean\tablenotemark{[2]}} & & & $-0.830 \pm 0.047$ & $ -1.222 \pm 0.044$ \enddata \tablecomments{Column~(1)-(2): \emph{Hipparcos} ID and \emph{GAIA} sourceId number of those Magellanic Cloud stars previously identified by Kroupa \& Bastian (1997) and analyzed here. Columns~(3)-(6): right ascension $\alpha$, declination $\delta$, proper motion ${\rm PM}_{\rm W(est)}$ ($\equiv - {\rm PM}_\alpha \cos \delta$), and ${\rm PM}_{\rm N(orth)}$ ($\equiv {\rm PM}_\delta$) from the TGAS catalog. All stars have known LOS velocities (Barbrier-Brossat \etal 1994; Kroupa \& Bastian 1997; Neugent \etal 2012; Kordopatis \etal 2013) consistent with LMC or SMC membership. The stars HIP 22237 and 25815 in the LMC were rejected because they had the two highest TGAS {\tt astrometric\_excess\_noise} values ($> 1.02$) in the sample, as well as strongly outlying PM values. HIP 7912 and 8470 near the SMC were excluded because they reside in the Magellanic Bridge. HIP 23500, 24907, 25146, 25822, and 27655 in the LMC, and HIP 5397 in the SMC are not listed in the TGAS catalog. There are no additional \emph{Hipparcos} stars with both position and kinematics (SIMBAD LOS velocity and TGAS PM) consistent with Magellanic Cloud membership. The straight and weighted mean for each Magellanic Cloud are listed (accounting also for correlations between the TGAS PM components).} \tablenotetext{[1]}{The uncertainty in the ``straight'' mean is based exclusively on the observed scatter, and doesn't use the individual PM uncertainties.} \tablenotetext{[2]}{The uncertainty in the weighted mean is based exclusively on the individual PM uncertainties, and doesn't use the observed scatter. This underestimates the PM uncertainty in the COM motion of each Magellanic Cloud.} \end{deluxetable*} The \emph{HST} studies showed that the Magellanic Clouds move faster about the Milky Way than previously believed based on models of the Magellanic Stream. So instead of being long-term satellites, they are most likely on their first Milky Way passage (Besla \etal 2007). These results have refined our understanding of the Magellanic Clouds, as well as the formation of Magellanic Irregulars in general (Besla \etal 2012). van der Marel \& Kallivayalil (2014; hereafter vdMK14) studied the variations in the \emph{HST} PM measurements across the face of the LMC. They measured the PM rotation curve, and demonstrated consistency with LOS velocity studies. \begin{figure*}[t] \begin{center} \epsfxsize=0.49\hsize \epsfbox{fignew1a.eps} \hfill \epsfxsize=0.49\hsize \epsfbox{fignew1b.eps} \caption{Spatially variable component of the observed TGAS PM fields for the LMC (left) and SMC (right), overlaid on a representation of the Gaia DR1 source density. Each panel is centered on the dynamical center (cross; a triangle for the SMC indicates the photometric center of the old stars), with the horizontal and vertical extent representing an equal number of degrees on the sky. Solid dots show the positions of the sample stars. The PM vector for each star is the observed PM from Table~\ref{t:TGAS}, minus the best-fit COM PM from Tables~\ref{t:param} and~\ref{t:paramS} (bottom left inset). PM vectors have a size that indicates the mean predicted motion over (arbitrarily) the next $7.2 \Myr$. For the LMC, clockwise rotation is clearly evident. The bottom right inset shows the median random PM errors for the sample.\footnote{A figure that shows the individual PM uncertainties is available at http://www.cosmos.esa.int/web/gaia/iow\_20160916 .} The $\chi^2$ values of our model fits suggest that these may be overestimated by a factor $\sim 1.85$ (confirmed visually by the good agreement between the PMs of adjacent stars). Overstimated errors have also been suggested for Gaia DR1 parallax values (Casertano \etal 2016). \label{f:obsvar}} \end{center} \end{figure*} Historically, one of the first measurements of the Magellanic Cloud PMs was obtained by Kroupa \& Bastian (1997), using data for 36 LMC stars and 11 SMC stars from the \emph{Hipparcos} satellite. These are young massive stars with apparent V-magnitudes between 9--12 (absolute magnitudes brighter than $-6.5$). High-quality TGAS data exist for 29 of the LMC and 8 of the SMC stars. We retrieved these data from the \emph{Gaia} archive using \texttt{pygacs}.\footnote{\url{https://github.com/Johannes-Sahlmann/pygacs}} While the \emph{Hipparcos} PM errors ranged from one to a few mas/yr, the new TGAS PM errors, listed in Table~\ref{t:TGAS}, are much smaller. The 0.15 mas/yr median error is similar to the \emph{HST} PM errors for the K13 two-epoch fields. So while the TGAS measurements do not improve upon the \emph{HST} measurements, they do allow for an independent verification. We therefore analyze here the Magellanic Cloud TGAS PMs with the same methodologies presented in K13 and vdMK14. We do this for the LMC in Section~2, and the SMC in Section~3. Section~4 discusses the results in the context of previous work. Section 5~summarizes the conclusions. | \label{s:conc} We have used the \emph{Gaia} DR1 to obtain new insights into the motions and internal kinematics of the Magellanic Clouds. The results do not improve upon the accuracy of existing \emph{HST} studies, but they have similar accuracy and are consistent to within the uncertainties. Since these missions use different methods with different systematics, this provides an external validation of each approach.\footnote{With future Gaia DRs it will be possible to do star-by-star comparisons, since $\gtrsim 100$ stars in the observed HST fields are bright enough for Gaia PM measurements (Kallivayalil et al.~2006a, fig.~6).} The TGAS results confirm the large PM of the Magellanic Clouds, which has previously been used to revise our understanding of their orbital history and cosmological context (K13). Both \emph{Gaia} and \emph{HST} (vdMK14) confidently detect and quantify the rotation of the LMC disk. Comparison of the LMC rotation curves from PM and LOS data yields a kinematic distance estimate that is independent from, but consistent with, that from photometric methods and the cosmological distance ladder. The results presented here are the first from the \emph{Gaia} mission on the topic of Local Group dynamics. \emph{Gaia}'s future data releases will contain many more stars and have higher PM accuracy. With the methods used here, this is guaranteed to further improve our understanding of the Magellanic Clouds. When combined with studies of other nearby targets, this will revolutionize our understanding of the Milky Way and its satellites. For PM studies further out into the Local Group, and especially for dwarf galaxies with old stellar populations, \emph{HST} will continue to be the telescope of choice due to its ability to measure accurate PMs for faint stars ($V \lesssim 25$) over small fields (e.g., Sohn \etal 2015). | 16 | 9 | 1609.04395 |
1609 | 1609.00780_arXiv.txt | {We report the results of $Swift$/XRT observations (2008$-$2015) of a {hyper}-luminous X-ray source, ESO 243-49 HLX-1. We found % a strong observational evidence that ESO 243-49 HLX-1 underwent % spectral transitions from the low/hard state to the high/soft state during these observations. The spectra of ESO 243-49 HLX-1 are well fitted by the so-{called} bulk motion Comptonization model for all spectral states. We have established the photon index ($\Gamma$) saturation level, $\Gamma_{sat}$=3.0$\pm$0.1, in the correlation of $\Gamma$ versus mass accretion rate ($\dot M$). This $\Gamma-\dot M$ correlation allows us to estimate the black hole (BH) mass in ESO 243-49 HLX-1 to be $M_{BH}\sim 7\times 10^4 M_{\odot}$, assuming the % distance to ESO 243-49 of 95 Mpc. % For the BH mass estimate we used the scaling method, taking Galactic BHs XTE~J1550-564, H~1743-322 and 4U~1630-472, and an extragalactic BH source, M101 ULX-1 as reference sources. The $\Gamma-\dot M$ correlation revealed in ESO 243-49 HLX-1 is similar to those in a number of Galactic and extragalactic BHs and it clearly shows the correlation along with the strong $\Gamma$ saturation at $\approx 3$. This is a {reliable} % observational evidence of a BH in ESO 243-49 HLX-1. We also found that the seed (disk) photon temperatures are quite low, of order of 50$-$140 eV which are consistent with a high BH mass in ESO 243-49 HLX-1. } | The prominent edge-on galaxy ESO 243-49, located at 95 Mpc away in the constellation Phoenix (see Afonso et al. 2005), { hosts a hyper-luminous X-ray source commonly known as HLX-1, which is possibly an intermediate-mass black hole (IMBH).} This black hole candidate (BHC) was first observed in 2004 as a source emitting X-rays in the vicinity of the spiral galaxy ESO 243-49 and it was catalogued as 2XMM J011028.1-460421. Later, in 2008 the field of this X-ray source was deeply re-imaged by a team led by Natalie Webb (the Institut de Recherche en Astrophysique et Planetologie in Toulouse, France). Farrell et al. 2009 suggested that HLX-1 is an intermediate-mass black hole candidate with mass of $\sim 10^4$ M$_{\odot}$ because of very high X-ray luminosity of HLX-1 ($\sim 10^{42}$ erg/s in the 0.2 -- 10 keV range) and because its disk blackbody spectrum peaked at $kT_{in}\sim$2 keV along with its X-ray spectral variability. X-ray spectral analysis (see Godet et al. 2009, 2012; Servillat et al. 2011; Lasota et al. 2011; Farrell et al. 2009; Davis et al. 2011), optical observations (see Farrell et al. 2012; Wiersema et al. 2010; Soria et al. 2010) and radio observations (see Webb et al. 2012) support the presence of an intermediate-mass BH in ESO 243-49 HLX-1. Long-term monitoring with the $Swift$/XRT has shown that X-ray luminosity of HLX-1 changes by a factor of $\sim$50 (Godet et al. 2009; Yan et al. 2015), and its % spectral variability is reminiscent of that seen in Galactic stellar-mass BHs (see Servillat et al. 2011). % Specifically, the X-ray light curve demonstrates a recurrent fast rise-exponential decay'' (FRED) type of pattern in the range of $\sim$370 -- 460 days. This recurrency has been interpreted as an orbital period of the companion star (see Lasota et al. 2011 and Soria 2013). However, the last 2 outbursts have been too late to be consistent with that explanation. The interval between the last two outbursts is almost 3 months longer than the interval between the first two [Soria (2015), a private communication]. Recently, Webb et al. (2012), hereafter W12, reported a detection of transient radio emission at the location of HLX-1, which agrees with a discrete jet ejection event. These observations also allowed W12 to re-estimate the BH mass to be between $\sim$9$\times$10$^3$ M$_{\odot }$ and $\sim$9$\times$10$^4$ M$_{\odot }$. % In contrast, King \& Lasota (2014) suggested that HLX-1 may be a stellar mass binary like SS~433 (see also Lasota et al. 2015), in which the X-ray emission possibly comes from the beamed jet. HLX-1 is projected in the sky at $\sim$0.8 kpc out of the plane and $\sim$3.3 kpc ($\approx$8 {\tt "}) of the nucleus of the S0/a galaxy ESO 243-49 (the luminosity distance $\sim$ 96 Mpc). Galaxy ESO 243-49 is a member of the cluster Abell 2877 (e.g. Malumuth et al. 1992). The association of HLX-1 with ESO 243-49 is confirmed by the redshift measurements of the observed H$_{\alpha}$ emission line of the counterpart (Soria et al. 2013, hereafter SHP13; Wiersema et al. 2010), although the velocity offset between this and the bulge of ESO 243-49 is $\sim$430 km/s, close to the escape velocity from the S0 galaxy (SHP13). This allows to suggest that HLX-1 might be in a dwarf satellite galaxy or a star cluster near ESO 243-49 are not than in the galaxy itself (SHP13). The HII region in which the HLX is located could be the remnant of a dwarf satellite galaxy that has been accreted (Farrell et al. 2012). The optical counterpart of HLX-1 was detected in various bands, from near-infrared to far-ultraviolet (FUV, Wiersema et al. 2010; Soria et al. 2010, 2012; Farrell et al. 2012), but its nature remains puzzling. Cseh et al. (2015) used radio observations of ESO 243-49 HLX-1 in 2012 based on the Australia Telescope Compact Array (ATCA) and Karl G. Jansky Very Large Array (VLA). They esimated the BH mass as $2.8^{+7.5}_{2.1}\times 10^6$ M$_{\odot}$. Yan et al. (2015) have analyzed $Swift$ monitoring observations of ESO 243-49 HLX-1 and compared the HLX-1 outburst properties with those of bright Galactic low-mass X-ray binary transients (LMXBTs). Furthermore, they stated that HLX-1 spends progressively less time in the succeeding outburst state and much more time in quiescence, but its peak luminosity remains approximately constant. The spectral analysis by Yan et al. strengthened the similarity between the state transitions in HLX-1 and those in Galactic LMXBTs. A very high luminosity of ESO~243-49 HLX-1 is considered as evidence for the existence of IMBH in HLX-1 (Farrell et al. 2009). However, luminosities up to $\sim$10$^{41}$ erg/s can be explained by stellar-mass BHs undergoing super-Eddington accretion (see Begelman 2002) that is followed. As a result, the apparent luminosity can exceed the Eddington limit estimated for isotropic radiation (King 2008; Freeland et al. 2006). Highly collimated sources are not expected to have a disk-blackbody or thermal-dominant spectrum, like we see in HLX-1 in the high/soft state. Therefore HLX-1 may not be a strongly beamed source. Consequently, luminosity above $\sim 10^{41}$ erg/s is difficult to explain without considering a massive BH source. Generally, two scenarios for an interpretation of HLX/ULX phenomena have been proposed. First, these sources can be stellar-mass BHs ($<$100 M$_{\odot}$) % radiating at Eddington or super-Eddington rates [% see e.g. \cite{Mukai05}]. Alternatively, they can be intermediate-mass BHs ($>$100 M$_{\odot}$) % whose luminosities are essentially sub-Eddington. The exact origin of such objects still remains uncertain, and there is still no general consensus on the causes of the poweful outbursts. Recently, \cite{Bachetti14} discussed another scenario for ULX. Using the {\it NuSTAR} mission { \cite{Harrison13}}, Bachetti and collaborators detected pulsations of X-ray emission with an average period 1.37 s modulated by a 2.5-day cycle % from ULX-4 located in the nuclear region of the galaxy M82. Bachetti et al. also argued that these pulsations are results of the rotation of a magnetized neutron star, while the modulation arises from its binary orbital motion. We note that the X-ray luminosity of M82 ULX-4 is about $L_X \sim 2\times 10^{40}$ erg s$^{-1}$ in 0.3 -- 10 keV energy range, which suggests a luminosity $\sim 100\times L_{Edd}$ % for a 1.4 M$_{\odot}$ neutron star (NS). Such a source is ten times brighter than any known accreting pulsar. The discovery of M82 ULX-4 and its possible interpretation as a NS can expand possible scenarios for ULXs. It is desirable for ESO~243-49 HLX-1 to independently identify the BH for its central object and also determine the mass of its BH as an alternative to previously employed methods (based on luminosity estimates alone). A new method for determining the BH mass was developed by Shaposhnikov \& Titarchuk (2009), hereafter ST09, who used a correlation scaling between X-ray spectral and timing (or mass accretion rate) properties observed from many Galactic BH binaries during the spectral state transitions. This method has also been applied to study of another class of X-ray sources, ULXs sources, NGC 5408 X-1 (Strohmayer \& Mushotzky (2009) and M101 ULX-1 (Titarchuk \& Seifina, 2015). We note, this method is commonly used for a BH mass determination of supermassive BHs, such as % NGC 3227, NGC 5548 NGC 5506 and NGC 3516 (Papadakis et al. 2009; Sobolewska \& Papadakis, 2009) and NLS1 galaxy {Mrk 766} (Giacche et al. 2014), using a sample of Galactic BHC binaries as reference sources. % This scaling method can also be applied for BH mass estimates when the conventional dynamical method cannot be used. We applied the ST09 method to {\it Swift}/XRT data of ESO ~243-49 HLX-1. Previously, many properties of HLX-1 were analyzed using $Swift$/XRT observations (e.g., Soria et al. 2010; Farrell et al. 2013; Webb et al. 2014; Yan et al. 2015). In particular, Soria et al. (2010) assessed {\it Swift} (2008 -- 2009) % observations by fitting their X-ray spectra. They used a few % models, in particular, an additive model of the {blackbody/diskbb} plus power-law. % They found that in these X-ray spectra the photon index changes from 1.8 to 2.95 but they were unable to present any argument that this source to be intermediate-mass BH or foreground NS. \cite{{ft11}}, \cite{STSS15}, \cite{STF13}, \cite{ST12}, \cite{ST11}, hereafter ST11, have shown that BH and NS sources can be distinguished using $\Gamma$-$\dot M$ correlation. ST11 predicted a BH source in ESO~243-49 HLX-1 and ruled out a quiescent neutron star in this source. Only in BH sources % the photon index $\Gamma$ can increase from $\Gamma\sim 1.6$ to $\Gamma\sim 3$ with mass accretion rate, in contrast to neutron stars, % for which we usually find the constant photon index around $\Gamma\sim 2$ (see e.g. ST11). Furthermore, Wiersema et al. (2010) % measured a redshift of z=0.0223 for HLX-1, which clearly indicates that HLX-1 cannot be a neutron star (NS) source because its luminosity is too high for a NS. In this paper we present an analysis of available {\it Swift} % observations of ESO~243-49~HLX-1 made during 2008 -- 2015 to re-examine our previous conclusions on a BH nature of HLX-1 and to find further indications on intermediate-mass BH in HLX-1. In Sect. 2 we present the list of observations used in our data analysis, while in Sect. 3 we provide details of the X-ray spectral analysis. We discuss the evolution of the X-ray spectral properties during the high-low state transitions and present the results of the scaling analysis to estimate the BH mass of ESO~243-49~HLX-1 in Sect. 4. % We conclude on our results in Sect. 5. | } We found the low$-$high state transitions observed in HLX-1 using the full set of $Swift$-/XRT observations (2008 -- 2015) and % we showed the observed spectra can be fitted by the BMC model for all observations, independently of the spectral state of the source. We investigated the X-ray outburst properties of HLX-1 and confirmed the presence of spectral state transitions during the outbursts using of hardness-intensity diagrams (Godet et al. 2009; Servillat et al. 2011) and the index$-$normalization (or $\dot M$) correlation observed in HLX-1, which were similar to those in Galactic BHs. In particular, we found that HLX-1 follows the $\Gamma-\dot M$ correlation previously obtained for extragalactic IMBH source M101 ULX-1 and Galactic BHs, 4U~1630-472, XTE~J1550-564 and H~1743-322 taking into account the % particular values of the $M_{BH}/d^2$ ratio (Figure~\ref{three_scal}). The photon index $\Gamma$ of ESO~243-49 HLX-1 spectrum is in the range $\Gamma = 1.6 - 3.0$. We also estimated the peak bolometric luminosity, which is about $4\times 10^{42}$ erg s$^{-1}$. We used the observed index-mass accretion rate correlation to estimate $M_{BH}$ in HLX-1. This scaling method was successfully implemented to find BH masses of Galactic (e.g. ST09, STS13) and extragalactic black holes [TS16; \citet{sp09}; \cite{ggt14}]. An application of the scaling technique to the X-ray data from XRT/Swift observations of ESO~243-49 HLX-1 allowed us to estimate $M_{BH}$ for this particular source. We found values of $M_{BH}\geq 7.2\times 10^4 M_{\odot}$. Furthermore, our BH mass estimate agrees % the previously established IMBH mass of $\sim 10^4 - 10^5$ M$_{\odot}$ derived using the detailed X-ray spectral modelling (Farrell et al. 2010; Davis et al. 2011; Servillat et al. 2011; Godet et al. 2012; Webb et al. 2012). Combining all these estimates with the inferred low temperatures of the seed disk photons $kT_s$, we can state that the compact object of ESO~243-49 HLX-1 probably is an intermediate-mass black hole with a mass at least $M_{BH}> 7.2\times10^4 M_{\odot}$. This research was performed using data supplied by the UK $Swift$ Science Data Centre at the University of Leicester. We also acknowledge the interesting remarks and points of the referee. | 16 | 9 | 1609.00780 |
1609 | 1609.02785_arXiv.txt | {We perform a detailed analysis on a primordial gravitational-wave background amplified during a Kasner-like pre-inflationary phase allowing for general triaxial anisotropies. It is found that the predicted angular distribution map of gravitational-wave intensity on large scales exhibits topologically distinctive patterns according to the degree of the pre-inflationary anisotropy, thereby serving as a potential probe for the pre-inflationary early universe with future all-sky observations of gravitational waves. We also derive an observational limit on the amplitude of such anisotropic gravitational waves from the $ B $-mode polarisation of the cosmic microwave background.} | There has been an accumulation of observational evidence for cosmic inflation \cite{Guth:1980zm,Sato:1980yn} in the past decades, one of the most crucial being the precise measurements of the cosmic microwave background (CMB) \cite{Ade:2015lrj}. Among others, a subject currently attracting a particular attention in this field is the search for the primordial gravitational waves (PGWs) emerging from the quantum nature of space-time during an early accelerated expansion \cite{Mukhanov:1981xt}, which is thought to be a \emph{direct} evidence of the occurrence of inflation. Direct detections of such PGWs in low-frequency bands are indeed one of the primary aims of future planned laser-interferometer experiments in space, such as eLISA \cite{AmaroSeoane:2012je}, DECIGO \cite{Seto:2001qf}, and Big-Bang Observer \cite{Crowder:2005nr}. There are, however, still many challenges to overcome in laser-interferometer experiments in spite of the recent success of the first observation of gravitational waves from coalescing binary black holes \cite{Abbott:2016blz}. As an alternative approach, there have been attempts at measuring the $ B $-mode polarisations of the CMB as an imprint of the PGWs \cite{Seljak:1996gy,Kamionkowski:1996zd,Kamionkowski:1996ks}. Past and ongoing projects for CMB $ B $-mode polarisation measurement at low multipoles include POLARBEAR \cite{Ade:2014afa}, ACTpol \cite{Naess:2014wtr}, BICEP2/Keck array and Planck \cite{Ade:2015tva} (see also \cite{Ade:2014xna}), and SPTpol \cite{Keisler:2015hfa}. Many future experiments are also planned, such as POLARBEAR-2 and Simons Array \cite{Suzuki:2015zzg}, and LiteBIRD \cite{Matsumura:2013aja}. Several constraints on tensor perturbations from the current bound on the CMB $ B $-mode have been obtained in \cite{Ade:2015tva,Ade:2015xua}. One of the goals beyond confirming the occurrence of cosmic inflation would be determination of the initial condition of inflation. If there are earlier stages preceding the onset of inflation, it is well anticipated that there were anisotropies and/or inhomogeneities of order the energy scale of unified theories such as Grand Unification Theories (GUTs) or superstrings. Investigations of early anisotropies may bring us useful information to construct the theory of elementary particles beyond the Standard Model and even quantum gravity. This serves as another motivation for investigating the anisotropic stages before an isotropic inflation. Then, what is to be understood is how the universe has evolved into the currently observed homogeneous and isotropic state. A key clue to this issue would be Wald's cosmic no-hair theorem \cite{Wald:1983ky}, stating that the Bianchi models for homogeneous anisotropic universe \cite{Ellis:1968vb} inevitably evolve towards isotropic de Sitter space in the presence of a large enough positive cosmological constant $ \Lambda $\,. It is generically expected that anisotropies of cosmological expansion would have great impacts on the evolution of cosmological perturbations. Indeed, several observational signatures of an anisotropic pre-inflation were discussed in \cite{Gumrukcuoglu:2007bx,Gumrukcuoglu:2008gi,Pitrou:2008gk}. Among others, a remarkable finding is that amplification of gravitational waves occurs during the pre-inflationary Kasner regime \cite{Gumrukcuoglu:2008gi,Kofman:2011tr}, whose efficiency varies with the direction in the sky. In particular, in \cite{Gumrukcuoglu:2008gi}, G{\"{u}}mr{\"{u}}k\c{c}{\"{u}}o\u{g}lu et al.\ investigated such gravitational waves from an inflationary background driven by a scalar field. The purpose of the present paper, therefore, is to give further insights into the connection between direction-dependent gravitational waves and primordial pre-inflationary anisotropies. While G{\"{u}}mr{\"{u}}k\c{c}{\"{u}}o\u{g}lu et al.'s analysis in \cite{Gumrukcuoglu:2008gi} was restricted to a particular background with axisymmetry, in contrast, we treat general \emph{triaxial} backgrounds. To do so, we take the so-called Kasner-de Sitter metric as a simpler background in which initially anisotropic expansion of space is isotropised due to a cosmological constant rather than a scalar field. As analysed in \cite{Gumrukcuoglu:2008gi,Kofman:2011tr}, the amplification of gravitational waves originates from an instability in the tensor sector and we expect even our simple model captures its essential features. This simple model also allows us to generate the all-sky map of gravitational-wave intensity from which we could decode the degree of the primordial anisotropy. Also we give some tentative constraints on the model parameters from the current bounds on the CMB $ B $-mode polarisation. The organisation of the paper is as follows. In section~\ref{sec:basic}, we describe the basic equations for the background and perturbations. In particular, we employ a gauge-invariant formulation for cosmological perturbations in the Bianchi type-I universe recently constructed by Pereira et al.\ \cite{Pereira:2007yy} (see also \cite{Tomita:1985me} for an earlier attempt). In section~\ref{sec:gws}, we show how gravitational waves evolve depending on the direction of wavevectors as well as on the anisotropy of the background universe. In section~\ref{sec:limit}, we demonstrate how limits can be given to the initial anisotropy and the initial power spectrum of the pre-inflationary gravitational waves from future all-sky observations of the PGWs. Finally, in section~\ref{sec:concl}, we conclude. Throughout the paper we use natural units with $ c = \hbar = k_\mathrm B = 1 $. The Latin indices $ i,j $ are spatial and run through $ 1,2,3 $. We will use the arrow notation to denote spatial contravariant vectors such as $ \vec V \equiv (V^1,V^2,V^3) $. | 16 | 9 | 1609.02785 |
|
1609 | 1609.02266_arXiv.txt | Recently, the High Energy Stereoscopic System (H.E.S.S.) reported two new interesting results for a $\gamma$-ray emitting supernova remnant, RX J1713.7$-$3946 (G347.3$-$0.5). The first result is the establishment of a broken power-law spectrum of GeV-TeV $\gamma$-rays. The other is a more extended $\gamma$-ray spatial profile than the one in the X-ray band. In this paper, we show both of these results can be explained by inverse Compton emission from accelerated electrons. If the maximum energy of electrons being accelerated decreases with time, the broken power-law spectrum can be generated by accumulation. Furthermore, the extended component of $\gamma$-ray profile can be interpreted as a CR precursor of currently accelerated electrons. | \label{sec:1} Supernova remnants (SNRs) are the most plausible candidate of the origin of Galactic cosmic rays (GCRs) mainly composed of protons, electrons and nuclei. In fact, X-ray and $\gamma$-ray observations showed that electrons and protons (or nuclei) are accelerated in SNRs \citep{koyama95,ackermann13}. The diffusive shock acceleration (DSA) \citep{axford77,krymsky77,bell78,blandford78} is the most plausible acceleration mechanism of GCRs, where it is assumed that accelerated particles diffusively move around a shock. It predicts a power-law momentum spectrum of the accelerated particles, that is almost consistent with radio observations of SNRs \citep{reynolds12}. Another important prediction of the DSA is a CR precursor ahead of the shock front. Furthermore, linear analysis and several numerical simulations show that the CR precursor generates magnetic-field fluctuation \citep{bell78,bell04,niemiec08,ohira09,riquelme09,ohira10,caprioli13}. Recently, \citet{katsuda16} found that the upstream plasma of the SNR Cygnus loop is abruptly heated in the vicinity of shocks explained via damping of magnetic-field fluctuation in an unresolved thin CR precursor. However, the CR precursor of SNRs has never been directly imaged so far. The length scale of the CR precursor tells us the diffusion coefficient of CRs in the upstream region and includes information about magnetic-field fluctuation generated by CRs. The imaging observation of the CR precursor at high energies is crucial for identifying that DSA actually works at SNR shocks, thus it is eagerly anticipated. The SNR RX J1713.7$-$3946 is one of the best studied SNRs to understand CR acceleration \cite[for a recent review, see ][]{zhang16}, detected in radio, X-ray, and GeV-TeV $\gamma$-ray bands. In particular, the origin of $\gamma$-rays from RX J1713.7$-$3946 has attracted attention over the years. One is the hadronic origin, that is, the $\gamma$-rays originate from accelerated protons \citep{berezhko06,yamazaki09,ellison10,zirakashvili10,inoue12,gabici14,federici15}. The other is the leptonic origin in which the $\gamma$-rays are generated by inverse Compton emission from accelerated electrons \citep{porter06,ellison10,zirakashvili10,finke12}. At present, the origin of $\gamma$-rays from RX J1713.7$-$3946 is an open problem. Recently, some new data about RX J1713.7$-$3946 were reported. \citet{katsuda15} reported the first detection of thermal X-ray line emission from RX J1713.7$-$3946 and proposed that RX J1713.7$-$3946 resulted from a type Ib/c SN. The High Energy Stereoscopic System (H.E.S.S.) reported two interesting results \citep{naurois15,abdalla16}\footnote{Details for \citet{naurois15} were provided as a full paper by \citet{abdalla16} which was submitted after this paper was submitted to arXiv.}: \begin{enumerate}[(1)] \item The new GeV-TeV $\gamma$-ray spectrum breaks at about $100~{\rm GeV}$. \item The radial profile of $\gamma$-rays is more extended than that of X-rays. \end{enumerate} The former has already suggested by \citet{abdo11} although the spectrum of GeV $\gamma$-rays had a large uncertainty. In a simple leptonic model, the recently observed $\gamma$-ray spectrum tells us the existence of a break at a few TeV in the spectrum of accelerated electrons. However, it is hardly explained by the cooling break because it requires a strong magnetic field or a very high photon field energy density, that conflict with other observations. Moreover, a one-zone leptonic model cannot explain the extended $\gamma$-ray profile. Therefore, a simple leptonic model seems to be confronted by the severe challenge \citep{naurois15,abdalla16}. In this paper, we show that if the maximum energy of accelerated electrons is decreasing with time and it is now about a few TeV, the time-integrated spectrum of accelerated electrons breaks at a few TeV, that can explain the new GeV-TeV gamma ray spectrum by inverse Compton emission. In addition, our model can naturally explain the $\gamma$-ray profile by the CR precursor of currently accelerated electrons with energy of a few TeV. Hence, the leptonic model is still plausible and the extended component of $\gamma$-ray image is the first observation of the CR precursor of SNRs. | \label{sec:5} In this paper, we assumed that all particles previously accelerated do not escape from the SNR. In order to supply CRs to the interstellar medium from SNRs, CRs have to escape from SNRs. In fact, $\gamma$-ray observations shows that middle-aged or old SNRs actually supply CR protons (or nuclei) to the interstellar medium \citep{ohiraetal11,uchiyama12}. Hence, accelerated electrons have to escape from the SNR eventually. In this model, $\gamma$-rays above $250~{\rm GeV}$ from the CR precursor ($\theta>0.45^\circ$) are mainly emitted by highest-energy electrons currently accelerated ($E=5~{\rm TeV}$). If higher-energy $\gamma$-rays extend more than $250~{\rm GeV}$, it could be an evidence that electrons previously accelerated ($E>5~{\rm TeV}$) have already started to escape from the SNR. As long as the diffusion coefficient has an energy dependence, the diffusion length scale has an energy dependence. However, it would be difficult to identify the energy dependence by current experiments because the expected energy dependence is very weak. The Cherenkov Telescope array \citep[CTA,][]{acharya13} will be able to observe many SNRs with better sensitivity and angular resolution, that will allow us to identify the CR precursor or escaping CR halo. In this paper, we consider only the acceleration of electrons. However, it is expected that protons and nuclei are accelerated and they produce the CR precursor. Therefore, the extended $\gamma$-ray profile could be explained by hadronic models \citep{zirakashvili10,federici15}. For the parameters adopted in this paper, the maximum energy of accelerated particles in the past does not reach $10^{15.5}~{\rm eV}$ (the knee), which is shown in Figure~\ref{fig:1}. However, other parameter sets, for example, a smaller $r_{\rm tr}$ makes $E_{\rm max}(t_{\rm tr})$ larger. If so, $\gamma$-rays originated from hadrons could appear in $100~{\rm TeV}$ range, that might be observed by CTA \citep{nakamori15}. | 16 | 9 | 1609.02266 |
1609 | 1609.00055_arXiv.txt | \small General Relativity predicts that the emission close to a black hole must be lensed by its strong gravitational field, illuminating the last photon orbit. This results in a dark circular area known as the black hole 'shadow'. The Event Horizon Telescope (EHT) is a (sub)mm VLBI network capable of Schwarzschild-radius resolution on Sagittarius A* (or Sgr A*), the 4 million solar mass black hole at the Galactic Center. The goals of the Sgr A* observations include resolving and measuring the details of its morphology. However, EHT data are sparse in the visibility domain, complicating reliable detailed image reconstruction. Therefore, direct pixel imaging should be complemented by other approaches. Using simulated EHT data from a black hole emission model we consider an approach to Sgr A* image reconstruction based on a simple and computationally efficient analytical model that produces images similar to the synthetic ones. The model consists of an eccentric ring with a brightness gradient and a two-dimensional Gaussian. These elemental forms have closed functional representations in the visibility domain, which lowers the computational overhead of fitting the model to the EHT observations. For model fitting we use a version of the Markov chain Monte-Carlo (MCMC) algorithm based on the Metropolis-Hastings sampler with replica exchange. Over a series of simulations we demonstrate that our model can be used for determining geometric measures of a black hole, thus providing information on the shadow size, linking General Relativity with accretion theory. \\ | The Event Horizon Telescope (EHT) is a project to observe supermassive black holes, including Sagittarius A* (Sgr A*) and M87, at an angular resolution comparable to the black hole Schwarzschild radius. Upgrades to EHT instrumentation that are currently underway will increase the sensitivity and baseline coverage of the array, making it possible to produce images of these sources. Because of the small number of antennas and, hence, sparsity of the $uv$ coverage the reconstructed image of Sgr A* black hole and its accretion flow will have severe uncertainty or ambiguity. Therefore, additional constraints on the Sgr A* image are required. Previous observations with smaller number of the baselines allowed to make preliminary estimates of the Sgr A* event horizon size ($40-60\;\mu$as), spin (close to zero) and the viewing angle ($\sim 68^\circ$) \citep{Doeleman2008Nature, Broderick2009estim, Fish2011detect, Broderick2011lowspin, Broderick2011constr}. Other constraints, derived from theoretical considerations, describe subtler details of the Sgr A* morphology. The size and shape of the black hole shadow depend on the nearby space-time metric, and the no-hair theorem infers that the black hole space-time has the Kerr metric. \citet{Johannsen2012testsgra, Johannsen2010testqk, Johannsen2010testbhim} elaborated a framework for testing the no-hair theorem. They suggested a parameterized non-Kerr metric and considered the changes in the shadow morphology due to its deviations from the Kerr metric. Two major techniques can be used to analyze VLBI data: direct imaging and model fitting. In order to reconstruct the brightness image from the sparse set of visibilities, maximum entropy (MEM) or similar methods are used \citep[see, for example,][]{Narayan1986, Baron2008, Baron2010, Kluska2014, RusenLu2014}. Of all possible images corresponding to the observation data the method selects an image with the maximum entropy. The benefit of direct imaging is its model independence. However, due to the non-linearity of MEM and other similar methods (e.g. CLEAN), the relationship between visibility data errors and the noise in the resultant image is not clear. In the alternative model fitting technique, the possible brightness distribution is described by a parametric model with well-determined linear mapping on the visibility domain. Such a model can be used to calculate the expected visibility measurements. The parameters are then adjusted to minimize a criterion such as $\chi^2$. This approach allows estimation of model parameter errors arising from errors in the measured visibilities, which is a substantial advantage of the model fitting technique. However, with all its advantages, the model-fitting approach has one inherent disadvantage: to ``see" the object as its model we first must know how it ``looks" to design its model. This drawback does not devaluate the approach because both imaging and model fitting should be utilized together. Namely, the first model-independent images can be obtained via imaging. Studying the images with theoretical insight is instrumental in designing models. Thus elaborated models can be fitted to the observational data to produce much more plausible images. The main value of the fitted model is its ability to quantitatively measure the features of the observed object. We use a Markov Chain Monte Carlo (MCMC) method for finding best-fit model parameters along with their posterior probability distributions. Generally, the posterior distributions may be complicated---multi-modal or not bell-shaped at all. However, if the model is well designed and plausibly reflects the view of the observed object, the parameter statistics from MCMC are usually close to normal distributions with statistical moments conditioned by those in the visibility measurements. Thus the errors in estimated parameters of the model can be characterized by the standard deviations of the posterior distributions. By now, a variety of models of the accretion flow have been created, some based on the electron concentration and temperature profiles \citep{Yuan2003nonthermal, Broderick2006freqdepshift}, others on magnetohydrodynamics and radiative transport processes \citep{Monica2009radmod, Monica2011numeric, Fish2009constrriaf}. Direct estimation of the physical model parameters based on the observations is problematic. The existing physical models of Sgr A* are non-linear and complex. They have to take into account the effects of multiple orbiting of the photons, and the ray-tracing \citep{Psaltis2012raytr} consumes significant computational resources and time. A statistical algorithm of parameter estimation for these physical models would require an unacceptably long time. Therefore, for the Sgr A* image reconstruction a simple geometric model reflecting only the overall geometric features produced by the physical models may be preferred. A possible view of the black hole and its image geometry is determined by the nearby physical processes. Strong gravitational lensing makes the emission from behind the black hole appear to come from around it. Also, due to relativistic beaming the approaching side of the accretion disk appears to be many times brighter than the receding side. If the inclination is close to $90^\circ$, the black hole looks like an eccentric ring or crescent, as in the left panel of Fig.~\ref{quasikerr_f1}. Conversely, in the case of low inclination the black hole will look like a funnel, shown in the right panel of Fig.~\ref{quasikerr_f1}. In the visibility domain these simple forms can be represented by algebraic expressions only using elementary functions to form a visibility model in the $uv$-plane that is fit to the observational data points. The $\chi^2$ distribution is calculated on the visibility magnitudes and closure phases. The inverse Fourier transform (IFT) of the best-fit model is then used to reconstruct the brightness image of the observed black hole. The analytical model must be flexible enough to resemble both states shown in Fig.~\ref{quasikerr_f1}. This significant simplification is justified by the computational speed. A similar approach has been recently used by \citet{Kamruddin_Dexter_2013}. They offered a geometric crescent model, composed of two eccentric cylinders of the opposite sign. This yields an eccentric ring crescent of uniform brightness. Our 9-parameter xringaus model provides a more detailed black hole accretion image by introducing a gradient in the crescent brightness and a two-dimensional Gaussian enhancement at the brightest part of the image. In the second section we describe two geometric models: the simplest ``slashed ring" and the 9-parameter ``xringaus" model. The third section is devoted to a description of the model fitting method, Markov Chain Monte Carlo with replica exchange. The fourth section describes simulations using the model and outlines the limits of the models' usability. Section five discusses our results. \begin{figure*} % \begin{center} \pdfimageresolution=350 \includegraphics{fig_Quasi_Kerr_000_006.png} \end{center} \caption{\small Simulated Quasi-Kerr Images for different inclinations of the accretion disk \citep{BJPL2013}. Left panel: the disk is close to the edge-on orientation. Right panel: the disk is close to the face-on orientation. \label{quasikerr_f1}} \end{figure*} | The described \emph{xringaus} (or 9-parameter) model is an intensional simplification of a real black hole accretion image. However, it can provide valuable information on the most general parameters such as the black hole shadow size, its relative position, the spin axis inclination, differences between the brightest and the dimmest parts etc. The \emph{xringaus} model is a development of the \emph{crescent} model independently designed by \citet{Kamruddin_Dexter_2013}. The \emph{xringaus} model provides a more detailed and hence more informative image. One of the interesting properties of the 9-parameter model is that it is capable to significantly eliminate the effects of interstellar scattering. We chose modeling in the visibility domain mostly for computational speed. A model in the brightness domain would impose an overhead of a large number of fast Fourier transforms (FFTs) during the MCMC fitting process for every variation of the model parameters. However, modeling in the brightness domain could provide greater flexibility: we would not be restricted to the circular pillboxes and Gaussians. Instead, it would be possible to use any conceivable mathematical forms, non-circular and asymmetric shapes. For example, some authors \citep{deVries2000,Vries2005limacon,Cruz_etal2011,Villanueva_etal2013} consider the Durer-Pascal lima\c{c}on as the mathematical curve describing the shadow. Suppose a parametric image with a non-circular shadow is specified in the brightness domain. Note that the $\chi^2$ computation does not require the Fourier transform of the whole $N\times N$ brightness image. With a moderate number of observational data points, the direct discrete Fourier transform (DFT) of the model brightness into the visibility for only those particular points can be an order of magnitude faster than the FFT producing the whole visibility image. Therefore, the next step in this work is envisioned as Sgr A* image modeling in the brightness domain. In this numerical study we assumed slow variation of the black hole object, such that it can be considered static over the full track of the observations (over 24 hours). However, Sgr A* is highly variable on a time scale of minutes. M.~Moscibrodzka and J.~Dolence \citep{Monika2012galacenter} developed GRMHD and RIAF models of the black hole accretion flow. Their simulation results in the form of 24 hour Sgr A* ``movies" with the frames only 10 s apart, providing valuable material for future testing of our model-fitting approach on the dynamic images. \clearpage | 16 | 9 | 1609.00055 |
1609 | 1609.09497_arXiv.txt | \noindent We investigate the symmetry structure of inflation in 2+1 dimensions. In particular, we show that the asymptotic symmetries of three-dimensional de Sitter space are in one-to-one correspondence with cosmological adiabatic modes for the curvature perturbation. In 2+1 dimensions, the asymptotic symmetry algebra is infinite-dimensional, given by two copies of the Virasoro algebra, and can be traced to the conformal symmetries of the two-dimensional spatial slices of de Sitter. We study the consequences of this infinite-dimensional symmetry for inflationary correlation functions, finding new soft theorems that hold only in 2+1 dimensions. Expanding the correlation functions as a power series in the soft momentum $q$, these relations constrain the traceless part of the tensorial coefficient at each order in $q$ in terms of a lower-point function. As a check, we verify that the ${\cal O}(q^2)$ identity is satisfied by inflationary correlation functions in the limit of small sound speed. | As we learn from A Square~\cite{abbott1884flatland}, things are often simpler in lower-dimensional settings. For instance, gravity in 2+1 dimensions is far simpler than gravity in our world, primarily because it has no local degrees of freedom~\cite{Deser:1983tn}. However it is not completely trivial because there can still be global and boundary degrees of freedom, leading to nontrivial solutions, {\it e.g.}, the BTZ black hole~\cite{Banados:1992wn,Banados:1992gq}. This makes 2+1 dimensions a nice testing ground, in which we have gained a variety of insights into the nature of gravitational physics (for a review, see~\cite{Carlip:1995zj}). We are therefore motivated to investigate the (2+1)-dimensional version of cosmological inflation. Just as with pure gravity, the dynamics of inflation is much simpler in three dimensions.\footnote{Some work has been done on lower-dimensional inflation in the past:~\cite{Martinec:2014uva,Moore:2014sia} considered the dynamics of eternal inflation and the properties of perturbations in $(1+1)$-dimensional inflation. The question of starting inflation and some aspects of perturbations in $2+1$ dimensions were explored in~\cite{Banks:1984np,Samiullah:1991qv}. In~\cite{Kaplan:2014dia}, the authors considered aspects of the effective theory of holographic renormalization of 2-dimensional field theories, which is related to three-dimensional inflation by analytic continuation.} Because there are no gravitational waves, the only propagating degrees of freedom are the inflaton, plus any spectator fields that may be present. It has recently become clear that viewing inflation as a process of spontaneous symmetry breaking is a powerful approach. This is exemplified by the effective field theory of inflation~\cite{Creminelli:2006xe,Cheung:2007st}, in which inflation is seen as a spontaneous breaking of time diffeomorphism invariance. It is also useful to think of gauge-fixed inflation as a process of global symmetry breaking, where the curvature perturbation, $\zeta$, is the corresponding Nambu--Goldstone mode~\cite{Creminelli:2012ed,Hinterbichler:2012nm,Assassi:2012zq}. The nonlinearly realized symmetries of inflation then lead to Maldacena's consistency relation~\cite{Maldacena:2002vr,Creminelli:2004yq} as a Ward identity~\cite{Assassi:2012zq,Hinterbichler:2013dpa,Kehagias:2012pd,Goldberger:2013rsa}. Including tensor perturbations, one finds an infinite set of soft theorems as Ward identities of an infinite number of non-linearly realized global symmetries~\cite{Hinterbichler:2013dpa}. These identities are the cosmological analogue of Adler's zero for soft pions~\cite{Adler:1964um}. The consistency relations have been generalized and extended in many directions: for example, they have been derived from CFT arguments~\cite{Schalm:2012pi,Mata:2012bx,McFadden:2014nta}, from the underlying diffeomorphism invariance~\cite{Berezhiani:2013ewa,Pimentel:2013gza,Collins:2014fwa,Armendariz-Picon:2014xda,Berezhiani:2014kga,Berezhiani:2014tda,Ferreira:2016hee}, extended to multiple soft momenta~\cite{Joyce:2014aqa,Mirbabayi:2014zpa}, and generalized to large scale structure~\cite{Kehagias:2013yd,Peloso:2013zw,Creminelli:2013mca,Creminelli:2013poa,Creminelli:2013nua,Horn:2014rta,Horn:2015dra,Hui:2016ffo}. At their core, the single field soft theorems follow from the fact that $\zeta$-gauge does not fully fix the diffeomorphism symmetry of Einstein gravity. Rather, there remain residual large gauge transformations -- corresponding to conformal transformations of the spatial ${\mathbb R}^3$ slices -- under which $\zeta$ shifts nonlinearly. In $(2+1)$-dimensional inflation, the relevant group of symmetries is the conformal group of ${\mathbb R}^2$. This group is infinite-dimensional -- it is the Virasoro group familiar from two dimensional conformal field theory -- and correspondingly there is an infinite number of symmetries of $\zeta$.\footnote{In fact, in higher dimensions there is already an infinite number of residual large gauge transformation symmetries once one includes tensor modes and allows them to transform as well~\cite{Hinterbichler:2012nm,Hinterbichler:2013dpa,Bordin:2016ruc}. The difference in this case is that there is an infinite number of {\it scalar} symmetries.} One of our goals is to elucidate the nature of these symmetries and investigate how they act on fields during inflation. Parallel to the investigation of soft limits in cosmology, there has been much recent interest in connecting soft theorems of quantum field theory on flat space to asymptotic symmetries ({\it e.g.},~\cite{Strominger:2013lka,Cachazo:2014fwa,Larkoski:2014bxa,Avery:2015rga}). For example, Weinberg's soft graviton theorem~\cite{Weinberg:1965nx} can be thought of as a consequence of the Bondi--van der Burg--Metzner--Sachs (usually called BMS)~\cite{Bondi:1962px,Sachs:1962wk} invariance of gravitational scattering~\cite{Strominger:2013jfa,He:2014laa}. It seems natural that these two approaches should be closely connected. This connection has been made in one direction by~\cite{Mirbabayi:2016xvc}, who showed that the flat space identities for a U$(1)$ gauge theory can be derived from a generalization of Weinberg's construction of adiabatic modes in cosmology~\cite{Weinberg:2003sw}, and~\cite{Kehagias:2016zry}, who considered the cosmological analogue of the BMS group. Here we wish to further explore this connection in cosmology. We show that adiabatic modes are in one-to-one correspondence with the asymptotic symmetries of dS$_3$, so that either can be derived from the other. Our hope is that this will give some insight into extending this connection to cosmology in higher dimensions \cite{Ferreira:2016hee}. Three dimensional de Sitter space has an infinite-dimensional asymptotic symmetry group~\cite{Brown:1986nw,Strominger:1997eq}. This can be thought of as a manifestation of the putative dS/CFT correspondence~\cite{Strominger:1997eq}, where theories on dS$_3$ have dual descriptions in terms of a 2d CFT, with corresponding Virasoro symmetry. In Sec.~\ref{sec:asympsymm} we review the derivation of the asymptotic symmetry transformations of dS$_3$ and how they close to form two copies of the Virasoro algebra. We then derive how these symmetries act on the curvature perturbation, $\zeta$. As anticipated, on the future boundary asymptotic symmetry transformations act as conformal transformations of ${\mathbb R}^2$. In Sec.~\ref{sec:zetasymms} we derive the same transformations for $\zeta$ by applying Weinberg's adiabatic mode construction to find residual large gauge transformations which may be smoothly connected to a physical solution. We find that the adiabatic modes for $\zeta$ specialized to de Sitter space reproduce precisely the asymptotic symmetry transformations with Brown--Henneaux boundary conditions. Recall that in 3+1 dimensions the non-linearly realized symmetries, the dilation and special conformal transformations on ${\mathbb R}^3$, induce respectively a constant and linear gradient profile for~$\zeta$. In 2+1 dimensions, the additional Virasoro symmetries can induce profiles to all orders in the coordinates. Specifically, at each order in $n$, the holomorphic and anti-holomorphic symmetry generators can be arranged into a symmetric, traceless $n$-index tensor, which acts on $\zeta$ as \be \delta_{{i_1\cdots i_n}}\zeta \,\propto\, x^{(i_1}\cdots x^{i_n)_{\rm T}}+\ldots\,, \label{eq:tracelessintro} \ee where $x^{(i_1}\cdots x^{i_n)_{\rm T}}$ denotes the fully symmetric and traceless combination. These transformations are reminiscent of the tensor symmetries in 3+1 dimensions~\cite{Hinterbichler:2013dpa}. In Sec.~\ref{sec:Ward} we derive the Ward identities associated to these symmetries. In momentum space they relate the symmetric, traceless part of the correlation function at each order $q^n$ in the soft momentum to a symmetry transformation on a lower-point function without the soft mode. We then go on to check some of these identities involving the 3-point function in Sec.~\ref{sec:check}. Computing the squeezed limit of the 3-point function analytically in odd space-time dimensions is somewhat tricky, because the mode functions are Hankel functions of integer order. Instead we calculate the squeezed limit in arbitrary even dimensions and continue the expression to $D=3$. This requires constructing the EFT of inflation in arbitrary dimension and computing its quadratic and cubic action. We comment on future directions in Sec.~\ref{sec:concl}. Some technical appendices collect useful results. \vspace{-.4cm} \paragraph{Conventions:} We use the mostly-plus metric signature. We use $D$ to represent the space-time dimension and $d$ to represent the spatial dimension, hence $D = d+1$. In many cases it will be useful to work in terms of the complex coordinates $z = x+iy$ and $\bar z = x-iy$. Derivatives with respect to these coordinates are denoted by $\partial$ and $\bar{\partial}$. See Appendix~\ref{app:complexcoords} for more details. | \label{sec:concl} We have investigated how the asymptotic symmetry group of three dimensional de Sitter space acts on correlation functions during inflation. The infinite number of asymptotic symmetry transformations are in one-to-one correspondence with the adiabatic modes which generate nontrivial backgrounds for the curvature perturbation, $\zeta$. These nonlinearly realized symmetries lead to soft theorems which partially restrict the form of correlation functions in the soft limit -- where one of the momenta is taken to be smaller than the others -- at each order in the soft momentum. We have provided an initial check of these identities, including the first novel identity not present in higher-dimensional versions of inflation. Looking forward, there are a number of interesting directions to pursue. Our analysis reinforces the notion that there is a close relationship between the asymptotic symmetries of a space-time, cosmological adiabatic modes, and soft theorems. It appears that the asymptotic symmetries are precisely those transformations which lead to physical soft insertions of the metric -- precisely what adiabatic modes are. It has been shown that higher-dimensional inflation possesses an infinite number of adiabatic modes~\cite{Hinterbichler:2012nm}, with corresponding Ward identities~\cite{Hinterbichler:2013dpa}. It would be interesting to understand these symmetries more directly in the language of asymptotic symmetries (see~\cite{Ferreira:2016hee} for some work in this direction). Further, the non-linearly realized components of the four-dimensional symmetries are similar to the ones discussed in this note: they consist of traceless polynomials in the coordinates. It would be interesting to understand the relationship between these two sets of symmetries, perhaps through dimensional reduction. Staying within the realm of three dimensional inflation there are also a number of intriguing directions to pursue. It has long been known that three-dimensional gravity possesses a formulation as a Chern--Simons theory with ${\rm SL}(2,{\mathbb R})\times{\rm SL}(2,{\mathbb R})$ gauge group \cite{Achucarro:1987vz,Witten:1988hc}. It would be very interesting to consider inflation from this perspective, as opposed to the metic formulation we have used here. It may also be interesting to consider generalizations of the identities we have considered, for example to multiple soft external legs, along the lines of~\cite{Joyce:2014aqa,Mirbabayi:2014zpa}. In~\cite{Kaplan:2014dia}, the EFT of holographic RG flows was considered, which is essentially inflation on its side; it would be interesting to understand whether the soft theorems for the dilaton have any important consequences in that setup. Additionally, we have focused primarily on the dynamics and Ward identities of the curvature perturbation itself; it should be possible to extend these arguments to include correlation functions of spectator fields during inflation. Since the vacuum is only invariant under the global SL$(2,{\mathbb C})$ subgroup of the Virasoro symmetries, we expect that correlation functions of spectator fields will only be annihilated by $\delta_{-1},\delta_0, \delta_1$ and their conjugates (indeed, this can be explicitly checked). The higher Virasoro symmetries correspond to insertions of ``boundary gravitons,'' which correspond to insertions of moments of the stress tensor in the dual CFT, leading to a late-time identity of the form (see also~\cite{Fitzpatrick:2014vua}) \be \langle L_n\phi(z_1)\phi(z_2)\cdots\phi(z_N)\rangle = -\sum_{a=1}^{N}\left(\frac{(n+1)\Delta_a}{2}z_a^{n}+z_a^{n+1}\right)\langle\phi(z_1)\phi(z_2)\cdots\phi(z_N)\rangle\,, \label{eq:specIDs} \ee where $L_n$ is the operator which generates the vector field $\ell_n$ on the boundary, $z_a$ are points on the future boundary, and $\Delta$ is set by the mass of the field $\phi$ through $\Delta = 1-\sqrt{1-\frac{m_\phi^2}{H^2}}$. It would be interesting to derive the identity~\eqref{eq:specIDs} directly from the bulk physics, and check it on multi-field correlators. Similarly, it would be interesting to investigate the consequences of the purely tensor adiabatic modes and elucidate their relation to non-Brown--Henneaux boundary conditions. Three-dimensional inflation provides a simplified arena in which to explore the relationship between adiabatic modes, asymptotic symmetries, and soft theorems in the context of cosmology. Aside from being of interest in their own right, we hope that the lessons abstracted from this situation may be usefully applied to gain a better understanding of these phenomena in higher dimensions. \vspace{-.4cm} \paragraph{Acknowledgements:} We thank Paolo Creminelli, Wayne Hu, Lam Hui, Emil Martinec, Rachel Rosen, Marko Simonovi\'c and Junpu Wang for helpful discussions. We would like to thank the Sitka Sound Science Center for hospitality while some of this work was completed (A.J. \& K.H.). This work was supported in part by NASA ATP grant NNX16AB27G, National Science Foundation Grant No. PHYS-1066293 and the hospitality of the Aspen Center for Physics, and also by the Kavli Institute for Cosmological Physics at the University of Chicago through grant NSF PHY-1125897, an endowment from the Kavli Foundation and its founder Fred Kavli, and by the Robert R. McCormick Postdoctoral Fellowship (A.J.). J.K. is supported in part by NSF CAREER Award PHY-1145525. \appendix | 16 | 9 | 1609.09497 |
1609 | 1609.05994_arXiv.txt | In this work, we study the properties of magnetized white dwarfs taking into account possible instabilities due to electron capture and pycnonuclear fusion reactions in the cores of such objects. The structure of white dwarfs is obtained by solving the Einstein-Maxwell equations with a poloidal magnetic field in a fully general relativistic approach. The stellar interior is composed of a regular crystal lattice made of carbon ions immersed in a degenerate relativistic electron gas. The onsets of electron capture reactions and pycnonuclear reactions are determined with and without magnetic fields. We find that magnetized white dwarfs violate the standard Chandrasekhar mass limit significantly, even when electron capture and pycnonuclear fusion reactions are present in the stellar interior. We obtain a maximum white dwarf mass of around $2.14\,M_{\odot}$ for a central magnetic field of $\sim 3.85\times 10^{14}$~G, which indicates that magnetized white dwarfs may play a role for the interpretation of superluminous type Ia supernovae. Furthermore, we show that the critical density for pycnonuclear fusion reactions limits the central white dwarf density to $9.35\times 10^9$ g/cm$^3$. As a result, equatorial radii of white dwarfs cannot be smaller than $\sim 1100$~km. Another interesting feature concerns the relationship between the central stellar density and the strength of the magnetic field at the core of a magnetized white dwarf. For high magnetic fields, we find that the central density increases (stellar radius decrease) with magnetic field strength, which makes ultramagnetized white dwarfs more compact. The opposite is the case, however, if the central magnetic field is less than $\sim 10^{13}$~G. In the latter case, the central density decreases (stellar radius increases) with central magnetic field strengths. | It is generally accepted that stars born with masses below around 10 solar masses end up their evolutions as white dwarfs (WDs) \cite{weber1999pulsars,shapiro2008black,glendenning2012compact}. With a typical composition mostly made of carbon, oxygen, or helium, white dwarfs possess central densities up to $\sim 10^{11}\,{\rm g/cm}^{3}$. They can be very hot \citep{0004-637X-704-2-1605}, fast rotating \cite{arutyunyan1971rotating,boshkayev2013general,hartle1967slowly} and strongly magnetized \cite{2014ApJ...794...86C,lobato_magnetars_2016,Banibrata_2016}. The observed surface magnetic fields range from $10^{6}\,$ G to $10^{9}\,$ G \cite{Terada:2007br,Reimers:1995ia,Schmidt:1995eh,Kemp:1970zz,putney1995three,% angel1978magnetic}. The internal magnetic fields of white dwarfs are not known, but they are expected to be larger than their surface magnetic fields. This is due to the fact that in ideal magneto hydrodynamics (MHD), the magnetic field, $B$, is `frozen-in' with the fluid and $B\propto \rho$, with $\rho$ being the local mass density (see, e.g., Refs.~\cite{mestel2012stellar,landau_quantum_1958}). A simple estimate of the internal magnetic field strength follows from the virial theorem by equating the magnetic field energy with the gravitational binding energy, which leads to an upper limit for the magnetic fields inside WDs of about $\sim 10^{13}$ G. On the other hand, analytic and numeric calculations, both in Newtonian theory as well as in General Relativity theory, show that WDs may have internal magnetic fields as large as $10^{12-16}\,$ G (see, e.g., Refs.~\cite{angel1978magnetic,shapiro2008black,das_maximum_2014,bera2014mass,bera2016mass,Franzon:2015gda,Franzon:2016gzf,das_grmhd_2015-1}). The relationship between the gravitational stellar mass, $M$, and the radius, $R$, of non-magnetized white dwarfs was first determined by Chandrasekhar~\cite{chandrasekhar1939}. Recently, mass-radius relationships of magnetic white dwarfs have been discussed in the literature (see, e.g., Refs.~\cite{suh2000mass,bera2014mass,Franzon:2015gda}). These studies show that the masses of white dwarfs increase in the presence of strong magnetic fields. This is due to the Lorentz force, which acts against gravity, therefore supporting stars with higher masses. Based on recent observations of several superluminous type Ia supernovae (SN 2006gz, SN 2007if, SN 2009dc, SN 2003fg) \cite{silverman2011fourteen, Scalzo:2010xd, Howell:2006vn, Hicken:2007ap,Yamanaka:2009dp, taubenberger2011high,Kepler11032007}, it has been suggested that the progenitor masses of such supernovae significantly exceed the Chandrasekhar mass limit of $M_{\rm Ch}\sim 1.4\, M_{\odot}$ \citep{Ilkov11012012}. Super-heavy progenitors were studied as a result of mergers of two massive white dwarfs \cite{Moll:2013mpa,0004-637X-773-2-136,0004-637X-827-2-128}. Alternatively, the authors of Ref.~\cite{liu2014one} obtained super-Chandrasekhar white dwarfs for magnetically charged stars. In addition, super-Chandrasekhar white dwarfs were investigated in the presence of strong magnetic fields in Refs.~\cite{das_revisiting_2014}. In Refs.~\cite{adam1986models,ostriker1968rapidly1}, WDs models with magnetic fields were calculated in the framework of Newtonian physics. A recent study of differential rotating, magnetized white dwarfs has shown that differential rotation might increase the mass of magnetized white dwarfs up to 3.1 $\rm{M_{\odot}}$ \cite{Subramanian21112015}. Also, as shown in Ref.~\cite{bera_massradius_2016}, purely toroidal magnetic field components can increase the masses of white dwarfs up to $5\, M_{\odot}$. According to Refs.~\cite{das_strongly_2012}, effects of an extremely large and uniform magnetic field on the equation of state (EOS) of a white dwarf could increase its critical mass up to $2.58 \, M_\odot$. This mass limit is reached for extremely large magnetic fields of $\sim 10^{18}$ G. Nevertheless, as already discussed in Refs.~\cite{coelho_dynamical_2014,chamel_stability_2013}, the breaking of spherical symmetry due to magnetic fields and micro-physical effects, such as electron capture reactions and pycnonuclear reactions, can severely limit the magnetic field inside white dwarfs. In Ref.~\cite{Franzon:2015gda}, mass-radius relationships of highly magnetized white dwarfs were computed using a pure degenerate electron Fermi gas. However, according to Ref.~\cite{salpeter_energy_1961}, many-body corrections modify the EOS and, therefore, the mass-radius relationship of white dwarfs. The purpose of our paper is two-fold. Firstly, we model white dwarfs using a model for the equation of state which takes into account not only the electron Fermi gas contribution, but also the contribution from electron-ion interactions \cite{PhysRevD.92.023008}. Secondly, we perform a stability analysis of the matter in the cores of white dwarfs against electron capture and pycnonuclear fusion reactions. The Landau energy levels of electrons are modified by relativistic effects if the magnetic field strength is higher than the critical QED magnetic field strength of $B_{cr}=4.4\times 10^{13}$~G. However, as already shown in Ref.~\cite{Bera:2014wja}, the global properties of white dwarfs, such as masses and the radii, are nearly independent of Landau quantization. For this reason, we do not take into account magnetic fields effects in the equation of state to calculate the global properties of WD's. Our paper is organized as follows. In Sec.\ \ref{sec:stellarint}, we discuss the stellar interior of white dwarfs and details of the equation of state used in our study to model white dwarfs. This is followed, in Sec.\ \ref{sec:equations}, by a brief discussion of the equations that are being solved numerically to obtain the structure of stationary magnetized white dwarfs. In Sec.\ \ref{sec:axisymm}, we briefly discuss the Einstein-Maxwell tensor and the metric tensor used to solve Einstein's field equations of General Relativity. The results of our study are discussed in Sec.\ \ref{sec:results} and summarized in Sec.\ \ref{sec:summary}. | \label{sec:summary} In this work, we presented axisymmetric and stationary models of magnetized white dwarfs obtained by solving the Einstein-Maxwell equations self-consistently and taking into stability considerations related to neutronization due to electron capture reactions as well as pycnonuclear fusion reactions among carbon nuclei in the cores of white dwarfs. We investigated also the influence of magnetic fields on the structure of white dwarfs. This is an important problem, since super-massive magnetized WD's, whose existence is partially supported by magnetic forces, could simplify the explanation of observed ultra-luminous explosions of supernovae Type Ia. The Lorentz force induced by strong magnetic fields breaks the spherical symmetry of stars and increases their masses, since the force acts in the radial outward direction against the inwardly directed gravitational pull. In this paper, we make use of an equation of state for a degenerate electron gas with electron-ion interactions (body-centered-cubic lattice structure) to describe the matter inside of white dwarfs. We have shown that the equation of state becomes softer if nuclear lattice contributions are included in addition to the electron pressure. This is due to the fact that the repulsive force between electrons is smaller in the presence of an ionic lattice, causing a softening of the equation of state (see Fig.~\ref{eos_carbono}). We note that the density thresholds for pycnonuclear fusion reactions and inverse $\beta$-reactions are reduced when magnetic fields are present in the stellar interior, as can be seen in Table \ref{t1}. We have shown that the masses of white dwarfs increase up to $M=2.14 \, M_{\odot}$ (with a corresponding magnetic dipole moment of $\mu=2.0\times 10^{34}$ Am$^2$ (see, e.g., Fig.~\ref{MRHO}) if microphysical instabilities are considered. This star has an equatorial radius of $\sim 1100$ km with magnetic fields of $B_{c}=3.85\times10^{14}$ G and $B_{s}=7.21\times10^{13}$ G at the center and at the stellar surface, respectively. For this white dwarf, the ratio between the magnetic pressures and the matter pressure at the center is 0.789. Although the surface magnetic fields obtained here are higher than the observed ones for white dwarfs, these figures provide an idea of the maximum possible magnetic field strength that can be reached inside of these objects, and may also be used to assess the effects of strong magnetic fields on both the microphysics and the global structure of magnetized white stars. The maximum magnetic field found in this work is an order of magnitude smaller than that of Ref.~\cite{Franzon:2015gda}. This is because we modeled the stellar interior with a more realistic equation of state than just a simple electron gas, and we considered the density threshold for pycnonuclear fusion reactions for a 10 Gyrs fusion reaction time scale, which restricts the central density of white dwarfs to $\sim 9.25\times 10^9$ g/cm$^3$ (see Table \ref{t1}), limiting the stellar masses and, therefore, their radii, which for very massive and magnetized white dwarfs cannot be smaller than R$\sim 1100$ km. However, it is important to mention that the pycnonuclear reaction time scales are somewhat uncertain. In our case, for example, we have a factor of uncertainty of approximately 3.5 in the calculation of the astrophysical S-factor (see Refs. \cite{gasques_nuclear_2005,yakovlev_fusion_2006}). Our results show that the surface magnetic field, $B_s$, is about one order of magnitude smaller than the magnetic field reached at the stellar center, $B_c$. If the magnetic field weakens for massive white dwarfs, we found that the magnetic dipole moments of such stars may increase (Fig.\ \ref{globalproperties1}), which is due to the fact that, for a fixed baryon mass, the magnetic field is determined by the interplay between the magnetic dipole moment and the stellar radius. The situation is reversed for less massive white dwarfs, for which smaller the magnetic fields imply smaller stellar magnetic dipole moments. The radii of massive (light) white dwarfs are found to increase (decrease) for decreasing central magnetic fields (Fig.\ \ref{globalproperties2}). This opens up the possibility that massive white dwarfs, with central magnetic fields greater than $B\sim 10^{13}$ G, increase their magnetic fields through continued compression. This phenomenology differs from previous studies carried out for magnetic fields less than $\sim 10^{13}$ G \cite{suh2000mass,ostriker1968rapidly1}, where an increase of the central magnetic field was found to make stars less dense and therefore bigger in size. We note that stellar configurations which contain only poloidal magnetic fields (no toroidal component) are unstable (see, e.g., \cite{armaza2015magnetic, mitchell2015instability, braithwaite2006stability}). Moreover, according to Ref.~\cite{goldreich_magnetic_1992}, many different mechanisms can affect the magnetic fields and their distributions inside of white dwarfs. In this work, in the framework of a fully general relativistic treatment, we model the properties of magnetized white dwarfs with purely poloidal magnetic field components. Although this is not the most general magnetic field profile, and a dynamical stability of these stars still needs to be addressed, magnetic fields considerably increase the masses of white dwarfs, even when microphysical instabilities are considered. As a consequence, such white dwarfs ought to be considered as possible candidates of super-Chandrasekhar white dwarfs, thereby contributing to our understanding of superluminous type-Ia supernovae. Lastly, we note that for a typical magnetic field value of $\sim 10^{14}$ G and a density of $\sim10^{9}$ g/cm$^3$, we obtain an Alfven velocity of $v=10^{9}$ cm/s, which, for a white dwarf with a typical radius of $R=1500$ km, leads to an Alfven crossing time of $\sim 0.1$ s \cite{durisen1973viscous, yakovlev1980thermal, cumming2002magnetic}. This is close to the hydrostatic equilibration time of white dwarfs. As a consequence, although magnetized white dwarfs seem to be short-lived stars, they might still be supported by magnetic fields. Our results represent magnetostatic equilibrium conditions. The stability analysis of such systems is beyond the scope of this study, which constitutes a first step toward a more complete discussion of the possible existence of super-Chandrasekhar white dwarfs. Studies which address issues such as the role of different (poloidal and toroidal) magnetic field configurations, stellar rotation, and different compositions of the stellar cores will be presented in a series of forthcoming papers. | 16 | 9 | 1609.05994 |
1609 | 1609.09032_arXiv.txt | On behalf of the International Astronomical Consortium for High Energy Calibration (IACHEC), we present results from the cross-calibration campaigns in 2012 on \qcs\ and in 2013 on \pksb\ between the then active X-ray observatories \chandra, \nustar, \suzaku, \swift\ and \xmm. We compare measured fluxes between instrument pairs in two energy bands, 1--5\,keV and 3--7\,keV and calculate an average cross-normalization constant for each energy range. We review known cross-calibration features and provide a series of tables and figures to be used for evaluating cross-normalization constants obtained from other observations with the above mentioned observatories. | It is common to have simultaneous or near simultaneous X-ray coverage of astrophysical sources with multiple observations. The community is often faced with the question on how to properly fit joint data sets spanning multiple observatories. It is the mission of the International Astronomical Consortium for High Energy Calibration \citep[IACHEC,][]{Sembay2010} to provide the proper guidance and cross-calibration information to help the community avoid pitfalls and approach cross-observatory fitting in the correct manner. Several papers have been published as a result of IACHEC effort, using a variety of methods and targets. \citet{Nevalainen2010,Kettula2013, Schellenberger2015} used galaxy clusters to measure the differences in measured temperatures between instruments, and \citet{Tsujimoto2011} used the Pulsar Wind Nebula G21.5-0.9 to measure power-law slopes and fluxes. These studies were focused on extended sources and the differences in measured spectral parameters. For the soft X-ray CCD instruments \citet{Plucinsky2012, Plucinsky2016} used the supernova remnant 1E\,0102.2-7219 to compare the fluxes of the line spectrum, developing an empirical model as a reference spectrum for future cross-calibrations campaigns. For point source flux comparison \citet{Ishida2011} used \pksb. Furthermore, recent cross-calibration studies have been made by \citet{Guver2016} using simultaneous observations of thermonuclear X-ray bursts from GS\,1826-238. Observatory calibration is under continuing development as instruments age and change. Most calibration updates deal with time dependent changes such as the evolution of instrument gain or contamination, but occasionally errors are discovered and corrected that affect data from the entire mission lifetime. It is therefore necessary to repeat and update cross-calibration campaigns on a regular basis using the newest instrument calibrations available. As instruments get decommissioned and new ones launched, it is also beneficial to the community to relate the newest member to the rest of the group. We examine in this paper two cross-calibration campaigns conducted in 2012 and 2013 on two sources, the quasar \qcs, and the BL Lac object \pksb. Both sources have been used as calibration targets in the past, and they are well suited for several reasons: they are not too bright to cause severe pileup issues for the CCD instruments, their absorbing Galactic column is very low, and the spectra can be well fit by a power-law between 1--20 keV for \qcs\ and 1--10 keV for \pksb. Both targets are variable so that calibration observations must be simultaneous. In addition, \qcs\ can enter states where it has a curving spectrum above 20 keV, so caution is required for comparing slopes across a wide broadband \citep{madsen2015a}, and \pksb\ is very soft with $\Gamma \sim 2.7$, so that very long integration times would be required for sufficient statistics above 10\,keV. In this paper we perform two different analyses. First, we find the best fit for each instrument and compare the differences between them, focusing primarily on the flux from which we will derive the cross-calibration constant. Second, we explore the change in flux and cross-normalization constant when we require the same spectral parameters for all data sets, rather than allowing each to take on its best fit. This second situation is what most astronomers do when fitting data from multiple instruments. It is therefore important to understand what systematics one might encounter due to systematic calibration errors that are different among instruments. The participating instruments were: \chandra\ with HETGS for \qcs\ and LETGS for \pksb, \nustar, \suzaku\ with XIS for both targets and HXD-PIN for \qcs\ (there was no detection of the source in GSO), \swift\ with XRT only (no BAT), and \xmm. This paper is a summary of the activity of a working group aiming at calibrating the effective areas of different X-ray missions within the framework of the IACHEC. The consortium aims to provide standards for high-energy calibration and to supervise cross calibration between different missions. We refer the readers to the website\footnote{International Astronomical Consortium for High Energy Calibration, http://web.mit.edu/iachec/} for more details on IACHEC activity and meetings. | We have calculated flux ratios between the five observatories \chandra, \nustar, \suzaku, \swift, and \xmm\ for restricted energy bands 1--5\,keV, 3--7\,keV for those involving \nustar, and 20--40\,keV for \nustar\ and \suzaku/HXD. We stress that the cross-normalization constants derived from the fluxes are valid only in the specified energy bands, and do not inform on the differences in spectral slopes between instruments. Results from multiple observatories should be judiciously evaluated against the information provided in this paper, and it should be understood that in the absence of an absolute calibration source there is no instrument that is more ``correct" than the other. | 16 | 9 | 1609.09032 |
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