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1404 | 1404.7179.txt | We present an optical/NIR imaging survey of the face-on spiral galaxy M83, using data from the {\it Hubble Space Telescope} Wide Field Camera 3 (WFC3). Seven fields are used to cover a large fraction of the inner disk, with observations in nine broadband and narrowband filters. In conjunction with a deep \chandra\ survey and other new radio and optical ground-based work, these data enable a broad range of science projects to be pursued. We provide an overview of the WFC3 data and processing and then delve into one topic, the population of young supernova remnants. We used a search method targeted toward soft X-ray sources to identify 26 new supernova remnants. Many compact emission nebulae detected in \FeiiL\ align with known remnants and this diagnostic has also been used to identify many new remnants, some of which are hard to find with optical images. We include 37 previously identified supernova remnants that the data reveal to be $<$0\farcs5 in angular size and thus are difficult to characterize from ground-based data. The emission line ratios seen in most of these objects are consistent with shocks in dense interstellar material rather than showing evidence of ejecta. We suggest that the overall high elemental abundances in combination with high interstellar medium pressures in M83 are responsible for this result. Future papers will expand on different aspects of the these data including a more comprehensive analysis of the overall supernova remnant population. | } M83 (NGC\,5236) is an iconic face-on ($i$ = 24$^{\circ}$) grand-design SAB(s)c spiral galaxy, with a starburst nucleus, active star formation along the arms, and prominent dust lanes \citep{{talbot79}, {elmegreen98}}. Adopting the Cepheid distance of 4.61 Mpc to M83 \citep{saha06} means that 1\arcsec\,=\,22 pc. With its proximity and nearly face-on orientation, M83 has been the subject of numerous studies at wavelengths across the electromagnetic spectrum \citep[to mention a few]{{crost02}, {soria03}, {herrmann08}}, and as each new facility or improved instrument comes on-line, observers return to this galaxy to improve the available data. This is because M83 provides an exceptional example for studying the entire cycle of star formation and destruction, and the impacts of this activity on the structure and evolution of the galaxy itself. Over time, the integrated effects of these ongoing processes reveal themselves in the form of high overall metallicity \citep{{bres02}, {pily06}, {pily10}} and chemical abundance gradients across the $\sim$10\arcmin\ diameter bright optical disk \citep{{bres02}, {bres09}}. GALEX UV imaging and deep H~I surveys show a fainter and much more extended and distorted disk, indicative of past interactions and active feeding of new material to the inner galaxy \citep{{hucht81}, {thilker05}, {bigiel10}}. One direct indicator of the ongoing activity in M83 is the observed supernova (SN) rate. To date, M83 has hosted six recorded supernovae (SNe) since 1923, although none since 1983 \citep{{cowan85}, {stockdale06}}, second in number only to NGC\,6946 which has had nine. Three of the six have spectroscopically determined types of Ib or II, consistent with them resulting from the core-collapse of massive stars \citep{barbon99}. Projecting this observed rate backwards in time, there must have been dozens of core-collapse SNe in M83 within the past millennium, and many more older supernova remnants (SNRs) as well since expectations are that SNRs remain visible for tens of thousands of years. This is consistent with existing SNR surveys that have identified well over 200 SNR candidates in M83 \citep[see][henceforth B12, and references therein; see also Blair et al. 2013]{blair12}. We are pursuing a multi-wavelength observational campaign to obtain new optical/IR, X-ray, and radio data for M83 to better understand the various populations of objects and how they interact with each other and with the galaxy as a whole. As part of this campaign, B12 used IMACS imaging data from the Magellan-I 6.5m telescope to identify some 225 ISM-dominated SNRs and some additional relatively strong \oiii\ sources that are potential SNRs, expanding on the earlier work of \citet[][henceforth BL04]{blair04}. In addition, \citet{long14} conducted an extensive \chandra\ campaign totaling 729 ks (plus 60 ks from much earlier in the \chandra\ mission) that shows over 400 point sources and extensive diffuse X-ray emission filling the spiral arms and star forming regions. Radio observations with ATCA (also reported by \cite{long14}) and the Jansky EVLA (Stockdale et al., in preparation) have also been conducted. Early results include the discovery and characterization of a new ultraluminous X-ray source \citep{soria12}, an improved characterization of the young remnant of SN1957D \citep{long12}, and the discovery of a new microquasar near the nucleus \citep{soria14}. In this paper, we provide an overview of the \hst\ portion of our multi-wavelength campaign, which includes imaging in nine broadband and narrow emission-line filters in the optical and near-IR of seven fields in M83, two of which are from the Early Release Science Program (ID 11360; R. O'Connell, PI) and five of which are from a cycle 19 \hst\ General Observer program (12513; W. Blair, PI). The excellent spatial resolution of WFC3 ($0\farcs0396$ per pixel for UVIS, $0\farcs13$ per pixel for the IR camera) permits accurate stellar photometry in relatively crowded fields and also resolves the emission-line gas at the parsec level. After this overview, we report initial results from our analysis of the smallest diameter SNR candidates uncovered by \hst/WFC3. \citet[henceforth D10]{dopita10} performed what in many ways was a precursor to the current SNR investigation, using \hst/WFC3 data from what we will call Field 1 to investigate the SNR population in the M83 nuclear region and an inner spiral arm. They identified 60 SNRs and candidates within this one WFC3 field, including 20 objects in the complex nuclear region, a possible (but spectroscopically unconfirmed) young ejecta-dominated SNR on the eastern edge of the nucleus, and a tentative optical identification of the counterpart to SN1968L (also deep in the nuclear region). The next section describes the \hst\ observations and data processing. In \S3, we describe the candidate SNRs and their properties, concentrating on the subset for which \hst\ data provide the most leverage. In \S4 we discuss the implications of these results, and we summarize our findings in \S5. We will address various other aspects of these data or specific objects of interest in future papers, including a more comprehensive treatment of the full SNR population and its relation to the underlying stellar component. | } The \hst\ data resolve many complex regions of star formation, dust lanes, and nebular emission that are unresolved even at the best ground-based resolutions available. This resolution provides several distinct advantages for studying SNRs. Accurate sizes and morphologies can be determined for many of the SNRs first identified in the ground-based data. Objects in complex regions can be more readily identified and separated from contaminating stellar or nebular contamination. Also, the direct determination of the sizes of the smallest SNRs ($\leq$10 pc in diameter) allows identification of the population of the youngest SNRs. Many of these SNRs were missed in ground-based surveys because they were either too faint or simply smeared out by atmospheric seeing. Below we show a few example objects to demonstrate these points, discuss our initial assessment of the small SNR population, and highlight the use of \fe2\ emission as a diagnostic of shocks and SNRs in particular. \subsection{Selected SNR Candidate Identifications\label{sec_examples}} A small (6\arcsec\ square) region from Field 4 is shown in Figure \ref{fig_triplesnr}, where the four panels show the subtracted \fe2, 3-color continuum subtracted emission lines, 3-color continuum (all from WFC3) and a 3-color representation of the \chandra\ data. (Details are given in the figure caption.) Three patches of bright \fe2\ emission are evident, and correspond to three regions of enhanced \sii\ and to a lesser extent \oiii\ emission (causing the yellow-green and/or bluish-white appearance in the upper right panel). Only the brighter and larger object below center in the figure was identified in the Magellan survey. The morphology seen with \hst\ resolution and the \fe2\ emission both indicate these are three separate but closely spaced SNRs, two of which were previously unknown. %The extinction should not differ greatly for these three objects, and so the apparent changes in the relative intensities of \fe2\ emission to the optical emission are real, as discussed further below. Although a \chandra\ source was identified at this position, it is extended compared to most point sources and may involve emission from more than one of the objects. The continuum data (lower left panel) show a combination of hot, young stars and red supergiants in the vicinity, indicating the progenitor of the SN arose from within a young population. In Figure \ref{fig_5snrs}, we show a 16\arcsec\ $\times$ 20\arcsec\ region from the southern portion of Field 5 as another example. The green circles denote four B12 catalog objects in the field. %While these objects were identified in the Magellan search, The subtracted WFC3 emission-line data resolves each object into knots, shells, or partial shells, and reasonable measurements of the size of each object can be made. Although the IR camera resolution is lower, all four of these objects are nonetheless well detected in \fe2\ and show reasonably similar morphologies to the UVIS emission line data. While stars are present near each object, the stellar contamination is not severe. The smallest SNR at upper left, B12-45, is well-detected in X-rays, and two neighboring SNRs are within more diffuse X-ray emission but were not identified as separate point sources in the \chandra\ data. Of particular interest is the yellow-circled object in the \fe2\ panel of the Figure. This object is comparable in size and \fe2\ surface brightness to the other SNRs, and yet no optical or X-ray counterparts are evident at the position. The yellow circle projects onto a dark dust lane in the continuum image panel. We posit that this is a previously unknown SNR, listed as object \#3 in our Tables \ref{table_snrlist1} and \ref{table_snrlist2}, whose optical (and possibly soft X-ray) emissions are blocked from our vantage point. In Figure \ref{fig_newsnr}, we show an example of a source (\#7 in our list) identified both from its X-ray and \fe2\ emission, located on the northern edge of Field 5. We were initially drawn to this location by the moderately strong soft X-ray emission (source X067 from \citet{long14}), for which no optical candidate had been identified. In the subtracted emission-line panel, a very compact knot of optical emission is present with characteristics consistent with a SNR identification, directly adjacent to a bright \hii\ region and active star-forming region. The \fe2\ data show that the same object is clearly detected while the optically much brighter \hii\ region to the NW is not seen in \fe2. Because of the larger pixel size for the IR camera, it is not immediately obvious whether only a portion object \#7 is bright optically, or whether the optical emission represents the SNR's true size. The object appears projected against a fairly dark, dusty region on the outskirts of the star-forming region to the NW, but in this case it must be primarily on the near side of the obscuration, and thus not as heavily reddened as the new SNR highlighted in Figure \ref{fig_5snrs}. The proximity of this SNR to the star forming region is suggestive of a core-collapse progenitor. \subsection{Where are the Ejecta-dominated SNRs? \label{sec_noejecta}} Pertaining to the smallest diameter SNRs, one thing is immediately obvious from Table \ref{table_snrlist2}: while many of the small objects are moderately strong \oiii-emitters, none of them is dominated by \oiii\ emission the way the prototype ejecta-dominated remnants are. Cas A in our Galaxy (age $\simeq$ 340 years, diameter=5 pc) shows primarily lines of O and S ejecta up to velocities in excess of 8000 $\VEL$ \citep{{kirshner77},{fesen06}} and has no comparable associated \ha\ emission. The Small Magellanic Cloud object 1E0102-7219 (hereafter E0102; kinematic age $\simeq$ 2000 years, diameter=11 pc) is also dominated by high velocity ($\sim$6000 $\rm km ~ s^{-1}$) O emission lines, and while it is adjacent to an \hii\ region, it has no directly associated \ha\ component \citep{{dopita84}, {blair00}, {vogt10}}. Thus, to first order, E0102 simply looks like an older (and larger) version of Cas A. The object N132D in the Large Magellanic Cloud is more than 3000 years old and still shows evidence of O-rich ejecta \citep{vogt11}, although an outer shell swept up by the main blast wave is starting to show regions of radiative shock emission \citep{{morse96},{blair00}}. However, with a diameter of 25 pc, this outer shell would be readily resolved with WFC3 for a similar object in M83. \hst\ images of the extraordinary young SNR in NGC~4449 \citep{milis12} seem to show \ha\ as well as very bright \oiii\ emission at the source position, although spectra show the \ha\ to be narrow while the \oiii\ lines are broad and hence, are due to the expanding ejecta. The fact that in our M83 imagery both \ha\ and \sii\ are comparable to the \oiii\ emission in nearly all of the small diameter SNRs points toward emission from normal radiative ISM shocks rather than an ejecta-dominated interpretation, which is not what was expected for these small diameter (presumably young) SNRs. Spectra are currently only available for selected objects from our list in Table \ref{table_snrlist1}, but they appear to corroborate the conclusion from imagery. In Figure \ref{fig_spectrum}, we show spectra of two objects obtained as part of an ongoing Gemini-S GMOS program on M83 (P. F. Winkler, PI) that will be reported separately. B12-150 (\#41 in our Tables), which was also observed spectroscopically by BL04 (coincidentally also their object BL04-41) has a diameter of 11.3 pc, similar to E0102. However, the spectrum of this object is fully consistent with ISM-dominated radiative shocks: \oiii\ $\lambda$5007 is comparable in strength to \ha\ with no evidence of high velocities that would indicate emission from ejecta. This object is only 0.8 kpc from the center of the galaxy and has very strong \nii\ and \sii\ lines compared with \ha. The \sii\ doublet line ratio of 0.85 implies high electron densities near 700 $\rm cm^{-3}$. The second spectrum in Fig. \ref{fig_spectrum}, B12-115 (\#18), poses an even more extreme example. Only 5.3 pc in diameter, it is essentially the same size as Cas A, and yet its spectrum shows no signs of broad ejecta emission lines. This object is 1.8 kpc from the center of the galaxy, and shows somewhat weaker lines of \nii\ and \sii\ compared with \ha, although some modest contamination by nearby \hii\ emission may be present in the spectrum. As with B12-150, this object has moderately strong but narrow \oiii\ emission consistent with bright radiative shocks. The \sii\ doublet line ratio of 0.75 implies an even higher electron density of about 1000 $\rm cm^{-3}$ in this case. Published spectra for a number of M83 SNRs were provided by BL04, but only two are from the current ``small SNR'' sample, the aforementioned B12-150, and B12-147 (our \#40, also BL04-40). The BL04 spectrum of B12-150 is consistent with the higher quality GMOS spectrum discussed above. The B12-147 spectrum is also consistent with a classic ISM shock, with strong forbidden line emission no evidence of high velocity ejecta. An interesting point is that, once again, the electron density for B12-147 implied by the \SiiL\ ratio of 0.97 is moderately high at 300 $\rm cm^{-3}$. From the evidence at hand, we conclude that the conditions in M83 are such that the young SNR population is evolving very quickly beyond the ejecta-dominated phase and into the radiative phase. A detailed assessment of this finding is beyond the scope of this initial report, but it seems likely that the high pressure/high density ISM conditions and quite possibly the high elemental abundances in M83 are both contributing to this situation. In a statistical analysis of Field 1 SNRs and comparison to shock models, D10 found indications of high pressure ISM conditions, both generally and especially within the spiral arms. The bright, diffuse X-ray emission seen with \chandra\ \citep{long14} is another indication of this high pressure ISM, as is the \ha\ luminosity function for M83 SNRs reported by B12 and shown corrected in \cite{blair13}, which is offset toward significantly higher luminosities than seen for SNRs in M33. The high \sii\ electron densities in the spectra reported above are further evidence that the shocks in these young SNRs are encountering relatively dense surrounding interstellar or circumstellar material. The elevated abundances in M83 may contribute by enabling enhanced stellar wind mass loss from the precursor stars \citep{{vink01}, {kudrit02}}, and it could be this material, at least in some cases, that is responsible for the dense, radiative shocks inferred for these young SNRs. SN1957D (our object \#46) remains the only confirmed case of a young ejecta-dominated remnant in M83, but it may provide a clue to young SNR evolution in M83. This $\sim$56 year old SNR has already experienced substantial decline of its ejecta-dominated optical emission over the last two decades \citep{{milis12}, {long12}}, very different from Cas A, which is still bright (and even brightening) more than 300 years after the explosion. In Cas A, dense ejecta knots light up optically as they encounter the reverse shock, and then fade. The overall brightening indicates more new ejecta knots are encountering the reverse shock than are disappearing as they cool below detectability. The rapid fading of the broad O lines for SN1957D is consistent with the idea that the bulk of the ejecta have already encountered the reverse shock and that overall the ejecta emission is decreasing. This indicates that the ejecta-dominated phase will be short-lived compared with objects such as Cas A and E0102, which is consistent with the picture outlined above. \subsection{[Fe II] as a Shock Indicator \label{sec_iron}} The WFC3/IR data using the F164N filter provide an excellent tool for locating shock-heated gas, and many SNRs in particular. As we inspected the seven fields of \hst\ data, the only compact optical nebulae that aligned with \fe2-emitting sources were D10 or B12 SNRs. Many (but not all) of the known SNRs, including both small diameter SNRs and larger objects not reported here, were found to be strong \fe2\ sources. One exceptional object in the \hst\ data just to the NE of the bright nucleus was initially identified by D10 as a nuclear SNR candidate (object 16 in Table 3 of D10). However, a new assessment \citep{soria14} indicates this object is a microquasar similar to SS 433/W50 in our Galaxy; it is a strong X-ray and ATCA radio source and it is exceptionally bright in \fe2. Hence, even though it may not be a SNR in the usual sense, this object clearly involves a strong shock-heated emission component, consistent with our findings for the more conventional SNRs. In support of this conclusion, we examined the positions of dozens of PNe, both from the listings of \citet{herrmann08} and \citet{herrmann09}, and from our own inspection of objects with similar character in the \hst\ data but not in those listings, and found no \fe2\ emission from any of them. We also compared to many dozens of W-R stars/nebulae cataloged by \citet{hadfield05} (see their Appendix A, Tables A1 and A2), and found no \fe2\ counterparts. Occasionally one can see very faint, diffuse \fe2\ emission associated with the positions of very high surface brightness \hii\ regions, but \hst\ is not the right tool for assessing faint diffuse emission. If M83 were more distant and unresolved, this faint diffuse emission could conceivably compete with or even dominate a global assessment of \fe2\ emission. \citet{alonso03} and \citet{labrie06} concluded that point \fe2\ sources (e.g. SNRs) accounted for up to a few 10's of percent of the total \fe2\ emission in a number of nearby starburst galaxies, and that the overall \fe2 emission was a good indicator of the star-formation rate and supernova activity. It would require deeper integrations with the F164N filter in M83 to obtain a quality measurement of the total \fe2\ emission. As we pursued our targeted search of X-ray source positions, we occasionally found corresponding compact \fe2\ emission sources that were not previous optical SNR identifications. On closer inspection of the \hst\ optical emission line data at these positions, faint new optical counterparts consistent with an SNR identification were sometimes found, as was the case with the object shown in Figure \ref{fig_newsnr}. Also, some new compact \fe2\ sources were found buried in bright or confused regions of \ha\ emission; these are likely buried SNRs for which the usual optical diagnostics for shocks are less effective. Finally, a small number of well-detected \fe2\ sources did not have obvious optical or X-ray counterparts but were projected against regions of high extincttion), as with the SNR highlighted by the yellow circle in Figure \ref{fig_5snrs}. Hence, \fe2\ provides an effective way of finding SNRs that are difficult to locate using the usual optical and X-ray diagnostics, thus permitting a more complete sample to be assembled. As discussed in section \ref{sec_find} and shown in Table \ref{table_snrlist2}, significant variations in the ratio of \fe2\ to optical lines is observed, but until spectroscopy and/or other means of estimating extinction to individual objects becomes available the intrinsic variations in the strength of \fe2\ relative to the optical lines cannot be assessed. This is because of the differential extinction between optical and IR wavelengths that has the effect of artificially enhancing the observed relative \fe2\ line strength. For instance, the spectrum of B12-150 in Figure \ref{fig_spectrum} shows an observed ratio of F(\ha)/F(\hb) = 5.0 which, using a standard extinction curve \citep{cardelli89} with R=3.1, implies an extinction of $A_V$= 1.64. Using \sii\ as a clean reference (since \ha\ is not measured directly by F657N), the observed ratio F(\fe2)/F(\sii) = 0.29 corrects to an intrinsic ratio of 0.11. For other objects with more or less extinction than B12-150, the correction would obviously be larger or smaller. Hence, quantitative comparison to shock models cannot yet be done for most of our objects.\footnote{The other object with a spectrum in Figure 8, B12-115, coincidentally has nearly the same extinction as B12-150, but B12-115 was not covered in the WFC3/IR observations.} In contrast with the reddened objects that have artificially high observed \fe2\ emission are some optical SNRs that have little or no \fe2\ emission detected. Columns 5 and 6 of Table \ref{table_snrlist2} show some objects with only upper limits on their \fe2\ emission even though one or more optical lines are well detected. In addition, there are some fairly bright optical SNRs in the sample of larger diameter SNRs not reported here that have little or no detectable \fe2\ emission. Hence, we can say that variable extinction is not the only cause of the observed variations in the relative strength of \fe2\ to the other lines. The observational result that there are optical SNRs with little or no detectable \fe2\ indicates there is some region of parameter space that produces relatively weak \fe2\ emission compared to the optical lines. There are many factors that could contribute to the relative strength of \fe2\ emission, including variable shock conditions, variable amounts of dust destruction in the SNR shocks, the possible contribution of Fe ejecta emission (or not), in addition to variable extinction. We will investigate these possibilities further once the larger SNR data set has been analyzed more fully, including additional spectroscopy of many of the objects to properly account for extinction effects. For now we conclude that \fe2\ emission provides an important new diagnostic for identifying shock-heated nebulae, especially in dusty or confused regions, but that it is not a universal diagnostic. } We have performed a detailed imaging survey of seven \hst-WFC3 fields covering much of the bright optical disk of M83 in nine continuum and emission line bands. We describe the acquisition and processing for the entire data set and then discuss results of a preliminary targeted search of these data for supernova remnants. Comparisons between deep \chandra\ X-ray images and the \hst\ data have directed us to a number of new SNRs missed in ground-based surveys but that are apparent at \hst\ resolution. As part of this search, we have also found the WFC3/IR data using the F164N filter of particular interest since the \fe2\ emission from many SNRs makes them stand out clearly even in dusty or optically-confused regions of the galaxy. We have also inspected the positions of SNRs previously known from ground-based surveys and selected those that are measured with \hst\ to be less than 0\farcs5 (11 pc) in diameter, and thus must represent the younger population of SNRs in M83. In total, we tabulate information for 63 SNRs, 32 of which have an associated X-ray source in the deep \chandra\ survey data \citep{long14}. The observed line ratios for this young SNR population, mostly from the \hst\ imagery but with some spectral confirmation, indicate the objects are dominated by radiative ISM shocks rather than ejecta, which was not expected {\it a priori}. This may be related to both the super-solar abundances, which allow more significant winds and mass loss from the precursor stars, and the apparently high-pressure ISM in M83 which helps to constrain this material to the vicinity of the SN. The young SNR shocks then encounter this dense material, causing the apparent rapid evolution into the radiative stage. This interaction would also create a strong reverse shock and the optically-emitting ejecta must pass through this shock and fade quickly in comparison to local examples of young SNRs such as Cas A and E0102. Additional spectra of this small SNR population, and in particular some of the objects newly discovered with \hst, might be able to find additional transitional cases similar to SN1957D, where the rapidly-moving ejecta are still visible. This would help confirm this picture of rapid evolution for these young SNRs. When a more thorough and systematic search is completed for the new fields, and when the complex nuclear region is included (an additional 19 SNR candidates already known; see D10), we expect the total SNR population in M83 to top the 300 mark. One of several future papers will provide a more complete analysis of the entire SNR population as seen by \hst, including an analysis of the stellar populations near many SNRs to constrain the main sequence turn-off masses of associated stars and hence constrain the masses of many of the SN precursors. | 14 | 4 | 1404.7179 |
1404 | 1404.2120_arXiv.txt | { Transit observations in the Mg\,{\sc i} line of HD\,209458b revealed signatures of neutral magnesium escaping the upper atmosphere of the planet, while no atmospheric absorption was found in the Mg\,{\sc ii} doublet. Here we present a 3D particle model of the dynamics of neutral and ionized magnesium populations, coupled with an analytical modeling of the atmosphere below the exobase. Theoretical Mg\,{\sc i} absorption line profiles are directly compared with the absorption observed in the blue wing of the line during the planet transit. Observations are well-fitted with an escape rate of neutral magnesium $\dot{M}_{\mathrm{Mg^{0}}}$=2.9$\stackrel{+0.5}{_{-0.9}}\times10^{7}$\,g\,s$^{-1}$, an exobase close to the Roche lobe (\mbox{$R_\mathrm{exo}$=3$\stackrel{+1.3}{_{-0.9}}$$\,R_\mathrm{p}$}, where $R_\mathrm{p}$ is the planet radius) and a planetary wind velocity at the exobase $v_{\mathrm{pl-wind}}$=25\,km\,s$^{-1}$. The observed velocities of the planet-escaping magnesium up to -60\,km\,s$^{-1}$ are well explained by radiation pressure acceleration, provided that UV-photoionization is compensated for by electron recombination up to $\sim13\,R_\mathrm{p}$. If the exobase properties are constrained to values given by theoretical models of the deeper atmosphere ($R_\mathrm{exo}$=2$\,R_\mathrm{p}$ and $v_{\mathrm{pl-wind}}$=10\,km\,s$^{-1}$), the best fit to the observations is found at a similar electron density and escape rate within 2$\sigma$. In all cases, the mean temperature of the atmosphere below the exobase must be higher than $\sim6100$\,K. Simulations predict a redward expansion of the absorption profile from the beginning to the end of the transit. The spatial and spectral structure of the extended atmosphere is the result of complex interactions between radiation pressure, planetary gravity, and self-shielding, and can be probed through the analysis of transit absorption profiles in the Mg\,{\sc i} line. } | \label{intro} The hot-Jupiter HD\,209458b has been the source of many detections of atomic and molecular species over the years (see \citealt{VM2013} and references therein). Transit observations of this planet in the H\,{\sc i} Lyman-$\alpha$ line led to the first detection of atmospheric escape (e.g., \citealt{VM2003,VM2008}; \citealt{BJ2007,BJ2008}; \citealt{Ehrenreich2008}). Heavier elements were identified at high altitudes in the extended exosphere of the planet in the lines of O\,{\sc i}, C\,{\sc ii}, and Si\,{\sc iii} (\citealt{VM2004}; \citealt{Linsky2010}, \citealt{BJ_Hosseini2010}), Si\,{\sc iv} (\citealt{Schlawin2010}) and more recently Mg\,{\sc i} (\citealt{VM2013}), supporting the idea that its atmosphere is in a state of ``blow-off''. \\ A large range of models have been developed to characterize the structure of the upper atmosphere of close-in giant exoplanets and to explain the evaporation process, either from theory or from observations (see \citealt{Bourrier_lecav2013} and references therein). Here we use the 3D numerical model detailed in Bourrier \& Lecavelier (2013), revised to interpret the observed escape of magnesium from the atmosphere of HD\,209458b. Transit observations of the planet in the Mg\,{\sc i} and Mg\,{\sc ii} lines are described in Section~\ref{obs}. We present our new model in Section~\ref{model}, notably the analytical modeling of the atmosphere below the exobase and the description of the ionization and recombination mechanisms. In Section~\ref{dyn}, we analyze the dynamics of an escaping magnesium atom, and in Section~\ref{regimes}, we describe the ionization state of the gas around HD\,209458b. In Section~\ref{model results}, we compare simulated spectra with the observations and put constraints on the exobase properties as well as the physical conditions in the extended atmosphere of HD\,209458b. Predictions of spectro-temporal variations in the absorption profile are presented in Section \ref{tempvar}.\\ | \label{conclu} We used a revised version of the 3D particle model described in Bourrier \& Lecavelier (2013) to simulate the escape of magnesium from the atmosphere of HD\,209458b and to calculate theoretical transmission spectra to be compared to transit and post-transit observations obtained in the Mg\,{\sc i} and Mg\,{\sc ii} lines in the UV by \citet{VM2013}. The main improvement to the previous model is a detailed analytical modeling of the atmosphere below the exobase which takes its shielding effect and its absorption in the core of the neutral magnesium line into account. We found that the mean temperature below the exobase must be higher than $\sim6100$\,K. The free parameters of the model are otherwise the escape rate of neutral magnesium, the electron density, the altitude of the exobase, and the velocity of the planetary wind at the exobase. \\ Observations are best explained if the exobase is close to the Roche lobe (\mbox{$R_\mathrm{exo}$=3$\stackrel{+1.3}{_{-0.9}}$$\,R_\mathrm{p}$}) and magnesium atoms escape the atmosphere at the exobase level with a radial velocity $v_{\mathrm{pl-wind}}$=25\,km\,s$^{-1}$. Because of the V-shape of the stellar Mg\,{\sc i} line, radiation pressure is not too efficient on low-velocity neutral magnesium atoms close to the planet but impart strong accelerations to atoms with high radial velocities, as they receive more UV flux far from the line core. The velocity range of the absorption signature, up to -60\,km\,s$^{-1}$ in the blue wing of the line, is thus well reproduced by a radiative blow-out, provided the quick stellar UV-photoionization of the escaping particles is compensated for by electron recombination up to an equilibrium altitude between the two mechanisms, which is estimated to be $R_{\mathrm{eq}}$=13.4$\stackrel{+3.1}{_{-4.5}}$$\,R_{\mathrm{p}}$. Beyond this Mg-recombining layer of the exosphere the magnesium is mostly ionized and subjected to a low radiation pressure from the Mg\,{\sc ii} line. The non-detection of excess absorption in this line is well-explained by low densities of ionized magnesium at all altitudes. The global best fit to the observations is obtained with an escape rate $\dot{M}_{\mathrm{Mg}}=2.9\times10^{7}$\,g\,s$^{-1}$ ($2.0\times10^{7}$ -- $3.4\times10^{7}$\,g\,s$^{-1}$). Assuming a solar abundance these results are consistent with standard values of hydrogen escape rates in the range $2.1\times10^{10}$ -- $3.5\times10^{10}$\,g\,s$^{-1}$. Observations are best reproduced with electron density at $3R_{\mathrm{p}}$ in the order of 10$^{10}$cm$^{-3}$. This value is possibly overestimated; or if the electron density is correct, it could mean that electrons are more abundant than ions in this collisionless part of the upper atmosphere. With the addition of electron-impact ionization to UV-photoionization, electron-recombination is dominated by ionization close to the planet (below 2.7$R_{\mathrm{p}}$), but this has little influence on the quality of the best fit since particles are launched above the Roche lobe. In any case, the rates used by \citet{Voronov1997} for electron-impact ionization may not be valid for temperatures below 11000\,K because they were calculated for plasmas with far higher temperatures. \\ Constraining the exobase radius and planetary wind velocity to lower values consistent with theoretical model predictions ($R_\mathrm{exo}$=2$\,R_\mathrm{p}$ and $v_{\mathrm{pl-wind}}$=10\,km\,s$^{-1}$) we found that the observations can still be explained with similar escape rates and electron densities, albeit with larger error bars: $\dot{M}_{\mathrm{Mg}}$=6.3$\times10^{7}$\,g\,s$^{-1}$ ($1.4\times10^{7}$ -- $4.7\times10^{8}$\,g\,s$^{-1}$). Although in this case the exobase radius was chosen arbitrarily, halfway between the planet surface and the Roche lobe, a different value in this range does not significantly change our conclusions.\\ Simulations show that the absorption profile results from complex interactions between radiation pressure, planetary gravity, and self-shielding. In a previous work, the analysis of transit observations in the Lyman-$\alpha$ line of neutral hydrogen allowed us to characterize atmospheric escape at high altitudes in the exosphere. Here the absorption signature in the line of neutral magnesium has been used to analyze the structure of the atmosphere at lower altitudes both in the escaping cloud and below the exobase. Simulations predict that the absorption profile should expand toward positive velocities during the transit because the atmosphere close to the planet follows its circular orbital motion. Observation of the magnesium lines thus appears to be a powerful tool to probe an exoplanet's upper atmosphere in the thermosphere-exosphere transition region. We can anticipate that several host stars of transiting planets may be bright enough in the Mg\,{\sc i} line for their atmosphere to be probed in such a way. | 14 | 4 | 1404.2120 |
1404 | 1404.0313_arXiv.txt | We review the case for testing preferred acceleration scale theories of gravity (sometimes falling under the guise of MOdified Newtonian Dynamics) in the Solar System using the forthcoming LISA Pathfinder (LPF) mission. Using a combination of analytical and numerical results, we suggest that different types of theory should be detectable using the predicted anomalous tidal stresses effects around the saddle points of the Newtonian gravitational field. The saddle point bubbles expected extent of $\sim 400$ km are to be contrasted with potential miss parameters of $\leq 10$ km, making such a test in easy reach of LPF. We also consider routes to constraining our theories from data, based on scenarios of both null and positive results. | The concordance model of modern cosmology rests soundly on two cornerstones, a universe filled mostly with cold dark matter (CDM) and dark energy (described by a cosmological constant), i.e. $\Lambda$CDM, with underlying dynamics characterised by Einstein's theory of General Relativity (GR). Whilst this model explains the early universe with ever increasing accuracy~\cite{Planck}, as long as there remains the lack of direct detection of a dark matter particle (baring unviable candidates such as neutrinos~\cite{DMastro,DMthesis}), it remains prudent to consider alternatives. One such pathway available is to modify the underlying dynamics themselves, subject to the condition that above certain scales we restore our familiar Newtonian limit. MOdified Newtonian Dynamics (MOND) provides just such a scheme. The MONDian paradigm seeks to explain away galactic dynamics through the use of a modified force law, introducing a preferred acceleration scale, on the scale of typical galactic accelerations (see~\cite{MONDreview} for a detailed review). On galactic scales, these modified effects become dominant, but at larger accelerations, gravity becomes idyllically described by Newtonian dynamics. Although ideas of ``modifying'' gravity are in some way nothing new, it was Milgrom in 1983 who first proposed a theory of modified inertia~\cite{Milgrom:1983ca}. This was subsequently developed in 1986 into the theory known as AQUAL~\cite{aqual} by Bekenstein and Milgrom, formulating a Lagrangian theory which would satisfy energy and momentum conservation. Investigating the equations of motion from that leads us to a modified Poisson relation - a common way to present such theories. In the past decade, the potential accomplishments of MONDian theories have been put on an equal pedestal to GR with the development of fully relativistic modified gravity (MG) theories. We find in the literature now a litany of examples of such\footnote{The original work on AQUAL~\cite{aqual} did describe a relativistic extension for MOND, however it was soon realised it could not take into account observations of light deflection from galaxies nor could it properly restrict the tachyonic behaviour of its field.}, starting in 2004 with Bekenstein's ground breaking theory of T$e$V$e$S~\cite{teves}. T$e$V$e$S attempted to overcome previous issues in this field by introducing a vector and scalar field into the mix, fixing acausal and light deflection issues, at least at the payoff of having to fix more variables. Similarly with the Lorentz violating work of Einstein \AE ther theories~\cite{jacobmatAE, aether}\footnote{In fact the original Einstein \AE ther theory reduces just to Newtonian dynamics in its weak field, but its construction introduces an acceleration scale, a feature that was later used in generalisations to reduce to MOND.}, these various ideas were expanded on and generalised by Zlosnik, Ferreira and Starkman in 2006~\cite{aether1,aether2,AESS}, as well as attempts by Skordis and others to generalise and investigate the cosmology of these theories~\cite{kostasrev,SkordisGenTeves,tevesstrucform}. Since 2009, Milgrom has produced bimetric theories~\cite{bimetric}, motivating a quasi-linear MONDian theory from a relativistic perspective. There have been various other ideas for gravity theories in this way~\cite{BSTV,Clifton11,Fam-gaugh}. Whilst the MONDian paradigm provides a useful framework for making connection to observables, the free functions and parameters in these theories remain relatively unconstrained, leading problems of fine tuning. These theories have the danger of explaining an observations at the cost of being purely empirically fitted to data. Much work has been done investigating these modified effects on the largest scales, for instance applying constraints from galactic data when seeking dark matter alternatives~\cite{Zhao,binney,yusaf,yusaf1,yusaf2}. The much hailed Bullet Cluster (1E 0657-558) has been considered for what it can tell us about the necessity or needlessness of dark matter and MOND~\cite{Angus,bullet,bullet1,bullet2,bullet3}. These gravitational lensing studies in the past decade have suggested that CDM fits the data very well and modified gravitational force laws are statistically unlikely to explain away the results. There remains however a lack of consensus on interpreting the weak lensing survey and also there are clusters, such as Abell 520~\cite{AbellDM}, which are not easily explained by any current paradigm. Quite a different tack has come from applying Lorentz violating mechanisms (typically well constrained in the matter sector) to the gravity sector~\cite{withers, lviolationcosmo}. Constraints from high energy experiments, such as those at the LHC, especially in the light of the most recent data, have provided some of the best detailed constraints to be seen in the Solar System. Perhaps a good way to investigate general modified non-relativistic theories is to examine deviations from the inverse square law, as considered in~\cite{Blanchet, Sereno,Milgromss}. Little more however seems to be known about constraining modified gravity theories purely in the Solar System. A more pragmatic way to approach these issues is to consider that there appears to be a ubiquitous acceleration scale in the universe, $ a_0\sim 10^{-10}\unit{ms}^{-2}$. It crops up variously in cosmology and astrophysics, e.g. the cosmic expansion rate and galactic rotation curves appear curiously linked to this value. Such an observation has prompted the investigation of alternative theories of gravity endowed with such a preferred acceleration, whatever its eventual physical effect. Such ideas were first proposed with the motivation of bypassing the need for dark matter, but they may also be considered independently from this, simply as mature alternative theories of gravity~\cite{Clifton11} into which this acceleration scale has been embedded. In such a guise, they constitute prime targets for experimental gravitational tests inside the Solar System. A chance of extending the forthcoming LISA Pathfinder (LPF) mission~\cite{bekmag,LISA,companion}, to include probing the low acceleration regime around gravitational saddle points (SP), appears to provide just such an opportunity, both for testing and also cleanly constraining these theories. We organise this paper as follows, in Section \ref{techniques} we will consider on both analytical (Section \ref{Uformalism}) and numerical (Section \ref{SOR}) investigations in to preferred acceleration scale theories. Section \ref{LISApathfinder} introduces the LISA Pathfinder spacecraft and Section \ref{GWtech} shows how methods from experimental gravitational wave searches can be applied to characterise such a test, with results for various theories in Section \ref{secsnr}. Section \ref{constrain} attempts to explore the wider parameter space of these theories, varying both constants as well of the free function itself, in order constrain such theories from data. We conclude with some future thoughts and directions in this field. \subsection{Finding $a_0$ - Saddle Points in the Solar System} Here we will introduce the techniques we will need later to characterise theoretical and experimental ideas in MONDian tests. We will follow the notation and formalism first developed in~\cite{bekmag}, as well as numerical ideas presented in~\cite{bevis}. Obviously to test MONDian theories, we will need a regime where the {\it total} acceleration on test masses will be small enough to be approaching galactic acceleration scales, which we will take as $a_0$. Such regions do in fact exist in the Solar System, our own cosmic backyard. Before we continue, we will need to understand where these regions are located and solve our MONDian equations of motion in these regimes, before examining how we can test these ideas concretely. We start by considering a two body gravitational system, with masses $m$ and $M$, such that $M \gg m$, separated by some distance $R$ along the $\ve_z$ axes linking them. We centre the coordinates on mass $M$ and look at the resultant acceleration along $\ve_z$, \be \vF_N = -\Del \Phi_N = \left(-\frac{G M}{r^2} + \frac{G m}{(R-r)^2}\right)\ve_z \label{2bodyFN}\ee The stationary point of this force is thus located at \be r_{s} = \frac{R}{1 + \sqrt{m/M}}\simeq R\left(1 - \sqrt{\frac{m}{M}}\right)\ee The form of the force shows that moving along $\ve_z$ towards either mass results in an attractive force, however moving perpendicular to the axes results in a restoring force towards the stationary point - we have a gravitational saddle point (SP). We should be clear to distinguish these points from the well known Lagrange points, which exist {\it only} in a system of rotating bodies, whereas this saddle always exists (the effect of two attractive forces along the line linking them, in opposite directions). We find that the Newtonian force is linearised about the saddle, taking the form \be \vF_N = -\Del \Phi_N = A\,(r-r_{s})\,\ve_z \label{linearFN}\ee where $A$ is the Newtonian tidal stress at the saddle, defined as the derivative of the force \be S_{ij}^N = \frac{\partial^2 \Phi_N}{\partial x_i \partial x_j}\ee Here $S_{ij}^N $ is simply a constant, found when we compute the Taylor expansion coefficients in the linear expression (\ref{linearFN}) from the full two body expression (\ref{2bodyFN}) \be A = 2\frac{G M}{r_s^3}\left(1 + \sqrt{\frac{M}{m}}\right) \label{2bodyNewtS}\ee We can make two observations, one being that since $F_N \rightarrow 0$, it will indeed pass through the acceleration barrier of $a_0$, suggesting MONDian effects should be visible around saddles. For the Earth-Sun SP, such a low acceleration region is located at $r \leq 2.2$m around the saddle - a poor prospect for a satellite target. If however we consider the rule of thumb for MONDian systems, i.e. \bea F \leq a_0 &\Rightarrow& F\rightarrow\sqrt{F_N a_0}\eea then the (previously linear) force near the SP is now of the form \be F \rightarrow \sqrt{A a_0 |r-r_s|}\ee and the tidal stresses look like \be S = \frac{\partial F}{\partial _r} \sim \frac{1}{\sqrt{r - r_s}}\ee it would appear these diverge as we approach the saddle! Clearly we need to investigate the calculation using a fully relativistic theory, but this simple calculation provides at least a proof-of-concept for a tidal stress based MOND saddle test. A second relevant point to make concerns the other contributions to the Newtonian tidal stresses at the saddle, surely the Solar System and the galaxy will play a role here? At leading order, only the Earth and Sun play a role in this calculation, as (\ref{2bodyNewtS}) shows. The effect of the Moon, providing a truly 3-body system, can be computed using a numerical treatment of the saddle system, as we will shortly show in Section \ref{SOR}. One conclusion of that work is that the position of the Earth-Sun saddle is shifted with respect to the phase of the Moon (and hence at different times of the month the saddle is shifted to a known, but differing location), on the order of a few tens of km. Taking the effect of most of the mass of the solar system (from Saturn and Jupiter) into account shifts the saddle a few more km. Taking the contribution from the galaxy into account shifts it a tiny bit more. Given this, we can consider the total Newtonian tidal stress at the saddle taking the form \be A_{SP} \simeq A_{ES} + A_{M} + A_{SS} + A_{G} + \dots\ee where $ES$ denotes Earth-Sun, $M$ denotes Moon, $SS$ denotes Solar System and $G$ denotes the galactic contribution. The ordering here is such that each contribution is smaller in magnitude than the one previous. Given that each contribution to the saddle is an attractive force component, there will always be a saddle (and at a location close to the 2-body case) and hence an observable for a tidal stress experiment. \subsection{Classifying MONDian theories}\label{theory} In the wider modified gravity literature, one can find a large number of relativistic modified gravity theories. Their complexity and differences arise from the requirement that they should explain relativistic phenomena (such as lensing and structure formation) without appealing to dark matter, whilst in the non-relativistic regime have some MONDian and Newtonian limit. In general, the large profusion of relativistic MONDian theories reduce to just three different non-relativistic limits: Our job is to approach theories where such modified behaviour is present and see if they represent good prospects for detection. Their complexity and differences arise from the requirement that they should explain relativistic phenomena (such as lensing and structure formation) without appealing to dark matter, whilst in the non-relativistic regime have some Newtonian and other modified limit. The manner in which such effects are manifest may however vary widely and there have been many previous studies as to the phenomenology of these ideas, particularly in this non-relativistic regime~\cite{typeIIpaper,ali,Milgromss,aether,teves}. We will briefly outline some of these here, with the caveat that this list is neither exhaustive, nor represents the final story on gravity theories at the time of writing and for a more in depth look at gravity theories, we point the reader towards~\cite{Clifton11}. \begin{itemize} \item{\bf Type I:} Here the total potential acting on non-relativistic particles is given by the sum of the usual Newtonian potential $\Phi_N$ and a fifth force field, $\phi$: \be \Phi = \Xi\Phi_N+\phi\ee where $\Xi$ is some constant usually set to unity and the Newtonian potential satisfies the usual Poisson equation \mbox{$\nabla^2 \Phi_N=4\pi G \rho$}, and the field $\phi$ is governed by: \be \nabla \cdot \left(\mu(z)\nabla \phi\right) = \kappa G \rho \label{type1} \ee The argument of $\mu(z)$ is given by \be z=\frac{\kappa}{4\pi}\frac{\vert\nabla\phi\vert}{a_0} \ee where $\kappa$ is a dimensionless coupling constant. $\mu$ is a free function, typically chosen limits of the theory are $\mu\rightarrow 1$ when $z\gg 1$ and $\mu \simeq z$ for $z\ll 1$. The effect of these fields is twofold, in the large $z$ regime, $\phi \rightarrow \frac{\kappa}{4\pi} \Phi_N$ mimicking the Newtonian, this makes the physical potential have the form \be \Del \Phi \rightarrow \left(\Xi + \frac{\kappa}{4\pi}\right)\Del\Phi_N\ee or equivalently the form of Newton's constant is altered \be G_{ren} \rightarrow \left(\Xi + \frac{\kappa}{4\pi} \right)G_N \ee Cosmology sets bounds on the variation of $G$, from BBN and effects in the CMB~\cite{CarrollLim, Nconstraint}. Additionally these two fields mean that the Newtonian behaviour is always present in the non-relativistic regime and non-linear behaviour in $\phi$ gets triggered at a certain acceleration \be a_{\text{trig}} = \left(\frac{4\pi}{\kappa}\right)^2 a_0\ee The field however remains sub-dominant until $a_N = a_0$ and this is when fully modified behaviour is seen (in the galactic regime). It is this onset of non-linearity that we hope to probe with LPF. \item{\bf Type II:} These are similar in set-up to type {\bf I}, with $\Phi = \Phi_N +\phi$ and $\phi$ governed by a driven linear Poisson equation:\be \nabla^2 \phi = \frac{\kappa}{4\pi}\nabla\cdot\left(\nu(w)\nabla \Phi_N \right) \label{type2} \ee The argument of $\nu$ is given by \be w = \left(\frac{\kappa}{4\pi}\right)^2\frac{\vert\nabla\Phi_N \vert}{a_0} \ee Once again $\nu$ is a free function and typically we give it the form $\nu\simeq 1/\sqrt{w}$ for $w\ll 1$ and $\nu \rightarrow \unit{constant}$ for $w\gg 1$. We divide this up in the subtypes of {\bf IIA} or{ \bf IIB} with qualitatively very different implications, which can we seen more clearly if we return to using the physical potential form \bea \Del^2 \Phi &=& \Del \cdot\left( \hat{\nu} \Del\Phi_N\right) \\ \hat{\nu} &=& 1 + \left(\frac{\kappa}{4\pi}\right)\nu\eea Consider in the large $w$ regime: \begin{itemize} \item{In type {\bf IIA}, $\nu \rightarrow 0$ which implies no $G$ renormalisation occurs and $a_{\text{trig}} = a_0$. The whole theory in fact hinges on $\Phi$, all other fields are considered auxiliary.} \item{In type {\bf IIB}, $\nu \rightarrow 1$ means a trigger acceleration similar to type {\bf I}. }\end{itemize} \item{\bf Type III:} Crucially, here non-relativistic particles are sensitive to a single field $\Phi$, satisfying a non-linear Poisson equation: \be \nabla\cdot\left(\tilde{\mu}(x) \nabla \Phi \right) = 4 \pi G \rho \label{type3} \ee where the argument of $\tilde\mu$ is \be x = \frac{\vert\nabla\Phi\vert}{a_0}\ee so that $\tilde \mu\rightarrow 1$ when $x\gg 1$ and $\tilde \mu\sim x$ for $x\ll 1$. Again no renormalisation of $G$ and a trigger acceleration $a_{\text{trig}} = a_0$ \end{itemize} As the trigger acceleration sets the scale of the SP bubble, using the current estimates for our parameters ($\kappa = 0.03$, $a_0 = 10^{-10}\unit{ms}^{-1}$) we find these to be \bea {\bf I,IIB}:\nonumber\\a_{\text{trig}} &=& \left(\frac{4 \pi}{\kappa}\right)^2 a_0 \simeq 10^{-5}\unit{ms}^{-2} \Rightarrow r_0\sim 383 \unit{km}\nonumber\\{\bf IIA,III}:\nonumber\\ a_{\text{trig}} &=& a_0 = 10^{-10} \unit{ms}^{-2} \Rightarrow r_0 \sim 2.2 \unit{m}\nonumber\eea These distinctions group together types {\bf I} and {\bf IIB} as the best candidates for detection with LPF; types {\bf IIA} and {\bf III} would easily escape any negative result. An important distinction here stems from the fact that we have a curl term (often called a magnetic field) in type {\bf I} and {\bf III} theories. This is easiest seen when one attempts to linearize the non-linear Poisson equations present by introducing an auxiliary vector field (e.g. $\mu\nabla\phi$ for type {\bf I} theories) - such a field has non-zero curl. The same is not true for type {\bf II} theories, being already linear in $\phi$ and driven by a function of the Newtonian field, $\nu\nabla \Phi_N$, (a quantity which has a curl). This turns out to have a significant quantitative effect upon the magnitude of the saddle tidal stresses, as the magnetic field is known to soften the anomalous tidal stresses around the saddle points in type {\bf I} theories. A scan of the relativistic MONDian theories proposed in the literature suggests that they fall into these categories. Bekenstein's TeVeS~\cite{teves} as well as Sanders' stratified theory~\cite{BSTV} have type I limits. Milgrom's Bimetric theory~\cite{Milgrom:2009gv,Milgrom:2010cd} can be either type I or type II, depending on details. GEA theories~\cite{aether,aether1} and Galileon k-mouflage~\cite{k-mouflage} have a non-relativistic limit of type III. Often authors have attended to different considerations and constraints, so the parameter $\kappa$ has been taken to be different. However, as we will point out, if in each case the same considerations have been employed, the value of $\kappa$ would have to be comparable. | \label{concs} \begin{figure}[t!]\begin{center} \resizebox{1\columnwidth}{!}{\includegraphics{deltaFQN.eps}} \caption{\label{fig:ssconstraints}{Comparing Solar System fifth force constraints~\cite{ssconst} with models of free function. Such a plot would a starting point to consider current constraints on MG theories. Recall that for fiducial parameter values, the bubble boundary is at $a_{trig} \simeq \frac{4\pi}{\kappa}{a_0} \simeq 10^{-5} \unit{ms}^{-2}$ and here we have subtracted off the rescaled Newtonian contribution from the $\delta F$ and $\kappa = 0.03$ unless stated otherwise. The function $\mu_{fid}$ corresponds to the $\mu$ of Equation \ref{mufid}. The errors on the constraints from Uranus and Neptune remain high, even so note that our fiducial models would not satisfy the constraint from Jupiter - changes to either the fall off $n$ and/or $\kappa$ would be required. }}\end{center} \end{figure} In this work, we considered the case for testing and constraining theories of modified gravity with a preferred acceleration scale. Such ideas were originally conceived in the guise of MOND as a replacement for dark matter but now have been elevated to fully relativistic, consistent alternatives to GR. The weak field limits of these theories can produce phenomenology suitable for such purposes on galactic scales, however cosmological and other probes~\cite{tevescaustics, tevesstrucform, TimTom} can be problematic. In Section \ref{theory}, we showed how to attack these problems by first classifying the different modified poisson equations that result from these theories. Theories we labelled type I and IIB provide the best prospect for such a test, producing large regions of observable MONDian behaviour (due to the particular way their dynamics are triggered). In such theories, the fifth force field $\phi$ present moves from taking the form of a rescaled Newtonian potential ($\phi \rightarrow \frac{\kappa}{4\pi} \Phi_N$, with $\kappa$ taken suitably small to escape detection on, say, Solar System scales) to producing a truly MONDian form. When the total acceleration drops some preferred acceleration scale (which we denote $a_0$), this $\phi$ field becomes the dominant contribution. Whilst this region around the Earth-Sun SP would only be $\sim 2.2$m in size, the anomalous tidal stress ``bubble'' of behaviour would be $\sim 383$km - providing a viable target for a satellite fly-by test. We also considered the Earth-Moon SP and showing that provided we approach ``close enough'' and at the ``right phase'' in the Moon's cycle, very high SNRs are within arms reach, as illustrated in Figure \ref{fig:moon}. The LPF space probe, designed to test the feasibility of space based, low frequency gravitational wave detection, could provide just the experimental test for a tidal stress experiment. We find the peak of a potential MONDian tidal stress signal would be exactly around the lowest point in the expected noise spectrum - a useful coincidence. Other theories, which we labelled types IIA and III, would fair less favourably, due to their one field approach for producing modified gravity effects - the effects which are the tiny saddle bubbles. In Section \ref{secsnr}, we used the framework of experimental gravitational waves to estimate the SNRs for a LPF test. Further to this, we considered experimental systematics such as different noise profiles, spacecraft velocity and self gravity and as such the nominal requirements of the mission should be ample, as Figure \ref{fig:SNR contours} shows. In Section \ref{constrain}, we considered how these Solar System tests would be able to constrain the parameter space, based on a null result. Whilst a precise statement would be model dependent, we can obtain an order magnitude answer on the functional form of the free functions $\mu$ and $\nu$, as Figure \ref{fig:null SNR 1} shows. Such constraints suggest it would be hard to wriggle out of a negative result (unless certain types of free functions are considered e.g. they diverge). The different types of theory appear to have different behaviours in the regime we will be testing and so different constraints will apply to each - perhaps this can be used a discriminator between them. We suggest therefore that a mission extension for LPF to probe these ideas would be scientifically feasible and provide good constraints on modified gravity theories (whatever the eventual result). Looking to the future, we can consider a few prospects for additional work. A consistent study of how to reconcile Solar System based constraints, such as the SP test and fifth force constraints, with galactic and other astrophysical settings for MOND should be made. A proper fit of all the constraints available over {\it all} regimes has to date not been considered. By way of a start, we can consider inner and outer Solar System constraints (e.g.~\cite{ssconst}) and see how our free functions compare on these scales, as outlined Figure \ref{fig:ssconstraints}. A proper assessment of the weak-field limits of these theories should be considered, e.g. BiMOND~\cite{Milgrom:2009gv,Milgrom:2010cd} can produce different NR limits~\cite{qmond} using a different form of free function. The FRW cosmology of such theories~\cite{TimTom} investigated generalisations of these theories and so the phenomenological implications of such should also be considered in this context. It is well known preferred acceleration scale effects are not properly covered by the PPN formalism, e.g. time delay effects across MONDian bubbles as characterised in~\cite{MagTimeDelay}. Perhaps a way forward would be developing a Post Parametrised Saddle formalism? Characterising MOND from a more geometric point of view, as in~\cite{SkordisZlosnik} could be a starting point. | 14 | 4 | 1404.0313 |
1404 | 1404.3310_arXiv.txt | Several nearby solar-type dwarfs with variable radial velocity were monitored to find their spectroscopic orbits. Orbital elements of HIP 179, 1989, 2981, 5276, 6439, 11218, 21443, 96434 are determined, as well as tentative orbits for HIP 28678 and 41214. We discuss each of those objects. Three of the four double-lined binaries are twins with nearly equal components. All four orbits with periods shorter than 10 days are circular, the remaining orbits are eccentric. | \label{sec:intro} Current interest in nearby solar-like stars is largely driven by search of exo-planets. These stars are also ideally suited for the study of binary statistics, which gives clues to the origin of stellar and planetary systems. The 25-pc sample of \citet{R10} was recently extended to a larger volume to increase the significance of binary statistics and to access the statistics of higher-order hierarchies \citep{FG67}. Extensive data on F- and G-type stars within 67\,pc of the Sun are available in the literature and cover the full range of orbital periods. The detection of spectroscopic binaries is mostly based on the Geneva-Copenhagen Survey (GCS) by \citet{N04}. They addressed about 80\% of the sample, typically with 2 or 3 radial velocity (RV) measurements per star. However, many spectroscopic binaries discovered by GCS from variable RV or from the appearance of double lines have no orbits determined so far. This leaves their periods and mass ratios indeterminate and adds uncertainty to the multiplicity statistics. A large number of these binaries were followed by D.~Latham at Center for Astrophysics, leading to hundreds of orbital solutions (D.~Latham, in preparation). Still, not all spectroscopic binaries are covered. Our aim is to complement the existing work and to determine, whenever possible, spectroscopic orbits. We focus on stars with the largest (hence fastest) RV variations and derive here orbital solutions for some of them from the data of two seasons. The objects covered in this study are listed in Table~\ref{tab:list}, where visual magnitudes and spectral types are taken from SIMBAD, trigonometric parallaxes from the {\it Hipparcos-2} catalog \citep{HIP2}, and masses are estimated from absolute magnitudes \citep{FG67a}. All stars are bright; their spectral types range from F2V to G5V. | \label{sec:concl} The database on solar-type binaries within 67\,pc \citep{FG67a} suffers from the missing data (periods and mass ratios) on 260 spectroscopic binaries discovered by the GCS. Our work reduced this number by 4\%; its results are already included in the statistical analysis of this sample \citep{FG67}. Several other stars with variable RV and/or double lines were observed, but do not have yet sufficient data to derive their orbits. We plan to continue the observations. | 14 | 4 | 1404.3310 |
1404 | 1404.3126_arXiv.txt | Generally, eclipsing binary systems (hereafter EBs) offer unique information for the calculation of stellar absolute parameters and the evolutionary status of stars. Especially, the cases of binaries with $\delta$~Sct components are extremely interesting, since they provide additional information (i.e. pulsation characteristics) for this part of the stellar lifetime. Therefore, the calculation of their absolute parameters and the identification of their oscillating characteristics help us to obtain useful conclusions for this 'unstable' part of stellar lifetime. V1464~Aql ($m_{\rm{V}}$=8.98~mag, $P$=0.69777$^{\rm d}$) was observed spectroscopically by \cite{RU06}, who revealed that it is an eclipsing binary of F1-2 spectral type and measured the radial velocity of the primary component as $K_{1}$=31~(1)~km/s. The most detailed study of the system was made by \cite{DA13}, who found, using their own data, one pulsation frequency and calculated the absolute parameters of the system using the $q$-search method. In the present work, we use our new $BVRI$ light curves to create our model and to perform a detailed Fourier analysis in order to find the main characteristics of the pulsating component. | We analysed new multicolour LCs of V1464~Aql. New results for the absolute elements are derived and new pulsation frequencies were detected. The differences between our results and those of \cite{DA13}, regarding the evolutionary status of the components, probably come from the $q$-search method. More detailed spectroscopic observations are needed for final conclusions. Two more pulsation frequencies for the primary component were found in comparison with the work of \cite{DA13} increasing the total detected frequency number to 3. In $M-R$ diagram (Fig.\ref{Fig1}) it is shown that the present results for the pulsating component of V1464~Aql are compatible with other for $\delta$~Scuti stars in binaries. \noindent | 14 | 4 | 1404.3126 |
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1404 | 1404.4640_arXiv.txt | Comet C/2013~A1 (siding Spring) will experience a high velocity encounter with Mars on October 19, 2014 at a distance of 135,000 km $\pm$ 5000 km from the planet center. We present a comprehensive analysis of the trajectory of both the comet nucleus and the dust tail. The nucleus of C/2013~A1 cannot impact on Mars even in the case of unexpectedly large nongravitational perturbations. Furthermore, we compute the required ejection velocities for the dust grains of the tail to reach Mars as a function of particle radius and density and heliocentric distance of the ejection. A comparison between our results and the most current modeling of the ejection velocities suggests that impacts are possible only for millimeter to centimeter size particles released more than 13 au from the Sun. However, this level of cometary activity that far from the Sun is considered extremely unlikely. The arrival time of these particles spans a 20-minute time interval centered at October 19, 2014 at 20:09 TDB, i.e., around the time that Mars crosses the orbital plane of C/2013~A1. Ejection velocities larger than currently estimated by a factor $>2$ would allow impacts for smaller particles ejected as close as 3 au from the Sun. These particles would reach Mars from 43 to 130 min after the nominal close approach epoch of the purely gravitational trajectory of the nucleus. | \label{sec:intro} Comet C/2013~A1 (Siding Spring) was discovered on January 2013 at the Siding Spring observatory \citep{McNaught13}. Shortly after discovery it was clear that C/2013~A1 was headed for a close encounter with Mars on October 19, 2014. C/2013~A1 is on a near parabolic retrograde orbit and will have a high relative velocity with respect to Mars of about 56 km/s during the close approach. If the comet has no significant nongravitational perturbations, the trajectory of the nucleus consistent with the present set of astrometric observations rules out an impact on Mars. However, comet orbits are generally difficult to predict. As the comet gets closer to the Sun cometary activity can result in significant nongravitational perturbations \citep{Marsden73} that in turn can lead to significant deviations from the purely gravitational (``ballistic'') trajectory. In the case of C/2013~A1, cometary activity was already visible in the discovery observations, when the comet was at more than 7 au from the Sun. Beside the effect of nongravitational perturbations, dust grains in the tail of the comet could reach Mars and possibly damage spacecrafts orbiting Mars, i.e., NASA's Mars Reconnaissance Orbiter, NASA's Mars Odyssey, ESA's Mars Express, NASA's MAVEN, and ISRO's MOM. \citet{Vaubaillon14} and \citet{Moorhead14} show that dust grains can reach Mars if they are ejected from the nucleus with a sufficiently high velocity. The modeling of the ejection velocity is in continuous evolution. As the comet gets closer to the inner solar system we have additional observation that provide constraints to the ejection velocities of dust grains. In particular, by making use of observations from HST/WFC3, Swift/UVOT, and WISE, \citet{Farnham14} and \citet{Tricarico14} find ejection velocities lower than those derived by \citet{Vaubaillon14} and \citet{Moorhead14}, thus significantly reducing the hazard due to dust grains in the comet tail. In this paper we study the trajectory of C/2013~A1's nucleus, including the contribution of nongravitational perturbations. We also present an analysis of the required ejection velocities for the dust grains to reach Mars. This analysis can be used as a reference as the understanding and the modeling of the dust grain ejection velocities evolve. | To study the Oct 19, 2014 encounter with Mars, we analyzed the trajectory of comet C/2013~A1 (Siding Spring). The ballistic orbit has a closest approach with Mars at 135,000 km $\pm$ 5000 km at 18:30 TDB. Nongravitational perturbations are not yet detectable for C/2013~A1, so we assumed known nongravitational parameters for known comets in the catalog. In case of typical nongravitational perturbations there are no relevant differences from the ballistic trajectory. On the other hand, unexpectedly large nongravitational accelerations would produce significant deviations that should become detectable in the observation dataset by the end of July 2014. However, even in the case of unexpectedly large nongravitational perturbations, the nucleus C/2013~A1 cannot reach Mars. To analyze the risk posed by dust grains in the tail, we computed the required ejection velocities as a function of the heliocentric distance at which the particle is ejected and the particle's $\beta$ parameter, i.e., the ratio between solar radiation pressure and solar gravity. By comparing our results to the most updated modeling of dust grain ejection velocities, impacts are possible only for $\beta$ of the order of $10^{-4}$, which, for a density of 1 g/cc, corresponds to millimeter to centimeter particles. However, the particles have to be ejected at more than 13 au, which is generally considered unlikely. See \citet{Kelley14} for a discussion of the maximum liftable grain size at these distances. The arrival times of these particles are in an interval of about 20 minutes around the time that Mars crosses the orbit of C/2013~A1, i.e., Oct 19, 2014 at 20:09 TDB. In the unlikely case that ejection velocities are larger than currently estimated by a factor $>2$, impacts are possible for particles with $\beta = 0.001$ that are ejected as close as $\sim 3$ au from the Sun. These impacts would take place from 43 min to 130 min after the nominal ballistic close approach of the nucleus. As the comet gets closer to the inner solar system, new observations will be available and will allow better constraints on the dust grain ejection velocity profile. Our analysis can be used as a reference to quickly figure out what particles can reach Mars and the heliocentric distance at which they would have to have been ejected. In the unlikely case that future astrometry reveals unexpectedly large nongravitational perturbations, the required velocity to reach Mars for particles ejected within 2 au from the Sun can change and the presented analysis will need to be refined. | 14 | 4 | 1404.4640 |
1404 | 1404.3583_arXiv.txt | In this letter I report the \textit{Fermi} Large Area Telescope (LAT) detection of Very High Energy (VHE; $E>100$ GeV) $\gamma$-ray emission from the BL Lac object RBS 0970. 5.3 years of LAT observations revealed the presence of 3 VHE photon events within 0\ensuremath{^{\circ}}.1 of RBS 0970, with a subsequent unbinned likelihood analysis finding RBS 0970 to be a source of VHE photons at the $6.5\sigma$ level of confidence. The $\geq1$ GeV flux, binned in monthly periods, did not indicate any flux brightening of RBS 0970 accompanying the emission of the VHE photons. However, a likelihood analysis of the $0.1-100$ GeV flux, binned in 28 day periods centered on detection of the VHE photons, revealed that the emission of the lowest energy VHE photons coincided with a hardening of the $\gamma$-ray spectrum. Interestingly, the same analysis did not find any significant $\gamma$-ray emission from RBS 0970 during the emission of the highest energy VHE event. The discovery of RBS 0970 as a VHE emitter, combined with the spectral variability, suggest RBS 0970 to be a good candidate for follow-up observations with ground-based $\gamma$-ray observatories. | The \textit{Fermi} $\gamma$-ray Space Telescope affords an ideal opportunity to investigate the inner workings of Active Galactic Nuclei (AGN). Since 2008 August 4, the vast majority of data taken by \textit{Fermi} has been in the default \textit{all-sky-survey} observing mode, whereby the Large Area Telescope (LAT) onboard \textit{Fermi} points away from the Earth and rocks north and south of its orbital plane. This rocking motion, coupled with \textit{Fermi}-LAT's large effective area, allows \textit{Fermi} to scan the entire $\gamma$-ray sky every two orbits, or approximately every three hours (\citet{ritz}). With this ability to scan the sky every 3 hours, the LAT has allowed us to catch AGN during brief flares of $\gamma$-ray activity (e.g. \citet{dickinson}), with these flares sometimes resulting in the discovery of Very High Energy (VHE; $E_{\gamma}>100$ GeV) emission from the flaring AGN (e.g. \citet{ong} \& \citet{aliu}). While it's 3 hour scan period is important for catching brief periods of flare activity from AGN, coupling \textit{Fermi}-LAT's continual scanning of the sky with a long mission livetime allows us to construct a deep exposure of the extragalactic sky. This deep exposure affords us the ability to perform searches for faint VHE sources which would otherwise go undetected by the pointed observations of ground-based Imaging Atmospheric Cherenkov Telescope (IACT) arrays. RBS 0970 is a point-like radio source, with a redshift of z$=0.124$ (\citet{gommi}). Detected by successive X-ray surveys using the EINSTEIN, ROSAT and BEPPO-SAX satellites (\citet{einstein}, \citet{rosat}, \citet{beppo}), RBS 0970 has been optically identified as a BL Lac object with SDSS observations (\citet{sdss}). As a member of the blazar sub-class of AGN, it is no surprise that RBS 0970 is present in both the 1 and 2 year \textit{Fermi}-LAT AGN catalogues (\citet{1agn}; \citet{acker3}). Furthermore, the recent $E_{\gamma}>10$ GeV LAT catalogue also lists RBS 0970 as a source (\citet{hecat}). This letter reports the discovery of VHE emission from RBS 0970. Utilising 5.3 years of \textit{Fermi}-LAT data, 3 \textsc{ultraclean} events were discovered to be clustered within 0\ensuremath{^{\circ}}.1 of RBS 0970. The emission of some of these VHE photons was observed to occur during periods of spectral hardening, suggesting a harder-when-brighter property for the VHE emission. In \textsection 2 the \textit{Fermi}-LAT observations and analysis routines used in this study are described, along with the results of the 1-300 GeV likelihood analysis. The results on the VHE emission study of RBS 0970 are shown in \textsection 3. A brief investigation into the global $\gamma$-ray characteristics of RBS 0970 when the VHE emission occurs is presented in \textsection 4, with the conclusions given in \textsection 5. | With 5.3 years of \textit{Fermi}-LAT data, RBS 0970 has been found to be a source of VHE $\gamma$-ray photons. With 3 \textsc{ultraclean} $E_{\gamma}>100$ GeV photon events within 0.1\ensuremath{^{\circ}} of RBS 0970, an unbinned likelihood analysis revealed the significance of this discovery to be at the $6.5\sigma$ confidence level. The 5.3 year integrated $E_{\gamma}>100$ GeV flux was found to be $(2.47 \pm 1.26) \times 10^{-11} \text{ photons cm}^{-2} \text{s}^{-1}$. An indepth analysis of the $0.1-100$ GeV flux from RBS 0970 during a 28 day window centered on the detection of the VHE photons revealed that the emission of the 114 and 117 GeV photons coincided with a hardening of the $\gamma$-ray spectrum when compared to the 5.3 year average. However, the same analysis did not find any significant $\gamma$-ray emission from RBS 0970 during the emission of the 273 GeV event. This non-detection is hard to accommodate in a pure SSC model description of $\gamma$-ray emission from RBS 0970. The detection of 3 \textsc{ultraclean} events within 0.1\ensuremath{^{\circ}}, coupled with the results of the $100-300$ GeV unbinned likelihood analysis suggest the VHE detection of RBS 0970 is a robust result. As such, RBS 0970 is a promising target for follow-up observations with IACTs. Such observations are highly recommended. | 14 | 4 | 1404.3583 |
1404 | 1404.1065_arXiv.txt | The simplest inflationary model $V=\frac12 m^2\phi^2$ represents the benchmark for future constraints. For a quadratic potential, the quantity $(n_s-1)+r/4+11 (n_s-1)^2/24$ vanishes (up to corrections which are cubic in slow roll) and can be used to parametrize small deviations from the minimal scenario. Future constraints on this quantity will be able to distinguish a quadratic potential from a pseudo-Nambu-Goldstone boson with $f \lesssim 30 \mpl$ and set limits on the deviation from unity of the speed of sound $| c_s-1| \lesssim 3\times 10^{-2}$ (corresponding to an energy scale $\Lambda\gtrsim 2\times 10^{16}\, \mathrm{GeV}$), and on the contribution of a second field to perturbations ($\lesssim 6 \times 10^{-2}$). The limiting factor for these bounds will be the uncertainty on the spectral index. The error on the number of e-folds will be $\Delta N \simeq 0.4$, corresponding to an error on the reheating temperature $\Delta T_\mathrm{rh}/T_\mathrm{rh}\simeq 1.2$. We comment on the relevance of non-Gaussianity after BICEP2 results. | 14 | 4 | 1404.1065 |
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1404 | 1404.0006_arXiv.txt | The possibility of matter coupling to two metrics at once is considered. This appears natural in the most general ghost-free, bimetric theory of gravity, where it unlocks an additional symmetry with respect to the exchange of the metrics. This double coupling, however, raises the problem of identifying the observables of the theory. It is shown that if the two metrics couple minimally to matter, then there is no physical metric to which all matter would universally couple, and that moreover such an effective metric generically does not exist even for an individual matter species. By studying point particle dynamics, a resolution is suggested in the context of Finsler geometry. \PACS{04.20.Cv, 04.80.Cc, 98.80.Jk, 95.30.Sf, 98.80.-k} | 14 | 4 | 1404.0006 |
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1404 | 1404.5415_arXiv.txt | % The {\sl Wilkinson Microwave Anisotropy Probe} ({\sl WMAP}) mapped the distribution of temperature and polarization over the entire sky in five microwave frequency bands. These full-sky maps were used to obtain measurements of temperature and polarization anisotropy of the cosmic microwave background with the unprecedented accuracy and precision. The analysis of two-point correlation functions of temperature and polarization data gives determinations of the fundamental cosmological parameters such as the age and composition of the universe, as well as the key parameters describing the physics of inflation, which is further constrained by three-point correlation functions. {\sl WMAP} observations alone reduced the flat $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological model (six) parameter volume by a factor of $>68,000$ compared with pre-{\sl WMAP} measurements. The {\sl WMAP} observations (sometimes in combination with other astrophysical probes) convincingly show the existence of non-baryonic dark matter, the cosmic neutrino background, flatness of spatial geometry of the universe, a deviation from a scale-invariant spectrum of initial scalar fluctuations, and that the current universe is undergoing an accelerated expansion. The {\sl WMAP} observations provide the strongest ever support for inflation; namely, the structures we see in the universe originate from quantum fluctuations generated during inflation. | The {\sl WMAP} \citep{bennett/etal:2003a} spacecraft was designed to measure the full-sky distribution of temperature differences (anisotropy) and polarization of the cosmic microwave background (CMB). {\sl WMAP} is the successor of the legendary {\sl Cosmic Background Explorer} ({\sl COBE}) satellite, whose spectrograph provided a precision-measurement of the CMB blackbody, implying that matter and radiation were in thermal equilibrium, consistent with the expectation of the hot Big Bang theory of the universe \citep{mather/etal:1990}. The {\sl COBE} differential radiometers discovered the primordial ripples in spacetime that existed in the early universe \citep{smoot/etal:1992}. With 35 times better angular resolution and 40 times better sensitivity than {\sl COBE}, {\sl WMAP} took the cosmological research with CMB to the next level. {\sl WMAP} was proposed to NASA as a MIDEX (Medium-Class Explorers) mission in 1995. Four of eight Co-Investigators\footnote{The Co-Investigators on the {\sl WMAP} proposal are C.~L. Bennett, G. Hinshaw, N. Jarosik, S.~S. Meyer, L. Page, D.~N. Spergel, D.~T. Wilkinson (deceased), and E.~L. Wright. Among them, Bennett, Hinshaw, Wilkinson, and Wright were previously on the {\sl COBE} Science Team.} of {\sl WMAP} were previously on the {\sl COBE} Science Team. After being selected in 1996, {\sl WMAP} launched on June 30, 2001, and arrived in its orbit around the second Lagrange point (L2), 1.5 million kilometers from Earth, three months later. Since then, {\sl WMAP} operated almost flawlessly for nine years until it left its L2 orbit on September 8, 2010, to pass the baton to its successor, the {\sl Planck} satellite, which arrived at L2 in July 2009. The {\sl WMAP} team issued five data releases. The first-year data release (February 11, 2003) came with 13 papers \citep{bennett/etal:2003b,bennett/etal:2003c,jarosik/etal:2003b,page/etal:2003a,page/etal:2003b,barnes/etal:2003,hinshaw/etal:2003a,hinshaw/etal:2003b,komatsu/etal:2003,kogut/etal:2003,spergel/etal:2003,verde/etal:2003,peiris/etal:2003} and later with one more paper \citep{nolta/etal:2003}; the third-year data release (March 16, 2006) came with 4 papers \citep{jarosik/etal:2007,hinshaw/etal:2007,page/etal:2007,spergel/etal:2007} and later with one more paper \citep{kogut/etal:2007}; the five-year data release (March 5, 2008) came with 7 papers \citep{hinshaw/etal:2009,hill/etal:2009,gold/etal:2009,wright/etal:2009,nolta/etal:2009,dunkley/etal:2009a,komatsu/etal:2009} and later with one more paper \citep{dunkley/etal:2009b}; the seven-year data release (January 25, 2010) came with 6 papers \citep{jarosik/etal:2011,gold/etal:2011,larson/etal:2011,bennett/etal:2011,komatsu/etal:2011,weiland/etal:2011}; and the final, nine-year data release (December 21, 2012) came with 2 papers \citep{bennett/etal:2013,hinshaw/etal:2013}. In addition, detailed descriptions of the mission, data processing, calibration, as well as of the data products for each release are given in the Explanatory Supplement document \citep{greason/etal:2012}. In this article, we give a brief review on the {\sl WMAP} experiment, the data analysis, and the main science results from the nine-year observations. | The nine years of observations of the {\sl WMAP} satellite have taught us many things. The current universe is 13.77 billion years old, and consists of 4.6\% atoms, 24\% cold dark matter, and 71\% dark energy \cite{bennett/etal:2013,hinshaw/etal:2013}. The nature of dark energy is consistent with that of a cosmological constant. The spatial geometry of the universe is consistent with Euclidean geometry. The universe is filled with neutrinos, whose abundance is consistent with the standard model of particle physics. The mass of neutrinos is much less than 1~eV. The measured properties of primordial fluctuations such as adiabaticity, Gaussianity, and near scale invariance all point toward a remarkable scenario: the observed fluctuations originate from quantum fluctuations generated during inflation driven by a single energy component. {\sl WMAP} offered a number of stringent tests of the simplest inflation scenarios: (1) flat universe, (2) adiabatic fluctuations, (3) super-horizon fluctuations, (4) nearly, but not exactly, scale-invariant initial power spectrum, and (5) Gaussian fluctuations. The simplest scenarios passed all of these tests. The {\sl Planck} 2013 data have confirmed all of these findings with greater precision. Yet, neither the {\sl WMAP} nor the {\sl Planck} 2013 data detect the signature of primordial gravitational waves from inflation in CMB. Detecting and characterizing the B-mode polarization of the CMB is the next milestone in cosmology. While the BICEP/Keck Array collaboration claims to have found the B-mode polarization from inflationary gravitational waves at 150~GHz, confirmation of the signal at other frequencies and with an independent experiment must be made before we claim a victory in observing all of the inflation predictions. | 14 | 4 | 1404.5415 |
1404 | 1404.5623_arXiv.txt | We anticipate the first direct detections of gravitational waves (GWs) with Advanced LIGO and Virgo later this decade. Though this groundbreaking technical achievement will be its own reward, a still greater prize could be observations of compact binary mergers in both gravitational and electromagnetic channels simultaneously. During Advanced LIGO and Virgo's first two years of operation, 2015 through 2016, we expect the global GW detector array to improve in sensitivity and livetime and expand from two to three detectors. We model the detection rate and the sky localization accuracy for binary neutron star (BNS) mergers across this transition. We have analyzed a large, astrophysically motivated source population using real\nobreakdashes-time detection and sky localization codes and higher\nobreakdashes-latency parameter estimation codes that have been expressly built for operation in the Advanced LIGO/Virgo era. We show that for most BNS events the rapid sky localization, available about a minute after a detection, is as accurate as the full parameter estimation. We demonstrate that Advanced Virgo will play an important role in sky localization, even though it is anticipated to come online with only one\nobreakdashes-third as much sensitivity as the Advanced LIGO detectors. We find that the median 90\% confidence region shrinks from $\sim$500\,deg$^2$ in 2015 to $\sim$200\,deg$^2$ in 2016. A few distinct scenarios for the first LIGO/Virgo detections emerge from our simulations. | We expect this decade to bring the first direct detection of gravitational waves (GWs) from compact objects. The LIGO and Virgo detectors are being rebuilt with redesigned mirror suspensions, bigger optics, novel optical coatings, and higher laser power~\citep{aLIGO, aVirgo}. In their final configuration, Advanced LIGO and Virgo are expected to reach $\sim10$ times further into the local universe than their initial configurations did. The best\nobreakdashes-understood sources for LIGO and Virgo are binary neutron star (BNS) mergers. They also offer a multitude of plausible electromagnetic (EM) counterparts~\citep{MostPromisingEMCounterpart} including collimated short\nobreakdashes-hard gamma\nobreakdashes-ray bursts (short GRBs; see for example \citealt{1986ApJ...308L..43P,1989Natur.340..126E,1992ApJ...395L..83N,2011ApJ...732L...6R}) and X\nobreakdashes-ray/optical afterglows, near\nobreakdashes-infrared kilonovae \citep[viewable from all angles;][etc.]{kilonova, BarnesKasenKilonovaOpacities}, and late\nobreakdashes-time radio emission~\citep{NakarPiranRadioFlares,PiranNakarRosswogEMSignals}. Yet, typically poor GW localizations of $\gtrsim 100\text{\,deg}^2$ will present formidable challenges to observers hunting for their EM counterparts. Several planned optical astronomy projects with a range of fields of view and apertures are preparing to pursue these elusive events. These include the Zwicky Transient Facility~\citep{ZTF}, PanSTARRS\footnote{\url{http://pan-starrs.ifa.hawaii.edu/public/}}, BlackGEM\footnote{\url{https://www.astro.ru.nl/wiki/research/blackgemarray}}, and LSST~\citep{LSST}, to name a few. Advanced LIGO is scheduled to start taking data in 2015~\citep{LIGOObservingScenarios}. Preparations for joint EM and GW observations require a complete understanding of when and how well localized the first GW detections will be. Plausible scenarios for the evolution of the configuration and sensitivity of the worldwide GW detector network as it evolves from 2015 through 2022, as well as rough estimates of sky localization area, are outlined in \citet{LIGOObservingScenarios}. To provide a more realistic and complete picture, we have conducted Monte Carlo simulations of the 2015 and 2016 detector network configurations, probing the transition from two to three detectors as Advanced Virgo is scheduled to begin science operation. Prior work has focused on various aspects of position reconstruction with advanced GW detectors \citep{FairhurstTriangulation,WenLocalizationAdvancedLIGO,FairhurstLocalizationAdvancedLIGO,2011PhRvD..84j4020V,RodriguezBasicParameterEstimation,NissankeLocalization,NissankeKasliwalEMCounterparts,KasliwalTwoDetectors,Grover:2013,SiderySkyLocalizationComparison}, but ours is the first to bring together a large astrophysically motivated population, an educated guess about the detector commissioning timetable, a realistic \ac{SNR} distribution, and the Advanced LIGO/Virgo data analysis pipeline itself. We have simulated hundreds of GW events, recovered them with a real\nobreakdashes-time detection pipeline, and generated sky maps using both real\nobreakdashes-time and thorough off\nobreakdashes-line parameter estimation codes that will be operating in 2015 and beyond. This study contains some of the first results with \textsc{bayestar}, a rapid Bayesian position reconstruction code that will produce accurate sky maps less than a minute after any BNS merger detection. The \textsc{lalinference\_mcmc} \citep{2008ApJ...688L..61V,Raymond:2009}, \textsc{lalinference\_nest} \citep{LALINFERENCE_NEST}, and \textsc{lalinference\_bambi} \citep{BAMBI,SKYNET} stochastic samplers were also used to follow up a subset of detected GW events. Though these analyses are significantly more computationally costly than \textsc{bayestar}, taking hours to days, they can provide improved sky location estimates when the GW signal is very weak in one detector, and also yield not just sky localization but the full multidimensional probability distribution describing the parameters of a circularized compact binary merger. All four algorithms are part of the \textsc{lalinference} library \citep{S6PE}, developed specifically for estimating the parameters of GW sources from ground-based detectors. Together, these analyses will be able to provide sky localizations on time scales that enable searching for all expected electromagnetic counterparts of compact binary mergers (except the GRB itself). With the benefit of a much larger sample size, important features of the 2015 and 2016 configurations come into focus. First, we find that even in 2015 when only the two LIGO detectors are operating (or in 2016 during periods when the Virgo detector is not in science mode), there is at least a 60\% chance of encountering the source upon searching an area of about 200\,deg$^2$. Second, many of these two\nobreakdashes-detector events will not be localized to a single simply connected region in the sky. We elucidate two nearly degenerate sky locations, separated by 180$^\circ$, that arise when only the two LIGO detectors are operating. When a GW source falls within this degeneracy, its sky map will consist of two diametrically opposed islands of probability. Third, in our simulations, we add a third detector, Advanced Virgo, in 2016. Even though at that time Virgo is anticipated to be only one\nobreakdashes-third as sensitive as the other two detectors due to differing LIGO and Virgo commissioning timetables, we find that coherence with the signal in Virgo generally breaks the previously mentioned degeneracy and shrinks areas to a third of what they were with two detectors. Fourth and most importantly, a picture of a typical early Advanced LIGO event emerges, with most occurring in a limited range of Earth\nobreakdashes-fixed locations, and most sky maps broadly fitting a small number of specific morphologies. | Summary of the 2015 and 2016 Scenarios, Listing the Participating Detectors, BNS Horizon Distance, Run Duration, and Fractions of Events Localized within 5, 20, 100, 200, or 500\,deg$^2$.} \tablecomments{A dash (---) represents less than 1\% of detections.} \tablehead{\colhead{} & \colhead{} & \multicolumn{2}{c}{2015} & \multicolumn{2}{c}{2016}} \startdata \multicolumn{2}{r}{Detectors} & \multicolumn{2}{c}{HL} & \multicolumn{2}{c}{HLV} \\ \multicolumn{2}{r}{LIGO (HL) BNS range} & \multicolumn{2}{c}{54 Mpc} & \multicolumn{2}{c}{108 Mpc} \\ \multicolumn{2}{r}{Run duration} & \multicolumn{2}{c}{3 months} & \multicolumn{2}{c}{6 months} \\ \multicolumn{2}{r}{No. detections} & \multicolumn{2}{c}{0.091} & \multicolumn{2}{c}{1.5} \\ \tableline \colhead{} & \colhead{} & \colhead{rapid} & \colhead{full PE} & \colhead{rapid} & \colhead{full PE} \\ \tableline \input{table1} \enddata \end{deluxetable} \begin{figure*} \begin{minipage}[b]{3.5in} \begin{center} \includegraphics{2015_area50_hist} (a) 2015, HL \end{center} \end{minipage} \begin{minipage}[b]{3.5in} \begin{center} \includegraphics{2016_area50_hist} (b) 2016, HLV \end{center} \end{minipage} \begin{minipage}[b]{3.5in} \begin{center} \includegraphics{2015_area90_hist} (c) 2015, HL \end{center} \end{minipage} \begin{minipage}[b]{3.5in} \begin{center} \includegraphics{2016_area90_hist} (d) 2016, HLV \end{center} \end{minipage} \begin{minipage}[b]{3.5in} \begin{center} \includegraphics{2015_searched_area_hist} (e) 2015, HL \end{center} \end{minipage} \begin{minipage}[b]{3.5in} \begin{center} \includegraphics{2016_searched_area_hist} (f) 2016, HLV \end{center} \end{minipage} \caption{\label{fig:area_hist}Cumulative histogram of sky localization areas in the 2015 (HL) and 2016 (HLV) scenarios. Plots in the left column (a,~c,~e) refer to the 2015 configuration and in the right column (b,~d,~f) to the 2016 configuration. The first row (a,~b) shows the area of the 50\% confidence region, the second row (c,~d) shows the 90\% confidence region, and the third row (e,~f) shows the ``searched area,'' the area of the smallest confidence region containing the true location of the source. The red lines comprise all detections and their sky maps produced with \textsc{bayestar}, and the blue lines represent sky maps for the random subsample of 250 detections analyzed with \textsc{lalinference\_nest}/\textsc{mcmc}. The light shaded region encloses a 95\% confidence interval accounting for sampling errors \citep[computed from the quantiles of a beta distribution;][]{BinomialConfidenceIntervalsAstronomy}. The left axes show the number of detections localized within a given area assuming the ``realistic'' BNS merger rates from \citep{LIGORates}. The right axes show the percentage out of all detected events. \\ (A color version of this figure is available in the online journal.)} \end{figure*} \subsection{2015} \label{sec:2015} Our 2015 scenario assumes two detectors (HL) operating at an anticipated range of 54\,Mpc. About 0.1 detectable BNS mergers are expected, though there are nearly two orders of magnitude systematic uncertainty in this number due to the uncertain astrophysical rates. A detection in 2015 is possible, but likely only if the BNS merger rates or the detectors' sensitivity are on the modestly optimistic side. A typical or median event (with a localization area in the 50th percentile of all detectable events) would be localized to a 90\% confidence area of $\sim 500$\,deg$^2$. We find that the area histograms arising from the \textsc{bayestar} rapid sky localization and the full parameter estimation agree within sampling errors, and that the sky maps resulting from the two analyses are comparable for any individual event. Put differently, the rapid sky localization contains nearly all of the information about sky localization for these events, with the full probability distributions over masses and spins becoming available when the stochastic samplers finish on a timescale of a day. \begin{figure*} \begin{minipage}[b]{3.5in} \begin{center} \includegraphics{2015_offset_hist} (a) 2015, HL \end{center} \end{minipage} \begin{minipage}[b]{3.5in} \begin{center} \includegraphics{2016_offset_hist} (b) 2016, HLV \end{center} \end{minipage} \caption{\label{fig:offset_hist}Normalized histogram of the cosine angular separation between the location of the simulated GW source and the \underline{maximum} a posteriori location estimate, for (a) the 2015 configuration and (b) the 2016 configuration. The red line encompasses all detections and their \textsc{bayestar} localizations, and the blue line the subsample of 250 events analyzed by \textsc{lalinference\_nest}/\textsc{mcmc}. The inset shows the distribution of angle offsets for angles less than 60$^\circ$. \\ (A color version of this figure is available in the online journal.)} \end{figure*} Figure~\ref{fig:offset_hist}(a) shows a histogram of the cosine of the angular separation between the true location of the simulated GW source and the maximum a posteriori estimate (the mode of the sky map, or the most probable location). The main feature is a peak at low separation. However, there is a second peak at the polar opposite of the true location, 180$^\circ$ away; about 15\% of events are recovered between 100 and 180$^\circ$ away from the true location. Correspondingly, for any one event, it is common to find the probability distributed across two antipodal islands on opposite sides of the mean detector plane. We define this plane by finding the average of the two vectors that are normal to the planes of the two detectors' arms, and then taking the plane to which this vector is normal. This plane partitions the sky into two hemispheres. We find that one hemisphere is favored over the other by less than 20\% (which is to say that the odds favoring one hemisphere over the other are as even as 60\%/40\%) for 20\% of events. The second peak admits a simple explanation as an unavoidable degeneracy due to the relative positions of the H and L interferometers. Before the Hanford and Livingston sites were selected, it was decided that the detectors' arms would be as closely aligned as possible~\citep[section V\nobreakdashes-C\nobreakdashes-2]{LIGOProposal}. Significant misalignment would have created patches of the sky that were accessible to one detector but in a null of the other detector's antenna pattern, useless for a coincidence test. The near alignment maximized the range of the detectors in coincidence, though at certain expenses for parameter estimation. Observe that the sensitivity of an interferometric GW detector is identical at antipodal points (i.e., symmetric under all rotations by 180$\arcdeg$). Therefore, any source that lies in the plane of zero time delay between the detectors is always localized to two opposite patches. Because the HL detectors were placed nearby (at continental rather than intercontinental distances) on the surface of the Earth so as to keep their arms nearly coplanar, their combined network antenna pattern has two maxima that lie on opposite sides of that great circle. As a consequence, a large fraction of sources are localized to two islands of probability that cannot be distinguished based on time or amplitude on arrival. See Figure~\ref{fig:degeneracy} for an illustration of these two degenerate patches. A second undesirable side effect of the aligned antenna patterns is that GW polarization, observed as the phase difference on arrival at these two detectors, is of limited help for parameter estimation. \begin{figure*} \caption{\label{fig:degeneracy}HL degeneracy. This, like all sky plots in this paper, is a Mollweide projection in geographic coordinates to emphasize spatial relationships with respect to the Earth\nobreakdashes-fixed GW detector network as well as possible ground\nobreakdashes-based telescope sites. Pluses denote the locations of signals whose best-estimate locations are offset by $\geq 100 ^\circ$, comprising the large\nobreakdashes-offset peak that is evident in Figure~\ref{fig:offset_hist}(a). The locations of zero time delay (simultaneous arrival at the H and L detectors) is shown as a thick black line. Shading indicates the \ac{RMS} network antenna pattern, with darker areas corresponding to high sensitivity and white corresponding to null sensitivity. \\ (A color version of this figure is available in the online journal.)} \includegraphics{degeneracy} \end{figure*} A fairly typical sky map morphology, even at modestly high $\mathrm{SNR}_\mathrm{net}$, will consist of two extended arc-shaped modes, one over North America and a mirror image on the opposite side of the Earth. See Figure~\ref{fig:typical} for a typical event exhibiting this degeneracy. In this example, it is also possible to discern two narrow stripes resembling the forked tongue of a snake. This is a reflection of the HL network's limited polarization sensitivity. It occurs when the GW phases on arrival support two different binary inclination angles, with the orbital plane nearly facing the observer but with opposite handedness (usually peaked at $\iota \approx 30\arcdeg$ and $\iota \approx 150\arcdeg$; see \citealt{ShutzThreeFiguresOfMerit}). The two forks cross at a sky location where the GW data cannot distinguish between a clockwise or counterclockwise orbit. The HL degeneracy is even apparent in earlier works on localization of GW bursts with networks of four or more detectors: \citet{CWBLocalization} drew a connection between accurate position reconstruction and sensitivity to both the `$+$' and `$\times$' GW polarizations, and noted that the close alignment of the HL detector network adversely affects position reconstruction. (They did not, however, point out the common occurrence of nearly $180^\circ$ errors, or note that the worst GW localizations paradoxically occur where the HL network's sensitivity is the greatest.) The HL degeneracy affects most events that occur $\lesssim 30\arcdeg$ from one of the antenna pattern maxima. Most events that are $\gtrsim 50\arcdeg$ away have localizations that consist of a single long, thin arc or ring. See Figure~\ref{fig:typical-unimodal} for an example. \begin{figure*} \caption{\label{fig:typical}Localization of a typical circa 2015 GW detection. This is a Mollweide projection in geographic coordinates. Shading is proportional to posterior probability per deg$^2$. This is a moderately loud event with $\rho_\mathrm{net}=15.0$, but its 90\% confidence area of 630\,deg$^2$ is fairly typical, in the 60th percentile of all detections. The sky map is bimodal with two long, thin islands of probability over the north and southern antenna pattern maxima. Neither mode is strongly favored over the other. Each island is forked like a snake's tongue, with one fork corresponding to the binary having face\nobreakdashes-on inclination ($\iota \approx 0^\circ$) and the other fork corresponding to face\nobreakdashes-off ($\iota \approx 180^\circ$). \\ This is event ID 18951 from Tables~\ref{table:2015-sim}~and~\ref{table:2015-coinc} and the online material (see the Appendix for more details). \\ (A color version of this figure is available in the online journal.)} \includegraphics{2015_18951} \end{figure*} \begin{figure*} \caption{\label{fig:typical-unimodal}Localization of a typical circa 2015 GW detection. This is a Mollweide projection in geographic coordinates. Shading is proportional to posterior probability per deg$^2$. This event's $\rho_\mathrm{net}=12.7$ is near the threshold, but its 90\% confidence area of 530\,deg$^2$ near the median. The sky map consists of a single, long, thin island exhibiting the forked-tongue morphology. \\ This is event ID 20342 from Tables~\ref{table:2015-sim}~and~\ref{table:2015-coinc} and the online material (see the Appendix for more details). \\ (A color version of this figure is available in the online journal.)} \includegraphics{2015_20342} \end{figure*} \begin{figure} \includegraphics{2015_mode_hist} \caption{\label{fig:mode_hist}Frequency with which GW sky maps have one, two, or more disconnected modes during 2015. From top to bottom are the number of modes contained within the smallest confidence contour containing each simulated signal, the smallest 90\% contour, and the smallest 50\% contour. In 2015, roughly half of the sky maps will be unimodal, with most of the remainder being bimodal. \\ (A color version of this figure is available in the online journal.)} \end{figure} In Figure~\ref{fig:mode_hist}, we have plotted a histogram of the number of disconnected modes comprising the 50\% and 90\% confidence regions and the searched area, for the rapid localizations in the 2015 configuration. The ratios of events having one, two, or three or more modes depend weakly on the selected confidence level. In 2015, using either the 50\% contour or the searched area, we find that about half of events are unimodal and about a third are bimodal, the rest comprising three or more modes. Using the 90\% contour, we find that about a third of the events are unimodal and about half are bimodal. \subsection{2016} In our 2016 scenario, the HL detectors double in range to 108\,Mpc and the V detector begins observations with a range of 36\,Mpc. Over this six\nobreakdashes-month science run we expect $\sim$1.5 detections, assuming a BNS merger rate of 1\,Mpc$^{-3}$\,Myr$^{-1}$. Figure~\ref{fig:demographics} shows how livetime and duty cycle breaks down according to detector network (HLV, HL, LV, or HV). About half of the time all three detectors are online, with the remaining time divided in four almost equal parts among the three pairs of detectors or $\leq 1$~detector. However, the HLV network accounts for about three\nobreakdashes-quarters of detections and the HL network for most of the rest. When all three detectors (HLV) are operating, most detections are comprised of H and L triggers, lacking a trigger from V because the signal is below the single\nobreakdashes-detector threshold of $\rho=4$. Slightly more than half (57\%) of all detections have a signal below threshold in one operating detector (almost always~V) while slightly less than half (43\%) consist of triggers from all operating detectors. \begin{figure} \includegraphics{2016_demographics} \caption{\label{fig:demographics}Breakdown of 2016 scenario by detector network. The top row shows the duty fraction of each subset of the detector network, the fraction of time when all three detectors~(HLV) are observing, when any pair of detectors are observing~(HL, LV, or HV), or when zero or one detector is observing~(---). The second row shows the fraction of coincident detections that occur under any given network~(HLV, HL, LV, or HV). The last row shows the fraction of coincident detections for which the given detectors have signals above the single-detector threshold of $\rho=4$.\\ (A color version of this figure is available in the online journal.)} \end{figure} The first half consists mainly of HLV events that are detected by HL but not Virgo. For these events, the stochastic samplers provide a marked improvement in sky localization; their 90\% confidence regions have about one\nobreakdashes-third as much area as their rapid localizations. This is because the rapid localization makes use of only the triggers provided by the detection pipeline, lacking information about the signal in Virgo if its \ac{SNR} is $< 4$. The stochastic samplers, on the other hand, can use data from all operating detectors, regardless of \ac{SNR}. Therefore, in the present analysis, an improved sky localization would be available for half of the detections on a timescale of a day. Fortunately, for BNS sources, it is immediately known whether an improved localization is possible, since this statement only depends on what detectors were online and which contributed triggers. On the other hand, it may be possible to provide prompt sky localizations for all events by simply lowering the single\nobreakdashes-detector threshold. If the single-detector threshold was dropped to unity, essentially no event would lack a Virgo trigger. There are also efforts to do away with the single\nobreakdashes-detector threshold entirely \citep{2012PhRvD..86l3010K,2013arXiv1307.4158K}. Simultaneously, there is promising work under way in speeding up the full parameter estimation using reduced order quadratures \citep{roq-pe}, interpolation \citep{interpolation-pe}, jump proposals that harness knowledge of the multimodal structure of the posterior \citep{KDEJumpProposal}, hierarchical techniques \citep{HierarchicalParameterEstimation}, and machine learning techniques to accelerate likelihood evaluation \citep{BAMBI,SKYNET}. It seems possible that the the delayed improvement in sky localization may be a temporary limitation that can be overcome well before 2016. The second half consists of HLV events with triggers from all three detectors and events that occur when only HL, HV, or LV are operating. For these, the \textsc{bayestar} analysis and the full stochastic samplers produce comparable sky maps. For nearby loud sources ($\rho_\mathrm{net} \gtrsim 20$), the HLV network frequently produces compact sky localizations concentrated in a single island of probability. However at low SNR ($\rho_\mathrm{net} \lesssim 20$), and especially for the events that are detected as only double coincidence (HL), the refined localizations from the full stochastic samplers often identify many smaller modes. An $\rho_\mathrm{net} =13.4$ example is shown in Figure~\ref{fig:typical-hlv}. In this event, the rapid sky localization has two modes and has a morphology that is well\nobreakdashes-described by the HL degeneracy explained in Section~\ref{sec:2015}. However, the refined, full parameter estimation breaks this into at least four smaller modes. \begin{figure*} \caption{\label{fig:typical-hlv}Localization of a typical circa 2016 GW detection in the HLV network configuration. This is a Mollweide projection in geographic coordinates. This event consists of triggers in H and L and has $\rho_\mathrm{net} = 13.4$. The rapid sky localization gives a 90\% confidence region with an area of 1100\,deg$^2$ and the full stochastic sampler gives 515\,deg$^2$. \\ This is event ID 821759 from Tables~\ref{table:2016-sim}~and~\ref{table:2016-coinc} and the online material (see the Appendix for more details). \\ (A color version of this figure is available in the online journal.)} \begin{center} \includegraphics{2016_821759_bayestar} (a) \textsc{bayestar} \includegraphics{2016_821759_mcmc} (b) \textsc{lalinference\_mcmc} \end{center} \end{figure*} Of the remaining events, most occur when only the two HL detectors are operating. These look qualitatively the same as the 2015 case; their sky maps generally exhibit one or two slender islands of probability. However, percentage\nobreakdashes-wise, two\nobreakdashes-detector events are localized worse in the 2016 scenario than in the 2015 scenario. This unusual result is easily explained. Though the LIGO detectors improve in sensitivity at every frequency, with the particular noise curves that we assumed, the signal bandwidth is actually slightly lower with the 2016 sensitivity compared to 2015. This is because of improved sensitivity at low frequency. Applying Equation~(\ref{eq:sigmat}), we find that for a $(1.4, 1.4)\,M_\odot$ binary at $\rho=10$, one of the 2015 LIGO detectors has an \ac{RMS} timing uncertainty of 131\,{\textmu}s, whereas one of the 2016 LIGO detectors has a timing uncertainty of 158\,{\textmu}s. Clearly, the 2016 detectors will produce more constraining parameter estimates for sources at any fixed distance as the \ac{SNR} improves. However, for constant \ac{SNR} the 2016 LIGO detectors should find areas that are $(158/131)^2=1.45$ times larger than events at the same \ac{SNR} in 2015. This is indeed what we find. \begin{figure*} \caption{\label{fig:typical-hv}Rapid localization of a typical circa 2016 GW detection in the HV network configuration. This is a Mollweide projection in geographic coordinates. This event's $\rho_\mathrm{net} = 12.2$ is near the detection threshold. Its 90\% confidence area is 4600\,deg$^2$, but the true position of the source (marked with the white pentagram) is found after searching 65\,deg$^2$. \\ This is event ID 655803 from Tables~\ref{table:2016-sim}~and~\ref{table:2016-coinc} and the online material (see the Appendix for more details). \\ (A color version of this figure is available in the online journal.)} \includegraphics{2016_655803} \end{figure*} Two\nobreakdashes-detector events involving Virgo (HV and LV) are rare, accounting for only about 6\% of detections. Sky maps for these events sometimes exhibit multiple fringes spread over a quadrant of the sky. These are in part due to the increased importance of phase\nobreakdashes-on\nobreakdashes-arrival due to the oblique alignment of the LIGO and Virgo antenna patterns, which gives the network a limited ability to measure GW polarization. Occasionally there are also diffuse clouds of probability near the participating LIGO detector's two antenna pattern maxima, which may be a vestige of the antenna pattern. A typical HV event that exhibits both features is shown in Figure~\ref{fig:typical-hv}. | 14 | 4 | 1404.5623 |
1404 | 1404.2145_arXiv.txt | We discuss a novel instability in inertia-less electron magneto-hydrodynamics (EMHD), which arises from a combination of electron velocity shear and electron density gradients. The unstable modes have a lengthscale longer than the transverse density scale, and a growth-rate of the order of the inverse Hall timescale. We suggest that this \dsi\ may be of importance in magnetic reconnection regions on scales smaller than the ion skin depth, and in neutron star crusts. We demonstrate that the so-called Hall drift instability, previously argued to be relevant in neutron star crusts, is a resistive tearing instability rather than an instability of the Hall term itself. We argue that the \dsi\ is of greater significance in neutron stars than the tearing instability, because it generally has a faster growth-rate and is less sensitive to geometry and boundary conditions. We prove that, for uniform electron density, EMHD is ``at least as stable'' as regular, incompressible MHD, in the sense that any field configuration that is stable in MHD is also stable in EMHD. We present a connection between the \dsi\ in EMHD and the magneto-buoyancy instability in anelastic MHD. | Electron magneto-hydrodynamics (EMHD) is a regime of plasma physics in which positive and neutral particles are approximately immobile, so that only the dynamics of the (lighter) electrons needs to be considered \cite{Kingsep-etal87,Gordeev-etal94}. The flow of electrons induces \Bfs\ via the Hall effect, and the \Bf\ influences the electrons via the Lorentz force. EMHD was first studied in the context of laboratory plasma experiments \cite{GordeevRudakov69}, where it is applicable on scales smaller than the ion skin depth, and has also been used to explain (nearly) collisionless reconnection in the solar corona and magnetotail \cite{Mandt-etal94,Avinash-etal98,DengMatsumoto01}. Another important application of EMHD is in neutron stars \cite{GoldreichReisenegger92,Cumming-etal04}. Within the outermost 1km of a neutron star, called the crust, the ions are locked into a solid lattice, and the dynamics of the \Bf\ is therefore governed by the EMHD equations. The structure and topology of the \Bf\ determines the pattern of radiation from the star, and thus its observational signature, thermal evolution, and spin-down timescale \cite{Pacini67,*Gold69}. Furthermore, the evolution of the \Bf\ in the crust can trigger radiation bursts and flares, either via internal crustal failure \cite{ThompsonDuncan95,*ThompsonDuncan96,LevinLyutikov12} or by twisting the external \Bf\ lines until they undergo fast reconnection \cite{Lyutikov03,Lyutikov06}. An important question then is whether \Bfs\ in EMHD have a preferred structure, and whether some field configurations are unstable. Although there have been many studies of instability and turbulence in EMHD, almost all of the known instabilities require either finite ohmic resistivity \cite{Gordeev70} or finite electron inertia \cite{Bulanov-etal92,Califano-etal99,GaurDas12}. In the crust of a neutron star, however, electron inertia is entirely negligible in comparison with the Lorentz and Coulomb forces. Furthermore, most studies of EMHD turbulence have only considered the structure of the field in spectral space \cite{Biskamp-etal96,Biskamp-etal99,Dastgeer-etal00,ChoLazarian04,Galtier08b}. More recently, numerical simulations have suggested that the \Bf\ in a neutron star crust evolves towards a quasi-equilibrium, ``frozen-in'' state on a relatively short timescale ($\lesssim 1\Myr$) \cite{HollerbachRudiger02,HollerbachRudiger04,PonsGeppert07,WareingHollerbach09a,WareingHollerbach10,GC14}. However, these studies are all either two-dimensional, or else neglect variations in the electron density. Whether the quasi-equilibrium states found in these studies would be dynamically stable under more realistic conditions is unknown. \defcitealias{RheinhardtGeppert02}{RG02}% \citet{RheinhardtGeppert02}, \citetalias{RheinhardtGeppert02} hereafter, have presented numerical results demonstrating an instability in the inertia-less EMHD equations, which they argue is caused by Hall drift in the presence of a non-uniform \Bf, and which they called the ``Hall drift instability''. % However, they find that the growth-rate of the instability is very sensitive to the choice of boundary conditions, and also seems to vanish in the limit of high electrical conductivity. These observations suggest that the instability may, in fact, be a resistive tearing mode rather than an instability of the Hall term itself. The distinction is important, because tearing instability occurs only for rather particular \Bf\ configurations, which calls into question the general applicability of \citetalias{RheinhardtGeppert02}'s results to neutron stars. Tearing instability generally occurs only if the \Bf\ has a null surface, within which the ideal EMHD equations become singular. The goal of this paper is to determine the stability properties of inertia-less EHMD equilibrium states, for both finite and infinite electrical conductivity. We also consider the effect of non-uniform electron density, which was neglected in \citetalias{RheinhardtGeppert02}'s original model, but included in a subsequent work \cite{Rheinhardt-etal04}. % This effect is almost certainly important in real neutron star crusts, in which the electron density scale-height is typically only a few percent of the crust thickness \cite{ChamelHaensel08}. We show that electron velocity shear together with density gradients can produce an instability, which resembles an instability described originally in Ref.~\onlinecite{GordeevRudakov69}. We suggest that this \dsi\ was present in the results of Ref.~\onlinecite{Rheinhardt-etal04}, % which explains the significant discrepancies between their results and those % of \citetalias{RheinhardtGeppert02}. % We present an explicit, analytical instance of the \dsi, and discuss its implications for the evolution of \Bfs\ in neutron star crusts. | Most known instabilities in EMHD require either finite conductivity or finite electron inertia. We have demonstrated the existence of a very different instability that, instead, requires electron density gradients and electron velocity shear. This \dsi\ may play an important role in the evolution of \Bfs\ in the crusts of neutron stars, as well as in nearly-collisionless plasmas on scales smaller than the ion skin depth. The possibility of such an instability was first recognized in Ref.~\onlinecite{GordeevRudakov69} in the context of laboratory fusion devices, and has received very little attention in other contexts. The instability grows on the Hall timescale, which is generally faster than the growth-rate of any resistive tearing instability, such as the so-called Hall drift instability of \citetalias{RheinhardtGeppert02}. Moreover, the \dsi\ does not require peculiar \Bf\ configurations or boundary conditions to operate. It is highly likely that the instabilities observed in Ref.~\onlinecite{Rheinhardt-etal04}, in a numerical model of a neutron star crust, include both the resistive tearing instability and the \dsi. Although they interpreted all of their results in terms of the Hall drift instability, in fact the instabilities they described clearly form two distinct families. One family occurs close to magnetic null surfaces and has a growth-rate that depends on resistivity, as we would expect for a resistive tearing instability. The other family occurs in the region where density and magnetic pressure gradients are parallel and has a growth-rate that is independent of resistivity, as we would expect for the \dsi. We have demonstrated a connection between the stability properties of EMHD and those of incompressible/anelastic MHD, which shows the futility in seeking EMHD instabilities for field configurations that are already known to be stable in MHD. The \dsi\ is analogous to magneto-buoyancy instability in an anelastic fluid. Under this analogy, the EMHD fluid, which has zero mass and finite charge, becomes an anelastic fluid, which has finite mass and zero charge, and the electric potential becomes the gravitational potential. We have not found any instabilities in ideal, inertia-less EMHD with uniform density; at present, it is not known whether any such instabilities exist. By analogy with magneto-buoyancy instability in the solar interior \cite{Parker55-buoyancy} we suggest that the \dsi\ will greatly enhance the transport of magnetic flux from the superconducting core of a neutron star to its surface. This could explain the rapid decrease in the \Bf\ strengths observed in young neutron stars \cite{Lyne-etal85,NarayanOstriker90}. This might also be the explanation for the magnetic spots suggested by Ref.~\onlinecite{Geppert-etal13}. Of course, the EMHD equilibrium states and \Bf\ geometries considered in this paper are rather idealized, and the true situation in neutron star crusts is surely more complex. A full appreciation of the relevance of these results to neutron stars can only come from more realistic, direct numerical simulations, such as those of Refs.~\onlinecite{HollerbachRudiger04,Geppert-etal13,GC14}. | 14 | 4 | 1404.2145 |
1404 | 1404.5286_arXiv.txt | {} {We present a case study to demonstrate the potential of multi-wavelength polarization measurements. The aim is to investigate the effects that dichroic polarization and thermal re-emission have on tracing the magnetic field in the interstellar medium (ISM). Furthermore, we analyze the crucial influence of imperfectly aligned compact dust grains on the resulting synthetic continuum polarization maps.} {We developed an extended version of the well-known 3D Monte-Carlo radiation transport code MC3D for multi-wavelength polarization simulations running on an adaptive grid. We investigated the interplay between radiation, magnetic fields and dust grains. Our results were produced by post-processing both ideal density distributions and sophisticated magnetohydrodynamic (MHD) collapse simulations with radiative transfer simulations. We derived spatially resolved maps of intensity, optical depth, and linear and circular polarization at various inclination angles and scales in a wavelength range from $7\ \rm{\mu m}$ to $1\ \rm{mm}$.} {We predict unique patterns in linear and circular polarization maps for different types of density distributions and magnetic field morphologies for test setups and sophisticated MHD collapse simulations. We show that alignment processes of interstellar dust grains can significantly influence the resulting synthetic polarization maps. Multi-wavelength polarization measurements allow one to predict the morphology of the magnetic field inside the ISM. The interpretation of polarization measurements of complex structures still remains ambiguous because of the large variety of the predominant parameters in the ISM.} {} | Magnetic fields in the interstellar medium (ISM) affect astrophysical processes in various environments and scales in a crucial way. Especially the collapse of molecular clouds and the driving forces behind star formation are topics of ongoing research \citep{1999osps.conf..305M,2000ApJ...530..277E, 2007ARA&A..45..565M}. So far, vital questions about the role of magnetic fields remain unanswered. \\ The current paradigms of what drives star formation (magnetically supported \citep{1999osps.conf..305M} or turbulent models \citep{2004ASPC..322..299K} make different predictions of the magnetic field geometry. In models preferring magnetic support, gas falls parallel to the field lines. The magnetic field lines are frozen in to the matter, mass-dragged field lines form an hourglass morphology \citep{2005ApJ...631..411N}. In general, the magnetic field lines are expected to be smooth, with a regular structure. \\ The turbulent model, in turn, predicts a magnetic field that is too weak to resist the deformation by the local turbulent ISM environment. In this case, the magnetic field lines have an irregular and chaotic structure. Such irregularities should be easily recognizable in polarization measurements because of a correlation between polarization patterns and the density distribution.\\ To test the role of magnetic fields in the star formation process proper knowledge of the magnetic field strength and field morphology involved are required. Different methods are available for determining the magnetic field strength, such as the Chandrasekhar-Fermi method \citep[][]{1953ApJ...118..113C, 2004ApJ...600..279C}, Zeeman measurements \citep[e.g.][]{2008arXiv0808.1150C} and the field morphology by taking advantage of the polarization effects of non-spherical aligned dust particles inside the ISM \citep[e.g.][]{1999ApJ...525L.109G,2004MNRAS.352.1347L,2010ApJ...717.1262T}. However, from an observational point of view, the difficulty is that the reliability of polarization measurements and their interpretation depends on a wide range of physical parameters that are still discussed.\\ So far, knowledge about magnetic field morphologies in star formation regions has been accumulated by measurements of thermal dust re-emission by aligned dust grains at far-infrared (FIR) to sub-millimeter (sub-mm) wavelength \citep[e.g][]{2011AA...535A..44F}. Although the polarization of light by interstellar dust was discovered in the middle of the last century \citep{1949Natur.163..283H}, its potential as a tool for tracing the magnetic field in the ISM is still high. Especially circular polarization is an often neglected source of additional information. In the mid-/far-infrared wavelength range where extinction is not dominated by scattering one can expect significant insights into the magnetic field structures by polarization measurements in combination with the ongoing research in grain alignment mechanisms. Existing theories of grain alignment \citep[e.g.][]{1951ApJ...114..206D,2007JQSRT.106..225L} agree that rotating non-spherical dust grains align with their shorter axis parallel to the magnetic field direction. As a result, previously unpolarized light will be polarized by thermal dust remission and dichroic extinction perpendicular and parallel, respectively, to the magnetic field lines. This makes multi-wavelength observation on multiple scales a powerful tool completing our understanding of the fundamental physics of star formation processes. \\ The paper is arranged in the following order: In Sect. \ref{sq:pol} in detail we present the theoretical basis for the considered mechanisms of dichroic polarization. In Sect. \ref{sect:dust} the parameters of the applied dust grain model are described. We introduce the considered mechanisms of grain alignment in Sect. \ref{sq:PDG} and \ref{sq:IDG}. To investigate the effects of polarization and alignment we apply these mechanisms in Sect. \ref{setupIDEAL} to simple setups of various density and temperature distributions with analytically modeled field configurations. In Sect. \ref{setupMHD} we extend the investigation to more realistic setups including sophisticated MHD collapse simulations. We discuss and summarize the effects observed in the resulting synthetic polarization maps in Sect. \ref{disc} and demonstrate that the magnetic field morphology can be traced from the complexity of the involved density distribution. | We demonstrated the influence of grain alignment mechanisms and magnetic field configurations by a first case study of the potential of multi - wavelength polarization measurements. For this reason we developed an extended version of the radiative transfer code MC3D \citep{2003CoPhC.150...99W} and demonstrateed its accuracy. We included a dust grain model consistent with observations and studied the effects of non-spherical dust particles with perfect alignment and imperfect alignment with respect to the direction of the magnetic field. The effects of dichroic polarization and thermal re-emission allowed us to calculate synthetic polarization maps. To do this we used ideal Bonnor - Ebert sphere setups and a sophisticated MHD collapse simulation as test models (see Tab. \ref{tab:1}.). We showed that measurements of linear polarization in combination with measurements of circular polarization as an additional source of information allow one to reveal the underlying morphology of the magnetic field for different inclination angles. The limiting factors for interpreting continuum polarization measurements are the current uncertainty of different physical parameters concerning alignment theory and dust composition. We demonstrated that the influence of imperfect grain alignment changes the behavior for circular and linear polarization radically. We conclude that possible ambiguities in the interpretation of observational data can be resolved by including additional measurements of circular polarization in future observation missions. However, it remains unclear whether the low values of circular polarization in the order of $10^{-4} - 10^{-6}$ as predicted by our models are accessible to observational equipment in the near future.\\ An additional source of ambiguity is inherent in the dichroic polarization mechanism itself. We identified two effects of rotation in the orientation angles of the vectors of linear polarization projected on the plane sky. The orientation of linear polarization is determined by a critical value of the cross sections for absorption and extinction (see Appendix \ref{apB}). Since the cross sections depend on wavelength and alignment this effect leads to a flip in the orientation of linear polarization by $90^{\circ}$. Additionally, thermal re-emission depends on dust temperature and number density. This results in a continuous rotation of the orientation angle of linear polarization as a function of wavelength. This might easily veil the underlying field morphology even for a symmetrical density distribution and field morphology. Therefore, measurements for linear polarization at a distinct wavelength alone are insufficient to identify the underlying magnetic field morphology because of effects of the wavelength-dependent rotations on the polarization vectors. \\ Resolving complex density and magnetic field structures, however, is currently ambiguous because of open questions about interstellar dust composition and the absence of a consistent theory of grain alignment mechanisms \citep{2007AAS...21113807H,2010MNRAS.404..265D}. A reliable theory about the dominating grain alignment mechanisms inside the ISM \citep[e.g.][]{2011ASPC..449..116L} and a sophisticated understanding of the dust composition is essential to resolve these uncertainties. \begin{figure}[] \begin{minipage}[c]{0.49\linewidth} \begin{center} \includegraphics[width=1.0\textwidth]{2lPolVec.pdf} \end{center} \end{minipage} \begin{minipage}[c]{0.49\linewidth} \begin{center} \includegraphics[width=1.0\textwidth]{1lPolVec.pdf} \end{center} \end{minipage} \caption{\small Orientation vectors of linear polarization with an inclination angle of $75^{\circ}$ for a wavelength of $\lambda = 46\ \rm{\mu m}$ (left) and $\lambda = 811\ \rm{\mu m}$ (right). The parameters are identical to those of $\rm{BE_{hour2}}$. However, the density is $n_0=10^{12}\ \rm{m^{-3}}$ in the center and the field strength is $6.0\times 10^{-8} T$. The linear polarization vectors have an offset angle of $90^{\circ}$ to match the projected magnetic hourglass field. The orientation angles of linear polarization in the center regions differ from each other because of the $90^{\circ}$ flip (see Appendix \ref{apB})}. \label{IDlPolFlip} \end{figure} \appendix | 14 | 4 | 1404.5286 |
1404 | 1404.6599_arXiv.txt | \PRE{\vspace*{.3in}} We investigate constraints on the properties of light dark matter which can be obtained from analysis of invisible quarkonium decays at high intensity electron-positron colliders in the framework of a low energy effective field theory. A matrix element analysis of all contact operators pertinent for these meson decays allows for a model-independent calculation of associated dark matter-nucleon scattering and dark matter annihilation cross sections. Assuming dark matter couples universally to all quark flavors, we then obtain bounds on nucleon scattering which complement direct dark matter detection searches. In contrast to similar analyses of monojet searches at high energy colliders, B and charm factories are more suitable probes of light dark matter interactions with less massive mediators. Relevant bounds on dark matter annihilation arising from gamma ray searches of dwarf spheroidal galaxies are also presented. | Despite strong observational evidence for non-baryonic dark matter (DM) which interacts gravitationally~\cite{Kolb:1990}, the detection of dark matter interactions with the Standard Model (SM) remains elusive. Many extensions of the SM predict dark matter candidates which should leave signatures in the direct and indirect dark matter detection experiments, and at hadron colliders. If the particles mediating dark matter-Standard Model interactions are much heavier than the energy scales involved, then the constraints on dark matter interactions arising from these disparate detection strategies can be related to each other in a model independent fashion via a generalized effective field theory (EFT) framework, in which the details of the ultraviolet (UV) physics have been integrated out of the Lagrangian~\cite{Goodman:2011,Hooper:2009,Cao:2011,Kumar:2013iva,Rajaraman:2013,Dreiner:2013,Buckley:2013,Rajaraman:2013-2, Busoni:2014,Buchmueller:2014,Crivellin:2014,Busoni:2014-2,Alves:2014,Fedderke:2014}, and dark matter-Standard Model interactions occur through contact operators. Weakly interacting massive particles (WIMPs) are stable dark matter candidates predicted by many models of physics beyond the SM~\cite{Kolb:1990}. Although recent hints of possible WIMP signals may be encouraging, the lack of clear and convincing evidence for the discovery of WIMP dark matter motivates consideration of dark matter candidates which deviate from the expectations of the WIMP paradigm. A well-motivated example is light dark matter (LDM), a class of dark matter candidates with masses typically $\sim 10 \mev - 10 \gev$. LDM would elastically scatter at direct detection experiments, with nuclear recoil energies which are relatively small and may be below the experimental threshold, rendering them undetectable. In this case, other experimental means aside from direct detection would be required to probe DM-SM interactions. For example, complimentary bounds on LDM scattering can be inferred from collider monojet searches~\cite{Feng:2005gj,Goodman:2010,Birkedal:2004,Hooper:2010,Bai:2010,Rajaraman:2011,Fox:2012,Bai:2013,Agrawal:2013, Goodman:2011-2,Bai:2011,Papucci:2014}. Nonresonant LDM production at low energy $e^+/e^-$colliders can also be used to set model independent limits on electron scattering and, if the LDM couples universally, nucleon scattering~\cite{Essig:2013}. In this work, we consider the prospects for probing LDM-quark interactions through bounds on invisible decays of heavy quarkonium states at colliders~\cite{Fayet:2007,Fayet:2010,Cotta:2013,Schmidt-Hoberg:2013hba,McElrath:2007}. Such bounds have already been considered in a variety of contexts, including $B$ and $D$ meson decays~\cite{Badin:2010}, and $\Upsilon$ decays into scalar LDM~\cite{Yeghiyan:2010,McKeen:2009rm}. However, the constraints which one can obtain on dark matter-quark interactions depend in detail on the quantum numbers of the heavy meson, as well on the choice of final state (i.e., $\rightarrow invisible$ or $\rightarrow \gamma +invisible$). The angular momentum and $C/P$ transformation properties of the initial state (as well as the presence or absence of a photon in the final state) together determine which of the possible dark matter-quark interaction structures can participate in the decay process (and can thus be bounded by constraints on invisible decays). We consider invisible decays of the heavy quarkonium states $\Upsilon (1S)$ and $J / \Psi $, mesons with $J^{PC} = 1^{--}$. As the quark constituents annihilate in an $s$-wave, the dependence of the meson decay matrix element on the associated nonrelativistic bound state wavefunction is very simple and can be determined experimentally, with relatively little uncertainty. Moreover, since the mesons which we consider each have a quark and anti-quark of the same flavor, the DM-SM interactions which we introduce are not constrained by bounds on flavor-violation and, given universal quark coupling, can contribute to nucleon scattering. At quark level, the matrix element relevant for meson decay ($\bar q q \rightarrow \bar X X$) is also relevant for monojet/photon/$W$,$Z$ searches at the LHC~\cite{CMS:2012, CMS:2012tea,ATLAS:2012ky,ATLAS:2012,ATLAS:2013}. As a result, these searches will share many features, and event rates will have the same dependence on the energy of the process. Moreover, bounds arising from both invisible meson decay rates and LHC monojet searches do not weaken as the dark matter mass decreases, in notable contrast to direct detection searches. However, if the particle mediating LDM interactions is light, then the interaction is poorly approximated by a contact operator for the purposes of LHC mono-anything searches, and model independent bounds on the interaction strength can no longer be obtained. Even given a mediating particle massive enough to warrant the use of the contact interaction approximation, the masses of LDM particles would be difficult to resolve at LHC searches due to the large center-of-mass energy of the beam. The bounds obtained from meson decays thus provide a unique handle on some dark matter interaction models, which is complementary to the information provided by other search strategies. In this paper, we use the limits on bound state decay widths to constrain the coupling of scalar, fermion or vector LDM to Standard Model quarks through all contact operators of dimension six or lower. In section II, we review the relevant effective contact interactions and calculate the resulting meson decay rates and dark matter annihilation and scattering cross sections. In section III we present constraints on all of the relevant dark matter-quark interaction structures arising from $\Upsilon (1S)$ decay and Fermi gamma-ray searches of dwarf spheroidal galaxies, and relate these constraints to those arising from direct detection experiments and LHC searches. We conclude in section IV with a discussion of our results. | We have presented bounds on dark matter-quark contact interactions which can be obtained from high luminosity $B$/charm-factories by constraining decays of the form $\Upsilon (1S), J/\psi \rightarrow \bar X X$. These bounds on low mass dark matter probe a mass range significantly below the threshold of direct dark matter detection experiments and complement bounds on dark matter interactions obtained from gamma ray searches of dwarf spheroidal galaxies and from monojet/monophoton/mono-$W$,$Z$ searches at hadron colliders. In particular, the effective interactions which permit decay of a $1^{--}$ meson state can also permit velocity-independent dark matter-nucleon scattering (either spin-independent or spin-dependent). For $m_X \sim 1-5~\gev$, the bounds obtained from meson decay can thus potentially complement those obtained from direct detection experiments. For the case of spin-independent scattering, direct detection experiments already place bounds which well exceed those obtained from meson decay. However, for spin-dependent scattering, bounds arising from $\Upsilon (1S)$ decay via the F9 and V5 operators are comparable to those obtained from direct detection experiments. This is not surprising, as direct detection experiments typically have much weaker sensitivity to spin-dependent scattering, due to the lack of constructive interference in coherent scattering. Moreover, bounds on spin-1 dark matter interactions improve dramatically as $m_X$ decreases, because of the enhancement in the matrix element which arises when the dark matter particles are longitudinally polarized. Relating the suppression scale $\Lambda$ to the mediator mass scale $m_{med.}$ and coupling $g$ by $\Lambda \sim m_{med.} /g$, this implies that interactions between spin-1 dark matter and quarks can be constrained even if the coupling is very weak. We have seen that invisible quarkonium decays probe the same parton-level process ($\bar q q \rightarrow \bar X X$) as monojet/photon/$W$,$Z$ searches at hadron colliders. However, quarkonium decays provide complementary information, allowing robust probes of models with relatively light mediators ($\gsim 10~\gev$) for which the contact operator approximation would fail at the LHC. It is also worth noting that, since the heavy quarkonium bound states are non-relativistic, searches based on invisible heavy quarkonium decays readily distinguish between DM-SM interactions which vanish in the limit of non-relativistic quarks and those which do not. This probe thus nicely complements LHC searches, in which the partons are highly relativistic. A similar analysis can be performed of heavy quarkonium decays to a photon and missing energy; although the set of relevant contact operators would be different for such an analysis, those branching fractions are much more tightly constrained. Improved bounds on the $\Upsilon (1S) \rightarrow nothing$ decay rate from Belle II~\cite{Browder} and a factor of $\sim 14$ enhancement in sensitivity to $J / \Psi \rightarrow nothing $ decay rate from BESIII~\cite{Harris} will allow for even tighter constraints on the interactions of low mass dark matter with Standard Model particles. {\bf Acknowledgements} We are grateful to Y.~G.~Aditya, T.~Browder, F.~Harris, D.~Marfatia, A.~Petrov, A.~Rajaraman, X.~Tata, S.~Vahsen, D.~Walker and A.~Wijangco for useful discussions. This work is supported in part by Department of Energy grant DE-SC0010504. \appendix | 14 | 4 | 1404.6599 |
1404 | 1404.3719_arXiv.txt | \sourcefull\ is an extraordinary neutron star low-mass X-ray binary. Albeit discovered when it exhibited a $\simeq$10-s long thermonuclear X-ray burst, it had faded to a 0.5--10 keV luminosity of $L_{\mathrm{X}}\lesssim8\times10^{32}~(D/\mathrm{7.1~kpc})^2~\lum$ only $\simeq$8~hr later. It is generally assumed that neutron stars are quiescent (i.e., not accreting) at such an intensity, raising questions about the trigger conditions of the X-ray burst and the origin of the faint persistent emission. We report on a $\simeq$51 ks \xmm\ observation aimed to find clues explaining the unusual behavior of \sourcefull. We identify a likely counterpart that is detected at $L_{\mathrm{X}}$$\simeq$$5\times10^{31}~(D/\mathrm{7.1~kpc})^2~\lum$ (0.5--10 keV) and has a soft X-ray spectrum that can be described by a neutron star atmosphere model with a temperature of $kT^{\infty}\simeq50$~eV. This would suggest that \sourcefull\ is a transient source that was in quiescence during our \xmm\ observation and experienced a very faint (ceasing) accretion outburst at the time of the X-ray burst detection. We consider one other potential counterpart that is detected at $L_{\mathrm{X}}$$\simeq$$5\times10^{32}~(D/\mathrm{7.1~kpc})^2~\lum$ and displays an X-ray spectrum that is best described by power law with a photon index of $\Gamma \simeq 1.7$. Similarly hard X-ray spectra are seen for a few quiescent neutron stars and may be indicative of a relatively strong magnetic field or the occurrence of low-level accretion. | When matter accretes onto the surface of a neutron star, it can undergo unstable thermonuclear burning resulting in a brief, intense flash of X-ray emission. Such thermonuclear X-ray bursts (type-I X-ray bursts; shortly X-ray bursts hereafter) are observed from low-mass X-ray binaries (LMXBs), in which a neutron star accretes matter from a sub-solar companion star that overflows its Roche lobe. X-ray bursts are a potential tool to constrain the fundamental properties of neutron stars \citep[e.g.,][]{vanparadijs1979,steiner2010,suleimanov2011_eos}, and can give valuable insight into the accretion flow around the compact object \citep[e.g.,][]{yu1999,ballantyne2004,zand2012,degenaar2013_igrj1706,worpel2013}. Wide-field monitoring with observatories such as \beppo, \inte, and \swift\ has led to the discovery of X-ray bursts for which no persistent emission could be detected above the instrument background \citep[e.g.,][]{zand1999_burstonly,cocchi2001,cornelisse02,chelovekov07_ascabron,delsanto07,wijnands09,linares09,degenaar2010_burst,degenaar2011_burst, degenaar2013_igrj1706}. This implies that these \textit{burst-only sources} are accreting at 2--10 keV luminosities of $L_{\mathrm{X}}\lesssim10^{36}~\lum$. This is lower than typically seen for neutron star LMXBs \citep[e.g.,][]{chen97,wijnands06,campana09,degenaar2012_gc}. The burst-only sources trace a relatively unexplored accretion regime and provide valuable new input for thermonuclear burning models \citep[e.g.,][]{cooper07,peng2007,degenaar2010_burst}. \begin{figure*} \begin{center} \includegraphics[width=8.0cm]{fig1a.eps}\hspace{0.5cm} \includegraphics[width=8.0cm]{fig1b.eps} \end{center} \caption[]{{\xmm\ images of the field around \source. Left: Combined EPIC X-ray image (0.5--10 keV). The \beppo/WFC positional uncertainty of the X-ray burst ($3.2'$) and that of the tentative counterpart identified in follow-up \beppo/MECS observations ($1.5'$) are indicated. Within the WFC error circle there were eight faint X-ray sources detected with all three EPIC detectors, which are indicated by numbered red circles ($15''$ in size). Right: OM $V$-band image. The insets show magnifications to indicate possible associations with optical objects (black circles). In those sub-images the size of the red circles correspond to the X-ray positional uncertainties of source 2 and 3 ($1.7''$ and $1.6''$, respectively). The ellipsoidal feature in the center of the image concerns an artifact (straylight). }} \label{fig:image} \end{figure*} Follow-up observations with more sensitive narrow-field instruments (e.g., onboard \beppo, \chan, \xmm\ and \swift) have revealed that the burst-only sources fall into two categories: 1) LMXBs accreting (quasi-) persistently at $L_{\mathrm{X}}\simeq10^{34-35}~\lum$ \citep[e.g.,][]{zand05,chelovekov07_ascabron,delsanto07,degenaar2010_burst}, and 2) transient LMXBs that exhibit weeks to months long outbursts of $L_{\mathrm{X}}\simeq10^{34-36}~\lum$, but are otherwise quiescent \citep[e.g.,][]{cocchi2001,cornelisse02,hands04,wijnands09,campana09}. In quiescence, neutron star LMXBs are dim with $L_{\mathrm{X}}\simeq10^{31-33}~\lum$ \citep[e.g.,][]{campana1998,jonker2004,heinke2009,guillot2013}. The quiescent spectra typically contain a soft component that is well-fitted by a neutron star atmosphere model. This emission is ascribed to thermal radiation from the surface of the neutron star, and may act as a probe of its interior properties \citep[e.g.,][]{vanparadijs1984,brown1998,rutledge1999,wijnands2004,cackett2006,degenaar2013_ter5}. With their low mass-accretion rates, the burst-only sources can provide valuable new insight into the thermal evolution of neutron stars \citep[][]{wijnands2012}. An additional, non-thermal spectral component is often present in the quiescent spectra. It can be described by a simple power law with a photon index of $\Gamma\simeq1-2$. This component has been associated with (stochastic) intensity variations and therefore tentatively ascribed to the presence of a residual accretion flow \citep[e.g.,][]{rutledge2002_aqlX1,cackett2005,cackett2011_aqlx1,fridriksson2011,degenaar2012_1745,bernardini2013,wijnands2013}. Since there are some indications that the hard power-law emission is particularly prominent in the quiescent spectra of accreting millisecond X-ray pulsars \citep[AMXPs; e.g.,][]{wijnands05_amxps,campana2008,heinke2009,degenaar2012_amxp,linares2013_M28}, it has also been explained as the result of accretion onto the magnetosphere of the neutron star, or a shock from a pulsar wind colliding with matter flowing out of the donor star \citep[e.g.,][]{campana1998,rutledge2001,linares2013_M28}. \subsection{The Peculiar X-Ray Burster \sourcefull} Perhaps the most tantalizing burst-only source is \sourcefull\ (\source\ hereafter). It was detected with the \beppo\ Wide Field Camera (WFC) as a $\simeq$10-s long X-ray flash on 1999 November 6 \citep[][]{gandolfi1999}. Initially dubbed GRB 991106, multi-wavelength follow-up observations failed to detect a fading afterglow and cast doubt on a GRB nature \citep[e.g.,][]{antonelli1999,gandolfi1999_3,frail1999,jensen1999,gorosabel1999}. \citet{cornelisse02} demonstrated that the properties of the event were consistent with a thermonuclear X-ray burst, which would identify \source\ as a new neutron star LMXB. A source distance of $D \lesssim 7.1$~kpc was inferred by assuming that the X-ray burst peak did not exceed the Eddington limit ($L_{\mathrm{edd}}=2\times10^{38}~\lum$). No accretion emission could be detected with the WFC around the time of the X-ray burst, implying a 2--28 keV luminosity of $L_{\mathrm{X}}\lesssim2\times10^{36}~(D/\mathrm{7.1~kpc})^2~\lum$ \citep[][]{cornelisse02}. Rapid follow-up observations with the \beppo\ Medium-Energy Concentrator Spectrometer (MECS), performed $\simeq$8~hr after the X-ray burst detection, revealed only one source within the WFC error circle that was detected at a 0.5--10 keV luminosity of $L_{\mathrm{X}}\simeq8\times10^{32}~(D/\mathrm{7.1~kpc})^2~\lum$ \citep[][]{antonelli1999}. This raises the question whether the X-ray burst was ignited when the neutron star was accreting at a very low level, or whether it exhibited a faint, undetected accretion outburst that had ceased within 8~hr of the X-ray burst detection. In this work we present a deep \xmm\ observation to search for an X-ray counterpart of \source, and to find clues to its nature and unusual behavior. \begin{table*} \begin{center} \caption{Positions and Basic Properties of Detected X-Ray Sources.\label{tab:sources}} \begin{tabular*}{0.99\textwidth}{@{\extracolsep{\fill}}lcccccc} \hline Source & R. A. & Dec. & Error & MOS Count Rate & PN Count Rate & PN Hardness Ratio \\ & (J2000) & (J2000) & $('')$ & $(10^{-3}~\cnts)$ & $(10^{-2}~\cnts)$ & \\ \hline 1 \dotfill & 22 24 52.94 & +54 22 38.2 & 1.6 & $3.9 \pm 0.3$ & $1.3 \pm 0.1$ & $0.94 \pm 0.17$ \\ 2 \dotfill & 22 25 07.87 & +54 21 30.2 & 1.7 & $3.2 \pm 0.3$ & $0.8 \pm 0.1$ & $0.73 \pm 0.15$ \\ 3 \dotfill & 22 24 40.99 & +54 24 54.4 & 1.6 & $3.8 \pm 0.3$ & $1.5 \pm 0.1$ & $0.06^{+0.37}_{-0.06}$ \\ 4 \dotfill & 22 24 49.65 & +54 23 10.1 & 2.3 & $0.7\pm0.2$ & $0.17 \pm 0.03$ & $0.22^{+0.58}_{-0.22}$ \\ 5 \dotfill & 22 24 50.64 & +54 22 05.1 & 2.4 & $0.6\pm0.2$ & $0.13 \pm 0.03$ & $1.22 \pm 0.46$ \\ 6 \dotfill & 22 24 43.99 & +54 20 59.9 & 2.2 & $0.6\pm0.2$ & $0.23 \pm 0.05$ & $1.54 \pm 0.52$ \\ 7 \dotfill & 22 24 33.82 & +54 21 48.9 & 2.2 & $0.7\pm0.2$ & $0.24 \pm 0.04$ & $1.99 \pm 0.34$ \\ 8 \dotfill & 22 24 53.74 & +54 24 54.9 & 2.1 & $0.6\pm0.2$ & $0.23 \pm 0.04$ & $2.29 \pm 0.32$ \\ \hline \end{tabular*} \tablecomments{The quoted positional uncertainties are at 90\% confidence level, and are a combination of the statistical error from the detection algorithm and an estimated systematic uncertainty of $1.5''$ \citep[][]{watson2009}. Count rates errors are at the 1$\sigma$ level of confidence. We consider sources 1 and 4 as possible counterparts for \source. } \end{center} \end{table*} | \label{sec:discussion} \subsection{The Counterpart to the X-Ray Burst}\label{subsec:counterpart} \source\ is one of several sources for which \beppo\ detected an X-ray flash without detectable accretion emission \citep[e.g.,][]{cornelisse02}. Follow-up observations were performed with \chan\ for some of these objects (several years later) and revealed weak candidate X-ray counterparts with $L_X \lesssim 5 \times 10^{32}~\lum$. This suggested that they were likely transient neutron star LMXBs that exhibited faint ($L_X \lesssim 10^{36}~\lum$) accretion outbursts when the X-ray bursts were ignited \citep[][]{cornelisse02_chan}. Indeed, several of these sources were later detected during faint accretion outbursts \citep[e.g., \saxeen, \saxtwee, and \saxdrie;][]{hands04,degenaar2008_1828,delsanto2010,altamirano2011_1806}. The quality of the WFC data of \source\ was very low, imposing considerable uncertainty on the interpretation of this event \citep[][]{cornelisse02}. However, the similarities between the X-ray flash from \source\ and that of the other sources (i.e., duration, peak flux, overall spectral properties, indication of softening during the decay, and location in the Galactic plane), renders it likely that \source\ too is a bursting neutron star \citep[][]{cornelisse02}. Here we identify two possible quiescent neutron star LMXBs within the WFC error circle, that might provide support for this interpretation. During our long \xmm\ observation we detected eight weak X-ray sources within the $3.2'$ \beppo/WFC uncertainty of \source. They had 0.5--10 keV luminosities in the range of $L_{\mathrm{X}}\simeq (0.5-5)\times10^{32}~(D/7.1~\mathrm{kpc})^2~\lum$, which is typical for transient neutron star LMXBs in quiescence \citep[see e.g.,][]{jonker2004}. However, based on the X-ray spectral properties and X-ray/optical luminosity ratio's we can discard six of these as potential counterparts to the X-ray burster, leaving only sources 1 and 4 as candidates. Source 1 was detected at $L_{\mathrm{X}}\simeq 5\times10^{32}~(D/7.1~\mathrm{kpc})^2~\lum$, with a spectrum best described by a power law model with an index of $\Gamma=1.7$. Emission from a neutron star atmosphere with $kT^{\infty}\lesssim61$~eV could contribute up to $\simeq$24\% to the total unabsorbed 0.5--10 keV flux. Only a handful of quiescent neutron star LMXBs have similarly hard X-ray spectra that lack detectable thermal emission. The small LMXB subclass of AMXPs (which display coherent X-ray pulsations during accretion outbursts) exhibit $\Gamma \simeq1.5$ power-law spectra with $\lesssim$40\% attributed to thermal emission \citep[e.g., \sax, \swiftpulsar, and \radiopulsar; ][]{campana2008,heinke2009,degenaar2012_amxp,linares2013_M28}. Their hard spectra are ascribed to their relatively strong magnetic field. The only non-pulsating neutron star with a very hard ($\Gamma \simeq1.7$) quiescent spectrum is the LMXB and X-ray burster \exo\ \citep[e.g.,][]{wijnands2005,degenaar2012_1745}. Its irregular quiescent properties have been interpreted in terms of ongoing low-level accretion. Thus, source 1 could be the counterpart of \source, but it would imply that it is an unusual neutron star (perhaps with a relatively strong magnetic field or exhibiting low-level accretion). Source 4, on the other hand, has a soft X-ray spectrum like the majority of quiescent neutron star LMXBs. This source was detected at $L_{\mathrm{X}}\simeq 5\times10^{31}~(D/7.1~\mathrm{kpc})^2~\lum$, and its spectrum can be described by a neutron star atmosphere model with $kT^{\infty}\simeq50$~eV. This relatively low temperature is consistent with the expectations for a neutron star that exhibits faint accretion outbursts \citep[][]{wijnands2012}. We therefore tentatively identify source 4 as the counterpart of the X-ray burst detected with \beppo\ in 1999. \subsection{The X-Ray Burst Trigger Conditions}\label{subsec:bursttheory} The duration, repetition rate, and energetics of X-ray bursts depend on the conditions of the ignition layer, such as its thickness, temperature profile, and chemical abundances. These conditions are sensitive to the (local) accretion rate onto the neutron star so that different accretion regimes give rise to X-ray bursts with distinct properties \citep[e.g.,][]{fujimoto81,fushiki1987}. X-ray bursts that ignite in a pure He layer are typically short (seconds), whereas the presence of H in the ignition layer prolongs the duration (minutes). Upper limits obtained for the accretion emission of the burst-only sources suggests they occupy the lowest accretion regime \citep[$\lesssim0.01~L_{\mathrm{Edd}}$;][]{cornelisse02}. Classical burning theory prescribes that in this regime unstable burning of H should trigger a mixed He/H X-ray burst with a duration of $\simeq100$~s \citep[e.g.,][]{fujimoto81}. This is much longer than the short ($\simeq10$~s) X-ray bursts detected from \source\ and other \beppo\ burst-only sources. This apparent discrepancy was addressed by \citet{peng2007}, who showed that for the low inferred mass-accretion rates sedimentation of heavy elements significantly reduces the amount of H in the ignition layer. This would alter the X-ray burst properties, possibly explaining the observations \citep[][]{peng2007}. The fact that no persistent X-ray emission was detected above $L_{\mathrm{X}}\simeq8\times10^{32}~(D/7.1~\mathrm{kpc})^2~\lum$ within $\simeq$8 hr after the X-ray burst detection raises the question whether \source\ may have been accreting at $\lesssim 1 \times 10^{-5}~L_{\mathrm{Edd}}$ when the burst ignited. This is right at the boundary below which theoretical models predict that no X-ray bursts can occur \citep[e.g.,][]{fushiki1987}. We consider this scenario unlikely, because the chance probability of detecting this $\simeq$10-s event would be very low; for a typical ignition column depth of $y\simeq10^{8}~\mathrm{g~cm}^{-2}$ and a mass-accretion rate of $\dot{M}\simeq10^{-13}~\mdot$, the time to accumulate enough material to produce this X-ray burst would be $\simeq$8~yr. Regardless whether source 1 or source 4 is the true counterpart, we consider it more likely that \source\ is a transient neutron star LMXB that exhibited an X-ray burst during the decay of a (short) faint accretion outburst. In particular, the behavior of \source\ is strikingly similar to that of the AMXP \swiftpulsar. This source rapidly decayed to a level of $L_{\mathrm{X}}\simeq 1\times10^{33}~\lum$ within a day after it was discovered through the detection of an X-ray burst \citep[][]{wijnands09}. Its behavior remained a puzzle until it exhibited a $\simeq$2-week long accretion outburst with an average 0.5--10 keV luminosity of $L_{\mathrm{X}}\simeq10^{36}~\lum$ several years later \citep[e.g.,][]{altamirano2011_amxp}. This suggests that the peculiar X-ray burst had likely occurred during the decay of its previous accretion outburst. A similar scenario can be envisioned for \sourcefull. | 14 | 4 | 1404.3719 |
1404 | 1404.7140_arXiv.txt | The upcoming detection of gravitational waves by terrestrial interferometers will usher in the era of gravitational-wave astronomy. This will be particularly true when space-based detectors will come of age and measure the mass and spin of massive black holes with exquisite precision and up to very high redshifts, thus allowing for better understanding of the symbiotic evolution of black holes with galaxies, and for high-precision tests of General Relativity in strong-field, highly dynamical regimes. Such ambitious goals require that astrophysical environmental pollution of gravitational-wave signals be constrained to negligible levels, so that neither detection nor estimation of the source parameters are significantly affected. Here, we consider the main sources for space-based detectors -- the inspiral, merger and ringdown of massive black-hole binaries and extreme mass-ratio inspirals~-- and account for various effects on their gravitational waveforms, including electromagnetic fields, cosmological evolution, accretion disks, dark matter, ``firewalls'' and possible deviations from General Relativity. We discover that the black-hole quasinormal modes are sharply different in the presence of matter, but the ringdown signal observed by interferometers is typically unaffected. The effect of accretion disks and dark matter depends critically on their geometry and density profile, but is negligible for most sources, except for few special extreme mass-ratio inspirals. Electromagnetic fields and cosmological effects are always negligible. We finally explore the implications of our findings for proposed tests of General Relativity with gravitational waves, and conclude that environmental effects will not prevent the development of precision gravitational-wave astronomy. | Today, we have convincing indirect evidence from binary pulsars~\cite{HT1} for the existence of gravitational waves (GWs), which are a generic prediction of General Relativity (GR) and other relativistic theories of gravity. The ground-based GW detectors LIGO and Virgo are currently being updated to advanced configurations~\cite{Harry:2010zz,virgo} expected to achieve sensitivities sufficient for detecting signals from binaries of stellar-mass black holes (BHs) and/or neutron stars within the end of this decade. Detection of these signals will allow measuring the masses and spins of the binary components with accuracies comparable to current X-ray probes~\cite{Vitale:2014mka}. On the same timescale, pulsar-timing arrays will target signals from widely separated massive-BH binaries~\cite{pta}, and on a longer timescale spaced-based detectors will detect these systems at smaller separations, including the binary's merger and ringdown phases. Also, ESA has recently selected GWs as the science theme for its L3 mission with launch slot 2034. One possible mission that would explore this science theme is given by the space-based detector eLISA~\cite{Seoane:2013qna}, whose ``Pathfinder'' mission will be launched in 2015~\cite{pathfinder}. Detectors such as eLISA will estimate the source parameters, and in particular the masses and spins of massive BHs, to within fractions of a percent and up to $z\sim 10-15$~\cite{Seoane:2013qna}, which will permit testing models for the symbiotic coevolution of massive BHs and their host galaxies [see e.g. Refs.~\cite{Sesana:2010wy,Gair:2010bx,berti_volonteri,Barausse:2012fy,Sesana:2014bea}]. Furthermore, GW detectors will allow for precision tests of GR in the currently unexplored highly dynamical, strong-field regime~\cite{Berti:2009kk,Gair:2012nm,Yunes:2013dva}. Estimates of the accuracy of GW detectors in measuring the source parameters usually do not account for the realistic astrophysical environments surrounding the sources --~such as electromagnetic fields, accretion disks and dark matter (DM)~-- based on the expectation/hope that their effect will be negligible. However, a careful examination is needed to assess the environment's impact on GW observables, so as to determine whether precision GW physics is possible at all: unmodeled deviations (due to environmental effects) from the pure ``vacuum'' gravitational waveforms predicted by GR may degrade the signal-to-noise ratio and the parameter estimation accuracy, potentially jeopardizing tests of gravity theories and astrophysical models. On the other hand, if these effects are non-negligible and can be modeled, they may provide important information about the environments of GW sources. This article examines the impact of environmental effects on the most powerful source of GWs, namely the inspiral, merger and ringdown of BH binaries, both with comparable and extreme mass-ratios. Our analysis follows that of Ref.~\cite{longer}, but we focus here in particular on the implications for GW astrophysics with an eLISA-like mission. | \label{sec:conclusions} We have quantified the impact of realistic astrophysical environments on GW signals from BH binaries, including the effect of electromagnetic fields, cosmological evolution, accretion disks and DM. Our analysis shows that GW astronomy has the potential to become a precision discipline, because environmental effects are typically too small to affect the detection of GW signals and the estimation of the source's parameters. The few and rather extreme cases in which environmental effects might leave a detectable imprint should be seen as an opportunity, i.e.~given a sufficiently sensitive detector and adequate modeling of these effects, GW astrophysics can be used to obtain information about the density and velocity of the matter surrounding GW sources. For example, the DM density profile in galactic nuclei is still poorly understood, e.g. DM spikes may grow around the massive BHs dwelling at the center of galaxies~\cite{GS}. Our analysis shows that if these DM spikes survive till $z\sim 0$ (as may be the case in satellite galaxies~\cite{SatelliteHalos}), their effect would be detectable by eLISA in EMRIs, and GW observations could be used to constrain DM profiles near massive BHs (c.f. also Ref.~\cite{silk}). Likewise, the corrections due to accretion disks depend on their geometry and on the accretion rate. EMRIs with exceptionally large SNR could be used to constrain models of accretion onto massive BHs. These intriguing possibilities requires more sophisticated modeling, which is beyond the scope of our analysis. (See however Ref.~\cite{Barausse:2007dy,Macedo:2013qea,Barausse:2006vt,Barausse:2007ph,Yunes:2011ws,Kocsis:2011dr} for some work in this direction.) A quantitative analysis of environmental effects is also vital to allow tests of GR to be performed with GW observations, without mistaking the effect of astrophysical matter for a breakdown of GR. Our results therefore yield intrinsic lower bounds on the magnitude of the deviations from GR that can be tested with space-based GW detectors. Although admittedly approximate, ours is a largely model- and theory-independent analysis. While sufficient for our purposes, more sophisticated modeling (e.g. including the effect of BH spins) would be required to estimate environmental effects from real GW data when they become available. Finally, our analysis has considered enviromental effects on a single source. If the effect under consideration is universal (as would be the case for a modification of gravity), one may enhance eLISA's sensitivity to it by combining different sources. One might try to apply a similar technique to matter effects such as those due to accretion disks, DM, etc. However, in that case the effects may be completely different in different sources, and it is not guaranteed that correlating several sources will help detect them. \subsection* | 14 | 4 | 1404.7140 |
1404 | 1404.0283_arXiv.txt | A number of correlations between observables have been found to exist for gamma-ray burst (GRB) afterglows, linking ejecta energy to prompt and afterglow energy release and linking early stage optical and X-ray luminosity to the end times of these stages. Here, these correlations are compared to thick and thin shell models for GRB afterglows. In the thick shell model, the time evolution of the underlying relativistic blast wave is still influenced by the original ejecta, while in the thin shell model most energy in the explosion has been transferred to the external medium. It is shown here that the observed correlations rule out basic thin shell models but not the basic thick shell model. In the thick shell case, both forward shock and reverse shock dominated outflows are shown to be consistent with the correlations, using randomly generated samples of thick shell model afterglows. | \label{introduction_section} In no small part due to the launch of the \emph{Swift} satellite about ten years ago \citep{Gehrels2004}, the amount of high quality, early time gamma-ray burst (GRB) afterglow data has increased considerably. The \emph{Swift} era has revealed new features that pose additional constraints on theoretical models, such as X-ray plateaus lasting up $10^{3-4}$ seconds for long GRBs \citep{Nousek2006, ZhangBing2006}, where the emission decays more slowly than expected for a decelerating afterglow blast wave. A plateau provides at least a flux level, light curve slope and a turnover time to normal light curve decay that need to be accommodated by any valid model. In addition, more early time optical afterglow data are becoming available from Swift-UVOT and ground based observatories, revealing the existence of a separate early stage in the light curves in these bands as well (see e.g. \citealt{PanaitescuVestrand2008, PanaitescuVestrand2011, Filgas2011, Li2012} for examples), and again implying additional afterglow blast wave evolution in addition to late time deceleration. Optical and X-ray early stages might not necessarily lie in the same spectral regime and therefore yield different constraints. Additionally, a number of recent studies report a series of correlations between various early stage parameters and other burst parameters that might serve to confirm or invalidate our previous notions about the GRB and afterglow mechanism \citep{Dainotti2008, Dainotti2010, Dainotti2011, PanaitescuVestrand2011, Li2012, Dainotti2013, Grupe2013, Margutti2013}. GRB afterglows are expected to be produced by non-thermal emission from highly relativistic outflows. For massive relativistic ejecta, two categories of models can traditionally be identified: those with a \emph{thin} shell and those with a \emph{thick} shell \citep{SariPiran1995, Kobayashi1999, KobayashiSari2000}. An afterglow blast wave shell is considered thin if its initial width is so small that it quickly ceases to leave an imprint on the ejecta dynamics, which will then be dictated by the current ejecta radius and Lorentz factor instead. Specifically, this will occur before the reverse shock (RS), generated by the impact between ejecta and environment and running back into the ejecta, becomes relativistic. For thick shells, the RS will become relativistic during crossing of the ejecta and this will alter the ejecta dynamics. In the collapsar scenario \citep{Woosley1993, MacFadyen1999}, the GRB is the result of the collapse of a massive star into a black hole. In this case, there is no clear mechanism to power outflows for $10^4$ seconds. Unless the ejecta are emitted with a range of Lorentz factors, where slower shells will fall behind faster shells initially before catching up (see e.g. \citealt{Nousek2006, GranotKumar2006}), the initial width of the ejecta will therefore be set by the size of the progenitor system or speed of light $c$ times the duration of the prompt emission. Combined with the ultra-high Lorentz factors that are typically inferred from the prompt emission, this naturally leads to a thin shell scenario where the shell starts to decelerate around $10^2$ s. (in the observer frame), and no plateau-type deviation from a standard decelerating shell afterglow light curve is expected. However, this also assumes that the initial Lorentz factor of the ejecta responsible for the afterglow emission is that of the outflow generating the prompt emission, which is not necessarily the case. For example, the production of a massive slower moving shell (``cocoon'') around the prompt emission outflow is a natural by-product of collapsar jet breakout. This cocoon is expected to be only mildly relativistic (see e.g. \citealt{RamirezRuiz2002, ZhangWeiqun2003, Morsony2007}). While still a thin shell in the previously defined sense, this would lead to an observer frame deceleration time around $10^4$ seconds, similar to the end time of the plateau. Two-component jet models (e.g. \citealt{RamirezRuiz2002, Peng2005, Granot2006}) therefore provide a natural candidate to explain afterglow plateaus (for optical and X-rays examples, see e.g. \citealt{Berger2003, Filgas2011}). Alternatively, the Lorentz factor of the blast wave could have dropped considerably early on due to a high mass density immediately surrounding the progenitor but not extending sufficiently far outward to impact the integrated column density at radii where the majority of afterglow emission takes place (and therefore not affecting the inferred values for afterglow densities from broadband modeling). Other favoured explanations for afterglow plateaus include some form of energy injection into the jet. These can lead to thick shell-type scenario's where the width of the shell is set by the duration of the energy injection, be it through a continuum of sufficiently energetic shells with decreasing Lorentz factor entering the reverse shock or through a continuing source luminosity. A leading candidate for the source of the injection of energy of the latter type is a magnetar, an extremely magnetic and (temporarily) stable neutron star formed at the moment of collapse, that sheds its rotational energy \citep{DuncanThompson1992, Usov1992, Dai1998, ZhangMeszaros2001}. Finally, there are explanations for differing early time afterglow behavior that do not include altering the jet dynamics. Examples of these include time evolution of the microphysics parameters \citep{Granot2006} and viewing angle effects \citep{EichlerGranot2006}. In this study, I discuss the implications of the separate correlations in optical and X-rays between early stage end time $T$ and X-ray and optical luminosities $L_X$ and $L_O$ at this time, and the absence of a clear correlation between break time and total energy, for thick and thin shell scenario's of GRB afterglows. The relevant (non-)correlations are described in section \ref{key_correlations_section}. In section \ref{model_implications_section}, the implications of the correlations for the thick and thin shell models are described, and reverse shock emission in a thick shell scenario is found to be favoured in theory. Section \ref{synthetic_section} explores these implications for randomly sampled synthetic light curves generated from reasonable underlying distributions of the model parameters. In practice, both reverse and forward shock thick shell emission are found to be consistent with the correlations, with the preference for reverse shock emission not sufficient to overcome the noise level in the statistics. Thin shells models remain ruled out. Section \ref{discussion_section} closes off with a summary and additional discussion. | \label{discussion_section} The existence of various correlations between parameters (e.g. luminosity, characteristic break times, fluence) describing GRB prompt emission and afterglow light curves at early and late times, is a striking result that emerges whenever large samples of GRBs are studied. Ideally, these correlations can be used to test model predictions (as done in e.g. \citealt{DadoDar2013}, for ``cannonball'' type models) and distinguish between models capable of reproducing the correlations and those that require either fine-tuning or are falsified altogether. One way of obtaining specific correlations is via introducing time dependency in the parameters describing the microphysics of the radiation (see e.g. \citealt{Granot2006, Hascoet2014} for examples involving $\epsilon_B$, $\epsilon_e$), but this additionally requires an underlying microphysical model justifying the precise nature of the newly introduced physics (e.g. why $\epsilon_e$ depends on circumburst density, not blast wave Lorentz factor, again see \citealt{Hascoet2014}). Here I take a more limited approach and stay with the standard non-changing microphysics assumption for relativistic blast waves in the context of thick and thin shell models. In the thin shell model, the afterglow plateau phase is the result of the pre-deceleration emission from a slower component in a two-component or jet-cocoon type model. For thick shells, the plateaus result from energy injection either in the form of late activity from the source of via additional kinetic energy from slower ejecta catching up with the blast wave, as long as the amount of energy injected remains sufficiently large to allow for a relativistic reverse shock. It is shown that thin shell models can not be reconciled with the observed LTX / LTO correlations between afterglow plateau end time and luminosity and that they imply the existence of a correlation between plateau end time and ejecta energy that is not seen in the data. Basic thin shell models where the underlying physics parameters, explosion energy, circumburst density and ejecta Lorentz factor, remain uncorrelated do not lead to a correlation between time and luminosity, while no three-point correlations between the three physics parameters are possible that can explain both the LTX and LTO correlation even when each of those is shaped by a different dominant emission region or spectral regime. This does not mean that successful data fits using a thin shell model are not possible. In theory, it might even be possible to successfully fit all bursts with plateau stages in this way. However, this study demonstrates that such an effort will inevitably lead to a sample whose properties as a whole can not be explained from the basic thin shell model alone, and within which additional model parameter correlations will have emerged. Thick shell models, on the other hand, can easily reproduce the LTX / LTO correlations across a range of uncorrelated underlying values for the model parameters. They do this so well, in fact, that it is unfortunately difficult to distinguish in this way between forward shock (FS) and reverse shock (RS) emission dominated models, or homogeneous and stellar wind-type environments. By definition, the observed flux is shaped by simultaneous emission from both regions. Whether one region dominates or whether the two contributions are comparable, depends on the values for the model parameters (and possibly on differences in their microphysics parameters, such as $\epsilon_B$). In the case of comparable contributions, the existence of a clear LTX correlation implies that both regions emit in one of the allowed spectral regimes, although not necessarily in the same one. It is tempting to take the falsification of the basic thin shell model in its simple form as an argument against the collapsar nature for GRBs with plateaus in their afterglows, since the traditional single thin shell and two-component jet-cocoon system cannot explain, respectively, the existence of plateaus and the luminosity - time correlations involving plateaus. However, this is likely an overintepretation of an overly simplified model, and collapsar outflows probably involve a range of Lorentz factors that thereby can account for late energy injection into the forward shock, moving the collapsar afterglow predictions into thick shell territory. In any case, the results from this study are certainly consistent with long term energy injection, as expected e.g. from a magnetar model. Thick shell models are capable of reproducing the LTX / LTO correlations independent of the value of $q$, which drops out of the equations at when observing at $T$. An interesting possibility for further study is the potential for FS and RS regions to jointly shape the afterglow light curve and together account for the observed correlations. Especially if the two regions have strongly differing magnetizations, they can dominate the total emission in different spectral regimes (which might account for the lack of correlation between decay slopes in optical and X-rays reported by \citealt{Li2012}). \begin{table} \centering \begin{tabular}{rrrrrr} \hline & & thick & thick & thick & thick \\ & & FS & RS & FS & RS \\ & & ISM & ISM & wind & wind \\ \hline $\left<m\right>$ & LTX & 0.9 & 1.3 & 0.9 & 0.8 \\ & LTO & 0.9 & 0.8 & 2.0 & 1.3 \\ $ \left< \rho \right>$ & LTX & $10^{-2}$ & $10^{-2}$ & $10^{-4}$ & $10^{-3}$ \\ & LTO & $10^{-2}$ & $10^{-2}$ & $10^{-3}$ & $10^{-2}$ \\ & $E-T$ & 0.5 & 0.5 & 0.5 & 0.5 \\ \hline \end{tabular} \caption{Same as table \ref{population_table}, now using $\epsilon_B = 10^{-6}$. } \label{population_B_table} \end{table} \begin{figure} \centering \includegraphics[width=\columnwidth]{regimetiles.eps} \caption{Overview of possible ordering of observation frequencies in optical ($\nu_O$) and X-ray ($\nu_C$), and characteristic frequencies $\nu_m$ (synchrotron injection break) and $\nu_c$ (synchrotron cooling break), for comparison with the burst populations plotted in fig. \ref{numnuc_figure}. Again, the diagonal line marks where $\nu_m = \nu_c$. The left vertical line / lower horizontal line marks the optical observation frequency, the right vertical line / upper horizontal line marks the X-ray frequency.} \label{tiles_figure} \end{figure} If the degree of magnetization is altered, going from $\epsilon_B = 10^{-2}$ to a far lower $10^{-6}$ (see e.g. \citealt{Santana2013} for studies yielding significantly lower afterglow magnetizations than $\epsilon_B \sim 10^{-2}$), the results are as tabulated in table \ref{population_B_table}. The odds of chance correlations increase, but genuine correlations remain likely. On the whole, it becomes slightly harder to reproduce the LTX / LTO correlations from the literature, leading to sample based correlation results and literature LTX / LTO correlations that are sometimes consistent only within their $2 \sigma$ error bars. On the one hand, this indicates that, if a combination of FS and RS emission with different magnetizations is used to explain plateaus, the amount of freedom within parameter space is limited. On the other hand, the fact that going from $\epsilon_B = 10^{-2}$ to an extreme $\epsilon_B = 10^{-6}$ still leaves the thick shell model viable as an explanation for the LTX / LTO correlations at all, is an indication of the robustness of this result. | 14 | 4 | 1404.0283 |
1404 | 1404.6977_arXiv.txt | We discuss the dynamics of extended test bodies for a large class of scalar-tensor theories of gravitation. A covariant multipolar Mathisson-Papapetrou-Dixon type of approach is used to derive the equations of motion in a systematic way for both Jordan and Einstein formulations of these theories. The results obtained provide the framework to experimentally test scalar-tensor theories by means of extended test bodies. | Scalar-tensor theories have a long history and they belong to the most straightforward generalizations of Einstein's general relativity (GR) theory. In the so-called Brans-Dicke theory \cite{Brans:Dicke:1961,Brans:1962:1,Brans:1962:2,Dicke:1962:1,Dicke:1964} a scalar field is introduced as a variable ``gravitational coupling constant'' (which is thus more correctly called a ``gravitational coupling function''). Similar formalisms were developed earlier by Jordan \cite{Jordan:1955,Jordan:1959}, Thiry \cite{Thiry:1951} and their collaborators using the 5-dimensional Kaluza-Klein approach. The interested reader may find more details on the history and developments of scalar-tensor theories in \cite{Fujii:Maeda:2003,Brans:2005,Goenner:2012,Sotiriou:2014}. Surprisingly little attention was paid to the equations of motion of extended test bodies in scalar-tensor theories. Some early discussions can be found in \cite{Brans:1962:2,Bergmann:1968,Wagoner:1970}, and in \cite{Damour:etal:1992} the dynamics of compact bodies was thoroughly studied in the framework of the post-Newtonian formalism. However, the complete system of generalized Mathisson-Papapetrou-Dixon \cite{Mathisson:1937,Papapetrou:1951:3,Dixon:1974,Dixon:1979,Dixon:2008} equations of motion of extended test bodies in scalar-tensor theories was never derived and analyzed. Our paper fills this gap. | We have explicitly worked out the field equations and the equations of motion for extended test bodies for a large-class of scalar-tensor theories, in the Jordan, as well as in the Einstein frame. Our results show that test bodies in the Einstein frame experience additional forces and torques, depending on the particular version of the underlying scalar-tensor theory. The mass of a body is not constant, and its dynamics is determined by the derivative of $\log F$ along a world line. This is consistent with earlier analysis \cite{Damour:etal:1992}. Furthermore, it is interesting to note, that qualitatively the structure of the equations of motion of test bodies in the Einstein frame resembles the one found in theories with nonminimal coupling to matter \cite{Puetzfeld:Obukhov:2013:1,Puetzfeld:Obukhov:2013:2,Puetzfeld:Obukhov:2013:3}. Our general results can be used for the systematic testing of different ``flavors'' of scalar-tensor theories. Together with our previous results in theories with nonminimal coupling \cite{Puetzfeld:Obukhov:2013:1,Puetzfeld:Obukhov:2013:2,Puetzfeld:Obukhov:2013:3}, we have now established the basis for further systematic tests and comparisons of very large classes of gravitational theories by means of extended test bodies. | 14 | 4 | 1404.6977 |
1404 | 1404.1620_arXiv.txt | In this work we investigate the interaction between dark matter and dark energy for a coupling that obeys the Wang-Meng decaying law, $\rho_{{\rm DM}}\propto (1+z)^{3-\epsilon}$, and the Barboza-Alcaniz dark energy parametric model, $w=w_0+w'_0z(1+z)/(1+z^2)$. Theoretically, we show that the coupling constant, $\epsilon$, should satisfy the physical constraint $\epsilon\ge0$. We use the most recent data of type Ia supernovae, baryon acoustic oscillations, cosmic microwave background and the Hubble expansion rate function to constrain the free parameters of the model. From a purely observational point of view, we show that is not possible to discard values of the coupling constant in the unphysical region $\epsilon<0$. We show that the uncoupled case, $\epsilon=0$, is in better agreement with the data than any of coupled models in the physical region. We also find that all physically acceptable interaction in dark sector lies in the narrow range $0<\epsilon\le0.034$ ($95\%$ CL). | In the last 15 years there has been a large amount of observational data coming from Type Ia Supernovae (SNe Ia) \cite{acc_exp}, Cosmic Microwave Radiation Background (CMB) \cite{cmb} and Large Scale Structure (LSS) \cite{lss} shown that the expansion rate of the Universe is increasing. Finding out the causes of this acceleration has been the biggest challenge to cosmologists. In order to keep general relativity untouched, a fluid of negative pressure, dubbed dark energy (DE), must be added to the universe content to yield an acceleration. In this scenario, the cosmological constant proposed by Einstein emerges as the most appealing candidate to DE since it acts on the field equations like a fluid with $p_{\Lambda}=-\rho_{\Lambda}$ and can be associated with the zero point energy of the quantum fields. However, in spite of its agreement with the majority of cosmological data, the cosmological constant leads to a tremendous discrepancy between theory and observation: its observed value is at least $60$ orders of magnitude lower than the theoretical value provided by the quantum field theory \cite {weinberg}. This enormous discrepancy has made DE models beyond the cosmological constant widely studied. Such models presume that some unknown symmetry cancels out the vacuum energy contribution. If the vacuum energy cannot be canceled, another attempt to alleviate the conflict between theory and observation is to assume that the cosmological constant evolves with time. Such an assumption means that dark matter (DM) and the vacuum energy are not conserved separately. Due the success of the cosmological term in explaining the current observations, phenomenological dark energy models, frequently characterized by the ratio between pressure and density, $w\equiv p_{{\rm DE}}/\rho_{{\rm DE}}$, and vacuum decay scenarios are almost always built to get the standard $\Lambda$CDM model as an special case. A most general approach can be achieved by assuming an interaction between DE and DM. In this paper we study an interaction scenario where the DE is described by the equation of state (EoS) parameter \cite{barboza} \begin{equation} \label{EoS} w(z)=w_0+w'_0\frac{z(1+z)}{1+z^2} \end{equation} and the DM density follows the Wang-Meng evolution law \cite{wang-meng}: \begin{equation} \label{wang-meng} \rho_{{\rm DM}}=\rho_{{\rm DM},0}(1+z)^{3-\epsilon}. \end{equation} \noindent In the above equations the subscript $0$ denotes the current value of a quantity, the prime denotes differentiation with respect to the redshift $z$ and $\epsilon$ is a constant that quantifies the matter dilution due the interaction. The main advantage of the EoS parameterization (\ref{EoS}) is that it is a well behaved function of the redshift during the entire history of the universe ($z\in[-1,\infty[$) which allows one to enclose in its functional form the important case of a quintessence scalar field ($-1<w(z)<1$) \cite{quintessence}. By noting that $w(z)$ has absolute extremes in $z_{\pm}=1\pm\sqrt{2}$ corresponding, respectively, to $w_-=w(z_-)=w_0-0.21w'_0$ and $w_+=w(z_+)=w_0+1.21w'_0$, it is possible to divide the parameter space $(w_0,w'_0)$ into defined regions associated with distinct dark energy models which can be confronted with the observational constraints to confirm or rule out a given DE model. For $w'_0>0$, $w_-$ is a minimum and $w_+$ is a maximum and for $w'_0<0$ this is inverted. Since for quintessence and phantom \cite{phantom} scalar fields the EoS is limited by $-1\leq w(z)\leq1$ and $w(z)<-1$, respectively, the region occupied in the $(w_0,w'_0)$ plane by these fields can be determined easily. For quintessence we get $-1\leq w_0-0.21w'_0$ and $w_0+1.21w'_0\leq1$ if $w'_0>0$ and $-1\leq w_0+1.21w'_0$ and $w_0-0.21w'_0\leq1$ if $w'_0<0$. For phantom fields we get $w'_0<-(1+w_0)/1.21$ if $w'_0>0$ and $w'_0>(1+w_0)/0.21$ if $w'_0<0$. Points out of these bounds corresponds to DE models that have crossed or will cross the phantom divide line. This {\it paper} is organized as follows: in Section II the basic equations employed in the analysis are developed; in Section III the constraints on the parameters $w_0$, $w'_0$ and $\varepsilon$ are obtained observationally from current SNe Ia, BAO, $H(z)$ and CMB data; in Section IV we obtain the quintessence and phantom scalar field description for the model under consideration and in Section V we present our conclusions and final comments. \begin{figure*}[t] \centerline{\psfig{figure=cl.ps,width=7.4truein,height=3.0truein,angle=270} \hskip 0.1in} \caption{The $w_0-\epsilon$ (left) and $w_0-w'_0$ (right) parametric spaces. The blank regions in the $w_0-w'_0$ plane indicate models that at some point of the cosmic evolution have switched or will switch from quintessence to phantom behaviors or vice-versa. The Early DE region corresponds to the region where DE dominates over matter in early times. The dashed contours in the $w_0-w'_0$ plane are the ones obtained when we allow that $\epsilon<0$. The contours are drawn for $\Delta \chi^2 = 2.30$ and 6.17.\label{fig:1}} \end{figure*} | 14 | 4 | 1404.1620 |
|
1404 | 1404.1402_arXiv.txt | We present ALMA Cycle-0 observations of the CO~(6-5) line emission (rest-frame frequency = 691.473 GHz) and of the 435$\mu m$ dust continuum emission in the nuclear region of NGC~34, a local luminous infrared galaxy (LIRG) at a distance of 84~Mpc ($\rm 1\arcsec = 407\; pc$) which contains a Seyfert~2 active galactic nucleus (AGN) and a nuclear starburst. The CO emission is well resolved by the ALMA beam ($\rm 0\farcs26\times 0\farcs23$), with an integrated flux of $\rm f_{CO~(6-5)} = 1004\; (\pm 151) \; Jy\; km\; s^{-1}$. Both the morphology and kinematics of the CO~(6-5) emission are rather regular, consistent with a compact rotating disk with a size of 200 pc. A significant emission feature is detected on the red-shifted wing of the line profile at the frequency of the $\rm H^{13}CN\; (8-7)$ line, with an integrated flux of $\rm 17.7 \pm 2.1 (random) \pm 2.7 (sysmatic)\; Jy\;km\; s^{-1}$. However, it cannot be ruled out that the feature is due to an outflow of warm dense gas with a mean velocity of $\rm 400\; km\; s^{-1}$. The continuum is resolved into an elongated configuration, and the observed flux corresponds to a dust mass of $\rm M_{dust} = 10^{6.97\pm 0.13}\; M_\sun$. An unresolved central core ($\rm radius \simeq 50\; pc$) contributes $28\%$ of the continuum flux and $19\%$ of the CO~(6-5) flux, consistent with insignificant contributions of the AGN to both emissions. Both the CO~(6-5) and continuum spatial distributions suggest a very high gas column density ($\rm \gsim 10^4\; M_\sun\; pc^{-2}$) in the nuclear region at $\rm radius \lsim 100\; pc$. | \begin{deluxetable*}{cccccccc} \tabletypesize{\normalsize} \setlength{\tabcolsep}{0.05in} % \tablecaption{ALMA Observations \label{tbl:obs}} \tablehead{ {SB} & Date & {Time (UTC)} & {Config} & {$\rm N_{ant}$} & {$\rm l_{max}$} & {$\rm t_{int}$} & {$\rm T_{sys}$}\\ & (yyyy/mm/dd) & & & & (m) & {(min)} & {(K)}\\ {(1)} & {(2)} & {(3)} & {(4)} & {(5)} & {(6)} & {(7)} & {(8)} } \startdata X40e374\_Xba3 & 2012/05/20 & 09:17:15 -- 10:35:34 & E & 16 & 375&24.7 &850 \\ X40e374\_Xd36 & 2012/05/20 & 10:48:14 -- 12:06:33 & E & 16 & 375&24.7 &653 \\ X40e374\_Xec9 & 2012/05/20 & 12:22:31 -- 13:07:05 & E & 16 & 375& 9.9 &654 \\ X41065b\_X334 & 2012/05/21 & 09:47:04 -- 11:06:00 & E & 16 & 375&24.7 &634 \\ X41065b\_X4c7 & 2012/05/21 & 11:20:00 -- 10:41:09 & E & 16 & 375&24.7 &528 \\ X4afc39\_X43b & 2012/08/25 & 03:30:38 -- 05:01:41 &E\&C&27 & 402&24.7 &1058 \enddata \tablecomments{Column (1) -- schedule-block number; (2) \& (3) -- observation date and time; (4) -- configuration; (5) -- number of antennae; (6) -- maximum baseline length; (7) -- on-target integration time; (8) -- median $\rm T_{sys}$. } \end{deluxetable*} Luminous infrared galaxies (LIRGs: $\rm L_{IR} [8 \hbox{--} 1000\mu m] > 10^{11} \; L_\sun$), including ultra-luminous infrared galaxies (ULIRGs: $\rm L_{IR} > 10^{12}\; L_\sun$), have a space density exceeding that of optically selected starburst and Seyfert galaxies at comparable bolometric luminosity \citep{Soifer1987}. They are an ensemble of single galaxies, galaxy pairs, interacting systems and advanced mergers \citep{Sanders1996, Wang2006}. Most (U)LIRGs of $\rm L_{IR} \gsim 10^{11.5}\; L_\sun$ are advanced mergers (including merger remnants), harboring extreme starbursts (star formation rate (SFR) $\rm \gsim 50\; M_\sun\; yr^{-1}$) and powerful AGNs \citep{Kim2002}. \citet{Toomre1978} was the first to suggest that merging can transform spirals into ellipticals, a theory that has been borne out observationally \citep{Schweizer1982, Genzel2001}. Strong outflows of neutral and ionized gas were widely detected among (U)LIRGs \citep{Armus1990, Heckman1990, Rupke2005}. Recently, massive molecular gas outflows have been found in (U)LIRGs with powerful AGNs \citep{Fischer2010, Feruglio2010, Sturm2011, Aalto2012b, Veilleux2013, Feruglio2013, Combes2013, Cicone2014}. Hence, feedback from merger induced extreme starbursts and AGNs is the most popular mechanism for explaining the star formation quenching in massive galaxies that lead to the formation of red sequence galaxies \citep{Faber2007, Hopkins2008a}, and (U)LIRGs are the best local laboratories for studying these processes. However, due to the enormous dust obscuration in (U)LIRGs \citep{Sanders1996}, it is very difficult to study them using high angular resolution optical/NIR instruments. Observations using space FIR/sub-mm observatories, such as Spitzer \citep{Werner2004} and Herschel \citep{Pilbratt2010}, can penetrate the dust obscuration. However, their angular resolutions ($\gsim$ a few arcsecs) are not sufficient to resolve the nuclei in most (U)LIRGs. The Atacama Large Millimeter Array (ALMA; \citealt{Wootten2009}) is changing the situation rapidly. Once completed, sub-mm/mm observations using the ALMA full array (66 antennae) will detect both the line emission of gas and the continuum emission of dust (heated either by starburst or AGN, or both) with an angular resolution of $\lsim 0.1''$, revealing interplays between gas, starbursts and AGNs in (U)LIRG nuclei down to linear scales of $\sim$ 10 pc in the nearest systems. In this paper, we report ALMA Cycle-0 observations (utilizing up to 27 antennae) of the CO~(6-5) line (rest-frame frequency = 691.473 GHz) emission and of 435$\mu m$ dust continuum emission in the nuclear region of NGC~34, a local LIRG ($\rm L_{IR} = 10^{11.49}\; L_\sun$, \citealt{Armus2009}) containing a Sy2 AGN and a nuclear starburst (see \citealt{Schweizer2007} for an overview). With an excitation temperature of $\rm T_{ex} = 116.2\; K$ and a critical density of $\rm n_{crit} = 2.9\times 10^{5}\; cm^{-3}$ \citep{Carilli2013}, the CO~(6-5) line probes the warm and dense gas that is much more closely related to the star formation activities than the cold and lower density gas probed by low J CO lines (e.g. CO~(1-0) and CO~(2-1)) commonly studied in the literature. Among the complete sample of 202 LIRGs of the Great Observatories All-sky LIRG Survey (GOALS; \citealt{Armus2009}), which were selected from the IRAS Revised Bright Galaxy Sample (RBGS; \citealt{Sanders2003}), NGC~34 (also known as NGC~17, Mrk~938, and IRAS~F00085-1223) was chosen for early ALMA observations because of the following features: (1) Among LIRGs that have the CO~(6-5) line flux $\rm f_{CO~(6-5)} \geq 1000\; Jy\; km\; s^{-1}$ observed in the the Herschel SPIRE Fourier Transform Spectrometer (FTS) survey of GOALS galaxies (angular resolution: $\sim 30''$; van~der~Werf et al., in preparation; Lu et al., in preparation), it is one of the closest with a distance of $\rm D = 84$ Mpc ($\rm 1'' = 407 pc$). This enables high signal-to-noise ratio observations of warm gas structures with the best linear resolution for a given angular resolution. (2) With a declination of $-12^\circ$, NGC~34 transits at $\sim 11^\circ$ from the zenith, therefore its Band 9 observations are affected by minimal atmospheric absorption. (3) The Keck-MIRLIN images of \citet{Gorjian2004} detected $\gsim 50\%$ of the 12$\mu m$ IRAS flux in the central $\sim 1$ kpc region of NGC~34, indicating strong nuclear star formation and/or AGN activities. Early observations of the CO~(6-5) emission in nearby starburst galaxies NGC~253, IC~342 and M~82 \citep{Harris1991} showed that the molecular gas in starbursts is warmer than in normal disk galaxies. \citet{Papadopoulos2012} carried out an extensive survey for higher J CO lines, including the CO~(6-5) line, for LIRGs using JCMT and found many of them have the global CO spectral line energy distribution (SLED) dominated by a very warm ($\rm T \sim 100 K$) and dense ($\rm n \geq 10^4\; cm^{−3}$) gas phase. The CO~(6-5) map of the central region of Arp~220 obtained by \citet{Matsushita2009} using the SMA has an angular resolution of $\sim 1\arcsec$ ($\rm \sim 400\; pc$), revealing two warm gas components associated with the two nuclei (separation $\rm \sim 400\; pc$), but the data were unable to resolve the individual components. The SMA observations of the CO~(6-5) line emission of VV~114 \citep{Sliwa2013} has a relatively coarse resolution of $\rm 2\farcs5$ ($\rm \gsim 1\; kpc$). The new ALMA observations reported here, with an angular resolution of $\rm \sim 0\farcs25$, resolved the warm and dense gas in the nuclear region of a LIRG with a linear resolution of $\sim 100$ pc for the first time. We aim to answer the following questions with these observations: (1) How is the warm dense molecular gas distributed in the inner most region of NGC~34? (2) How is the gas related to the starburst and the AGN, respectively? (3) Is the dust emission dominated by an extended component, or by an unresolved compact component? (4) Is there evidence for a molecular outflow? Comparing with the extensive literature on NGC~34 (a late stage major-merger, \citealt{Mazzarella1993, Schweizer2007}) and with high-resolution simulations \citep{Hopkins2013a}, our results shed new light on how various activities and their feedback set the stage for a major-merger remnant to become a red-and-dead elliptical galaxy \citep{Zubovas2012}. | \label{sect:summary} The CO~(6-5) line emission in the central region of NGC~34 ($\rm radius \lsim 500\; pc$) is well resolved by the ALMA beam ($\rm 0\farcs26\times 0\farcs23$). This is the first time the warm and dense gas in the nuclear region of a LIRG is resolved with a linear resolution of $\sim 100$ pc. Both the morphology and kinematics of the CO~(6-5) line emission are rather regular, consistent with a compact rotating disk which has a FWHM size of 200~pc and extends to a radius of $\rm r = 320\; pc$. The integrated CO~(6-5) line flux of the disk is $\rm f_{CO~(6-5)} = 1004 (\pm 151) \; Jy\; km\; s^{-1}$, recovering all the single dish CO~(6-5) line flux of NGC~34 measured by Herschel. The line profile shows a double-horn shape, with a FWHM of $\rm 406\; km\; s^{-1}$. A significant emission feature is detected on the red-shifted wing of the profile, coincident with the frequency of the $\rm H^{13}CN\; (8-7)$ line emission (rest-frame frequency = 690.552 GHz), with an integrated flux of $\rm 17.7 \pm 2.1 (random) \pm 2.7 (sysmatic)\; Jy\;km\; s^{-1}$. However, it cannot be ruled out that the feature is due to an outflow of warm dense gas with a mean velocity of $\rm 400\; km\; s^{-1}$. The $\rm 435\; \mu m$ continuum emission is resolved into an elongated configuration ($\rm P.A. =315^\circ$). The flux is $\rm f_{435\mu m} = 275\; (\pm 41) \; mJy$ ($53\pm 8 \%$ of the total 435$\mu m$ flux derived from Herschel observations), corresponding to a dust mass of $\rm M_{dust} = 10^{6.97\pm 0.13}\; M_\sun$. An unresolved central core ($\rm radius \simeq 50\; pc$) contributes $28\%$ of the continuum flux and $19\%$ of the CO~(6-5) flux detected by ALMA, consistent with insignificant contributions of the AGN to both emissions. The CO~(6-5) disk is a factor of 6 smaller than the CO~(1-0) disk found by \citet{Fernandez2014}. Comparison with radio continuum suggests that the nuclear starburst has about the same distribution of the warm and dense gas probed by CO~(6-5), while much of the diffuse gas probed by CO~(1-0) is not associated with star formation. Both the CO~(6-5) line and continuum distributions indicate a very high gas column density ($\rm \gsim 10^4\; M_\sun\; pc^{-2}$) in the nuclear region ($\rm radius \lsim 100\; pc$), consistent with the extremely high SFR density found in the same region. \vskip1truecm \noindent{\it Acknowledgments}: CKX acknowledges useful discussions with George Privon, Eckard Sturm, Francois Schweizer, and Ximena Fernandez. Kim Scott and Tony Remijan from NAASC are thanked for their helps on data reduction. Y.G. is partially supported by NSFC-11173059, NSFC-11390373, and CAS-XDB09000000. Y.Z. thanks the NSF of Jiangsu Province for partial support under grant BK2011888. V.C. would like to acknowledge partial support from the EU FP7 Grant PIRSES-GA-2012-316788. This paper makes use of the following ALMA data: ADS/JAO.ALMA-2011.0.00182.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. This research has made extensive use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. | 14 | 4 | 1404.1402 |
1404 | 1404.3631_arXiv.txt | {We study the resonant decay of the Higgs condensate into weak gauge bosons after inflation and estimate the corrections arising from the non-Abelian self-interactions of the gauge fields. We find that non-Abelian interaction terms induce an effective mass which tends to shut down the resonance. For the broad resonance relevant for the Standard Model Higgs the produced gauge particles backreact on the dynamics of the Higgs condensate before the non-Abelian terms grow large. The non-Abelian terms can however significantly affect the final stages of the resonance after the backreaction. In the narrow resonance regime, which may be important for extensions of the Standard Model, the non-Abelian terms affect already the linear stage and terminate the resonance before the Higgs condensate is affected by the backreaction of decay products.} | The measured Higgs mass in the range $M_{h}=125-126$ GeV \cite{ATLAS:2012ae,Chatrchyan:2012tx} ensures vacuum stability within the Standard Model (SM) up to very high energies -- orders of magnitude above the electroweak scale. In particular, for top masses sufficiently below the best fit value the SM remains stable up to $\rho_{\rm inf}^{1/4}\sim 10^{16}$ GeV. Assuming the detection of primordial gravitational waves by BICEP2 \cite{Ade:2014xna} will be confirmed, this is the energy scale of inflation. If the Standard Model is not significantly affected by new physics at these scales, one generically predicts that the Higgs is a light field during inflation ($m_{h}^2\ll H^2$) with a negligible contribution to the total energy density \cite{DeSimone:2012qr,Enqvist:2013kaa}. As a light field, during inflation the Standard Model Higgs acquires long-wavelength fluctuations which in general render the local Higgs value, averaged over the observable patch, different from the field value at the minimum of the potential. Small modifications of the SM Higgs potential, such as adding a non-minimal Higgs-gravity coupling of the form $\xi H^{\dag}H R$, are not expected to change the qualitative picture. On the other hand, it is well known that with an exceptionally large coupling, ($\xi \gg 1$), inflation might be realized with the Higgs field itself \cite{Bezrukov:2007ep}. The predicted tensor-to-scalar ratio of the Higgs inflation, $r=0.0033$ \cite{Bezrukov:2007ep}, is however significantly below the reported detection of $r=0.20^{+0.07}_{-0.05}$ by BICEP2, although the level $r\sim0.2$ could be achieved for a very specific choice of the SM parameters (see e.g. \cite{Bezrukov:2014bra,Masina:2014yga,Hamada:2014iga,Cook:2014dga}). After inflation the observable patch of the universe is filled by an effective Higgs condensate with small fluctuations around the homogeneous background value. For the non-minimally coupled Higgs inflaton the condensate dominates the energy density. If the non-minial coupling is small (or zero), the energy density is dominated by a non-Standard Model inflaton(s) (or its decay products) while the Higgs condensate constitutes only a tiny fraction of the total energy density. The Higgs fluctuations can however be imprinted on metric perturbations even in this case if the Higgs value affects the expansion history, for example through a modulation of the inflaton decay rate \cite{Dvali:2003em,Dvali:2003ar,Choi:2012cp}. The dominant decay process of both the Standard Model Higgs and the non-minimally coupled Higgs at zero temperature is the non-perturbative production of weak gauge bosons from the oscillating Higgs condensate \cite{Enqvist:2013kaa,Bezrukov:2008ut, GarciaBellido:2008ab}. However, so far the non-Abelian self-couplings of the SU$(2)$ gauge bosons have been neglected. In investigating the resonant Higgs decay, the gauge fields have been treated as if they were Abelian. While this arguably could be justified at the onset of the resonance, the non-Abelian interactions eventually become important as the number density of the resonantly produced gauge field quanta grows large. This can have a significant impact on the duration and efficiency of the resonance. In this work we investigate the non-perturbative decay of the Standard Model Higgs into weak gauge bosons accounting for the non-Abelian terms. Our primary goal is to estimate the time at which the non-Abelian terms become significant for the dynamics of the resonance. This should be compared with the time when the gauge field induced mass for the Higgs, given by $m_{\rm ind}^2\sim g^2 \langle A^2\rangle$, becomes comparable to the effective mass $\mosc^2\sim \lambda a^2h^2$ due to the Higgs amplitude $h$. The time at which $m_{\rm ind}\gtrsim \mosc$ yields an estimate for the beginning of backreaction of the resonantly produced gauge fields, which eventually shuts down the resonance \cite{Kofman:1997yn,Greene:1997fu}. If the non-Abelian terms were to start to influence the gauge field dynamics when $m_{\rm ind}\ll \mosc$, the Abelian approximation would fail already in describing the linear stage of the resonance before the onset of backreaction. We find that this is generically the case for the narrow resonance. In the regime of broad resonance the Abelian approximation fails and the non-Abelian terms grow large very soon after the linear stage of the resonance. The non-Abelian terms will therefore play a significant role in the subsequent non-linear regime after the backreaction. The non-Abelian terms can therefore significantly affect the decay of the Higgs condensate in the early universe. The paper is organized as follows. In Section~\ref{sec:2} we outline the initial conditions set by inflation and write down the relevant equations. In Section~\ref{sec:3} we describe resonant production of weak gauge bosons from an oscillating Higgs condensate for the Standard Model parameters and estimate the non-Abelian effects. In Section~\ref{sec:4} we focus on the narrow resonance which requires physics beyond the Standard Model. We conclude in Section~\ref{sec:5} with a discussion of the results and their implications. | 14 | 4 | 1404.3631 |
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1404 | 1404.4682_arXiv.txt | We describe the arrival time measurements and timing modeling of the periodic radio flares and optical brightness variations of the M9 ultracool dwarf, TVLM 513-46546. We confirm the stability of the observed period and determine its best-fit value to be 7054.468$\pm$0.007 s over the last 7 years, based on both the new and archival radio observations and the archival optical data. The period, when measured separately for the radio flare and the optical periodicities, is the same to within $\pm$0.02 s. We show that the radio flares are out of phase with respect to the optical brightness maxima by 0.41$\pm$0.02 of the period. Our analysis also reveals that, on shorter timescales, the period varies with the amplitude of $\pm$1-2 s about its long-term average and that these variations are correlated between the radio and the optical wavelengths. These results provide further evidence that TVLM 513-46546 is equipped with a stable, approximately dipolar magnetic field which powers the activity of the star observed over a wide wavelength range, and that the active area has been maintaining its identity and positional stability over no less than 7 years. A stepwise decline of the apparent radio flaring period of TVLM 513-46546 deduced from timing observations with the Arecibo radio telescope in late 2012 and early 2013 suggests that this effect may be the manifestation of differential rotation of the star. | Magnetic fields and rotation play an essential role in determining the internal structure and evolution of fully convective, very low mass stars and brown dwarfs (e.g. Mohanty et al. 2006; Browning 2008; McLean et al. 2012). However, despite the significant progress in our understanding of the magnetic properties of stars at the bottom of the main sequence, it remains unclear, how does the magnetic dynamo operate in these objects, and how is the magnetic energy released and conducted through their largely neutral atmospheres (Mohanty 2002; Berger et al. 2010; Reiners \& Basri 2010). In this context, radio detections of brown dwarfs and very low-mass stars cooler than the M7 spectral type, commonly referred to as the ultracool dwarfs (UCDs; Kirkpatrick et al. 1997), are important, because it is the radio emission from the UCDs, especially from the coolest ones, that provides the most direct means to diagnose their magnetic fields, trace the field geometry, and test its coupling to stellar atmospheres. Observations of circularly polarized, periodic radio emission from some UCDs, when interpreted in terms of the electron cyclotron maser mechanism (ECM, Treumann 2006, and references therein), indicate the presence of large-scale magnetic fields in these objects (Hallinan et al. 2006, 2008; McLean et al. 2011). The fields appear to have a strong, one to a few kG, dipole component (Hallinan et al. 2008), but more complicated geometries are also possible (Berger et al. 2009). Radio emitting UCDs include examples of five periodically varying sources, three of which, TVLM 513-46546 (Hallinan et al. 2006), 2MASSW J0746425+200032 (Berger et al. 2009), and LSR J1835+3259 (Hallinan et al. 2008), emit short duration, periodic outbursts that make them vaguely ``pulsar-like", because of this behavior. The other two, 2M J00361617+1821104 (Hallinan et al. 2008), and 2M J13142039+130011 (McLean et al. 2011) exhibit much slower, periodic variations, which, at least in the case of 2M J00361617+1821104, can be interpreted as longer duration pulses or flares. Each of the first four objects has nearly identical periodicity in its radio and optical components (Lane et al. 2007; Littlefair et al. 2008; Berger et al. 2009; Harding et al. 2013). Long term, precise monitoring of the stability of such periodicities provides a direct way to determine timescales for the corresponding magnetic field stability of the UCDs, which is yet another critical constraint that needs to be established in the quest to understand the physics of these objects (e.g. Osten et al. 2006; McLean et al. 2011; Harding et al. 2013). We have conducted a series of observations of radio flares from one of these dwarfs, TVLM 513-46546 (hereafter TVLM 513), to investigate its periodic behavior with the aid of the timing method. We have been guided by the idea that timing measurements of periodically flaring UCDs can be used to study their physics, very much like the pulsar timing has been used as a tool to study a variety of phenomena in physics and astrophysics, including the neutron stars themselves (e.g. Blandford et al. 1992). In principle, this approach should provide a higher precision alternative to the methods of period stability analysis of TVLM 513 and other UCDs employed in the past (e.g. Doyle et al. 2010; Harding et al. 2013). We have also examined a selection of the published radio and optical measurements of TVLM 513 (Berger et al. 2008; Doyle et al. 2010; Harding et al. 2013) in an effort to phase-connect the flares from this star detected in the past with our more recent observations. In this paper, we report the initial results of the timing monitoring program of TVLM 513 with the Arecibo radio telescope. Also, by combining our measurements with the published data, we reassess the stability of the flaring period and the nature of the observed activity of this UCD. Observations, data analysis and timing models of the radio and the optical brightness variations of the star are described in Sections 2 and 3. In Section 4, we discuss the timing results of radio flares and the periodic optical variability of TVLM 513 since 2006, and suggest an explanation of its timing behavior over $\sim$200 days in 2012 and 2013. Our conclusions are presented in Section 5. | In this paper, we demonstrate that the timing method, when applied to the periodic variations observed in the brightness of the ultracool dwarf, TVLM 513-46546, makes it possible to measure the period, detect its temporal evolution, and model it with the precision surpassing that of the techniques used in the past by an order of magnitude. This is because a modeling process that uses the TOAs of periodic brightness maxima deals with a cumulative error in phase, which makes it possible to measure very small deviations of model parameters from their correct values, given a sufficient timespan of the data (e.g. Lorimer \& Kramer 2005). We show that the behavior of the apparent period of TVLM 513 measured over the 7-year span of the available radio and optical data is adequately described by the long-term, average value of 7054.47 s, representing the star's rapid rotation, and the superimposed month-to-year timescale, $\sim$2 s variations, possibly due to the changing geometry of the emission region created by stellar magnetic activity. An upper limit to the fractional stability of the period, computed from the timing model of the entire dataset involving the period and its first time derivative, amounts to $\le$10$^{-5}$. Despite the fact that this value must still be biased by the observed shorter timescale period variations, it provides a useful quantification of the period stability of TVLM 513 and the related stability of its magnetic field deduced from earlier period measurements (Harding et al. 2013) and from the observed persistence of the star's radio emission (Hallinan et al. 2006; Hallinan et al. 2007; Doyle et al. 2010). Our analysis also reveals that the best-fit, long-term averaged period values computed separately from the optical and the radio measurements of TVLM 513 are practically the same. In addition, the TOA variations of brightness maxima observed in the two wavelength ranges are highly correlated but the radio peaks lead the optical ones by 0.4 of the period. Including this effect in the timing modeling shows that the phase offset has been maintained over the 7-year time baseline of the data to within 5\%. These new results point to a common origin of the observed radio and optical activity of TVLM 513, which must be powered by the star's approximately dipolar magnetic field. The deviation of the measured phase offset from its 0.5 value for the magnetic dipole is probably due to the field geometry not being exactly dipolar, or to the location of the active region with respect to the line of sight, or both. Finally, our modeling of the high cadence timing observations of TVLM 513 made over 200 days in 2012 and 2013 clearly shows that the apparent period of radio flares from the star has been gradually becoming shorter, with the process being interrupted by small but easily detectable phase jumps in flare arrival times. We suggest that this phenomenon may be caused by a combination of a slow migration of the magnetically active region with the differential rotation of the star, in analogy to the well-known behavior of spots on the Sun and other stars. In fact, single measurements of stellar rotation scattered over time reveal period variations caused by a ``randomizing'' effect of a changing spot coverage of the star combined with its differential rotation (e.g. Henry et al. 1995; Barnes et al. 2005). Our work suggests that it should be possible to track the behavior of active regions in the magnetospheres of periodically flaring UCDs by means of multiwavelength timing of their brightness variations. If the active regions behave like stellar spots, it may be possible to use such measurements to monitor changes in the geometry of magnetically active areas and map their differential rotation in unprecedented detail. Overall, our results demonstrate that future timing measurements of TVLM 513 and other periodically varying ultracool dwarfs will definitely be of great value in the process of improving our understanding of the physics of these fascinating objects. | 14 | 4 | 1404.4682 |
1404 | 1404.1772_arXiv.txt | {% A simple analytical relation of form $\alpha=2\kappa-1$ between the magnetic energy spectral exponent $\alpha$ of the turbulent magnetic field in the solar photosphere and its magnetic flux cancellation exponent $\kappa$, valid under certain restrictive assumptions, is tested and extended outside its range of validity in a series of Monte Carlo simulations. In these numerical tests artificial ``magnetograms'' are constructed in 1D and 2D by superposing a discrete set of Fourier modes of the magnetic field distribution with amplitudes following a power law spectrum and measuring the cancellation function on these simulated magnetograms. Our results confirm the validity of the analytical relation and extend it to the domain $\alpha<-1$ where $\kappa\rightarrow 0$ as $\alpha\rightarrow -\infty$. The observationally derived upper limit of 0.38 on $\kappa$ implies $\alpha<-0.24$ in the granular size range, apparently at odds with a small scale dynamo driven in the inertial range. } | The structure of the magnetic field in the solar photosphere is still far from being fully understood (for reviews see de Wijn et al. 2007, Mart\'{\i}nez Pillet 2012). The two main methods of studying solar magnetism are based on the Zeeman and Hanle effects, respectively. As the above mentioned effects display different sensitivity to various field configurations depending on their amplitude and spatial organization, we have a dichotomic view of the magnetism of the solar photosphere. The basic properties of the magnetic network, consisting of kilogauss strength flux tubes, have been clarified by longitudinal Zeeman magnetometry decades ago. The contribution of these elements to the large scale unsigned flux density $\Babs$ typically does not exceed a few Gauss in quiet sun regions. Yet the analysis of the Hanle effect depolarization of spectral lines indicates that the total value of $\Babs$ is well in excess of 100\,G (Trujillo Bueno et al. 2004). Most of this flux was, then, previously hidden to traditional Zeeman magnetometry, presumably due to its fine scale turbulent structuring that leads to the cancellation of the net Zeeman polarization signal inside a resolution element. It has long been suspected that the sporadic internetwork (IN) magnetic flux concentrations seen in longitudinal magnetograms represent the observable part of this hidden or turbulent magnetic field. Recent improvement in the resolution and sensitivity of polarimeters, in particular the SDO/HMI {\revone (Solar Dynamics Observatory/Helioseismic and Magnetic Imager)}, Hinode/SP {\revone (Spectropolarimeter)} and Sunrise/IMaX {\revone (Imaging Magnetograph eXperiment)} instruments, have led to a breakthrough in the 3D vector polarimetry of the photospheric magnetic field, clearly demonstrating the presence of a large number of IN flux concentrations. In contrast to the nearly vertical, kG network flux tubes, these IN concentrations only reach hectogauss field strengths and their orientation may be either more or less horizontal or vertical. Statistically, the distribution of magnetic field orientations in this turbulent field seems to be more or less isotropic, perhaps with some (currently debated) preference towards the horizontal direction. Given that this observed IN field now represents a non-negligible fraction of the formerly ``hidden'' turbulent flux, its detection offers a unique chance to empirically study MHD turbulence in a compressible, stratified plasma. In this respect, recent studies of the {\it cancellation function}{\revone ,} $\chi(l_0)${\revone ,} of the photospheric magnetic field are of interest. {\revone The function} $\chi(l_0)$ is defined as the unsigned flux density $\Babs$ seen at a finite resolution $l_0$ in a longitudinal magnetogram, normalized to the intrinsic total unsigned flux density $\Babs_0$: \begin{equation} \chi(l_0)=\Babs(l_0)/\Babs_0. \end{equation} \noindent Analyzing a Hinode{\revone /}SP magnetogram, Pietarila Graham, Danilovic and Sch\"ussler (2009) found that the shape of the cancellation function is a power law $\chi(l_0)\propto l_0^{-\kappa}$ in the range 0.2 to 20 Mm, with $\kappa=0.26$. The analysis was repeated by Stenflo (2011) upon recalibrating the magnetogram, yielding a value $\kappa=0.127$, independently confirmed also by the analysis of Hinode{\revone /}NFI magnetograms. Recently, Pietarila and Pietarila Graham (2012) have made an extensive comparative analysis of the cancellation functions resulting from SoHO/MDI, SDO/HMI and Hinode/SP magnetograms, finding that the derived $\kappa$ values are heavily influenced by instrument noise, seeing effects, net flux imbalance in the field and by the proper exclusion of field components not belonging to the turbulent field (such as netwok elements). They find that the $\kappa$ values derived for quiet regions decrease with improving instrument quality, i.e. along the MDI $\rightarrow$ HMI $\rightarrow$ SP series, so that the SP value of 0.38 can be considered a conservative upper bound for the true value of the cancellation exponent. Lower values reported in earlier studies were apparently due to improper masking of network fields and/or the use of fields of view with a higher flux imbalance (i.e. less typical quiet sun areas). As the most important theoretical tool in the study of the scaling behaviour of turbulent flows is the energy spectral function, the question naturally arises how $\chi({\revone l_0})$ is related to the magnetic energy spectral function, written as $E_k\sim k^\alpha$? In Section 2 we derive a simple analytical relation between the cancellation exponent{\revone ,} $\kappa${\revone ,} and the spectral exponent{\revone ,} $\alpha$, valid under some assumptions. The relation is extended beyond the limit of validity of the analytic formula in a set of Monte Carlo simulations in Section 3. Conclusions are drawn in Section 4. \begin{figure}[!t] \includegraphics[width=\columnwidth,height=50mm]{marschalkog_fig1} \caption{Cancellation exponent $\kappa$ as a function of the magnetic energy spectral exponent $\alpha$ in the 1D case, with the analitically derived relation (dashed line). } \label{label1} \end{figure} | Under the assumption of a self-similar (fractal) magnetic field structure we have derived a simple analytical relationship, equation (\ref{eq:analrel}), between $\kappa$ and $\alpha$. The relation is expected to be valid for $\alpha>-1$. The relation is tested and extended outside its range of validity in a series of Monte Carlo simulations. In these numerical tests artificial ``magnetograms'' are constructed in 1D and 2D by superposing a discrete set of Fourier modes of the magnetic field distribution with amplitudes following a power law spectrum and measuring the cancellation function on these simulated magnetograms. Our results confirm the validity of the analytical relation and extend it to the domain $\alpha<-1$ where $\kappa\rightarrow 0$ with decreasing $\alpha$ values. The observationally derived upper limit of 0.38 on $\kappa$ implies $\alpha<-0.24$. The lowest $\kappa$ values detected in any magnetogram field to date would correspond to $\alpha\simeq -0.95$. These findings provide evidence that the magnetic energy spectral function is a decreasing function of wavenumber in the granular size range (0.2 to 20 Mm), in contrast to the prediction of small scale dynamo simulations where $\alpha>0$ is found (Schekochihin et al. 2007, Pietarila Graham et al. 2010). The limits we derived do not exclude the possibility of an $\alpha=-1$ spectrum which is the hallmark of a larger scale field being passively advected by turbulent motions. This might indicate that the photospheric turbulent magnetic field results from passive field amplification; however, in this case we would expect $\Babs\sim|\langle B\rangle|$ which is not observed (Lites 2011). This suggests that the turbulent magnetic field in the solar photosphere does originate in a dynamo but this dynamo does not operate in the inertial range as in current simulations but rather at or above the integral scale. This may be due to the fact the magnetic Prandtl number $P_m$ in the solar plasma is much lower than in current numerical simulations. There are indications that at such low values of{\revone ,} $P_m${\revone ,} the critical magnetic Reynolds number{\revone ,} $R_m${\revone ,} for dynamo action is much higher than for $P_m\simeq 1${\revone ,} which may impede the operation of an inertial range dynamo. At larger scales, however, $R_m$ may be high enough to drive a dynamo; or alternatively a small scale dynamo driven by a fundamentally different process might be at work at or above the integral scale. Our constraints on $\alpha$ are in accordance with the value of $\alpha\simeq -1.3$ derived by Abramenko et al. (2001) for quiet sun regions from a direct analysis of magnetograms. The single most important remaining restriction in our numerical results is the assumption of random phases {\revone (i.e. lack of intermittency).} The photospheric turbulent magnetic field is known to be distributed in a very distinctive pattern, forming IN field concentrations, following intergranular lanes and mesogranular structure. This is very different from the amorphous superposition of Fourier modes with random phases. Whether, and to what extent non-random phases might influence our inferences should be the subject of future research. \begin{figure}[!t] \includegraphics[width=\columnwidth,height=50mm]{marschalkog_fig4} \caption{Cancellation function with different turbulent magnetic energy spectra. Dots: $\alpha = -0.7$; stars: $\alpha = -0.6$; squares: $\alpha = -0.5$.} \label{label4} \end{figure} | 14 | 4 | 1404.1772 |
1404 | 1404.2771_arXiv.txt | {The stresses produced by magnetorotational turbulence can provide effective angular momentum transport in accretion disks. However, questions remain about the ability of simulated disks to reproduce observationally inferred stress-to-gas-pressure ratios. In this paper we present a set of high resolution global magnetohydrodynamic disk simulations which are initialised with different field configurations: purely toroidal, vertical field lines, and nested poloidal loops. A mass source term is included which allows the total disk mass to equilibrate in simulations with long run times, and also enables the impact of rapid mass injection to be explored. Notably different levels of angular momentum transport are observed during the early-time transient disk evolution. However, given sufficient time to relax, the different models evolve to a statistically similar quasi-steady state with a stress-to-gas-pressure ratio, $\lb \alpha_{\rm P} \rb \sim 0.032-0.036$. Such behaviour is anticipated based on consideration of mean magnetic field evolution subject to our adopted simulation boundary conditions. The indication from our results is that {\it steady, isolated} disks may be unable to maintain a large-scale magnetic field or produce values for the stress-to-gas-pressure ratio implied by some observations. Supplementary simulations exploring the influence of trapping magnetic field, injecting vertical field, and rapidly injecting additional mass into the disk show that large stresses can be induced by these mechanisms. In the first instance, a highly magnetized disk is produced with $\lb \alpha_{\rm P} \rb \sim 0.21$, whereas the latter cases lead to a transient burst of accretion with a peak $\lb \alpha_{\rm P} \rb \simeq 0.1-0.25$. As a whole, the simulations highlight the common late-time evolution and characteristics of turbulent disks for which the magnetic field is allowed to evolve freely (i.e., without constraint/replenishment). In contrast, if the boundaries of the disk, the rate of injection of magnetic field, or the rate of mass replenishment are modified to mimic astrophysical disks, markedly different disk evolution occurs. } | \label{sec:intro} For disk accretion to occur angular momentum must be removed from orbiting material. It has long been thought that magnetic fields could play more than just a passive role in this situation \citep{Shakura:1973, Lynden-Bell:1974}. The magnetorotational instability \citep[MRI -][]{BH91,BH92,BH98} has since emerged as a robust mechanism for destabilising a differentially rotating disk, placing the importance of magnetic fields on a firm footing. Subsequent numerical work has demonstrated that the non-linear motions induced by the MRI lead to self-sustaining turbulence with the resulting stresses effectively transporting angular momentum \citep[e.g.][]{Hawley:1995, Brandenburg:1995, Stone:1996}. A large body of the numerical work on magnetorotational turbulence to-date has focused on a local patch of disk with the vertical component of gravity neglected - the unstratified shearing-box. Studies examining various magnetic field configurations have produced a wide range of values for the stress-to-gas-pressure ratio, $\lb \alpha_{\rm P} \rb \simeq 0.001- 0.3$ \citep[e.g.][to mention but a few]{Hawley:1995, Sano:2004, Fromang:2007a, Simon:2009, Guan:2009}. Values of $\lb \alpha_{\rm P} \rb \gtsimm 0.01$ are, however, only achieved by models initialised with a net vertical magnetic field. By construction, the unstratified shearing-box preserves an initial net vertical field. Hence, in these cases power can be effectively injected by vertical MRI modes on large spatial scales, feeding the turbulent cascade from the top down. Astrophysical accretion disks are, however, intrinsically global objects (by which we mean they are not periodic in the radial and/or vertical directions). Recent studies by \cite{Sorathia:2010, Sorathia:2012} and \cite{Beckwith:2011} have demonstrated that localised patches of global disks do not preserve their magnetic field configuration in the same manner as an unstratified shearing-box. Moreover, an initial vertical field is free to evolve in global models, and it is not clear whether global disks will achieve the large stresses implied by net-vertical flux unstratified shearing-box models. What dependence of the turbulent stresses on initial field configuration should one expect for a stratified global disk? Newtonian global disk models exhibit $\lb \alpha_{\rm P} \rb \sim 0.001-0.15$ \citep[e.g.][]{Hawley:2000, Fromang:2006, Flock:2011, Beckwith:2011, Hawley:2011, Hawley:2013, Parkin:2013, Parkin:2013b, Gressel:2013, Parkin:2014, Suzuki:2014}. Larger values of $\lb \alpha_{\rm P} \rb$ are typically associated with the saturation stress level during the initial transient phase of the simulation, with some evidence for stronger stresses when the disk initially possesses a poloidal magnetic field. There are mixed results from general relativistic global disk simulations. For instance, \cite{Beckwith:2008} find markedly similar disk properties irrespective of the initial field configuration. In contrast, \cite{McKinney:2012} \citep[see also -][]{Tchekhovskoy:2011} quote $\lb \alpha_{\rm P} \rb \sim 0.01-0.69$ with the lowest values for an initially toroidal field, whereas the largest values are for models where the disk initially contains a large quantity of poloidal magnetic flux. In the present study we investigate the dependence of magnetorotational turbulence in a global disk on the initial field configuration. The simulations include a mass source term which facilitates simulations with long run times. Thus, the late-time quasi-steady disk evolution can be studied without concerns about contamination from mass exhaustion. This differs from previous global disk models, with the exception of \cite{Flock:2011, Flock:2012, Flock:2012b} and \cite{Parkin:2014}. A key result is the ignorance of the quasi-steady state turbulent stress, and thus efficiency of angular momentum transport, to the initial field configuration; given sufficient time the disk expels and/or digests the initial field, evolving to a statistically almost identical state. The simulations produce $\lb \alpha_{\rm P} \rb \sim 0.032-0.036$ during the quasi-steady state, which falls short of observationally inferred values of $\sim 0.1-0.4$ \citep[see][and references therein]{King:2007}. We perform supplementary simulations to address this quandary, finding that $\lb \alpha_{\rm P} \rb \sim 0.2$ can be achieved by trapping field, and $\lb \alpha_{\rm P} \rb \sim 0.1-0.25$ results when mass or vertical magnetic field are injected. The former case is relevant for magnetically arrested \citep{Narayan:2003} and magnetically levitating \citep{Johansen:2008, Gaburov:2012} disk models. The remainder of this paper is organised as follows: the simulation setup and initial conditions are described in \S~\ref{sec:model}. A preparatory discussion of the evolution of mean magnetic fields subject to boundary conditions is given in \S~\ref{sec:mean_field}, followed by the results of the simulations in \S~\ref{sec:results}. A discussion of the implications of the results for astrophysical disks, and some potentially interesting avenues for future studies, are discussed in \S~\ref{sec:discussion}. Finally, we close with conclusions in \S~\ref{sec:conclusions}. | \label{sec:conclusions} The dependence of turbulent stresses on initial field configuration, magnetic field trapping due to inhibited radial outflow, magnetic field injection, and rapid mass injection has been investigated using global MHD disk simulations. Properties of the saturation stress level during the early-time transient phase of disk evolution show a dependence on the initial magnetic field. This finding is consistent with models presented by \cite{Hawley:2013} which focused on the transient phase during roughly the first $\simeq 10.3 \ts P^{\rm orb}_{30}$ of the simulation. However, a major new result in this work, and one which was achieved by utilising a mass source term to avoid the exhaustion of disk mass by ongoing accretion, is that irrespective of the strength and topology of the initial magnetic field an {\it isolated} magnetorotationally turbulent disk evolves to a statistically similar quasi-steady state that is characterised by: i) a volume-averaged stress-to-gas-pressure ratio, $\lb \alpha_{\rm P} \rb \simeq 0.032-0.036$, ii) a gas-to-magnetic pressure ratio, $\beta \simeq 16-18$, and, iii) zero-net time-averaged radial and azimuthal magnetic fields. Simulations exploring the influence of trapping of magnetic field, vertical field injection, and of rapid mass injection, on the turbulence reveal that these mechanisms lead to relatively large stresses in the disk. Trapping of magnetic field produces a strongly magnetized disk with $\lb \alpha_{\rm P} \rb \sim 0.2$ and considerable vertical mass flux in the form of an intermittent wind. The injection of a vertical magnetic field, even a relatively weak one that equates to an accumulation of a $\beta=2000$ field over a time interval of $40\;P^{\rm orb}_{30}$, is sufficient to trigger a burst in accretion with stresses reaching $\lb \alpha_{\rm P} \rb \sim 0.25$. Rapid mass injection leads to a sudden sharp increase in turbulent stresses, peaking at $\lb \alpha_{\rm P} \rb \sim 0.1$ and subsequently decaying to the pre-outburst level. The results of these simulations may be relevant for understanding accretion state changes, transient bursts, and large observationally inferred accretion efficiencies for astrophysical disks. Indeed limit cycle behaviour reminiscent of dwarf novae eruptions could be produced with the inclusion of a temperature (and perhaps also surface density) dependent resistivity, following similar suggestions by \cite{Balbus:2008b}, \cite{Lesaffre:2009}, and \cite{Latter:2012}. \subsection*{Acknowledgements} I thank Geoffrey Bicknell, Yuri Levin, and Daniel Price for helpful discussions, the Australian Research Council's Discovery Projects scheme (project number DP1096417) for financial support, and the National Computational Infrastructure for computational resources through access to the Raijin supercomputer. \newcommand{\noop}[1]{} | 14 | 4 | 1404.2771 |
1404 | 1404.5960_arXiv.txt | Nearly one-third of the $\gamma$-ray sources detected by \fer\ are still unidentified, despite significant recent progress in this effort. On the other hand, all the $\gamma$-ray extragalactic sources associated in the second \fer-LAT catalog have a radio counterpart. Motivated by this observational evidence we investigate all the radio sources of the major radio surveys that lie within the positional uncertainty region of the unidentified $\gamma$-ray sources (UGSs) at 95\% level of confidence. First we search for their infrared counterparts in the all-sky survey performed by the Wide-field Infrared Survey Explorer (\wse) and then we analyze their IR colors in comparison with those of the known $\gamma$-ray blazars. We propose a new approach, based on a 2-dimensional kernel density estimation (KDE) technique in the single [3.4]-[4.6]-[12] $\mu$m \wse\ color-color plot, replacing the constraint imposed in our previous investigations on the detection at 22$\mu$m of each potential IR counterpart of the UGSs with associated radio emission. The main goal of this analysis is to find distant $\gamma$-ray blazar candidates that, being too faint at 22$\mu$m, are not detected by \wse\ and thus are not selected by our purely IR based methods. We find fifty-five UGS's likely correspond to radio sources with blazar-like IR signatures. Additional eleven UGSs having, blazar-like IR colors, have been found within the sample of sources found with deep recent ATCA observations. | \label{sec:intro} The large majority of the point sources detected by the Compton Gamma-ray Observatory in the 1990s \citep[e.g.,][]{hartman99} are still lacking an association with a low-energy candidate counterpart, and given their sky distribution, a significant fraction of these unresolved objects are expected to have extragalactic origin \citep[e.g.,][]{thompson08,abdo10a}. Unveiling the origin of the unidentified $\gamma$-ray sources (UGSs) is also one of the key scientific objectives of the recent \fer\ mission that still lists about 1/3 of the $\gamma$-ray sources as unassociated in the second \fer-LAT catalog \citep[2FGL;][]{nolan12} . A large fraction of UGSs is expected to be blazars, the largest known population of $\gamma$-ray active galaxies, not yet associated and/or recognized due to the lack of multifrequency observations \citep{ackermann11a}. Therefore a better understanding of the nature of the UGSs is crucial to estimate accurately the blazar contribution to the extragalactic gamma-ray background \citep[e.g., ][]{mukherjee97,abdo10b}, and it is essential to constrain exotic high-energy physics phenomena \citep[e.g.,][]{zechlin12}. Many attempts have been adopted to decrease UGSs number and to understand their composition. Pointed \swf\ observations\\ \citep[e.g.,][]{mirabal09a,mirabal09b,ugs4} to search for X-ray counterparts of UGSs as well as radio follow up observations were already performed or are still in progress \citep[e.g.,][]{kovalev09a,kovalev09b,petrov13}. In addition, statistical approaches based on different techniques have been also developed and successfully used \citep[e.g.][]{mirabal10,ackermann12}. We recently addressed the problem of searching $\gamma$-ray blazar candidates as counterparts of the UGSs adopting two new approaches: the first is based on the Wide-field Infrared Survey Explorer (\wse) all-sky observations \citep{wright10} aiming at recognizing $\gamma$-ray blazar candidates using their peculiar IR colors \citep{paper1,paper2,paper4,ugs1} while the second employs the low-frequency radio observations \citep{ugs3}. In particular, this second method was indeed based on the combination of the radio observations Westerbork Northern Sky Survey \citep[WENSS;][]{rengelink97} at 325 MHz with those of the NRAO Very Large Array Sky survey \citep[NVSS;][]{condon98} and of the Very Large Array Faint Images of the Radio Sky at Twenty-Centimeters \citep[FIRST;][]{becker95,white97} at about 1.4 GHz. It is worth noting that all the \fer\ extragalactic sources associated in the 2FGL catalog have a clear radio counterpart \citep{nolan12}, this is the basis of the radio-$\gamma$-ray connection, that has been found in the case of blazars \citep[e.g.,][]{ghirlanda10,mahony10,ackermann11b}. Thus, motivated by this observational evidence we propose a different approach to search for the blazar-like counterparts of the UGSs. We combine the radio and the IR information available for the sources lying within the positional uncertainty regions of the \fer\ UGSs to select $\gamma$-ray blazar candidates. With respect to our previous IR based search for blazar-like counterparts\\ \citep[e.g.,][]{paper3,ugs1} our new analysis relaxes the constraint on the 22$\mu$m detection of the \wse-selected candidates, and does not take into account their [12]-[22] $\mu$m color, replacing these features with the presence of a radio counterpart. The number of $\gamma$-ray blazars undetected at 22$\mu$m is only a small fraction \citep[$\sim$8\%of the total number of $\gamma$-ray blazars][]{ugs1}, but includes several high redshift sources that lying at larger distance than the whole population. To perform our analysis, we search all the radio sources detected in the \\ NVSS \citep{condon98} and in the Sydney University Molonglo Sky Survey \citep[SUMSS;][]{mauch03} surveys that lie within the positional uncertainty region, at 95\% level of confidence, of the UGSs listed in the 2FGL. Then we associate them with their \wse\ counterparts to compare their IR colors with those of the known $\gamma$-ray blazars in the [3.4]-[4.6]-[12] $\mu$m plot using the kernel density estimation (KDE) technique \citep[e.g.,][]{richards04,dabrusco09,paper3}. We also verified if the radio sources found in the recent deep radio observations performed by Australia Telescope Compact Array (ATCA) and presented by Petrov et al. (2013) have an IR counterpart with \wse\ colors consistent with those of the $\gamma$-ray blazar population. Our analysis of the IR colors is restricted only to the [3.4]-[4.6]-[12] $\mu$m color-color plot. The paper is organized as follows: Section~\ref{sec:sample} is devoted to the definitions of the samples used while in Section~\ref{sec:kde} we describe the KDE technique used to perform our investigation; we then applied our selection in Section~\ref{sec:ugs} to identify those radio sources that could be considered blazar-like counterpart of the UGSs listed in the 2FGL catalog. We also verified the presence of optical and X-ray counterparts for the selected $\gamma$-ray blazar candidates and we compare our results with different approaches previously developed. Finally, Section~\ref{sec:summary} is dedicated to our conclusions. For our numerical results, we use cgs units unless stated otherwise. Spectral indices, $\alpha$, are defined by flux density, S$_{\nu}\propto\nu^{-\alpha}$ and \wse\ magnitudes at the [3.4], [4.6], [12], [22] $\mu$m (i.e., the nominal \wse\ bands) are in the Vega system respectively. All the magnitudes and the IR colors reported in the paper have been corrected for the Galactic extinction according to the formulae reported in Draine (2003) as also performed in our previous analysis \citep[e.g.,][]{ugs1,ugs2}. The most frequent acronyms used in the paper are listed in Table~\ref{tab:acronym}. \begin{table} \caption{List of most frequent acronyms.} \begin{tabular}{|lc|} \hline Name & Acronym \\ \hline \noalign{\smallskip} Multifrequency Catalog of blazars & \bzcat\ \\ Second \fer\ Large Area Telescope Catalog & 2FGL \\ \hline \noalign{\smallskip} BL Lac object & BZB \\ Flat Spectrum Radio Quasar & BZQ \\ Blazar of Uncertain type & BZU \\ Unidentified Gamma-ray Source & UGS \\ \hline \noalign{\smallskip} Training Blazar sample & TB \\ Northern UGS sample & NU \\ Southern UGS sample & SU \\ Southern Deep ATCA sample & SDA \\ \hline \noalign{\smallskip} Kernel Density Estimation & KDE \\ \noalign{\smallskip} \hline \end{tabular}\\ \label{tab:acronym} \end{table} | \label{sec:summary} In this paper we presented an non-parametric method to search for $\gamma$-ray blazar candiates within two samples of UGSs. First we identify all the radio sources in the two major surveys \citep[i.e., NVSS and SUMSS][respectively]{condon98,mauch03} that lie within the positional uncertainty region at 95\% level of confidence, then we investigate the IR colors of their \wse\ counterparts to recognize those with similar spectral properties in the simple [3.4]-[4.6]-[12] color-color plot. With respect to our previous \wse\ selection of $\gamma$-ray blazar candidates \citep[e.g.,][]{paper3,ugs1} the criteria adopted in the present analysis are less conservative, since the detection of the \wse\ counterpart at 22$\mu$m is not required. A small fraction ($\sim$8\%) of the \fer\ blazar are in fact not detected at 22$\mu$m. Thus, to compare the IR colors of the \fer\ blazars with those of the radio sources selected, we adopted a KDE technique as already presented in Massaro et al. (2011a), Massaro et al. (2012a) and more recently in Paggi et al. (2013). Our new approach, being less restrictive than those adopted in our previous associations, permits to search for faint $\gamma$-ray blazar candidates that were not previously selected because too faint at 22$\mu$m. By relaxing the requirement on the detection at 22$\mu$m and thus on the [12]-[22] color, this method would select candidate blazars at the cost of a larger contamination, mitigated by the requirement on the presence of a radio counterpart. We found 41 and 14 radio sources with IR similar to those of the \fer\ blazars within the NU and the SU samples, respectively. In addition, we investigated the sample of radio sources discovered with recent deep ATCA observations performed to search for radio counterparts of the UGS in the southern hemisphere. Among 416 radio objects listed in Petrov et al. (2013) only 11 sources have an IR counterpart consistent with the $\gamma$-ray blazars. The total number of $\gamma$-ray blazar candidates is 66 all listed in Table~\ref{tab:table1} and Table~\ref{tab:table2}. without no multiple candidates within the positional uncertainty regions of the UGSs analyzed. { We estimate a probability of spurious association for the $\gamma$-ray blazar candidates selected according to our method of the order of 4\% and 3\% for the NU and SU samples, respectively.} It is worth noting that the large majority of our candidates show IR colors more consistent with the region occupied by the BZBs in the [3.4]-[4.6]-[12] $\mu$m color-color diagram rather than that of BZQs. Thus they could be potential faint and so distant BZBs that were not previously selected with different methods because lacking of the IR flux at 22$\mu$m. More detailed investigations based on ground-based, optical and near IR, spectroscopic follow up observations will be planned for the selected $\gamma$-ray blazar candidates to confirm their nature and to obtain their redshifts. \begin{table} \tiny \caption{Optical magnitudes for the \wse\ counterparts.} \begin{tabular}{|lcccccc|} \hline WISE & B1 & R1 & B2 & R2 & I & $\theta$ \\ name & mag & mag & mag & mag & mag & arcsec \\ \hline \noalign{\smallskip} J003119.70+072453.6 & 19.03 & 18.17 & 19.84 & 18.63 & 18.67 & 0.14\\ J003908.14+433014.6 & 19.9 & 19.61 & 21.42 & 20.77 & & 0.14\\ J010345.73+132345.4 & 17.98 & 17.73 & 18.69 & 17.38 & 17.24 & 0.07\\ J011619.59-615343.5 & & 17.72 & 18.22 & 17.78 & 17.91 & 0.27\\ J013306.35-441421.3 & & 18.38 & 19.7 & 18.12 & 18.76 & 0.26\\ J014347.39-584551.3 & & 16.7 & 18.48 & 16.64 & 17.04 & 0.04\\ J015248.80+855703.6 & 20.57 & 18.84 & 19.63 & 18.71 & 17.82 & 0.38\\ J020020.94-410935.6 & & 19.84 & 21.1 & 18.79 & 18.75 & 0.6\\ J022744.35+224834.3 & & & 20.82 & 20.22 & 19.28 & 0.35\\ J031240.54+201142.8 & & 19.34 & 21.22 & 19.42 & 19.07 & 2.63\\ J031614.31-643731.4 & & 16.59 & 18.19 & 16.57 & 16.82 & 0.22\\ J033153.90+630814.1 & & & 20.66 & 19.92 & 18.35 & 0.35\\ J034022.89-242407.2 & & 19.56 & 20.07 & & & 0.21\\ J035309.54+565430.8 & 20.09 & 19.24 & 20.43 & 18.76 & 18.53 & 0.55\\ J040946.57-040003.4 & 19.45 & 19.18 & 17.53 & 16.98 & 16.86 & 0.07\\ J041605.81-435514.6 & & 18.49 & 18.7 & 18.17 & 18.0 & 0.18\\ J042025.09-374445.0 & & 20.44 & 20.73 & 19.71 & 18.17 & 0.38\\ J052313.07-253154.4 & & 19.2 & 20.83 & 20.07 & 18.95 & 0.17\\ J055618.74-435146.1 & & 19.23 & 18.88 & 19.08 & 18.08 & 0.31\\ J060102.86+383829.2 & & 19.11 & & 19.84 & 18.48 & 0.04\\ J064435.72+603851.2 & 20.01 & 19.58 & 20.7 & 18.75 & 18.37 & 0.3\\ J065845.02+063711.5 & 20.25 & & & 19.12 & 18.3 & 0.39\\ J072354.83+285929.9 & 19.78 & 19.05 & 19.97 & 18.72 & & 0.19\\ J074627.03-022549.3 & 19.03 & & 18.59 & 18.43 & 16.53 & 0.31\\ J092849.83-352948.9 & & 18.56 & 19.64 & 18.07 & 18.23 & 0.23\\ J093754.72-143350.3 & 18.82 & 17.92 & 18.64 & 17.73 & 17.56 & 0.1\\ J101544.44+555100.7 & 19.69 & 19.42 & 20.61 & 19.35 & & 0.37\\ J103015.35-840308.7 & & 19.36 & 19.26 & 18.84 & 18.03 & 0.15\\ J111511.74-070239.9 & & 19.86 & 20.68 & 19.05 & 18.66 & 0.14\\ J112325.38-252857.0 & 16.9 & 15.76 & 15.87 & 15.56 & 15.51 & 0.19\\ J112903.25+375657.4 & 19.9 & 19.23 & 19.35 & 19.48 & 18.58 & 0.65\\ J122358.17+795327.8 & & 17.6 & 20.18 & 18.46 & 17.63 & 1.04\\ J125422.47-220413.6 & & 19.88 & 18.67 & 19.11 & 18.22 & 0.41\\ J125949.80-374858.1 & & 17.44 & 18.07 & 16.78 & 17.35 & 0.17\\ J131552.98-073301.9 & 19.78 & 18.68 & 18.75 & 17.75 & 17.56 & 0.16\\ J132840.61-472749.2 & & 17.75 & 18.23 & 16.8 & & 0.98\\ J133916.44-234829.4 & 20.3 & 19.3 & 20.43 & 19.79 & 18.5 & 0.31\\ J134042.02-041006.8 & 18.21 & 17.21 & 17.59 & 16.46 & 17.08 & 0.19\\ J134543.05-335643.3 & & 17.98 & 19.58 & 18.65 & 18.12 & 0.38\\ J134706.89-295842.3 & 17.85 & 17.09 & 18.8 & 17.14 & 17.09 & 0.41\\ J151303.66-253925.9 & 19.92 & 18.96 & 19.77 & 20.35 & & 0.5\\ J151649.26+365022.9 & 20.9 & & 21.49 & 20.07 & 19.16 & 1.58\\ J154824.39+145702.8 & 20.51 & 18.29 & 19.86 & 17.74 & 17.45 & 0.41\\ J164619.95+435631.0 & 20.43 & 19.73 & 20.42 & 19.67 & & 0.34\\ J170409.59+123421.7 & 19.86 & 18.04 & 18.62 & 17.63 & 17.46 & 0.47\\ J170433.84-052840.6 & 19.62 & 18.97 & 18.42 & 17.28 & 17.98 & 0.45\\ J200506.02+700439.3 & 20.73 & 19.25 & 19.24 & 18.65 & & 0.45\\ J202155.45+062913.7 & 17.27 & 16.13 & 17.01 & 16.67 & 16.03 & 0.43\\ J203451.08-420038.2 & & 18.97 & 19.34 & 18.87 & 18.27 & 0.44\\ J204201.92-731913.5 & & 17.46 & 17.9 & 18.36 & 18.04 & 0.29\\ J211522.00+121802.8 & 18.15 & 18.15 & 17.68 & 17.31 & 17.58 & 0.16\\ J213253.05+261143.8 & 20.04 & 19.29 & 19.14 & 19.62 & 18.44 & 0.07\\ J213430.18-213032.6 & 19.77 & 18.65 & 18.96 & 16.8 & 17.7 & 0.09\\ J213349.21+664704.3 & & & & 19.37 & 18.8 & 0.45\\ J221330.33-475425.0 & & 18.12 & 18.6 & 18.34 & 18.33 & 0.05\\ J222830.19-163642.8 & 18.57 & 19.34 & 19.95 & 19.04 & 17.91 & 0.29\\ J224604.98+154435.3 & 19.14 & 18.27 & 19.57 & 18.53 & 17.65 & 0.13\\ J225128.69-492910.6 & & 18.8 & 19.21 & 18.45 & 18.03 & 0.42\\ J234302.29-475749.9 & & 19.84 & 18.92 & 21.3 & 18.32 & 0.29\\ J235836.83-180717.3 & 19.14 & 18.45 & 18.28 & 17.22 & 17.53 & 0.3\\ \noalign{\smallskip} \hline \end{tabular}\\ \label{tab:optical} \end{table} | 14 | 4 | 1404.5960 |
1404 | 1404.7012_arXiv.txt | The cold dark matter (CDM) model faces persistent challenges on small scales. In particular, taken at face value, the model significantly overestimates the number of satellite galaxies around the Milky Way. Attempts to solve this problem remain open to debate and have even led some to abandon CDM altogether. However, current simulations are limited by the assumption that dark matter feels only gravity. Here, we show that including interactions between CDM and radiation (photons or neutrinos) leads to a dramatic reduction in the number of satellite galaxies, alleviating the Milky Way satellite problem and indicating that physics beyond gravity may be essential to make accurate predictions of structure formation on small scales. The methodology introduced here gives constraints on dark matter interactions that are significantly improved over those from the cosmic microwave background. | \label{sec:intro} $N$-body simulations of `cold' dark matter (CDM), consisting of weakly-interacting particles with a low velocity dispersion and therefore, negligible free-streaming, agree remarkably well with observations of the Universe on the largest scales~\citep{Davis:1985rj}. However, as the resolution of the simulations improved, significant discrepancies emerged on small scales. For example, dark matter (DM) halo profiles for dwarf galaxies are less cuspy than predicted by CDM~(\citealt{Dubinski:1991bm}, although this is still under debate, see~\citealt{Frenk:2012ph}) and large CDM haloes do not form as many stars as expected (the `too big to fail problem';~\citealt{BoylanKolchin:2011de}). Here, we address the so-called `Milky Way satellite problem'~\citep{Klypin:1999uc,moore_dark_1999}, which describes the disagreement between the number of `satellite' galaxies in orbit around the Milky Way (MW) and the much larger abundance of DM subhaloes predicted by the CDM model. Whilst the observational data have been revised significantly since this problem was first discussed and their completeness is still under discussion (e.g.~\citealt{Tollerud:2008ze}), a clear discrepancy remains compared with the number of DM subhaloes around the MW. Several astrophysical processes have also been invoked to solve this problem. Star formation could have been suppressed due to the effects of supernova feedback, photoionization and reionization~\citep{Bullock:2000wn,Benson:2001au} and tidal stripping may have dramatically reduced the size of substructures or disrupted a fraction of them~\citep{Kravtsov:2004cm}. Alternatively, since the DM halo mass has a significant impact on the expected number of satellites, one may argue that the severity of the problem depends upon the choice of MW halo mass, which remains difficult to determine~\citep{2012MNRAS.424.2715W,Cautun:2014dda}. A more drastic solution is to abandon CDM and instead consider `warm' dark matter (WDM). In this scenario, one allows a small (but non-negligible) amount of free-streaming, which greatly reduces the expected number of satellites with respect to CDM~\citep{Lovell:2013ola}. Given that the free-streaming scale of a DM particle is typically governed by its mass and velocity distribution, the proposed WDM models require very light ($\sim$ keV) particles. However, recent work suggests that such light candidates cannot simultaneously solve the small-scale problems of CDM and satisfy the particle mass constraints from the Lyman $\alpha$ forest and other observations~\citep{Schneider:2013wwa,Viel:2013fqw}. Here, we explore an alternative route that allows us to reduce the MW satellite population without having to discard CDM. In standard $N$-body simulations, DM is represented as a collisionless fluid that responds only to gravity. However, it is entirely plausible (and indeed expected) that DM interacts through other forces, with various components of the Universe\footnote{We do not study self-interactions as these have been discussed already in~\citet{rocha_cosmological_2012}.}. Such interactions have been shown to suppress small-scale density fluctuations~\citep{boehm_constraining_2001,boehm_interacting_2001,Boehm:2003xr,Boehm:2004th,chen_cosmic_2002,2012PhRvL.109w1301V,dvorkin_constraining_2013} but the implications for the satellite galaxy abundance have not been studied using numerical simulations. Here, we simulate the formation of large-scale structure in a Universe where DM interacts with photons or neutrinos, to determine whether such a coupling can address the MW satellite problem. We focus on radiation as this dominates the energy density at early times and should therefore lead to the largest effect on DM primordial fluctuations. For the sake of illustration, we will study specifically a DM--photon coupling (hereafter referred to as $\gamma$CDM) but very similar effects are expected in the case of a DM--neutrino coupling ($\nu$CDM). We will use these results to extract constraints on the DM--photon scattering cross section. The other small-scale problems of CDM will be addressed in forthcoming work. The Letter is organized as follows. In Section~\ref{sec:background}, we discuss the theoretical framework of interacting DM models. In Section~\ref{sec:simulations}, we provide details regarding the setup of our simulations. In Section~\ref{sec:results}, we present the results of our simulations and in particular, the effect on the satellite galaxy abundance. Conclusions are provided in Section~\ref{sec:conc}. | \label{sec:conc} We have shown that studying the formation of cosmic structure, particularly on small scales, provides us with a powerful new tool to test the weakly-interacting nature of DM. By performing the first accurate cosmological simulations of DM interactions with radiation (in this case, photons), we find a new means to reduce the population of MW subhaloes, without the need to abandon CDM. The resulting constraints on the interaction strength between DM and photons are orders of magnitude stronger than is possible from linear perturbation theory considerations. Similar results are expected in the case of DM--neutrino interactions. It should be noted that the observed value of $V_{\rm max}$ may be underestimated by our approach of directly calculating it from the stellar velocity dispersion~\citep{bullock_notes_2010}. Combined with an expected increase in the number of satellites from additional completeness corrections, this would lead to even stricter constraints on the interaction cross section. A future paper will present the non-linear structure formation for such models in greater depth to examine whether one can solve the other small-scale problems of CDM (Schewtschenko et al. 2014). Recent simulations with DM and baryons have shown that baryonic physics can alter the appearance of the subhalo mass function~\citep{Sawala:2014baa}. A definitive calculation would include the full impact of these effects, in particular, supernovae feedback and photoionization heating of the interstellar medium, but this is deferred to a future paper. \begin{figure} \begin{centering} \includegraphics[width=7.3cm, trim = -0.4cm -0.4cm 0cm 0cm]{Figures/constraints_a} \includegraphics[width=6.8cm, trim = 0cm 0cm 0cm 0cm]{Figures/constraints_b} \caption{Constraints on the $\gamma$CDM cross section. Top panel: the overabundance of satellites versus the cross section for the MW halo mass bin $(2.3-2.7) \times 10^{12} {\rm M}_\odot$, where the shaded bands represent the 1$\sigma$ and 2$\sigma$ uncertainties. Bottom panel: constraints on the cross section are plotted with respect to the MW halo mass. The most recent CMB constraint~\citep{wilkinson_using_2013} and selected upper mass bounds for the MW halo are shown for comparison.} \label{fig:constraints} \end{centering} \vspace{-2ex} \end{figure} | 14 | 4 | 1404.7012 |
1404 | 1404.7538_arXiv.txt | The Kepler mission has allowed the detection of numerous multi-planet exosystems where the planetary orbits are relatively compact. The first such system detected was Kepler-11 which has six known planets at the present time. These kinds of systems offer unique opportunities to study constraints on planetary albedos by taking advantage of both the precision timing and photometry provided by Kepler data to monitor possible phase variations. Here we present a case study of the Kepler-11 system in which we investigate the phase modulation of the system as the planets orbit the host star. We provide predictions of maximum phase modulation where the planets are simultaneously close to superior conjunction. We use corrected Kepler data for Q1-Q17 to determine the significance of these phase peaks. We find that data quarters where maximum phase peaks occur are better fit by a phase model than a ``null hypothesis'' model. | The field of exoplanets is rapidly evolving. We have progressed from simply finding new planets to characterizing them. As of 2014 March 10, the NASA Exoplanet Archive\footnote{\tt http://exoplanetarchive.ipac.caltech.edu}\citep{ake13} reports 1,692 planets confirmed around 1,024 stars. Additionally, NASA's {\it Kepler} mission has announced several thousand more likely transiting exoplanet candidates \citep{bor11a,bor11b,bat13, bur14}. The abundance of high signal-to-noise data from {\it Kepler} is allowing us to obtain planetary radii measurements which facilitate characterization studies of planetary densities and therefore planetary interiors \citep{lop13,for13}. The exquisite data also allows for other forms of study such as detection of planetary signatures from phase variations as they orbit their host star. A few planets have been the subject of phase variation studies, including HAT-P-7b \citep{bor09,wel10}, Kepler-10b \citep{bat11}, Kepler-7b \citep{dem11}, TrES-2b \citep{kip11,bar12}, and Kepler-41b \citep{qui13}. The phase variations of an exoplanet are caused by the observed reflected light component of an exoplanet as it orbits the host star and changes phase. The first observations of phase variations \citep{har06,knu07} followed closely after measurements of secondary eclipses were used to infer the temperatures of the planets \citep{cha05,dem05}. Infrared exoplanetary phase curves can help to map the energy redistribution of the planet \citep{knu09a,knu09b} while optical phase curves provide insight into the scattering properties of an exoplanet's atmosphere \citep{sud05,bur08}. Along with the growing number of planets and planet candidates, the number of exoplanet systems with multiple planets has risen to almost 500. The advent of precise data from Kepler has brought about the opportunity to simultaneously observe the phase variations of these multi-planet systems. These systems offer unique opportunities to measure albedos thanks to the precision of not only the {\it Kepler} photometry, but also its timing measurements, which can accurately predict the times when maximum phase amplitude for each of planets in the system should occur. Detailed measurements of phase variations can significantly contribute to current theoretical models of exoplanet atmospheres. We have examined in detail the dependence of phase curves on eccentricity in \citet{kag10}, and \citet{kag11} examined the dependence on inclination. In addition, \citet{kag13} have developed techniques for decoupling the phase variations of planets in these multi-planet systems \citet{mad12} have created a technique which can be used to interpret phase curves as a function of orbital parameters and atmospheric reflective properties (Lambert versus Rayleigh, etc.). Other hypotheses have also been empirically derived. For example, based on a study of 24 planets with available secondary eclipse and phase variation constraints, \citet{cow11} suggest that very hot giant exoplanets may have low heat redistribution efficiency, while ``cooler'' hot Jupiters may have a variety of redistribution efficiencies. \begin{deluxetable*}{cccccccc} \tablecolumns{8} \tablewidth{0pc} \tablecaption{\label{planchar} Planetary Orbital Parameters and Derived Characteristics} \tablehead{ \colhead{Planet} & \colhead{$P\,^{\dagger}$} & \colhead{$T_0\,^{\dagger}$} & \colhead{$M_p\,^{\ddagger}$} & \colhead{$R_p\,^{\ddagger}$} & \colhead{$\rho_p\,^{\ddagger}$} & \colhead{$a\,^{\ddagger}$} & \colhead{$i\,^{*}$} \\ \colhead{} & \colhead{(days)} & \colhead{(date)} & \colhead{($M_\oplus$)} & \colhead{($R_\oplus$)} & \colhead{($g\,cm^{-3}$)} & \colhead{(AU)} & \colhead{(deg)} } \startdata b & $10.3039^{+0.0006}_{-0.0010}$ & $689.7378^{+0.0026}_{-0.0047}$ & $1.9^{+1.4}_{-1.0}$ & $1.80^{+0.03}_{-0.05}$ & $1.72^{+1.25}_{-0.91}$ & $0.091^{+0.001}_{-0.001}$ & $89.64^{+0.36}_{-0.18}$ \\ c & $13.0241^{+0.0013}_{-0.0008}$ & $683.3494^{+0.0014}_{-0.0019}$ & $2.9^{+2.9}_{-1.6}$ & $2.87^{+0.05}_{-0.06}$ & $0.66^{+0.66}_{-0.35}$ & $0.107^{+0.001}_{-0.001}$ & $89.59^{+0.41}_{-0.16}$ \\ d & $22.6845^{+0.0009}_{-0.0009}$ & $694.0069^{+0.0022}_{-0.0014}$ & $7.3^{+0.8}_{-1.5}$ & $3.12^{+0.06}_{-0.07}$ & $1.28^{+0.14}_{-0.27}$ & $0.155^{+0.001}_{-0.001}$ & $89.67^{+0.13}_{-0.16}$\\ e & $31.9996^{+0.0008}_{-0.0012}$ & $695.0755^{+0.0015}_{-0.0009}$ & $8.0^{+1.5}_{-2.1}$ & $4.19^{+0.07}_{-0.09}$ & $0.58^{+0.11}_{-0.16}$ & $0.195^{+0.002}_{-0.002}$ & $88.89^{+0.02}_{-0.02}$ \\ f & $46.6888^{+0.0027}_{-0.0032}$ & $718.2710^{+0.0041}_{-0.0038}$ & $2.0^{+0.8}_{-0.9}$ & $2.49^{+0.04}_{-0.07}$ & $0.69^{+0.29}_{-0.32}$ & $0.250^{+0.002}_{-0.002}$ & $89.47^{+0.04}_{-0.04}$ \\ g & $118.3807^{+0.0010}_{-0.0006}$ & $693.8021^{+0.0030}_{-0.0021}$ & $<25$ & $3.33^{+0.06}_{-0.08}$ & $<4$ & $0.466^{+0.004}_{-0.004}$ & $89.87^{+0.05}_{-0.06}$ \enddata \tablenotetext{$\dagger$}{From Table 1 of \citet{lis13}.} \tablenotetext{$\ddagger$}{From Table 4 of \citet{lis13}.} \tablenotetext{*}{From Table 2 of \citet{lis13}.} \end{deluxetable*} The Kepler-11 multi-planet system is one of the earliest discovered of the {\it Kepler} systems \citep{lis11} and has been studied and characterized in sufficient detail to greatly improve the phase model. Despite having a {\it Kepler} magnitude of 13.709 (NASA Exoplanet Archive), which places it midway between the brightest and faintest of the {\it Kepler} systems, Kepler-11 represents an idealized case of a compact multi-planet system comprised of relatively large, in a Kepler sense, planets which should produce the maximum cumulative flux ratio when all planets are near superior conjunction. Also, the planets in this system fall into a radius regime where the geometric albedos are largely unknown. Therefore, in this paper we investigate the phase variations of the tightly packed Kepler-11 mutli-planet system in an effort to constrain its planetary albedos. In Section 2, we present the characteristics of the overall system which are input in to the system's flux ratio model. We use an atmosphere model to calculate the system phase variations in Section 3 and also show the system configuration at times of peak flux amplitude. In Section 4, we describe the processing of the long cadence Kepler data. We present our results from fitting and extracting phase signatures for the Kepler-11 system along with our subsequent constraints for the planetary albedos in Section 5. | The Kepler multi-planet systems allow accurate orreries to be constructed. One advantage of this is the prediction of observable features which coincide with specific orbital configurations. One such time-variable observable is that of phase variations. Here we have used available system properties of the compact Kepler-11 system to predict the phase modulation due to the orbital motion of the planets. By connecting these predictions to the Kepler data from Q1 to Q17, we have investigated the possibility of that signatures of peak phase amplitude may be present in the data. Our results show that quarters with predicted maximum phase peaks, when there are a sufficient number of planets close to superior conjunction, are best fit by a phase model rather than a constant model. Although the signal-to-noise of the Kepler-11 data compared with the model does not allow this to be conclusively shown to be the cause of the correlation, it does demonstrate how this technique may be used to further investigate similar systems. We have additionally shown how the sensitivity of phase variations to planetary radius and albedo allows for a wider range of planetary systems to be explored in this way. The full list of Kepler candidates now contains many multi-planet systems for which precise timing information is available. A more thorough investigation of the phase properties of these systems will yield an additional step toward characterizing the planets contained therein. | 14 | 4 | 1404.7538 |
1404 | 1404.2401_arXiv.txt | { We present the archive of the wide-field plate observations obtained at the University Observatory Jena, which is stored at the Astrophysical Institute of the Friedrich Schiller University Jena. The archive contains plates taken in the period February 1963 to December 1982 with the 60/90/180-cm Schmidt telescope of the university observatory. A computer-readable version of the plate metadata catalogue (for 1257 plates), the logbooks, as well as the digitized Schmidt plates in low and high resolution are now accessible to the astronomical community.This paper describes the properties of the archive, as well as the processing procedure of all plates in detail.} | The large astronomical plate collections provide unique resources for photometric and astrometric studies of astronomical objects. The plates may serve as a unique and crucial opportunity to investigate e.g. the long-term photometric behaviour of stars, identify pre-supernovae, get positional information of asteroids or comets, etc. . From this point of view preservation of the fragile glass plates as digital copies for quick and informative access by the astronomical community is a timely and important enterprise. In this paper we present the results of the archiving of the plate collection, obtained in the period 1963 to 1982 with the 60/90/180-cm Schmidt camera of the University Observatory Jena, operated by the Astrophysical Institute of the Friedrich Schiller University (henceforward abbreviated as AIU). The archiving process comprises the setup of a plate inventory, the preparation of a computer-readable version of the plate metadata catalogue, the plate digitization with two different resolutions, as well as the astrometric solution of all images. At this time, this is the only fully digitized plate archive with astrometric solutions in Germany. | The archiving work on the Schmidt plate collection of the AIU was done as part of a long-term project to support preservation and repeated usage of the world-wide fund of astronomical wide-field photographic plate collections. This international project strives for general on-line access by the scientific community to archives, plate metadata, and digitized plate images with optimal photometric and astrometric accuracy. The preparation of the AIU plate catalogue together with some statistical evaluation, as well as the scanning procedure are described in this paper. The catalogue is included in the WFPDB, which is accessible online\footnotemark[1]. The database, among other things, provides information on the telescope, parameters of the observations, details from the logbook, and previews of the scanned Schmidt plates with limited resolution. Beyond that, the paper gives insights into the history of photographic observations carried out at the University Observatory Jena with the 60/90/180-cm Schmidt telescope between 1963 and 1982. An images of the digitized plates in their original file formats (FITS) are available upon request. | 14 | 4 | 1404.2401 |
1404 | 1404.5017_arXiv.txt | In the general scenario of Weakly Interacting Massive Particles (WIMP), dark matter (DM) can be observed via astrophysical gamma-rays because photons are produced in various DM annihilation or decay processes, either as broad-band or line emission, or because of the secondary processes of charged particles in the final stages of the annihilations or the decays. The energy range of the former processes is accessible by current ground-based Imaging Atmospheric Cherenkov telescopes (IACTs, like H.E.S.S., MAGIC and VERITAS). The strengths of this technique are: a) the expected DM gamma-ray spectra show peculiar features like bumps, spikes and cutoff that make them clearly distinguishable from the smoother astrophysical spectra, b) the expected DM spectrum is universal and therefore by observing two or more DM targets with the same spectrum, a clear identification (besides detection) of DM would be enabled. The role of IACTs may gain more importance in the future as the results from the LHC may hint to a DM particle with mass at the TeV or above, where the IACTs sensitivity is unsurpassed by other experiments. In this contribution, a review of the search for DM with the current generation of IACT will be presented. | \label{sec:intro} \vspace{-3mm} One of the most interesting and compelling observations that ground-based Cherenkov telescopes operating in the very-high-energy gamma-ray band can perform is that looking at targets in the sky where a large concentration of dark matter (DM) is expected. There are several reasons in support of this. {\bf First} of all, DM is indeed expected in the sky. 80\% of the total matter content of the Universe is constituted by one or more new types of particles. The DM has shaped the formation of the first stars and galaxies, so thoroughly that the concordance cosmological model is called $\Lambda$CDM where CDM stands for Cold DM. We also know that there are places in the sky where DM is expected to be particularly concentrated. We don't know the DM nature and if it could finally be detected via primary or secondary radiation associated with its annihilation or decay, but there are several models that predict such signatures and it is therefore worth ``sailing'' our telescopes to these promised lands, despite no ``Earth!'' signal has arrived so far. {\bf Secondly}, the gamma-ray band is a very privileged one, for several reasons: a) gamma-rays are neutral and trace back to the point of origin, where we expect DM, b) the gamma-ray spectrum emerging from DM interactions (either annihilations or decays) is universal. All DM targets are expected to show exactly the same gamma-ray spectrum. The observation of multiple spectra from different targets would therefore constitute an excellent result, c) gamma-ray spectra from DM annihilations or decay typically show several characteristic features, naturally depending on the specific dark matter type, but in general classifiable in sharp cutoff, bumps, or even line emissions. This makes the DM spectra hardly confusable with typical astrophysical spectra. {\bf Third}, the recent experimental results of the LHC experiments: the quite large Higgs boson mass and the non-evidence for New Physics beyond the Standard Model are possibly hinting to DM particle being more massive than expected, about the TeV or above~\cite{Feng:2013pwa}. The TeV region is where ground-based telescopes have highest sensitivity. And indeed this is what was done in the last decade, specially with the H.E.S.S., MAGIC and VERITAS experiments. These very successful experiments, all together, invested quite a large fraction of their observation times in the last years to cover % the targets where DM was expected. In this contribution, we will try to review these observations. For additional details on gamma-ray signals from dark matter, we refer the reader to Ref.~\cite{Bringmann:2012ez}. \vspace{-2mm} | \label{sec:conclusions} \vspace{-3mm} \begin{figure}[t] \centering \includegraphics[width=0.95\linewidth]{./figure2_mod.eps} \vspace{-3mm} \caption{\label{fig:compare} Comparison of some exclusion lines for the Fermi-LAT observation of 15 combined DSGs for $b\bar{b}$ (solid black)~\cite{Ackermann:2013yva}, H.E.S.S. observation of the galactic center halo for the NFW (dot-dashed blue~\cite{Abramowski:2011hc}) for the $b\bar{b}$ channel, MAGIC-stereo observations of the Segue~1 DSG for the $b\bar{b}$ (solid red) and $\tau^+\tau^-$ (dashed red) channels~\cite{Aleksic:2013segue}, Veritas observations of the Segue~1 DSG for $b\bar{b}$ (dashed green) \cite{Aliu:2012ga}, and for the estimation for 100~h observation at the galactic center halo with CTA (thick dashed blue)~\cite{Doro:2012xx}. More details in the text.} \end{figure} In Fig.~\ref{fig:compare} we collect few results on the exclusion curves for WIMP annihilation cross-section. On the bottom left side of the plot, we see the exclusion power of Fermi-LAT observation of 15 combined DSGs for the $b\bar{b}$ (solid black line)~\cite{Ackermann:2013yva} We also show the best limit obtained on DSG observation with Segue~1 observed during 158~h with the MAGIC stereo experiment again for the $b\bar{b}$ (solid red line) and $\tau^+\tau^-$ (dashed red line) channels~\cite{Aleksic:2013segue}. These two channels somehow represent two extreme cases, a very soft spectrum ($b\bar{b}$) and a very hard spectrum ($\tau^+\tau^-$). One can see that because of the better sensitivity of MAGIC at higher energies, the harder $\tau^+\tau^-$ channel is better constrained. The same target was observed in 48~h of observation with Veritas (dashed green) \cite{Aliu:2012ga}. In blue, we show the H.E.S.S. exclusion curve from the galactic center halo for the NFW (dot-dashed blue line) \cite{Abramowski:2011hc} for the $b\bar{b}$ channel only. Finally, we show estimates for 100~h observation of the Galactic Center halo region with CTA (thick dashed blue, \cite{Doro:2012xx}) considering again a NFW profile. The detection of gamma-rays provides complementary information to other experimental probes of particle DM, especially that of direct detection, because CTA could be able to access a fraction of the parameter space not accessible otherwise~\cite{Bergstrom:2010gh}. With respect to particle searches at the LHC, the comparison is not straightforward, as LHC results are usually strongly related to specific models, and general conclusions are somewhat model dependent. In any case, LHC discovery of DM, would prompt the need for proof that the particle is actually consistent with the astrophysical DM. A concrete scenario has been analyzed~\cite{Bertone:2011pq} in the case of a SUSY model in the so-called co-annihilation region. Simulated LHC data were used to derive constraints on the particle physics nature of the DM, with the result that the LHC alone is not able to reconstruct the neutralino composition. The situation improves if the information from a detection of gamma-rays after the observation of the Draco DSG by IACT like CTA is added to the game: the internal degeneracies of the SUSY parameter space are broken and including IACT results allows us to fully interpret the particle detected at the LHC as the cosmological DM. In the other case where the LHC will not detect any physics beyond the Standard Model, predictions were made in the context of the CMSSM~\cite{Bertone:2011kb} indicating that the mass of the neutralino will be bound to be close to the TeV scale. In this scenario, MAGIC, H.E.S.S. and VERITAS and, even more, CTA could be the only instrument to be able to detect and identify a WIMP candidate with masses beyond some hundreds GeV. Finally, we mention that CTA will open a new possibility in detecting DM with IACTs based on the detection of spatial anisotropies in the diffuse extragalactic gamma-ray sky~\cite{Fornasa:2012gu,Ripken:2012db}. \vspace*{3mm} \footnotesize{{\bf Acknowledgment:}{ I gratefully acknowledge J.~Conrad, C.~Farnier, R.~Ong, M.~Fornasa and A.~Smith for comments on the manuscript as well as the MAGIC and CTA collaborations. This work is funded by University of Padova.} | 14 | 4 | 1404.5017 |
1404 | 1404.1825_arXiv.txt | \PRE{\vspace*{.15in}} \noindent The tensor-to-scalar ratio ($r = 0.20^{+0.07}_{-0.05}$) inferred from the excess B-mode power observed by the Background Imaging of Cosmic Extragalactic Polarization (BICEP2) experiment is almost twice as large as the 95\% CL upper limits derived from temperature measurements of the WMAP ($r<0.13$) and Planck ($r<0.11$) space missions. Very recently, it was suggested that additional relativistic degrees of freedom beyond the three active neutrinos and photons can help to relieve this tension: the data favor an effective number of light neutrino species $N_{\rm eff} = 3.86 \pm 0.25$. Since the BICEP2 ratio implies the energy scale of inflation ($V_*^{1/4} \sim 2 \times 10^{16}~{\rm GeV}$) is comparable to the grand unification scale, in this paper we investigate whether we can accommodate the required $N_{\rm eff}$ with three right-handed (partners of the left-handed standard model) neutrinos living in the fundamental representation of a grand unified exceptional $E_6$ group. We show that the superweak interactions of these Dirac states (through their coupling to a TeV-scale $Z'$ gauge boson) lead to decoupling of right-handed neutrino just above the QCD cross over transition: $175~{\rm MeV} \alt T_{\nu_R}^{\rm dec} \alt 250~{\rm MeV}$. For decoupling in this transition region, the contribution of the three right-handed neutrinos to $N_{\rm eff}$ is suppressed by heating of the left-handed neutrinos (and photons). Consistency (within $1\sigma$) with the favored $N_{\rm eff}$ is achieved for $4.5~{\rm TeV} < M_{Z'} < 7.5~{\rm TeV}$. The model is fully predictive and can be confronted with future data from LHC14. | The concordance model of cosmology, with dark energy ($\Lambda$), cold dark matter (CDM), baryons, and three flavors of left-handed ({\it i.e.} one helicity state $\nu_L$) neutrinos (along with their right-handed antineutrinos $\overline \nu_R$), provides a consistent description of the late early universe: big-bang nucleosynthesis (BBN), at $\sim 20$ minutes, the cosmic microwave background (CMB), at $\sim 380~{\rm Kyr}$, and the galaxy formation epoch, at $\agt 1~{\rm Gyr}$~\cite{Beringer:1900zz}. Inflationary cosmology extends the $\Lambda$CDM model by postulating an early period where the scale factor of the universe expands exponentially: $a \propto e^{Ht}$, where $H = \dot a/a$ is the Hubble parameter~\cite{Guth:1980zm}. If the interval of exponential expansion satisfies $\Delta t \agt 60/H$, a small casually connected region can grow sufficiently to accommodate the observed homogeneity and isotropy, to dilute any overdensity of magnetic monopoles, and to flatten the spatial hyper-surfaces (i.e., $\Omega \equiv \frac{8\pi \rho}{3 M_{\rm Pl} H^2} \to 1$, where $M_{\rm Pl} = G^{-1/2}$ is the Planck mass and $\rho$ the energy density; throughout we use natural units, $c = \hslash = 1$). The simplest inflationary models adopt Einstein gravity sourced by a scalar field $\phi$ and a potential $V(\phi)$~\cite{Linde:1981mu,Albrecht:1982wi,Linde:1983gd,Freese:1990rb}. In co-moving coordinates an homogeneous scalar field with minimal coupling to gravity has the equation of motion \begin{equation} \ddot{\phi} + 3 H\dot{\phi} + V' = 0, \end{equation} where $V' = dV/d\phi$. The phase of quasi-de Sitter expansion ($H \approx {\rm const.}$), when the scalar field rolls slowly down the potential, can only be sustained for a sufficient long period of time if \be \thalf \dot{\phi}^2 \ll |V| \quad {\rm and} \quad \left| \frac{\ddot{\phi}} {3 H \dot{\phi}}\right| \ll 1 \, . \ee These conditions imply \be \epsilon \equiv \frac{\mpl^2}{16\pi} \left(\frac{ V'}{V}\right)^2\ll 1 \quad {\rm and} \quad \eta \equiv \frac{\mpl^2} {8\pi} \left| \frac{ V''} {V} - \frac{1}{2} \left(\frac{V'}{V} \right)^2\right| \ll 1 \,,\ee respectively. Quantum fluctuations in de Sitter space causally generate large-scale density fluctuations, which are necessary for the formation of galaxies and large-scale structure. As a bonus, small perturbations ($h_{ij}$, with $h_i^i = \partial^i h_{ij} =0$) in the metric of space-time, \begin{equation} ds^2 \equiv g_{\mu \nu} dx^\mu \, dx^\nu = dt^2 - a \, (\delta_{ij} + h_{ij}) \, dx^i dx^j \,, \end{equation} become redshifted out to the horizon~\cite{Mukhanov:1981xt,Hawking:1982cz,Bardeen:1983qw}. The gravity-wave fluctuations are nearly frozen on super-Hubble scales and their B-mode power spectrum, \begin{eqnarray} {\cal P}_h & = & A_t \lb \frac k {k_*} \rb^{n_t + \frac 1 2 \alpha_t \ln \lb \frac k {k_*} \rb + \cdots} \\ & \simeq & {128V\over 3M_{\rm{Pl}}^4}\left[1 - \left(2C + \frac 5 3 \right) \epsilon \right] \, \lb \frac k {k_*} \rb^{n_t + \frac 1 2 \alpha_t \ln \lb \frac k {k_*} \rb + \cdots} , \end{eqnarray} can be imprinted in the CMB temperature and polarization. Here, the pivot $k_* = a H$ typifies scales probed by the CMB, $C \equiv \gamma_E + \ln 2 -2 \approx -0.7296$. To second order in $\epsilon$ the spectral index and its running are given by \begin{equation} n_t \simeq -2\epsilon + \left(\frac 8 3 +4C \right) \xe \eta -\frac 2 3 (7+6C) \xe^2 \quad {\rm and} \quad \alpha_t \equiv {d n_t \over d \ln k} \simeq -4\epsilon(\epsilon-\eta)\,, \end{equation} respectively~\cite{Leach:2002ar}. On the other hand, the power spectrum of curvature perturbations is given by \begin{eqnarray} {\cal P}_\chi & = & A_s \lb \frac k {k_*} \rb^{n_s -1 + \frac 1 2 \alpha_s \ln \lb \frac k {k_*} \rb + \cdots} \nonumber \\ & \simeq & {8V\over 3M_{\rm{Pl}}^4\epsilon}\left[1 - (4C + 1) \epsilon + \lb 2C -\frac 2 3\rb\eta\right] \lb \frac k {k_*} \rb^{n_s -1 + \frac 1 2 \alpha_s \ln \lb \frac k {k_*} \rb + \cdots} \,, \end{eqnarray} where \be n_s \simeq 1-4\epsilon+2\eta+ \left(\frac {10} 3 +4C \right) \xe \eta - (6+4C) \xe^2 + \frac 2 3 \eta^2 - \frac{2}{3} (3 C-1) \left(2 \xe^2-6 \xe \eta +\xi ^2\right)\,, \ee \be \alpha_s \equiv {d n_s \over d \ln k} \simeq -8 \epsilon ^2+ 16 \epsilon \eta -2\xi^2\,, \quad {\rm and} \quad \xi^2 \equiv \frac {M_{\rm Pl}^4 V' V'''} {64 \pi^2 V^2} \, . \ee For single field inflation with canonical kinetic term, the tensor spectrum shape is not independent from the other parameters. Slow-roll expansion implies a tensor-to-scalar ratio at the pivot scale of \begin{equation} r\equiv {A_t \over A_s} \simeq 16 \epsilon + 32\lb C - \frac 1 3 \rb \xe (\xe - \eta) \, . \end{equation} Very recently, the BICEP2 Collaboration reported the measurement of low-multipole B-mode polarization~\cite{Ade:2014xna}. The observed B-mode power spectrum is well-fit by a $\Lambda$CDM $+ r$ model, with $r = 0.20^{+0.07}_{-0.05}$, and is inconsistent with the null hypothesis, $r=0$, at a significance of $7\sigma$. Such unexpectedly large value of $r$ corresponds to a Hubble rate, $H \simeq 1.1 \times 10^{14}~{\rm GeV}$, constraining the energy scale of inflation: $V_*^{1/4} \sim 2 \times 10^{16}~{\rm GeV}$. The BICEP2 dataset then provides the first experimental evidence for the existence of a new physics scale in between the electroweak and Planck scales, which is astonishingly closed to the grand unification scale (determined by extrapolation of the running coupling constants $\alpha_{\rm QCD}$, $\alpha_{\rm QED}$, and $\alpha_{\rm weak}$ to a common, ``unified'' value). BICEP2 data, however, is in significant tension with Planck's 95\% CL upper limit, \mbox{$r< 0.11$,} from the temperature anisotropy spectrum in the simplest inflationary $\Lambda$CDM~$+r$ model~\cite{Ade:2013uln}.\footnote{BICEP2 data is also in tension with the 95\% CL upper limit, \mbox{$r< 0.13$}, reported by the WMAP Collaboration~\cite{Hinshaw:2012aka}.} The conflict is a result of the fact that the large angle temperature excess foreshadowed by the gravitational waves is not observed. This apparent mismatch cannot be resolved by varying parameters in this very restrictive, seven parameter model: $\{ \Omega_{\rm CDM} h^2,$ $\Omega_b h^2,$ $\tau, \, \Theta_{\rm s},\, A_s \,, n_s,\, r\}$, where $\Omega_{\rm CDM} h^2$ is the CDM energy density, $\Omega_b h^2$ is the baryon density, $\Theta_{\rm s}$ is the ratio between the sound horizon and the angular diameter distance at decoupling, and $\tau$ is the Thomson scattering optical depth of reionized intergalactic medium. Several explanations have been put forward to help reconcile Planck and BICEP2 measurements (see {\it e.g.}~\cite{Ashoorioon:2014nta,Ko:2014bka,Smith:2014kka}) . Of particular interest here, it was pointed out that the tension can be relaxed if extra light species ({\it e.g.} massive sterile neutrinos) contribute to the effective number of relativistic degrees of freedom (r.d.o.f.)~\cite{Giusarma:2014zza,Zhang:2014dxk,Dvorkin:2014lea}. In this work we take a somewhat related approach to investigate the possibility of relaxing the tension by considering extra massless neutrino species. Specifically, we associate the extra r.d.o.f. with the right-handed partners of three Dirac neutrinos, which interact with all fermions through the exchange of a new heavy vector meson $Z'$. | Aside from exhibiting temperature fluctuations of one part in $10^{5}$, the CMB is partially polarized. The parity-odd polarization, or B-mode, arises from primordial tensor fluctuations, which manifest as gravitational waves. The temperature map provided by the Planck mission constrains the value of tensor-to-scalar perturbations, $r<0.11$ at 95 CL. However, recent BICEP2 B-mode polarization data is in tension with this constrain, as imply a value $r=0.20^{+0.07}_{-0.05}$. Very recently, it was suggested that additional relativistic degrees of freedom beyond the three active neutrinos and photons can help to relieve this tension: the data favor an effective number of light neutrino species $N_{\rm eff} = 3.86 \pm 0.25$. We have shown that we can accommodate the required $N_{\rm eff}$ with the contribution from the right-handed partners of the three, left-handed, SM neutrinos (living in the fundamental representation of $E_6$). The six additional fermionic r.d.o.f. can be suppressed to levels in compliance with the favored $N_{\rm eff}$, because the milli-weak interactions of these Dirac states (through their coupling to a TeV-scale $Z'$ gauge boson) may allow the $\nu_R$'s to decouple much earlier, at a higher temperature, than their left-handed counterparts. If the $\nu_R$'s decouple during the quark-hadron crossover transition, they are considerably cooler than the $\nu_L$'s and contribute less than 3 extra ``equivalent neutrinos'' to the early Universe energy density. For decoupling in this transition region, the 3\,$\nu_R$ generate $\Delta N_{\nu} = 3(T_{\nu_R}^{\rm dec}/T_{\nu_L}^{\rm dec})^{4} < 3$, extra relativistic degrees of freedom. These requirements strongly constrain the mass of the heavy vector field. Consistency (within $1\sigma$) with $N_{\rm eff}$ is achieved for an effective coupling $\overline g = 0.46$ and $Z'$ mass in the range $4.5~{\rm TeV} < M_{Z'} < 7.5~{\rm TeV}$. The model is fully predictive and can be confronted with future data from LHC14. | 14 | 4 | 1404.1825 |
1404 | 1404.1014_arXiv.txt | {A basic principle of long baseline interferometry is that an optical path difference (OPD) directly translates into an astrometric measurement. In the simplest case, the OPD is equal to the scalar product between the vector linking the two telescopes and the normalized vector pointing toward the star. However, in some circumstances, a too simple interpretation of this scalar product leads to seemingly conflicting results, called here "the baseline paradox".} { For micro-arcsecond accuracy astrometry, we have to model in full the metrology measurement. It involves a complex system subject to many optical effects: from pure baseline errors to static, quasi-static and high order optical aberrations. The goal of this paper is to present the strategy used by the "General Relativity Analysis via VLT InTerferometrY" instrument (GRAVITY) to minimize the biases introduced by these defects.} {It is possible to give an analytical formula on how the baselines and tip-tilt errors affect the astrometric measurement. This formula depends on the limit-points of three type of baselines: the wide-angle baseline, the narrow-angle baseline, and the imaging baseline. We also, numerically, include non-common path higher-order aberrations, whose amplitude were measured during technical time at the Very Large Telescope Interferometer (VLTI). We end by simulating the influence of high-order common-path aberrations due to atmospheric residuals calculated from a Monte-Carlo simulation tool for Adaptive optics (AO) systems.} {The result of this work is an error budget of the biases caused by the multiple optical imperfections, including optical dispersion. We show that the beam stabilization through both focal and pupil tracking is crucial to the GRAVITY system. Assuming the instrument pupil is stabilized at a 4\ cm level on M1, and a field tracking below $0.2\,\lambda/D$, we show that GRAVITY will be able to reach its objective of $10\ \mu$as accuracy.} {} | A particular interest of astronomical long baseline optical interferometers is their ability to perform high accuracy angular astrometry \citep{1992A&A...262..353S}. The basic idea is that they can leverage on the high resolution offered by baselines of several hundred of meters. However, the implementation of astrometry is not straightforward. The practical measurement is a monitoring of the paths of the stellar lights inside the facility. More precisely, it is a measurement of the difference in optical path (OP) length between each arm of the interferometer. This is usually done with an internal metrology system, going from the interferometric lab up to the telescopes. The idea behind this is that an homodyne interferometer converts an angular position on the sky to an optical path difference (OPD). In the first order approximation, this optical path difference is equal to the direction of the star in the sky ($\vec s$) projected onto the baseline vector of the interferometer ($\vec B$): \begin{equation} OPD=\vec s \cdot \vec B\,. \label{eq1} \end{equation} Within this simple equation is hidden a lot of complexity. Above all, how is the baseline vector defined? The intuitive answer is to define the baseline by the vector which links the geographical position of the two telescopes. But unfortunately, it only has a sense in the case of two perfectly identical telescopes. This immediately implies some questions : what happens when the two telescopes are not identical? What happens if, for one reason or another, the optical alignment of the two telescopes is not identical? When dealing with precision astrometry, these kind of problem gets pivotal. The main scientific objective of the GRAVITY instrument is to probe the event horizon of the Galactic Center black hole \citep{2011Msngr.143...16E}. It will have to reach an unprecedented astrometric accuracy between two one-arcsec-separated objects of the order of $10\,\mu$as (ten part par million). According to Eq.~(\ref{eq1}), it means that the baseline of the Very Large Telescope Interferometer (VLTI) must be know to a sub-millimeter level. To complicate the fact that the baseline must be known to an extreme precision, the literature defines several baselines \citep{1999ApJ...510..505C,2004SPIE.5491.1649H,2013A&A...551A..52S}. From the simple definition of the baseline by \citet{2000plbs.conf.....L} (the distance between two apertures), emerged the idea of a Wide Angle Baseline (WAB), a Narrow Angle Baseline \citep[NAB,][]{2009NewAR..53..344C} and an Imaging Baseline \citep[IMB,][]{PI}. The idea behind these definitions was that each baseline corresponds to a given usage of the interferometer. But all these baselines affect the astrometric measurement to various degrees. \citet{PI} used the so-called "limit-points" to define the baselines vectors. Instead of defining the vector by its direction and length, the baseline vector is defined by the point from where it emerges to the point where it goes: the vector is also defined by its geographical position. In this paper, we establish how the position of the various limit-points affect the OPD measurement. Errors due to optical aberrations are intrinsically linked to the position of the limit-points, and we will see that they are an important part of astrometric limitations. Throughout this paper, we will build an error budget, focusing on the biases that occur due to baseline errors and optical aberrations, and showing how GRAVITY, through pupil control, plans to keep these bias below $10\ \mu$as. Note that this paper does not intend to cover random process errors like photon noise, detector noise or background noise. This paper starts with a presentation of ``The baseline paradox of optical interferometry''. Described in section~\ref{secparad}, it shows in a pedagogical way how a too simple assumption on the concept of baseline leads to conflicting observations. In section~\ref{secBaselines}, we use a three dimensional model of the interferometer to calculate the impact of the different baselines limit-points on the OPD measurement. However, this analytical modeling is not enough to account for aberrations of order higher than the tip-tilt. So in section~\ref{secHO} we simplify the problem to two dimension to investigate how these aberrations modify the OPD. The rest of the sections apply those results to the GRAVITY instrument. Section~\ref{secgravity} describes how the instrument works, and the technical choices made for the astrometric measurement. Section~\ref{secerror} puts concrete numbers on the errors and the way they affect astrometry. The end-product of this section is the error budget presented in Table~\ref{table:1}. Section~\ref{secconclusion} concludes. | \label{secconclusion} \subsection{15 years of experimentation} The predominantly theoretical exercise of this paper is supported by 15 years of experimentation carried out on various interferometers. The first astrometric observations with a long baseline interferometer were achieved around 1999 on the Palomar Testbed Interferometer \citep{1999ApJ...510..505C}, based on the theoretical work of \citet{1992A&A...262..353S}. Using small siderostats on 100 meter-long baselines, the instrument reached 160\ $\mu$as precision measurements on bright pairs \citep{1999AAS...195.8714S}. PTI was a technology demonstrator in preparation to the four 1.8 m telescopes planned to be added to the Keck Interferometer. The Keck Outrigger astrometry project was the first to tackle the issue of implementing astrometric baselines on large telescopes. The concept foresees to transfer the metrology end-point to primary space by a dedicated baseline monitor \citep{2004SPIE.5491.1649H}. However, the project was cancelled in 2006 before seeing first light. Started in 2008, and even though it never managed an on-sky astrometric demonstration, the ASTRA project of astrometric extension of the two 10 meter Keck Interferometer was the occasion to further study the implementation of metrologies for astrometric interferometer on large telescopes. The design of PRIMA \citep{2008NewAR..52..199D}, the VLTI equivalent to ASTRA and the Keck Outriggers, started in 2000. In 2011, during its first on-sky observations, PRIMA achieved an astrometric precision of 30\ $\mu$as, but the astrometric accuracy was limited to about 3 mas, mainly because the metrology endpoints were located at the telescopes Coude foci, far from primary space \citep{2013A&A...551A..52S}. A second on-sky demonstration run in 2013, with the metrology extended to the telescope secondary mirror, resulted in an astrometric accuracy of order 100\ $\mu$as. The GRAVITY metrology \citep{2012SPIE.8445E..1OG} follows a slightly different concept than the previous experiments. Instead of measuring in double pass the optical path difference between two telescopes for each star, as done for PRIMA and ASTRA, the GRAVITY metrology measures the optical path difference between the two beams for each telescope in single pass. And other than in PRIMA and ASTRA, the GRAVITY metrology end points are mounted above the primary mirror on the telescope spider, therefore covering the full optical path and providing a physical realization of the narrow angle baseline endpoints. A second laser is send back from the telescope to actively track the pupil on the metrology endpoints \citep{2012SPIE.8445E..34A}. \subsection{On the GRAVITY astrometric error budget} A sophisticated error budget was a central design driver for GRAVITY. The idea is to cancel as many error terms as possible thanks to technical choices. For example, the metrology is sent up to the spider arms, above M1. It is located in geographical coordinates to minimize error when transposing the physical narrow angle baseline to the sidereal reference frame (Section~\ref{secNABi}). The metrology is also send by the same single-mode fibers that accept the star light. The difference in propagation direction between the metrology and the starlight is therefore minimized (Section~\ref{secIMBi}). The necessity of \textbf{an active control over the pupils} (the imaging baseline limit-points) is one of the main requirement given by the error budget. The imaging baselines introduce an error term if the instrument pupil and focal plane are not correctly stabilized to a given position (Section~\ref{secIMB}). This issue cannot be canceled out by technical design, so GRAVITY includes inside its own cryostat a pupil and field tracking system. This system controls in real time the position of the instrument pupil with respect to four laser beacons on the spider arms of the telescopes. It also monitors the position of the stellar objects to keep them accurately positioned (within $0.2\lambda/D$) on the fibers. \textbf{Field tracking is also a fundamental issue} to minimize the influence of common-path aberrations. At first sight, common path aberrations (eg., atmospheric perturbations) do not matter. This is not the case if there is an additional error on the field tracking: it is the cross-term between field error and atmospheric perturbation which matters. In section~\ref{secCPi}, we showed that atmospheric perturbations have the potential to be the major limit of the astrometric precision, depending on the level of star tracking. Moreover, we show that GRAVITY's accuracy will depend on the level of AO correction. Notably, the absence of AO on the ATs does put a stringent requirement on the affordable tip-tilt errors for the system to work (see Table~\ref{table:3}). The main result of the error budget is that GRAVITY should fulfill its objective of $10\ \mu$as accuracy on the UTs if: i) the telescope pupils are positioned within the instrument to an accuracy of 0.5\% of their diameter (4\ cm on M1) and ii) the two stellar objects are tracked within $0.2\,\lambda/D$. | 14 | 4 | 1404.1014 |
1404 | 1404.4631_arXiv.txt | A significant fraction (\(\sim 30\)\%) of the high-energy gamma-ray sources listed in the second \textit{Fermi} LAT (2FGL) catalog are still of unknown origin, being not yet associated with counterparts at lower energies. In order to investigate the nature of these enigmatic sources, we present here an extensive search of X-ray {sources lying in the positional uncertainty region} of a selected sample of these Unidentified Gamma-ray Sources (UGSs) that makes use of all available observations performed by the \textit{Swift} X-ray Telescope before March 31, 2013, available for 205 UGSs. To detect the fainter sources, we merged all the observations covering the {\textit{Fermi} LAT} positional uncertainty region at 95\% level of confidence of each UGSs. This yields a catalog of 357 X-ray sources, finding {candidate} X-ray counterparts for \(\sim 70\)\% of the selected sample. In particular, 25\% of the UGSs feature a single X-ray source within their positional uncertainty region while 45\% have multiple X-ray sources. For each X-ray source we also looked in the corresponding \textit{Swift} UVOT merged images for optical and ultraviolet counterparts, also performing source photometry. We found ultraviolet-optical correspondences for \(\sim 70\)\% of the X-ray sources. We searched several major radio, infrared, optical and ultraviolet surveys for possible counterparts within the positional error of the sources in the X-ray catalog to obtain additional information on their nature. Applying the kernel density estimator technique to infrared colors of WISE counterparts of our X-ray sources we select 6 \(\gamma\)-ray blazar candidates. In addition, comparing our results with previous analyses, we select 11 additional \(\gamma\)-ray blazar candidates. | \label{sec:intro} One of the biggest challenges of modern \(\gamma\)-ray astronomy and one of the main scientific objectives of the ongoing \textit{Fermi} mission is unraveling the nature of the Unidentified Gamma-ray Sources (UGSs) \citep[e.g.,][]{abdo09,2009ApJ...697.1071A}. Since the Third EGRET catalog (3EG)\footnote{\href{http://heasarc.gsfc.nasa.gov/W3Browse/cgro/egret3.html} {http://heasarc.gsfc.nasa.gov/W3Browse/cgro/egret3.html}} \citep[e.g.,][]{hartman99} the fraction of \(\gamma\)-ray sources without an assigned counterpart at low energies has been significant \(\sim 30\)\% \citep[e.g.,][]{2003ApJ...590..109S}. This situation was mostly unchanged in the revised EGRET catalog \citep[EGR;][]{2008A&A...489..849C}, even though the improved background modeling applied in the EGR resulted in fewer \(\gamma\)-ray detections (188 sources in total, in contrast to 271 listed in 3EG); 87 out of 188 EGR entries remain unassociated. The UGSs at low Galactic latitude (\(|b|<10 \degr\)) are expected to be associated with local objects lying in our Galaxy, such as molecular clouds (as consequence of interaction with cosmic-rays), supernova remnants, massive stars, pulsars and pulsar wind nebulae, or X-ray binaries \citep[see,e.g.,][]{1999APh....11..277G,2010PASJ...62..769C,2012ApJ...745..140Y,2013Sci...339..807A,2013A&A...553A..34D} although there are few rare cases of \(\gamma\)-ray blazars detected through the Galactic plane \citep[e.g. Fermi J0109+6134, see][]{2010ApJ...718L.166V}. On the other hand, the population of UGSs above the Galactic plane is generally believed to be dominated by extragalactic sources, although there is a suspected Galactic component as well \citep[e.g.,][]{1996ApJ...463..105O,2000ApJ...541..180M,2001ASSL..267...17R,nolan12}. According to one of the most recent \textit{Fermi} discoveries, several millisecond pulsars have been found at high Galactic latitudes \citep{2010ApJ...712.1209A,2010ApJ...712..957A,nolan12}. A large fraction of these UGSs could be blazars, the rarest class of radio-loud active galactic nuclei, whose emission dominates the gamma-ray sky \citep[e.g.,][]{mukherjee97,abdo10}. Their observational properties are generally interpreted in terms of a relativistic jet aligned within a small angle to our line of sight \citep{1978bllo.conf..328B}. The blazar spectral energy distributions (SEDs) typically show two peaks. The first one, lying in the range of {radio} - soft X-rays, is widely held to be due to synchrotron emission by highly relativistic electrons within their jet. The second one lies at hard X-ray or \(\gamma\)-ray energies, and is interpreted as inverse Compton upscattering by the same electrons of the seed photons provided by the synchrotron emission \citep{1996ApJ...463..555I,2008ApJ...686..181F} with the possible addition of seed photons from outside the jets yielding contributions to the non-thermal radiations due to external inverse Compton scattering \citep[see][]{1993ApJ...416..458D,2002ApJ...575..667D,2009ApJ...692...32D,2013ApJ...763..134F} often dominating their \(\gamma\)-ray outputs \citep{ackermann11}. Blazars are also know X-ray sources since \textit{ROSAT} DXRBS \citep{1998AJ....115.1253P,2001MNRAS.323..757L} and \textit{Einstein} IPC \citep{1992ApJS...80..257E,1999AAS...195.1601P} surveys \citep[see also][]{2000AIPC..515...53P}. Since then, the X-ray properties of blazars have been deeply investigated by many authors \citep[see for example][]{1994MNRAS.268L..51G,1995ApJ...444..567P,2011ApJ...739...73M,2011ApJ...742L..32M}. \citet{2008A&A...489.1047M} in particular studied \textit{Swift} observations of a sample of low and intermediate peaked BL Lacs, for which the X-ray emission is expected to lie in the ``valley" between the low and high energy spectral components, finding these sources to be bright in the X-ray with fluxes above \(\sim {10}^{-13}\mbox{ erg}\mbox{ cm}^{-2}\mbox{ s}^{-1}\). In addition we note that \(\sim 75\%\) of the \(\gamma\)-ray blazars listed in the Second LAT AGN Catalog \citep[2LAC,][]{ackermann11} are also X-ray sources with fluxes above \(\sim {10}^{-14}\mbox{ erg}\mbox{ cm}^{-2}\mbox{ s}^{-1}\). However, due to the incompleteness of the current radio and X-ray surveys used for the gamma-ray associations, it is not always possible to identify a blazar-like counterpart to a UGS\footnote{{We note that, in the following, we will refer to a source lying into the positional uncertainty region of a \(\gamma\)-ray source as ``candidate counterpart", while we will use the term ``blazar candidate" for the \(\gamma\)-ray source together with its unique blazar-like counterpart.}}. Radio follow up observations of UGSs have been performed or are still in progress \citep[e.g.,][]{kovalev09a,kovalev09b,2010ApJ...718..587M,2013MNRAS.432.1294P}. \citet{massaro2013b} recently proposed a method for searching \(\gamma\)-ray blazar-like {candidate} counterparts of the UGSs based on the combination of radio observations from Westerbork Northern Sky Survey \citep[WENSS;][]{1997A&AS..124..259R}, those of the NRAO Very Large Array Sky survey \citep[NVSS;][]{1998AJ....115.1693C} and the Very Large Array Faint Images of the Radio Sky at Twenty-Centimeters \citep[FIRST,][]{1995ApJ...450..559B,white97}. In addition, a procedure to recognize blazar-like {candidate} counterparts for UGSs on the basis of their infrared (IR) colors have been successfully implemented by \citet{paper2,2013ApJS..206...12D} and \citet{paper3,2013arXiv1303.3585M} making use of the Wide-Field Infrared Survey Explorer (WISE) all-sky data \citep{cutri12a}. WISE data also proven to be useful to address the widely entertained field of mid-infrared AGN selection (\citealt{2005ApJ...631..163S,2012ApJ...753...30S}, see also \citealt{2010ApJ...708..584E,2010ApJ...717.1181P}). Additional attempts have been recently developed to associate or to characterize the UGSs using pointed \textit{Swift} observations \citep[e.g.,][]{mirabal09a,mirabal09b,2012ApJ...757..176K}, and/or with several statistical approaches \citep[e.g.,][]{mirabal10,ackermann12}. Moreover, in the last two years the \textit{Chandra} and \textit{Suzaku} X-ray telescopes have been used to investigate the nature of the UGSs \citep[e.g.,][]{2011PASJ...63S.857F,2011ApJ...729..103M,2011PASJ...63S.873M,2012ApJ...756...33C,2012PASJ...64..112M}. The characterization of X-ray emission from UGSs is of particular interest. All \(\gamma\)-ray sources associated in the second \textit{Fermi} LAT (2FGL) catalog have a clear radio counterpart \citep{nolan12} leading to the so called radio-\(\gamma\)-ray connection in the case of blazars \citep[e.g.,][]{ghirlanda10,ackermann11,massaro2013b}. However this is not the case for the X-ray sources. It is not clear at the moment if all \(\gamma\)-ray sources feature an X-ray counterpart and therefore a systematic study of X-ray emission from UGS is useful to investigate their nature. Motivated by these researches, we investigate the X-ray-\(\gamma\) connection presenting in this paper a catalog of X-ray {sources lying in the positional uncertainty region of} all UGSs listed in 2FGL without any \(\gamma\)-ray analysis flag, making use of all available observations performed by \textit{Swift} X-ray Telescope (XRT) up to March 31, 2013, and we investigate their multi-wavelength properties. For {X-ray} sources with a WISE counterpart we then apply the Kernel Density Estimation (KDE) technique to compare their IR colors to those of known \(\gamma\)-ray blazars, selecting 44 new blazar-like {candidate} counterparts and 6 \(\gamma\)-ray blazars candidates as a result. The paper is organized as follows: Section \ref{sec:sample} is devoted to the UGS sample definition while Section \ref{sec:swift} describes the main data reduction procedure adopted for the \textit{Swift} XRT and \textit{Swift} UVOT observations. The complete list of X-ray sources that could be potential counterpart of UGSs in the 2FGL catalog is presented in Section \ref{sec:ugs}. In Section \ref{sec:kde} we illustrate our selection of new \(\gamma\)-ray blazar candidates. In Section \ref{sec:comparison} we compare our results with different, previous selections, and Section \ref{sec:summary} is dedicated to our conclusions. | \label{sec:summary} In this work we present a catalog of {X-ray sources lying in the positional uncertainty regions of} the 299 UGSs reported in the 2FGL catalog without any \(\gamma\)-ray analysis flag. To this end, we made use of all available observations performed by \textit{Swift} XRT in PC mode up to March 31, 2013, that where available for 205 UGSs. In order to detect the fainter sources, we merged all the observations corresponding to each UGSs, and applied to these merged observations different detection algorithms (i.e., \textsc{ximage} \textsc{detect} and \textsc{sosta}). The source list was cleaned from spurious and extended sources by visual inspection of all the observations, to yield a final catalog of 357 X-ray sources. We searched several major radio, IR, optical and UV surveys for any possible counterparts within the positional error of our X-ray sources to obtain additional information on their nature, providing a comprehensive list of X-ray sources with multi-wavelength properties. The main results of our analysis can be summarized as follows: \begin{itemize} \item We find X-ray {candidate} counterparts for \(\sim 70\)\% of the UGSs investigated. In particular, we have \(\sim 25\)\% UGSs featuring a single X-ray counterpart and \(\sim 45\)\% UGSs featuring multiple X-ray {candidate} counterparts falling in the positional uncertainty region at 95\% level of confidence. \item For each X-ray source we also looked in the corresponding UVOT merged images for UV-optical counterparts performing sources photometry, and finding UV-optical counterparts to \(\sim 71\)\% of the X-ray sources in our catalog. \item We find no X-ray counterparts for 62 UGSs in our sample (\(\sim 30\)\%), 46 of which have a total exposure \(\geq 3\mbox{ ks}\). \item Comparing our results with \citet{2013arXiv1303.3585M} and \citet{massaro2013b} we find X-ray {candidate} counterparts to 29 sources classified as \(\gamma\)-ray blazar-like. \item Applying the KDE technique to IR colors of WISE counterparts, we obtain an additional list of 37 \(\gamma\)-ray blazar-like sources for 33 UGSs (29 with a unique candidate and 4 with a double candidate). In particular, 10 out of these 33 2FGL sources have radio counterparts, and for 4 UGSs out of 33 we add a different \(\gamma\)-ray blazar-like sources from those selected by \citet{2013arXiv1303.3585M} and \citet{massaro2013b}. \item Among the 51 UGSs that have a single X-ray {counterpart}, 17 have their X-ray counterpart selected as \(\gamma\)-ray blazar-like source with the three methods discussed above, and are there considered as \(\gamma\)-ray blazar candidates. \item The source 2FGL1328.5-4728, a \(\gamma\)-ray blazar candidate selected with the KDE technique, is classified as PSR by \citet{2012ApJ...753...83A}. \end{itemize} Even though blazars are expected to be bright in X-rays, the methods discussed here to find \(\gamma\)-ray blazar-like sources in UGSs uncertainty regions show that this is not always the case. We note that 39 2FGL sources in our sample are in common with the analysis of 1FLG UGSs by \citep{2013arXiv1307.5581T}. Comparing our results with \citet{2012ApJ...753...83A} we note that 38 2FGL sources in our sample are classified as AGN the 1FGL catalog with high level of confidence, 11 2FGL sources in our sample are classified as PSR with low level of confidence, and 17 2FGL sources in our sample are unclassified. In particular, 8 2FGL sources with a \(\gamma\)-ray blazar-like source selected with the KDE technique are classified as AGN by \citet{2012ApJ...753...83A}. Ground-based, optical and near IR, spectroscopic follow up observations will be planned for the \textit{Swift} XRT sources selected as \(\gamma\)-ray blazar-like {candidate} counterparts because they are crucial to confirm the nature of the selected sources and to obtain their redshift, as shown for the unidentified INTEGRAL and \textit{Swift} sources \citep[e.g.,][and references therein]{2012A&A...538A.123M,2012A&A...545A.101P}. ~\\ | 14 | 4 | 1404.4631 |
1404 | 1404.3966_arXiv.txt | The additional resonant contribution to the potential model is examined in $\alpha$+$^{12}$C elastic scattering and the low-energy $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction. The excitation function of elastic scattering below $E_{c.m.}= 5$ MeV seems to be reproduced by the potential model satisfactorily, and it is not profoundly disturbed by the additional resonances. The weak coupling is good enough to describe the $^{16}$O structure in the vicinity of the $\alpha$-particle threshold, especially below $E_{c.m.}= 8$ MeV, corresponding to the excitation energy $E_x \approx 15$ MeV. The additional resonances give the complement of the astrophysical $S$-factors from the simple potential model. The $S$-factor of $^{12}$C($\alpha$,$\gamma$)$^{16}$O at $E_{c.m.}=300$ keV is dominated by the $E$2 transition, which is enhanced by the subthreshold 2$^+_1$ state at $E_x= 6.92$ MeV. The contribution from the subthreshold 1$^-_1$ state at $E_x= 7.12$ MeV is predicted to be small. The additional resonances do not give the large contribution to the thermonuclear reaction rates of $^{12}$C($\alpha$,$\gamma$)$^{16}$O at helium burning temperatures. | The $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction following the triple $\alpha$ reaction in stars plays the very important role in the production of heavier nuclei than carbon \cite{Rol88}. To scrutinize the origin of elements, the low-energy $^{12}$C($\alpha$,$\gamma$)$^{16}$O cross sections have been investigated at helium burning temperatures, corresponding to the center-of-mass energy $E_{c.m.}\approx 300$ keV. However, the cross sections are very small, owing to the Coulomb barrier, so the direct measurement is not feasible at the present laboratories. To cope with the difficulty, the theoretical model calculation has been performed with the simple potential model \cite{Kat12,Kat08}. In this model, $\alpha$+$^{12}$C elastic scattering has been scrutinized to illustrate the feature of the $\alpha$+$^{12}$C continuum state. Below $E_{c.m.}=5$ MeV, the elastic cross sections have been found to be described very well by the simple $\alpha$+$^{12}$C configuration \cite{Kat08,Kat10}. The resulting potential between $\alpha$-particle and $^{12}$C nuclei is concordant with the optical model potential reproducing elastic scattering at laboratory energies $E_\alpha \approx 100$ MeV where the ambiguity of the potential is eliminated \cite{Ing94,Nol87,Mic95,Mic83,Bra97,Sat83}. The $\alpha$+$^{12}$C rotational bands are well reproduced and the 8$^+$ and 9$^-$ states at the excitation energy $E_x\approx$ 30 MeV are predicted to be the known rotational band member \cite{Kat14,Kat13}. From the characteristic feature of the reaction mechanism and the $^{16}$O structure, the low-energy $^{12}$C($\alpha$,$\gamma$)$^{16}$O cross sections have been calculated and they have been converted into the astrophysical reaction rates \cite{Kat12,Kat08}. At $E_{c.m.}= 300$ keV, the radiative capture cross section is dominated by the $E$2 transition to the ground state. The cascade transitions are important above $E_{c.m.}= 1$ MeV, corresponding to $T_9\approx 1$. $T_9$ is the temperature in the unit of $T_9=10^9$ K. The microscopic models have also attempted to describe the $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction and the structure of $^{16}$O (e.g. \cite{Duf08}), theoretically. Recently, the devoted efforts of the progress in the experimental work have been made, as well as the theoretical predictions. At low energies, the $\gamma$-ray angular distribution and its ambiguities have been discussed \cite{Gai13,Pla12,Mak09,Ass06,Kun01}. To cultivate the knowledge of $^{12}$C($\alpha$,$\gamma$)$^{16}$O, the direct measurement of cross sections, the cascade transition through the excited states of $^{16}$O and the total capture reaction cross sections have been investigated experimentally (e.g. \cite{Sch12,Sch11,Sch05,Mat06,Kun02,Rot99,Red87,Ket82}). However, these measurable energies correspond to the relatively high temperatures, even though they use the current technologies. So, the extrapolated values are made by e.g. the $R$-matrix method \cite{Lan58}. To pave the way for the analyses, the phase shifts of $\alpha$+$^{12}$C elastic scattering have also been measured precisely \cite{Tis09,Tis02,Pla87}. The indirect measurements (e.g. \cite{Bru99,Bel07}) and the $\beta$-delayed $\alpha$ decay of $^{16}$N (e.g. \cite{Tan10,Buc06,Buc96,Azu94,Buc93}) have been demonstrated to evaluate the $\alpha$-particle width of the subthreshold 1$^-_1$ state ($E_x= 7.12$ MeV), alternatively. If the radiative capture cross sections are expressed by the Breit-Wigner form, the high energy side of the tail of the subthreshold state could contribute the enhancement of the reaction rates \cite{Rol88,Nacre}. The low-energy $E$1 cross sections are believed to be enhanced by the 1$^-_1$ state. Above $E_{c.m.}\simeq 5$ MeV, the $^{15}$N(p,$\alpha$)$^{12}$C and the $^{15}$N(p,$\gamma$)$^{16}$O reactions are available (e.g.~\cite{Cog07,Cog09,Bar08,Mar10,Imb12, Imb12e,Rol74,Nacre}). The branching ratio of these reactions determines the escape from the main CNO cycle to the CNO-II cycle, and it controls the energy production of the proton burning in a star. The low-lying two 1$^-$ resonant states ($E_x=12.44$ MeV and 13.09 MeV) in the p+$^{15}$N channel appear to be coupled to the $\alpha$+$^{12}$C continuum state. Even at higher energies, the study of the $\alpha$+$^{12}$C system is important in nuclear astrophysics. In our previous studies \cite{Kat12,Kat08}, we have investigated the $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction at sub-barrier energies (below $E_{c.m.}=3$ MeV), and we have provided the derived reaction rates below $T_9=3$. Above the barrier, we see the narrow resonances in the excitation function of elastic scattering (e.g. \cite{Til93,Mar72}) and $^{12}$C($\alpha$,$\gamma$)$^{16}$O (e.g. \cite{Sch12,Sch05}). The contribution from the resonances has not been explicitly discussed yet. At $T_9=3$, the so-called Gamov peak energy $E_0$ and width $\Delta E_0$ \cite{Rol88,Nacre} are $E_0=1.92$ MeV and $\Delta E_0=1.63$ MeV, respectively. If taking account of the numerical integration up to $E_0+3\Delta E_0=6.8$ MeV \cite{Nacre}, we might want to discuss the contribution from the cross sections above the barrier. In the present article, we investigate the additional resonant contribution to the potential model for $\alpha$+$^{12}$C elastic scattering and the $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction. We show whether the potential model reproduces the excitation function of $\alpha$+$^{12}$C elastic scattering and the astrophysical $S$-factors, including the known resonances. We estimate the difference in the derived reaction rates below $T_9=3$. The contribution from the subthreshold states is also discussed. The main purpose of the present study is to examine the additional resonant contribution to the calculated cross sections and reaction rates. In the following section, we explain the potential model with the additional resonances. In Section \ref{sec3}, the contribution from the additional resonances is discussed by showing the difference in the excitation function of $\alpha$+$^{12}$C elastic scattering and the $^{12}$C($\alpha$,$\gamma_0$)$^{16}$O $S$-factors. The derived reaction rates are also compared with the previous ones \cite{Kat12}. The summary is given in Section \ref{sec4}. | \label{sec4} We have examined the additional resonant contribution to the potential model for the $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction. We have calculated the excitation function of $\alpha$+$^{12}$C elastic scattering below $E_{c.m.}= 8$ MeV, the low-energy astrophysical $S$-factors and the reaction rates of $^{12}$C($\alpha$,$\gamma$)$^{16}$O below $T_9=3$. In the present calculation, we use the parity-dependent real potential and include the known resonances as the Breit-Wigner form. The excitation functions and phase shifts of $\alpha$+$^{12}$C elastic scattering below $E_{c.m.}= 5$ MeV seem to be satisfactorily reproduced. The potential scattering appears to give the smooth trend of the excitation function and the single-particle potential resonances below $E_{c.m.}= 8$ MeV. The remaining rapid variation on the excitation function originates from the additional resonances. From the comparison, we find that the weak coupling to other reaction channels is good enough to describe in outline the structure of $^{16}$O below $E_x\approx 15$ MeV. The additional resonances complement the astrophysical $S$-factors obtained from the potential model. However, they do not give the large contribution to the derived $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction rates below $T_9=3$. (below 5\%) The $S$-factor at $E_{c.m.}=300$ keV is dominated by the $E$2 transition because of the subthreshold 2$^+_1$ state. The $E$1 is not enhanced by the subthreshold 1$^-_1$ state. The $S$-factors at $E_{c.m.}= 300$ keV are found to be $S_{E1}\approx 3$ keV~b and $S_{E2}=152$ keV~b, and they are approximately the same as the results of \cite{Kat08}. The simple potential model \cite{Kat08} describes the fundamental process of the radiative capture reactions. Compared with the direct-capture component, the additional $E$1 resonant component is small, and it does not strongly couple to the direct-capture process at low energies. \ack The author thanks Professors K.~Langanke, G.~Mart\'inez-Pinedo, and I.J.~Thompson for their comments and hospitality during his visiting program. He also thanks Professors Y.~Ohnita and Y.~Sakuragi for their hospitality and encouragement and Professor Y.~Kond\=o for the early days of the collaboration. He is grateful to Professors M.~Arnould, A.~Jorissen, K.~Takahashi, and H.~Utsunomiya for their hospitality during his stay at Universit\'e Libre de Bruxelles (ULB). The part of this work has been supported by the Interuniversity Attraction Pole IAP 5/07 of the Belgian Federal Science Policy (Konan University -- ULB convention), and by the JSPS Institutional Program for Young Researcher Overseas Visits ``Promoting international young researchers in mathematics and mathematical sciences led by Osaka City University Advanced Mathematical Institute''. | 14 | 4 | 1404.3966 |
1404 | 1404.3157_arXiv.txt | Doppler planet searches revealed that many giant planets orbit close to their host star or in highly eccentric orbits. These and subsequent observations inspired new theories of planet formation that invoke gravitation interactions in multiple planet systems to explain the excitation of orbital eccentricities and even short-period giant planets. Recently, NASA's Kepler mission has identified over 300 systems with multiple transiting planet candidates, including many potentially rocky planets. Most of these systems include multiple planets with sizes between Earth and Neptune and closely-spaced orbits. These systems represent yet another new and unexpected class of planetary systems and provide an opportunity to test the theories developed to explain the properties of giant exoplanets. Presently, we have limited knowledge about such planetary systems, mostly about their sizes and orbital periods. With the advent of long-term, nearly continuous monitoring by Kepler, the method of transit timing variations (TTVs) has blossomed as a new technique for characterizing the gravitational effects of mutual planetary perturbations for hundreds of planets. TTVs can provide precise (but complex) constraints on planetary masses, densities and orbits, even for planetary systems with faint host stars. In the coming years, astronomers will translate TTV observations into increasingly powerful constraints on the formation and orbital evolution of planetary systems with low-mass planets. Between TTVs, improved Doppler surveys, high-contrast imaging campaigns and microlensing surveys, astronomers can look forward to a much better understanding of planet formation in the coming decade. | Radial velocity (RV) surveys have discovered over 400 planets, most with masses larger than that of Jupiter (http://www.exoplanets.org; \cite{Butler06,Wright11}. Many of the early RV discoveries were ``hot-Jupiters'', planets with orbital periods of up to several days and masses comparable to that of Jupiter or Saturn (e.g., \cite{MayorQueloz95}). As the timespan of observations has increased, the median orbital period of RV-discovered planets has steadily increased to more than a year. Now, we know that hot-Jupiers are a relatively rare outcome of planet formation. Nevertheless, their existence and their orbital properties provide important clues to the planet formation process. \subsection{Disk Migration} Prior to the discovery of hot-Jupiters, planet formation theories had been focused on explaining properties of the solar system \cite{Lissauer93}. The large masses of hot-Jupiters imply a substantial gaseous component and therefore rapid formation, before the protoplanetary disk is dispersed. {\em In situ} formation of the rocky cores of hot-Jupiters is problematic due to the high temperature and low surface density of the disk so close to their host star. Therefore, theorists explain hot-Jupiters starting with the formation of a rocky core at larger separations from the host star, followed by accretion of a gaseous envelope and migration to their current location. The mechanism for migration is less clear. There are two broad classes of models: a gradual migration through a disk \cite{KleyNelson12,Capobianco11} or the excitation of a large eccentricity followed by tidal circularization \cite{RasioFord96,WeidenschillingMarzari96,FabryckyTremaine07}. In principle, planets could migrate through either a gaseous protoplanetary disk or a planetesimal disk. If giant planet cores form beyond the ice line, then planetesimal disks would rarely be massive enough to drive the large-scale migration needed to form a hot-Jupiter. On the other hand, a gaseous protoplanetary disk could power a rapid migration, perhaps too rapid \cite{KleyNelson08}. It is unclear how the planets would avoid migrating all the way into the host star or why the migration would be halted to leave planets with orbital periods of $\sim$2-5 days \cite{FordRasio06}. The apparent pile-up of hot-Jupiters with orbital periods of a few days could be the result of censoring, i.e., those planet that continued to migrate closer to their host star were either accreted onto the star, destroyed or reduced in mass due to stellar irradiation and mass loss. Even in this case, a stopping mechanism must be invoked to produce the observed giant planets with orbital periods beyond $\sim$7 days, since tides rapidly become inefficient with increasing orbital separations. \subsection{Eccentricity Excitation plus Tidal Circularization} Unlike disk migration, eccentricity excitation followed by tidal circularzation naturally explains the ``pile-up'' of hot-Jupiters at orbital periods of 2-7 days due to the rapid onset of tidal effects. The large eccentricities required to initiate circularization could be generated in a variety of ways. The simplest scenario is planet-planet scattering, as it requires only one additional massive planet \cite{RasioFord96}. In the case of two planets and no additional perturbers, the initial ratio of semi-major axes must be small enough to permit close encounters. Such scenarios may arise naturally for giant planets due to rapid mass growth. Alternatively, a system with more than two planets \cite{WeidenschillingMarzari96,LinIda97,AdamsLaughlin03,Chatterjee08,JuricTremaine08} will naturally approach instability on a much longer timescale. Even for a simple three planet system, the timescale until close encounters can easily exceed ten million years \cite{Chatterjee08}, by which time the protoplanetary disk will have dissipated. Alternatively, a system of two (or more planets) may become unstable due to an external perturbation, such as secular interactions with a binary companion \cite{Holman97} or a stellar flyby \cite{LaughlinAdams98}. This can lead to strong planet scattering, often following a prolonged phase of weaker interactions \cite{Malmberg11,Boley12,Kaib13}. Each close encounter between giant planets leads to a small perturbation to their orbits \cite{Katz97}. Thus, it is typically a series of close encounters that excites the two planets' orbital eccentricities until one planet's pericenter is small enough to initiate tidal circularizaiton. In practice, planetary systems that form two giant planets may well form additional massive planets, leading to a series of planet-planet scattering events and substantially increasing the probability for one to achieve a pericenter of just a few stellar radii. Another possible mechanism for eccentricity excitation involves secular (i.e., long-term) perturbations by one or more distant bodies (e.g., more planets, a brown dwarf or binary stellar companion). If there is a large mutual inclination between the inner planet and the outer companion, then large eccentricities are possible, even for systems with large orbital period ratios \cite{MazehShahm79,Holman97,Ford00b,Naoz11}. This could be particularly relevant for planets orbiting one member of a binary (or higher multiple) star system, even though the orbital period of the two stars is often much larger than the orbital period of the planet. For small mutual inclinations, exciting an eccentricity large enough to trigger tidal circularization requires a substantial angular momentum deficit (AMD) and a series of planets that serve to couple the inner giant planet to outer planets which are more likely to have a significant initial AMD \cite{ZakamskaTremaine04}. If the planets are widely spaced, then it is possible to construct initial conditions that lead to the inner planet's pericenter dropping to only a few stellar radii \cite{WuLithwick11}. However, for more typical initial conditions, the secular interactions lead to close encounters between planets that result in collisions and/or ejections via planet-planet scattering \cite{LinIda97,Levison98,Chatterjee08,Nagasawa08,Matsumura10,MoeckelArmitage12}. \subsection{Distinguishing between Hot-Jupiter Formation Models} In practice, nature may provide multiple migration mechanisms for forming hot-Jupiters. For many years, observations provided little data to help distinguish between even the two broad classes of migration models. The major breakthrough was the measurement of the Rossiter-McLaughlin effect for many transiting hot-Jupiters. When the planet passes in front of a rotating star, the apparent radial velocity is perturbed due to the planet blocking a portion of the star that is rotating towards or away from the observer. The Rossiter-McLaughlin signature measures the angle between the star's rotational angular momentum and the planet's orbital angular momentum (after projecting both onto the sky plane). While many systems are well-aligned, a significant fraction of hot-Jupiters are severely misaligned \cite{Albrecht12}. Misaligned systems, including nearly polar and even retrograde configurations \cite{Sanchis-Ojeda13}, arise naturally in scenarios that include eccentricity excitation plus tidal circularization \cite{Nagasawa08,Naoz11}. While planet scattering and secular perturbations will only produce hot-Jupiters for a few percent of planetary systems \cite{FordRasio08,Naoz12}, this is consistent with the rate of hot-Jupiters observed, or at least a substantial fraction of them. Astronomers have begun to attempt to deconvolve the distribution of Rossiter-McLaughlin measurements into a mixture of systems formed through disk migration, planet scattering and secular perturbations \cite{MortonJohnson11b}. However, we caution that there may be systematic biases in the outputs of such analyses, due to uncertainties in the treatment of tidal circularization. Another potential confounding factor is the possibility of a primordial star-disk misalignment \cite{Batygin12,Lai12}. Finally, we caution that an apparent trend of obliquity with stellar temperature \cite{Winn10} calls into question even qualitative predictions of tidal theory. While the details remain unclear, the Rossiter-McLaughlin observations demonstrate that simple disk migration is inadequate to explain all hot-Jupiters. Of course, these observations do not preclude disk migration from having operated in systems that were later sculpted by planet scattering or secular perturbations. Indeed, planet scattering is more efficient at forming hot-Jupiters, if migration were to bring planets to ~1 AU prior to scattering \cite{MoorheadAdams05} than if scattering commenced at several AU. Another key observational result is the realization that hot-Jupiters are seldom accompanied by additional planets close to their host star. This was foreshadowed by radial velocity planet searches \cite{Wright11} and dramatically confirmed by \Kepler observations of transiting hot-Jupiters \cite{Steffen12a}, as these provide precise constraints on both small planets with orbital periods of weeks to months (via photometry) and low-mass planets in or near mean-motion resonances (via transit timing variations). This result is consistent with the broad predictions of hot-Jupiter formation via eccentricity excitation plus tidal circularization, but in stark contrast to the predictions of disk migration models \cite{Narayan05,CresswellNelson06}. Thus, the isolation of hot-Jupiters suggests that there is a strong upper limit to the fraction of hot-Jupiters formed via disk migration. Recent radial velocity follow-up of systems with hot-Jupiters has found long-term radial velocity accelerations in roughly half of the surveyed hot-Jupiters \cite{Knutson13}. The location of the second-closest planet in systems with hot-Jupiters bolsters the hypothesis that hot-Jupiters may frequently commence scattering while at an orbital distance $\sim$1 AU. \subsection{Summary of Hot-Jupiter Formation} In summary, planet formation from a gaseous disk likely leads to forming many planets on low-eccentricity orbits. Initially, close encounters lead to collisions and increasing planet masses. Once the planets become massive enough to eject bodies from the gravitational potential well of the star, ejections become more common. The recoil from scattering planets leads to eccentricity growth of giant planets, especially in the outer regions of the planetary system. The AMD of planets that effectively eject smaller bodies is redistributed among all the remaining planets of a planetary system. This leads to further close encounters and collision or ejections, depending on the masses and distances of the planets involved. This process repeats, gradually thinning the planetary system, so that the remaining planets have masses and spacings that result in an instability timescale comparable to the age of the planetary system. In a small fraction of systems, either the chaotic interactions of a multi-body system and/or the secular interactions of highly inclined system lead to the innermost giant planet passing close enough to the host star that tidal interactions circularize its orbit, leading to the formations of a hot-Jupiter. While the future hot-Jupiter is circularizing, it cleans out the inner solar system by scattering any rocky planets in the inner planetary system into the star or the outer regions of the planetary system \cite{Mandell07}. | 14 | 4 | 1404.3157 |
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1404 | 1404.6291_arXiv.txt | We present first results of sunspot oscillations from observations by the Interface Region Imaging Spectrograph (IRIS). The strongly nonlinear oscillation is identified in both the slit-jaw images and the spectra of several emission lines formed in the transition region and chromosphere. We first apply a single Gaussian fit to the profiles of the Mg~{\sc{ii}}~2796.35\AA{}, C~{\sc{ii}}~1335.71\AA{} and Si~{\sc{iv}}~1393.76\AA{} lines in the sunspot. The intensity change is $\sim$30\%. The Doppler shift oscillation reveals a sawtooth pattern with an amplitude of $\sim$10~km~s$^{-1}$ in Si~{\sc{iv}}. In the umbra the Si~{\sc{iv}} oscillation lags those of C~{\sc{ii}} and Mg~{\sc{ii}} by $\sim$3 and $\sim$12 seconds, respectively. The line width suddenly increases as the Doppler shift changes from redshift to blueshift. However, we demonstrate that this increase is caused by the superposition of two emission components. We then perform detailed analysis of the line profiles at a few selected locations on the slit. The temporal evolution of the line core is dominated by the following behavior: a rapid excursion to the blue side, accompanied by an intensity increase, followed by a linear decrease of the velocity to the red side. The maximum intensity slightly lags the maximum blue shift in Si~{\sc{iv}}, whereas the intensity enhancement slightly precedes the maximum blue shift in Mg~{\sc{ii}}. We find a positive correlation between the maximum velocity and deceleration, a result that is consistent with numerical simulations of upward propagating magneto-acoustic shock waves. | Solar magneto-hydrodynamic waves have been intensively studied both observationally and theoretically in the past decades since they are believed to play a crucial role in chromospheric and coronal heating. Moreover, the generation and propagation of these waves can provide valuable information on the thermal and magnetic structures of the solar atmosphere. Sunspot oscillations, discovered by \cite{Beckers1969}, are one of the most spectacular wave phenomena in the solar atmosphere. Sunspot oscillations often have a dominant period of five minutes at the photospheric level \citep[e.g.,][]{Beckers1972}. These 5-minute oscillations are the response of the sunspot to forcing by the 5-minute p-mode oscillations in the surrounding atmosphere \citep[e.g.,]{Thomas1985}. Three-minute oscillations have been frequently reported in both the photosphere and chromosphere of the sunspot umbrae. Compared to the photospheric lines, they are more easily observed in the brightness (also called umbral flashes) and velocity of the chromospheric Ca~{\sc{ii}} H\&K lines, as well as in velocities derived from the He~{\sc{ii}} 10830\AA{} triplet. Early theoretical efforts suggest that they are a resonant mode of the sunspot itself \citep[see a review in][]{Thomas1985}. However, the detection of 3-minute oscillations in the transition region (TR) and corona above sunspots supports the interpretation of propagating waves \citep[e.g.,][]{Brynildsen1999a,Brynildsen1999b,Brynildsen2002,Brynildsen2004,Maltby1999,OShea2002,DeMoortel2002}. Running penumbral waves (RPWs) are concentric acoustic waves propagating outward with a speed of 10-25 km~s$^{-1}$ from the umbra-penumbra boundary \citep[e.g.,][]{Giovanelli1972,Zirin1972}. Their periods are usually in the range of 200-300 seconds. The RPWs are suggested to be trans-sunspot waves of purely chromospheric origin \citep[e.g.,][]{Tziotziou2006} or magneto-acoustic waves propagated along expanding field lines from the photosphere \citep[e.g.,][]{Bloomfield2007,Jess2013}. For reviews of the observations and theories of sunspot oscillations, we refer to \cite{Lites1992}, \cite{Bogdan2000}, and \cite{Bogdan2006}. As pointed out by \cite{Bogdan2000}, our most profound ignorance centers on the nonlinear aspects of the sunspot oscillations. Although signatures of nonlinearity and upward propagating shock waves have been frequently reported in chromospheric lines \citep[e.g.,][]{Bard1997,Rouppe2003,Centeno2006,Felipe2010,delaCruz2013}, direct evidence of the shock wave nature for sunspot oscillations in the TR is very rare. For instance, \cite{Brynildsen1999a} did not find any clear signs of shocks for the sunspot oscillations in their moderate-resolution observations. \cite{OShea2002} mentioned that it was not possible to determine whether the oscillations they observed were linear or non-linear waves due to the poor resolution of the instrument. Nonlinear sunspot oscillations were identified and explained as nonlinear acoustic waves without shocks by \cite{Brynildsen1999b} and \cite{Brynildsen2004}, although Brynildsen et al. (1999b) suggested the possible presence of shocks. The recently launched Interface Region Imaging Spectrograph \citep[IRIS,][]{DePontieu2014} mission is now providing high-cadence, high-resolution, and continuous observations of the solar TR and chromosphere. Here we report the first result of sunspot oscillations observed with IRIS. The new IRIS observations provide direct and adequate evidences of the shock wave nature for sunspot oscillations in the TR and chromosphere. These evidences include a sharp change of the velocity and a clear correlation between the maximum velocity and deceleration. | We report the first results of sunspot oscillations observed with IRIS. Our results reveal several new aspects of the shock wave behavior for sunspot oscillations in the TR and chromosphere. We first apply a single Gaussian fit to the profiles of the Mg~{\sc{ii}}~2796.35\AA{}, C~{\sc{ii}}~1335.71\AA{} and Si~{\sc{iv}}~1393.76\AA{} lines in the sunspot since these line profiles are mostly close to Gaussian to some extent. The intensity oscillation has an amplitude of $\sim$30\% for all three lines. The Doppler shift oscillation reveals a sawtooth pattern with an amplitude of about 10~km~s$^{-1}$ in Si~{\sc{iv}} and slightly smaller values in C~{\sc{ii}}~and Mg~{\sc{ii}}. The Si~{\sc{iv}} oscillation lags the C~{\sc{ii}} and Mg~{\sc{ii}} oscillations by about 3 and 12 seconds, respectively. The correlated change between the intensity and blue shift of the TR lines, together with the time lags and the strong nonlinearities, suggest the presence of magneto-acoustic shock waves propagating from the chromosphere to the TR. Detailed analysis of the temporal evolution of the line profiles reveals a repeated pattern of the following behavior: the line core first experiences a sudden impulsive blueward excursion and an accompanied intensity enhancement, then starts a gradual and constant deceleration to the red side. The maximum red shift is correlated with the deceleration. Such behaviors have been previously found in the chromospheric emission of DFs and proven to be the signatures of upward propagating magneto-acoustic shock waves. The similar behavior in both the chromospheric and TR emission lines in our data suggests that the three-minute sunspot oscillations may be dominated by a similar process. Waves generated by convective flows and global p-mode oscillations in the photosphere leak upward, steepen, and form shocks in the sunspot chromosphere and TR. A plasma parcel passing through a shock will then experience a sudden impulse ascending motion, followed by a gradual and constant deceleration. We also found that the maximum intensity slightly lags the maximum blue shift for the TR lines. However, the intensity enhancement of Mg~{\sc{ii}} occurs before the maximum blue shift is reached. We have also demonstrated that the strongly nonlinear line width oscillation, observed both here and previously, is actually related to the superposition of multiple emission components. The line profiles clearly exhibit two distinct components during the impulsive change from red shift to blue shift. These two components represent the emission from the newly shocked plasma and the back-falling matter after the passage of the previous shock, respectively. They are likely caused by the behavior of the shocks - a new shock occurs before the complete fading of the previous shock. The greatly enhanced SGF line width is mainly caused by the superposition of the two emission components. | 14 | 4 | 1404.6291 |
1404 | 1404.5292_arXiv.txt | The ongoing discoveries of extrasolar planets are unveiling a wide range of terrestrial mass (size) planets around their host stars. In this letter, we present estimates of habitable zones (HZs) around stars with stellar effective temperatures in the range $2600$ K - $7200$ K, for planetary masses between $0.1$ M$_{\oplus}$ and $5$ M$_{\oplus}$. Assuming $\h2o$- (inner HZ) and $\co2$- (outer HZ) dominated atmospheres, and scaling the background N$_{2}$ atmospheric pressure with the radius of the planet, our results indicate that larger planets have wider HZs than do smaller ones. Specifically, with the assumption that smaller planets will have less dense atmospheres, the inner edge of the HZ (“runaway greenhouse” limit) moves outward ($\sim 10 \%$ lower than Earth flux) for low mass planets due to larger greenhouse effect arising from the increased $\h2o$ column depth. For larger planets, the $\h2o$ column depth is smaller, and higher temperatures are needed before water vapor completely dominates the outgoing longwave radiation. Hence the inner edge moves inward ($\sim 7 \%$ higher than Earth's flux). The outer HZ changes little due to the competing effects of the greenhouse effect and an increase in albedo. New, 3-D climate model results from other groups are also summarized, and we argue that further, independent studies are needed to verify their predictions. Combined with our previous work, the results presented here provide refined estimates of HZs around main-sequence stars and provide a step towards a more comprehensive analysis of HZs. | \label{intro} Recent observational surveys have discovered several potential habitable zone (HZ) planet candidates \citep{Udry2007, Vogt2010, Pepe2011a, Borucki2011, Bonfils2011, Borucki2012, Vogt2012, Tuomi2012b, Anglada-Escude2013}, and it is expected that this number will greatly increase as time passes \citep{DC2013, KoppM2013,Gaidos2013}. Accordingly, the circumstellar HZ is defined as the region around which a terrestrial mass planet, with favorable atmospheric conditions, can sustain liquid water on its surface \citep{Huang1959, Hart1978, Kasting1993, Selsis2007b,Kopp2013}. Currently, more than $1600$ extra-solar planetary systems have been detected and $> 2700$ additional candidate systems from the {\it Kepler} mission are waiting to be confirmed \citep{Batalha2013,Lissauer2014, Rowe2014}. Recently \cite{Kopp2013} obtained new, improved estimates of the boundaries of the HZ by updating \cite{Kasting1993} model with new $\h2o$ and $\co2$ absorption coefficients from updated line- by-line (LBL) databases such as HITRAN 2008 \citep{Rothman2009} and HITEMP 2010 \citep{Rothman2010}. Several other recent studies used 3D global circulation models (GCMs) to study the potential habitability of specific systems \citep{Wordsworth2010,Forget2013}. Specifically, a recent study by \cite{Yang2013} proposed that stabilizing cloud feedback can expand the inner HZ (IHZ) to roughly twice the stellar flux found from 1D climate calculations for tidally locked planets or planets that are in synchronous rotation around low mass stars. The stabilizing feedback arises from an increase in the planetary albedo due to the presence of thick water clouds at the sub-stellar point. In contrast, \cite{Leconte2013} found that for a rapidly rotating planet similar to Earth around a Sun-like star, clouds have a {\it destabilizing} feedback on the long-term warming. This is because of the displacement of the cloud formation layer to higher altitudes, increasing the greenhouse effect of the clouds compared to the cooling effect caused by their albedo. While clouds provide a positive feedback in their model, \cite{Leconte2013} show that Earth's troposphere is not saturated everywhere, and that these unsaturated regions radiate efficiently to space, thereby cooling the planet. Consequently, they find that the IHZ is closer to the Sun, at $0.95$ AU, than predicted by the 1-D model of \cite{Kopp2013}. A similar study by \cite{WT2013}, using the 3D Community Atmosphere Model 3 (CAM3), also found that the inner edge can be as close as $0.93$ AU for our Sun. These results highlight the importance of 3D GCMs in understanding the varying climate feedacks associated with both tidally locked and rapidly rotating planets. Further studies using 3D models will be necessary to obtain a consensus on the location of the inner edge of the HZ. Here, we consider planetary masses $M_{p}$ between $0.1$ M$_{\oplus}$ $\le M_{p} \le 5$ M$_{\oplus}$. The lower limit includes Mars-mass planets. The upper limit is based on the observation that the theoretical and observed mass-radius relationships have different slopes beyond $5$M$_{\oplus}$(see \S\ref{sec2}), suggesting the accumulation of an increasingly significant gas envelope for planets with sizes larger than $5$M$_{\oplus}$. The outline of the paper is as follows: In \S\ref{sec2} we briefly describe our 1-D cloud-free climate model. In \S\ref{results} we present results from our climate model and illustrate various HZ limits as a function of planetary mass. In \S\ref{discuss}, we provide an analytical equation to calculate HZs incorporating various 3D GCM results. We conclude in \S\ref{conclusions}. | \label{conclusions} The HZ boundaries change as a of function planetary mass and the amount of background N$_{2}$ gas. The conservative HZ limits for more massive planets should be wider than those for low mass planets if the atmospheric column depth scales with planet radius, as assumed here. The results summarized here are only a step towards a more comprehensive analysis of HZ boundaries. Further work with 3D climate models will be needed to accurately calculate the habitable zones around different types of stars. A FORTRAN code is available with the online version of the paper. An interactive webpage to obtain HZs is available at: \url{http://www3.geosc.psu.edu/~ruk15/planets/} or at \url {http://depts.washington.edu/naivpl/content/hz-calculator}. | 14 | 4 | 1404.5292 |
1404 | 1404.0012_arXiv.txt | Using self-consistent, physically motivated models, we investigate the X-ray obscuration in 19 Type 2 [OIII] 5007 \AA\ selected AGN, 9 of which are local Seyfert 2 galaxies and 10 of which are Type 2 quasar candidates. We derive reliable line-of-sight and global column densities for these objects, which is the first time this has been reported for an AGN sample; 4 AGN have significantly different global and line-of-sight column densities. Five sources are heavily obscured to Compton-thick. We comment on interesting sources revealed by our spectral modeling, including a candidate ``naked'' Sy2. After correcting for absorption, we find that the ratio of the rest-frame, 2-10 keV luminosity (L$_{\rm 2-10keV,in}$) to L$_{\rm [OIII]}$ is 1.54 $\pm$ 0.49 dex which is essentially identical to the mean Type 1 AGN value. The Fe K$\alpha$ luminosity is significantly correlated with L$_{\rm [OIII]}$, but with substantial scatter. Finally, we do not find a trend between L$_{\rm 2-10keV,in}$ and global or line-of-sight column density, between column density and redshift, between column density and scattering fraction or between scattering fraction and redshift. | Supermassive black holes in the centers of galaxies grow by accretion in which they are observed as Active Galactic Nuclei (AGN). X-ray emission is thought to originate in a corona surrounding the accretion disk where optical and ultraviolet photons from the disk are inverse-Compton scattered to higher energies. According to conventional unified models \citep{antonucci,urry}, this central engine is enshrouded by a circumnuclear obscuring medium of dust and gas which has a toroidal geometry. The inclination of this system to the observer's line of sight therefore determines the observable properties. In this classification scheme, Type 1 AGN represent a face-on system, allowing an unobscured view of the central engine where broad and narrow optical emission lines are apparent, as well as the ultraviolet continuum, mid-infrared emission from the circumnuclear obscuring matter, and X-ray emission from the corona. Conversely, the Type 2 systems are oriented so that the accretion disk and corona are hidden from the observer's sight line, blocking the optical and ultraviolet continuum and optical broad lines, and possibly significantly impacting the observed X-ray emission. The physical processes that X-ray photons undergo are imprinted in the observed spectrum. An X-ray photon that is injected from the corona into the obscuring medium can pass unimpeded directly into our line of sight, be absorbed, or undergo one or more Compton-scatterings, with multiple scatterings becoming more likely if the column density is Compton-thick (i.e., N$_H \geq (1.2 \times \sigma_T)^{-1} \simeq 1.25 \times 10^{24}$ cm$^{-2}$, where $\sigma_T$ is the Thompson cross-section for electron scattering). The probabilities of these outcomes depend on the column density of the reprocessor and the incident energy of the X-ray photon. Fluorescent line emission from continuum photons ejecting inner shell electrons from atoms or ions in the obscuring medium can potentially be a dominant component of the observed spectrum. AGN continuum photons can also not interact with the absorber by escaping through the opening of the torus and/or passing through gaps in a clumpy medium if the absorber is non-uniform and patchy, and then scatter off a more distant optically-thin medium, entering our line of sight. Simple {\it ad hoc} X-ray models that parametrize the emission with an absorbed power law model or partial covering model will fail to capture the detailed physics inherent in these systems, especially when the column density exceeds $10^{24}$ cm$^{-2}$, i.e., when Compton scattering becomes an important factor. Even models that treat relativistic reflection off an accretion disk are unsuitable for these systems as they assume a column density that is infinite and a disk geometry does not adequately describe the absorber that reprocesses the X-ray emission. Additionally, such modeling is one-dimensional, which does not allow a finite column density out of the line of sight to be measured, even though the Fe K fluorescence line can provide information about the global matter distribution in which it is produced. With recent advances in spectral modeling that self-consistently treat Compton scattering, fluorescent line emission, and scattering off a distant medium \citep{mytorus,spherical}, we can now delve into the details of the obscuration in AGN and obtain physically meaningful constraints on inclination angle, line-of-sight and global column density, and the percentage of scattered AGN light. Here we use physically motivated X-ray models to study the circumnuclear obscuration of a sample of Seyfert 2 galaxies (Sy2s) and Type 2 quasar (QSO) candidates selected based on their [OIII] 5007 \AA\ line emission, where the Sy2s are local ($z<0.15$), lower luminosity obscured AGN compared with quasars, which have bolometric luminosities exceeding $10^{45}$ erg s$^{-1}$. The [OIII] 5007 \AA\ line forms in the AGN narrow line region, 100s of parsecs above and below the circumnuclear obscuring medium, and it is primarily ionized by the AGN continuum, making it a reliable indicator of intrinsic AGN power \citep{bassani,kauff,tim04,cappi,panessa,me10}. These samples are thus unbiased with respect to the circumnuclear obscuration while X-ray selected samples are inherently biased against the most obscured sources as the combined effects of photoelectric absorption and Compton scattering modify the observed X-ray emission. The Sy2 and QSO samples have previously been analyzed and published in \citet{me} and \citet{jj}, respectively, using simple power law or double power law models to fit the spectrum. The amount of implied obscuration was determined by normalizing the observed X-ray flux by the intrinsic luminosity ([OIII] for the Sy2 and QSO sample, and by the mid-infrared [OIV] 26 $\mu$m line and mid-infrared continuum for the Sy2 sample) and analyzing the equivalent width of the Fe K$\alpha$ line, which can exceed 1 keV in Compton-thick sources as the fluorescent line in the reflection spectrum is superimposed on a depressed continuum \citep[e.g.,][]{ghisellini,levenson}. \citet{jj} also estimate the absorber column density by comparing the observed ratio of X-ray to [OIII] flux to a simulated unabsorbed ratio, using the unabsorbed (Type 1 AGN) values from \citet{tim} as the basis for simulating 1000 random draws per source, and determining the column density that can account for the attenuation between the absorbed and simulated unabsorbed X-ray fluxes. In neither work is the fitted column density used as representative of the true obscuration as this is poorly determined with the simple models used. Instead, the observed 2-10 keV fluxes and Fe K$\alpha$ EWs, which are largely model-independent, were used as diagnostics of the column density. In both works, these obscuration proxies suggested that a majority of the Sy2s and Type 2 QSO candidates are heavily obscured, and possibly Compton-thick. In this analysis, we use the models from \citet{spherical} and \citet[MYTorus]{mytorus} to unveil the physical properties of the obscuration responsible for reprocessing the emission from the central engine within a spherical and toroidal geometry, respectively. These models treat the transmitted continuum, Compton scattered emission and fluorescent line emission self-consistently, allowing for physically meaningful measurements of the global and line-of-sight column densities which are poorly determined with {\it ad hoc} models. We apply these model to the subset of [OIII]-selected Sy2s from \citet{me} and QSO2 candidates from \citet{jj} that have adequate signal-to-noise X-ray spectra to constrain the model parameters. We comment on what we can learn about the circumnuclear obscuration with the present data, including reliable measurements of the global as well as line-of-sight N$_{H}$, and highlight two interesting sources as revealed by our X-ray analysis. As the Fe K$\alpha$ emission is accommodated self-consistently within the global obscuring medium in these models, we overcome the shortcomings of previous analyses that used simple power-law modeling to measure the Fe K$\alpha$ emission either in front of or behind the line-of-sight absorbing screen. We then test whether the Fe K$\alpha$ luminosity indeed traces the intrinsic luminosity as reported in previous works \citep[e.g.,][]{ptak,me,jj}. We also investigate whether there are differences between these QSO2s and Sy2s in terms of their column densities and scattering fractions and if there is a relationship between the column density and AGN luminosity as posited by the ``receding torus'' model \citep[e.g.,][]{lawrence,lawrence2,ueda,simpson}. Throughout, we refer to sources as mildly obscured if the circumnuclear column density is below $<10^{22}$ cm$^{-2}$, moderately obscured for $10^{22}$ cm$^{-2}< N_H < 10^{23}$ cm$^{-2}$, heavily obscured for 10$^{23}$ cm$^{-2} < N_H < 10^{24}$ cm$^{-2}$, and Compton-thick if the column density exceeds $1.25\times10^{24}$ cm$^{-2}$. We adopt a cosmology of H$_{0}$=70 km Mpc $^{-1}$ s$^{-1}$, $\Omega_M$=0.27, and $\Omega_\Lambda$=0.73. \renewcommand{\thefootnote}{\arabic{footnote}} | We used the physically motivated, self-consistent spherical absorption model of \citet{spherical} and the MYTorus model \citep{mytorus} to unravel the complexities of the X-ray reprocessor in 19 Type 2 [OIII]-selected AGN, 9 of which are Seyfert 2 galaxies and 10 of which are obscured quasar candidates. We report, for the first time for an AGN sample, reliable measurements of the global, as well as line-of-sight, column densities. \begin{itemize} \item Along the line-of-sight, 1 Sy2 and 1 QSO2 are mildly obscured ($<10^{22}$ cm$^{-2}$), 1 Sy2 and 4 QSO2s are moderately obscured ($10^{22}$ cm$^{-2} <$ N$_{H} < 10^{23}$ cm$^{-2}$), 4 Sy2s and 2 QSO2s are heavily obscured ($10^{23}$ cm$^{-2} <$ N$_{H} < 10^{24}$ cm$^{-2}$), and 2 Sy2s and 3 QSO2s are heavily-obscured to Compton-thick ($> 1.25\times10^{24}$ cm$^{-2}$). One source is unabsorbed. \item 13 objects have evidence of scattering of the intrinsic AGN continuum off a distant medium. The scattering fraction is largely under 2\%, but reaches between $\sim$ 7-9\% for individual sources. \item In 4 AGN, we measure global column densities that are significantly different from the line-of-sight column density. In one of these objects, SDSS J082443.28+295923.5, the line-of-sight column density is Compton-thin while the global column density is Compton-thick, while in 1 other object, SDSS J093952.74+355358.0, the line-of-sight column density is heavily-obscured to Compton thick with a Compton-thin global column density. \item We identified a candidate changing-look AGN or naked Sy2 galaxy, Mrk 0609. If Mrk 0609 is a true Sy2, both its bolometric luminosity and Eddington rate exceed the predicted critical values of disk-wind models that explain such sources \citep{nicastro,trump}. We are pursuing simultaneous X-ray and optical observations to test this possibility. \item The spectral features of SDSS J093952.74+355358.0 indicate that the line-of-sight obscuration is in the form of Compton-thick toroidal ring which is embedded in a Compton-thin global matter distribution. This is the first Type 2 QSO where this geometry has been observed. \item The ratio of the intrinsic 2-10 keV luminosity to the [OIII] luminosity, 1.54$\pm$0.49 dex, is basically equivalent to that for Type 1 AGN \citep[1.59$\pm$0.48]{tim}, affirming that these sophisticated models reliably measure the circumnuclear column density, allowing the inherent X-ray luminosity to be revealed. \item We find a significant correlation between the Fe K$\alpha$ and [OIII] luminosities, though with wide scatter. Estimating the Fe K$\alpha$ luminosity from the [OIII] luminosity can lead to errors of over an order of magnitude. \item We compared N$_{\rm H,Z}$ and N$_{\rm H,S}$ with obscuration diagnostics used often in the literature from {\it ad hoc} spectral modeling, i.e., L$_{\rm 2-10keV}$/L$_{\rm[OIII]}$ and the Fe K$\alpha$ EW \citep[e.g.,][]{ghisellini,bassani, cappi, levenson, panessa, me,me11,jj}, where lower values of the former (i.e., $\lesssim$1) and higher values of the latter (i.e., $\sim$1 keV) imply heavy-to-Compton-thick obscuration. Sources that are flagged as heavily obscured via these proxies do indeed have measured column densities consistent with heavy or Compton-thick obscuration, but a couple of objects with values similar to unabsorbed AGN also have measured N$_{\rm H,Z}$ indicative of heavy obscuration. \item Though a larger percentage of the Sy2s are more heavily obscured than the QSO2s, no trend exists between line-of-sight or global obscuration and AGN luminosity, parametrized here as the intrinsic, rest-frame 2-10 keV luminosity. We also find no relationship between N$_{\rm H,Z}$ or N$_{\rm H,S}$ and scattering fraction, N$_{\rm H,Z}$ or N$_{\rm H,S}$ and redshift, scattering fraction and redshift, and scattering fraction and L$_{\rm 2-10keV}$/L$_{\rm[OIII]}$. We reiterate that these results hold for the objects we studied here which are not necessarily representative of Type 2 AGN in general. \end{itemize} | 14 | 4 | 1404.0012 |
1404 | 1404.2826_arXiv.txt | The solar wind is a structured and complex system, in which the fields vary strongly over a wide range of spatial and temporal scales. As an example, the turbulent activity in the wind affects the evolution in the heliosphere of the integral turbulent scale or correlation length [$\la$], usually associated with the breakpoint in the turbulent-energy spectrum that separates the inertial range from the injection range. This large variability of the fields demands a statistical description of the solar wind. In this work, we study the probability distribution function (PDF) of the magnetic autocorrelation lengths observed in the solar wind at different distances from the Sun. We use observations from {\it Helios}, ACE, and {\it Ulysses} spacecraft. We distinguish between the usual solar wind and one of its transient components (Interplanetary Coronal Mass Ejections, ICMEs), and study also solar wind samples with low and high proton beta [$\be_{\mathrm p}$]. We find that in the last 3 regimes the PDF of $\la$ is a log-normal function, consistent with the multiplicative and non-linear processes that take place in the solar wind, the initial $\la$ (before the Alfv\'enic point) being larger in ICMEs. | \label{S_Intro} The solar wind (SW) is a very complex and structured system, where the fields are highly variable over different temporal and spatial scales. However, despite its complexity, different types of phenomena generally associated with different scales in the SW can be identified. At the global scale, the SW steady expansion has direct consequences on the typical length scales at which the bulk physical quantities that characterize the state of the system vary ({\it e.g.}, mass density, magnetic-field components, temperature). Between 0.3 astronomical unit (AU) and 5 AU from the Sun, these quantities typically decay as a power law with a negative exponent of the order of one to three \cite{Mariani_libro_marron}. Then, at a distance $D$ from the Sun, the \textquotedblleft steady expansion\textquotedblright~typical length scale can be estimated as $\approx D$. Furthermore, different transient phenomena with origin at the solar surface produce disturbances to the steady SW. An example of these SW \textquotedblleft transient structures\textquotedblright~is the phenomenon of fast transient streams of plasma from coronal holes \cite{Coronal_holes} or interplanetary coronal mass ejections (ICMEs), which have a magnetic topology radically different from the steady SW ({\it e.g.}, \opencite{Dasso_rev_MC_2005AdSpR}). These composite structures (which can contain several smaller sub-structures such as shock waves, plasma sheaths, {\it etc.}) are meso-scale objects in the system, with a range of sizes that are some fraction of $D$. In SW turbulence, the largest spatial scale of the inertial range can be approximated by the turbulent integral scale [$\la$] (see Equation (\ref{E_def_lambda}) for a proper definition), which is also a proxy for the typical size of the \textquotedblleft energy-containing eddies\textquotedblright~({\it e.g.}, \opencite{Bill_JGR94_evol_turb_eddies}). The inertial range extends from $\la$ to much smaller scales, involving turbulent processes along several orders of magnitude. It is very rich in non-linear processes (see for example \opencite{Coleman68}), combined with an important level of wave activity (see for example \opencite{BelcherDavis71}). This complex turbulent activity affects the evolution of different aspects of the SW fluctuations, such as the fluctuating intensity, the integral length [$\lambda$], the level of Alfv\'enicity \cite{Tu-Marsch-1995}, anisotropy \cite{Matthaeus90,dasso05,Ruiz2011}, {\it etc}. In particular, it is well known that $\la$ increases with heliocentric distance \cite{Tu-Marsch-1995}. Near Earth $\lambda_{{\mathrm 1 AU}}$ is $\approx 0.0079$ AU \cite{Matthaeus05_msc} while $\lambda_{{\mathrm 10 AU}}$ is $\approx 0.046$ AU in the SW near Saturn \cite{Smith2001JGR}. All of these physical phenomena, associated with significantly different spatial scales, are coupled. For instance: i) the decay of the total solar-wind pressure (determined by its \textquotedblleft steady expansion\textquotedblright~scale) plays the major role during the long-term interaction between magnetic clouds and their environment \cite{Pascal-Dasso,Adri_inner,Adri_outer}, ii) the presence of shear in the velocity profile ({\it e.g.}, associated with CIRs or ICMEs) can produce instabilities and introduce energy into the outer scales of the turbulent inertial range \cite{Goldstein_MHD_rev_95}, iii) turbulent properties control the drag on ICMEs and many other large-scale processes \cite{bill_velli_who_needs_t}, {\it etc}. An important entity for studying fluctuations of turbulent fields is the autocorrelation function. For the magnetic field, the average trace of the two-point/two-time correlation tensor is \begin{equation}\label{E_R_def} R([\xx,t],[\rr, \tau])=\langle \bbb(\xx,t)\cdot \bbb(\xx + \rr,t + \tau) \rangle \end{equation} where $\bbb$ is the fluctuating component of $\bb$ and $[\rr,\tau]$ are the spatial and temporal lags, respectively. We can drop the $[\xx,t]$ dependence in Equation (\ref{E_R_def}) if we assume stationarity and homogeneity of the medium \cite{1982Matthaeus,2013LivRev}. Further, we may assume the Taylor frozen-in-flow hypothesis \cite{Taylor-1938} to be valid in the supersonic and super-Alfv\'enic SW; that is, the fluctuating fields are convected past the spacecraft in a shorter time than their characteristic dynamical timescale. Then we can ignore the intrinsic temporal dependence of the fluctuations in Equation (\ref{E_R_def}), resulting in \begin{equation}\label{E_R_taylorhyp} R(\rr)=\langle \bbb(\vec 0)\cdot \bbb(\rr) \rangle \end{equation} The spatial decorrelation of the turbulence can be characterized by the correlation length or integral scale \begin{equation}\label{E_def_lambda} \la=\frac{\int_0^{\infty}\langle\,\bbb(\vec 0)\cdot\bbb(\rr)\,\rangle}{\langle\bbb^2 \rangle {\mathrm d}r} \end{equation} Conventionally, this typical length-scale is understood as being a measure of the size of the turbulent energy-containing eddies in the flow \cite{Batchelor_turb}. Moreover, $\la$ can be linked to the scale associated with the spectral break that separates the injection range (meso-scales) from the inertial range: $\la$ can be seen as a kind of spatial frontier between the two domains. Any description of the complex SW physical system should be complemented by a statistical description of the fields, since important information about turbulent systems resides at a statistical level and, to this day, it is not possible to measure initial or boundary conditions \cite{burlaga2000}. Log-normal distributions are frequent in nature across the different branches of science \cite{Limpert01}, and are believed to be a consequence of multiplicative processes ({\it e.g.}, \opencite{Montroll}). In particular, in the field of space and solar physics, many authors have considered log-normal distributions when modelling quantities of interest such as the Dst index \cite{Campbell_Dst_Logn}, the magnitude of the magnetic field fluctuations \cite{Burlaga_lognB,PadhyeJGR01}, SW speed, proton density and temperature \cite{burlaga2000}, proton plasma beta and Alfv\'en speed \cite{Mullan2006}. As far as we know, the probability distribution functions (PDFs) of autocorrelation lengths [$\la$] of the solar-wind fluctuating magnetic field have not been studied. \inlinecite{Wicks2010SoPh} reported an asymmetric shape for the observed PDF of the correlation lengths of the magnetic field magnitude at 1 AU. \inlinecite{Matthaeus_PRL86} had theoretically postulated that $\la$ is log-normally distributed. The authors explained that the structures that initiate the cascade in the inertial range, amplify their initial size $\la_0$ during their transport into the SW from the solar surface, employing a mechanism of successive magnetic reconnection events to increase the size of magnetic structures. This occurs $M$ times each one by a factor $(1+\epsilon)$ yielding a final size given by $\la=\la_0(1+\epsilon)^M$ with $\la$ the correlation length of the fluctuations. If $M$ is sufficiently large, the random variable $\ln(\la)$ will be normally distributed and therefore $\la$ log-normally distributed. Thus, the discussion presented in this Section motivates us to study $\la$ in the SW and its evolution. One of the main aims of this article is to provide an observational characterization of the PDF of $\la$. | The spatial scales associated with the correlation length [$\la$] are related to the breakpoint in the spectrum, which separates the inertial range from the injection (low-frequency) range associated with large-scale structures in the SW ({\it e.g.}, presence of velocity shear). During the expansion of the wind, this breakpoint moves to the lower-frequency part of the spectrum \cite{TUetal1984,BrunoRev2005}. In this work, we have analyzed {\it Helios} 1 and 2, ACE, and {\it Ulysses} magnetic observations, restricted to the Ecliptic plane for different heliocentric distances [$D$]. From these observations, we characterized the distributions of $\lambda$ in the solar wind, in low and high proton $\be$ SW regimes, and in ICMEs at 1 AU. We quantitatively investigated the hypothesis that the PDF of $\lambda$ is log-normal. In particular, we fitted the two free parameters of a normal distribution to the observed PDF of $\ln(\la$). Qualitatively and with respect to the fitted parameters, all of the samples appear to be reasonably well described by a log-normal distribution. Then we applied the Jarque-Bera goodness-of-fit test in order to quantify departures from log-normality of the PDFs. We find, in the case of H1$+$H2 and {\it Ulysses} data, clear evidence (\textit{i.e.}, $Pv>\alpha=0.05$) in favor of concluding that $\la$ is log-normally distributed. On the other hand, evidence is not so conclusive regarding ACE data: such a low $Pv$ indicates that we should reject the hypothesis. We also studied the distribution of correlation lengths in low-$\be_{\mathrm p}$ and high-$\be_{\mathrm p}$ SW regimes and estimated moments of the distribution. In each case, moments of $\ln(\la)$ evolve towards what is expected for a Gaussian PDF. Evaluation of the hypothesis of a normal distribution for $\ln(\la)$ by means of the JB test yield $Pv>\alpha=0.05$ in all cases. We conclude that the distribution of magnetic-correlation lengths can be regarded as log-normal when considering individually the low-$\be_{\mathrm p}$ and high-$\be_{\mathrm p}$ solar-wind regimes. Evidently the conclusion is now equally strong for all three spacecraft; the identification of a log-normal distribution in the ACE analysis is much more conclusive when the data was sorted by proton $\be$. Furthermore, the $\la$-distribution for the high-$\be_{\mathrm p}$ plasma is narrower and displaced to the left with respect to the low-$\be_{\mathrm p}$ case. While in the former regime the fluctuating amplitude is larger than in the latter, correlation lengths take smaller values in the former (high-$\be_{\mathrm p}$ sample), contrary to what is expected from MHD turbulence theories such as the K\'arm\'an and Howarth HD approach \cite{Karman-Howarth-38}. We interpret this behavior of $\la$ as a consequence of the different initial conditions of the magnetic-field fluctuations at the solar corona for the two kinds of solar wind, with the initial $\la$ in high-$\be_{\mathrm p}$ smaller than in the low-$\be_{\mathrm p}$ SW. Besides its stationary component, the SW has several transient components, of which ICMEs are an example. We separate this transient component (only at 1 AU) from the usual SW retaining intervals with an observed temperature lower than one-half of the expected temperature for usual SW \cite{RC1995JGR}. The distribution of $\la$ is similar to but displaced to the right with respect to the low-$\be_{\mathrm p}$ case. The JB test yields in this case the largest $Pv$ so the hypothesis of a log-normal PDF for $\la$ can be again accepted. The PDF of $\lambda$ evolves with the distance to the Sun. For larger heliocentric distances we found a narrower distribution (a decreasing $\sigma^2$ with $D$), and nearer to a log-normal distribution of $\lambda$. From Table 1 is possible to see that for increasing heliocentric distance, the moments of the PDF of $\ln(\lambda$) [$\gamma$, $K$, and $M_6$] tend progressively to those values expected for a normal distribution. This result is consistent with multiplicative processes involving $\lambda$ occurring in the solar wind, and a consequent relaxation to a log-normal PDF. We confirmed that $\lambda$ increases with the heliocentric distance [$D$] and with the nominal SW aging [$T=D/V_{SW}$], and found that $\lambda(D)= 0.89 (D/1\,AU)^{0.43}\times10^6$\,km and $\lambda(T)= 0.11 (T/1\,\mathrm{hour})^{0.47}\times10^6$\,km, for the ranges [0.3\,-\,5.3]AU and [30\,-\,670] hours, respectively. We find this overall behavior also in the low-$\be_{\mathrm p}$ and high-$\be_{\mathrm p}$ regimes: $\la$ grows with $D$ and $T$ in both cases. In the near-Ecliptic structured solar wind, fluctuations of the magnetic field are present over a large range of spatial and temporal scales. These multiscale structures partially originate at the Sun and evolve due to the local turbulent dynamics in the solar wind. In this context we infer that near the Sun, before the Alfv\'enic critical point, $\la$ follows a log-normal probability distribution function in both high-$\be_{\mathrm p}$ and low-$\be_{\mathrm p}$ solar wind, whose parameters continue to evolve due to the solar-wind turbulent dynamics. The distribution remains approximately log-normal, and evolves more precisely towards this form due to multiplicative processes in the turbulent solar wind. \begin{acks} MER is a fellow from CONICET. SD is a member of the Carrera del Investigador Cient\'{\i}fico, CONICET. MER and SD acknowledge partial support by Argentinean grants UBACyT 20020120100220 (UBA) and PIP 11220090100825/10 (CONICET). WHM acknowledge partial support by NFS Shine AGS 1156094, Solar Terrestrial Program AGS 1063439, and the Solar Probe Plus ISIS Project. We thank E. Marsch for providing {\it Helios} data. \end{acks} \appendix | 14 | 4 | 1404.2826 |
1404 | 1404.1938_arXiv.txt | \noindent I review current efforts to measure the mean density of dark matter near the Sun. This encodes valuable dynamical information about our Galaxy and is also of great importance for `direct detection' dark matter experiments. I discuss theoretical expectations in our current cosmology; the theory behind mass modelling of the Galaxy; and I show how combining local and global measures probes the shape of the Milky Way dark matter halo and the possible presence of a `dark disc'. I stress the strengths and weaknesses of different methodologies and highlight the continuing need for detailed tests on mock data -- particularly in the light of recently discovered evidence for disequilibria in the Milky Way disc. I collate the latest measurements of $\rhodm$ and show that, once the baryonic surface density contribution $\Sigma_b$ is normalised across different groups, there is remarkably good agreement. Compiling data from the literature, I estimate $\Sigma_b = 54.2 \pm 4.9 \Msunpctw$, where the dominant source of uncertainty is in the \HI\ gas contribution. Assuming this contribution from the baryons, I highlight several recent measurements of $\rhodm$ in order of increasing data complexity and prior, and, correspondingly, decreasing formal error bars (see Table \ref{tab:measurements}). Comparing these measurements with spherical extrapolations from the Milky Way's rotation curve, I show that the Milky Way is consistent with having a spherical dark matter halo at $R_0 \sim 8$\,kpc. The very latest measures of $\rhodm$ based on $\sim 10,000$ stars from the Sloan Digital Sky Survey appear to favour little halo flattening at $R_0$, suggesting that the Galaxy has a rather weak dark matter disc (see Figure \ref{fig:darkdisc}), with a correspondingly quiescent merger history. I caution, however, that this result hinges on there being no large systematics that remain to be uncovered in the SDSS data, and on the local baryonic surface density being $\Sigma_b \sim 55 \Msunpctw$. I conclude by discussing how the new Gaia satellite will be transformative. We will obtain much tighter constraints on both $\Sigma_b$ and $\rhodm$ by having accurate 6D phase space data for millions of stars near the Sun. These data will drive us towards fully three dimensional models of our Galactic potential, moving us into the realm of precision measurements of $\rhodm$. | \label{sec:introduction} The local dark matter density ($\rhodm$) is an average over a small volume, typically a few hundred parsecs$^{\rm \footnotemark}$, around the Sun.\footnotetext{1 parsec = 3.26 light years = 3.086$\times 10^{16}$\,m.} It is of great interest for two main reasons. Firstly, it encodes valuable information about the local shape of the Milky Way's dark matter halo$^{\rm \footnotemark}$ near the disc plane. This provides interesting constraints on galaxy formation models and cosmology \citep[e.g.][]{1994ApJ...431..617D,2001ApJ...551..294I,2004ApJ...611L..73K,2007MNRAS.378...55M,2007arXiv0707.0737D,2012MNRAS.424L..16L}; on the merger history of our Galaxy \citep[e.g.][]{1989AJ.....98.1554L,2008MNRAS.389.1041R,2009MNRAS.397...44R}; and on alternative gravity theories \citep[e.g.][]{2001MNRAS.326.1261M,2004MNRAS.347.1055K,2005MNRAS.361..971R,2007MNRAS.379..597N}. Secondly, $\rhodm$ is important for direct detection experiments that hope to find evidence for a dark matter particle in the laboratory. The expected recoil rate (per unit mass, nuclear recoil energy $E$, and time) in such experiments is given by \citep[e.g.][]{1996APh.....6...87L}: \begin{equation} \frac{dR}{dE} = \frac{\rhodmlab \sigma_W |F(E)|^2}{2 m_W \mu^2} \int_{v>\sqrt{m_N E/2\mu^2}}^{v_\mathrm{max}} \frac{f({\bf v},t)}{v}d^3 {\bf v} \label{eqn:recoilrate} \end{equation} where $\sigma_W$ and $m_W$ are the interaction cross section and mass of the dark matter particle (that we would like to measure); $|F(E)|$ is a nuclear form factor that depends on the choice of detector material; $m_N$ is the mass of the target nucleus; $\mu$ is the reduced mass of the dark matter-nucleus system; $v = |{\bf v}|$ is the speed of the dark matter particles; $f({\bf v},t)$ is the velocity distribution function; $v_\mathrm{max} = 533^{+54}_{-41}$\,km/s (at 90\% confidence) is the Galactic escape speed \citep{2014A&A...562A..91P}; and $\rhodmlab$ is the dark matter density within the detector. It is clear from equation \ref{eqn:recoilrate} that the ratio $\sigma_W/m_W$ trivially degenerates with $\rhodmlab$. Thus, to measure the nature of dark matter from such experiments (in the event of a signal), we must have an independent measure of $\rhodmlab$. This can be obtained by extrapolating from $\rhodm$ to the lab, accounting for potential fine-grained structure \citep{2008arXiv0801.3269K,2008MNRAS.385..236V,2009MNRAS.394..641Z,2009PhRvD..79j3531P,2011MNRAS.418.2648F}; I discuss this in \S\ref{sec:cosmotheory}. We also need to know the velocity distribution function of dark matter particles passing through the detector: $f({\bf v},t)$. In the limit of small numbers of detected dark matter particles, this must be estimated from numerical simulations (\S\ref{sec:cosmotheory}). However, for several thousand detections across a wide range of recoil energy, it can be measured directly \citep{Peter_2011}. \footnotetext{I use the standard terminology `halo' to mean a gravitationally bound collection of dark matter particles. I also define here `subhalo' to mean a bound halo orbiting within a larger halo.} There are two main approaches to measuring $\rhodm$. Local measures use the vertical kinematics of stars near the Sun -- called `tracers' \citep[e.g.][]{1922ApJ....55..302K,oort_force_1932,1960BAN....15....1H,oort_note_1960,bahcall_self-consistent_1984,bahcall_k_1984,1987AA...180...94B,1989MNRAS.239..571K,1989MNRAS.239..605K,1989MNRAS.239..651K,1991ApJ...367L...9K,bahcall_local_1992,creze_distribution_1998,holmberg_local_2000,2003A&A...399..531S,2004MNRAS.352..440H,2006AA...446..933B,2012MNRAS.425.1445G,2012ApJ...746..181S,2012ApJ...751...30M,2012ApJ...756...89B,2013ApJ...772..108Z}. Global measures extrapolate $\rhodm$ from the rotation curve\footnote{Actually, many modern studies use the local surface density of matter as a constraint on their models, typically taking the value from \citet{1991ApJ...367L...9K}. However, \citet{1991ApJ...367L...9K} use a prior from the rotation curve that assumes a spherical halo (see \S\ref{sec:theory}, \S\ref{sec:tests} and \S\ref{sec:measurements}). For this reason, I still consider global models that include a prior from \citet{1991ApJ...367L...9K} as `spherical halo' models that measure $\rhodmext$.} \citep[e.g.][]{1998MNRAS.294..429D,1989ApJ...342..272F,1992AJ....103.1552M,sofue_unified_2008,weber_determination_2010,2010JCAP...08..004C,2011MNRAS.414.2446M}. More recently, there have been attempts to bridge these two scales by modelling the phase space distribution of stars over larger volumes around the Solar neighbourhood \citep{2013arXiv1309.0809B}. The global measures often result in very small error bars (\bcite{2010JCAP...08..004C}; though see \bcite{2010AA...523A..83S} and \bcite{2011JCAP...11..029I}). However, these small errors hinge on strong assumptions about the Galactic halo shape -- particularly near the disc plane \citep{weber_determination_2010}. By contrast, local measures rely on fewer assumptions, but have correspondingly larger errors \citep[e.g.][]{2012MNRAS.425.1445G,2012ApJ...746..181S,2013ApJ...772..108Z}. To avoid confusion, I will refer to results from global estimates that assume a spherically symmetric dark matter halo as an `extrapolated' dark matter density, denoted $\rhodmext$, while I will refer to local measures as $\rhodm$. Combining measures of $\rhodm$ and $\rhodmext$, we can probe the local shape of the Milky Way halo. If $\rhodm < \rhodmext$, then the dark matter halo at the Solar position $R_0 \sim 8$\,kpc is likely prolate (stretched) along a direction perpendicular to the disc plane. If $\rhodm > \rhodmext$, this could imply an oblate (squashed) halo, or a local dark matter disc (see Figure \ref{fig:combinedprobes}). I discuss the theoretical implications of these different scenarios in \S\ref{sec:cosmotheory}. \begin{figure}[t] \begin{center} \includegraphics[width = 0.65\textwidth]{combinedprobes.png} \end{center} \vspace{-5mm} \caption{\small A schematic representation of local versus global measures of the dark matter density. The Milky Way disc is marked in grey; the dark matter halo in blue. Local measures -- $\rhodm$ -- are an average over a small volume, typically a few hundred parsecs around the Sun. Global measures -- $\rhodmext$ -- are extrapolated from larger scales and rely on assumptions about the shape of the Milky Way dark matter halo. (Here I define $\rhodmext$ such that the halo is assumed to be spherical.) Such probes are complementary. If $\rhodm < \rhodmext$, this implies a stretched or prolate dark matter halo (situation {\it a}, left). Conversely, if $\rhodm > \rhodmext$, this implies a squashed halo, or the presence of additional dark matter near the Milky Way disc (situation {\it b}, right). This latter is expected if our Galaxy has a `dark disc' (see \S\ref{sec:cosmotheory}).} \label{fig:combinedprobes} \end{figure} Measurements of $\rhodm$ have a long history dating back to \citet{1922ApJ....55..302K} who was one of the first to coin the term {\it ``dark matter"}. Using the measured vertical velocity of stars near the Sun, he compared the sum of their masses to the vertical gravitational force required to keep them in equilibrium, finding that: \begin{quote} {\it ``As matters stand it appears at once that this} [{\it dark matter}\hspace{0.4mm}] {\it mass cannot be excessive."} \end{quote} However, this early pioneering work treated the stars as a collisional gas, whereas stars are really a {\it collisionless fluid} that obeys similar but different equations of motion. This was corrected the same year by \citet{1922MNRAS..82..122J}, who laid down the basic theory for mass modelling of stellar systems that I outline in \S\ref{sec:theory}. The technique was later refined and applied to improved data by \citet{oort_force_1932}, \citet{1960BAN....15....1H}, \citet{oort_note_1960}, and \citet{bahcall_k_1984,bahcall_self-consistent_1984}. However, there were several problems with these early works: i) their measurements relied on poorly calibrated `photometric' estimates of the distances (\S\ref{sec:tracers}); (ii) stars were chosen that were sometimes too young to be dynamically well mixed in the disc (see \S\ref{sec:theory}); (iii) populations were often assumed to be `isothermal' with the vertical velocity dispersion constant with height \citep[typically a poor approximation: ][]{1989MNRAS.239..651K,2011MNRAS.416.2318G}; and (iv) it was often unclear if the stars for which photometric density distributions could be estimated were the same stars for which the velocity distribution was measured \citep[][and see \S\ref{sec:theory}]{1989MNRAS.239..651K}. A key series of papers by \citet{1989MNRAS.239..571K,1989MNRAS.239..605K,1989MNRAS.239..651K,1991ApJ...367L...9K}, improved on this by collecting an unprecedented amount of data, and compiling a {\it volume complete} sample of K-dwarf stars (that are particularly good for measuring photometric distances; \S\ref{sec:tracers}) towards the South Galactic Pole. A quarter of these had radial velocity measurements. A further key improvement came with the {\it Hipparcos} satellite that launched in August 1989, providing positions and proper motions for $\sim 100,000$ stars within $\sim 100$\,pc of the Sun \citep{vanLeeuwen2007}. It was a boon for the field, since prior to this only radial Doppler velocities and photometric distances were available. Several new measurements of $\rhodm$ using these new data followed \citep{creze_distribution_1998,holmberg_local_2000,2003A&A...399..531S,2004MNRAS.352..440H,2006AA...446..933B}. Most recently, there have been a series of new measurements coming from new Galactic surveys -- the Sloan Digital Sky Survey (SDSS; \citealt{2012ApJ...746..181S,2013ApJ...772..108Z}), and the RAdial Velocity Experiment (RAVE; \citealt{2008MNRAS.391..793S}). These same surveys have recently found evidence for vertical density waves in the Milky Way disc \citep{2012ApJ...750L..41W,2013arXiv1302.2468W,2013arXiv1309.2300Y}, perhaps caused by the recent Sagittarius dwarf merger \citep{2013MNRAS.429..159G}. This is something that may prove both a blessing and a curse for attempts to measure $\rhodm$; I discuss this further in \S\ref{sec:disequilibria}. All of the above measurements use stellar kinematics to probe the total Galactic potential near the Sun. To extract the local dark matter density from this, we must assume some weak field theory of gravity (to link the potential to the matter density; see \S\ref{sec:cosmomodel} and \S\ref{sec:theory}), and we must subtract off the contribution from visible matter (i.e. stars, gas, stellar remnants etc.). I call this from here on the {\it baryonic} matter density $\rho_b$. Estimates of this have also evolved with time, from an early estimate of $\rho_b \sim 0.038\Msunpcth$$^{\rm \footnotemark}$ \citep{oort_force_1932} to the more modern value $\rho_b = 0.0914 \pm 0.009\Msunpcth$ \citep{2006MNRAS.372.1149F}. I discuss the latest constraints on $\rho_b$ in \S\ref{sec:massmodel}. \footnotetext{Particle physicists may be more used to seeing these mass densities in units of $\GeVcmth$; a useful conversion is: $0.008\Msunpcth = 0.3\GeVcmth$. I mark all densities also in $\GeVcmth$ along the right $y$-axis of Figure \ref{fig:rhodmhistory}, and in Table \ref{tab:measurements}.} In addition to the above improvements in data, there has been a concerted push to better understand the model systematics that go into the measurement of $\rhodm$. Early work by \citet{1989ApJ...344..217S} and \citet{1989MNRAS.239..571K} explored the effects of un-modelled coupling between radial and vertical star motions (see \S\ref{sec:theory}), while tests on simple mock data drawn from an analytic Galactic model have been useful in determining the effect of errors due to measurement uncertainties and poor sampling (\citealt{1991ApJ...367L...9K}; \citealt{2013A&A...555A.105I}; and see \S\ref{sec:tests}). But a full test of methods on dynamically realistic $N$-body mock data has only come recently with \citet{2011MNRAS.416.2318G}. This has exposed some rather surprising model biases that I discuss further in \S\ref{sec:theory} and \S\ref{sec:tests}. Finally, new methods to combat such systematics are being developed \citep[e.g.][]{2011MNRAS.416.2318G,2013MNRAS.433.1411M} resulting in further new measurements of $\rhodm$ \citep{2012MNRAS.425.1445G}. I discuss these techniques in \S\ref{sec:theory} and compare and contrast the latest measurements in \S\ref{sec:measurements}. \begin{figure} \begin{center} \includegraphics[width = 0.99\textwidth]{rhodmhistory.png} \end{center} \vspace{-8mm} \caption{\small A century of measurements of $\rhodm$. In all cases, I assume the same matter density and surface density of $\rho_b = 0.0914\Msunpcth$ and $\Sigma_b = 55\Msunpctw$ \citep{2006MNRAS.372.1149F}. Values derived from a surface density rather than a volume density have a blue filled circle; red data points indicate the use of a `rotation curve' prior (see \S\ref{sec:rotprior}). The green data point is derived from \citet{2012MNRAS.425.1445G} assuming a stronger prior on $\Sigma_b = 55 \pm 1 \Msunpctw$ (see \S\ref{sec:measurements}). All error bars represent either $1\sigma$ uncertainties or 68\% confidence intervals. Overlaid are: $\rhodmext$ extrapolated from the rotation curve assuming spherical symmetry (grey band); the launch dates plus 5 years for the Hipparcos and Gaia astrometric satellite missions; and the start date plus 5 years of the SDSS and RAVE surveys. Where no error bar was calculated for a given measurement, there is simply a horizontal line through that data point. All data and references (including definitions of abbreviations) are given in Table \ref{tab:measurements}.} \label{fig:rhodmhistory} \end{figure} A summary of measurements of $\rhodm$ from Kapteyn through to the present day is given in Figure \ref{fig:rhodmhistory}, where I mark also the latest limits on $\rhodmext$ from the rotation curve assuming a spherically symmetric dark matter halo (grey band\footnote{This is taken from \citealt{2011JCAP...11..029I}, but is consistent with other recent measures \citep{1998MNRAS.294..429D,1989ApJ...342..272F,1992AJ....103.1552M,sofue_unified_2008,2010AA...523A..83S,weber_determination_2010,2010JCAP...08..004C}.}); all data and references are given in Table \ref{tab:measurements}. I discuss this Figure in detail along with the latest constraints on $\rhodm$ in \S\ref{sec:measurements}. With the successful launch of the Gaia satellite, measurements of $\rhodm$ are set to enter a golden age \citep[e.g.][]{2001A&A...369..339P,2005MNRAS.359.1306W}. There are significant challenges to be overcome \citep{2013A&ARv..21...61R,2013arXiv1309.2794B}, but as has happened post-Hipparcos, Gaia will likely drive another step-wise improvement in the error bars on $\rhodm$. I discuss this in \S\ref{sec:gaia}. This article is organised as follows. In \S\ref{sec:cosmotheory}, I discuss theoretical expectations for $\rhodm$ and its laboratory extrapolation $\rhodmlab$ in our current cosmology. In \S\ref{sec:theory}, I present the key theory behind both local and global measures of the local dark matter density, with a particular focus on moment methods. In \S\ref{sec:tests}, I present tests of different methods on simple 1D mock data, determining what quality and type of data best constrain $\rhodm$. In \S\ref{sec:measurements}, I discuss historical measures of $\rhodm$ and summarise the latest measurements from different groups. I compare and contrast the advantages and disadvantages of different methods and data, and I assess where the key uncertainties remain. In \S\ref{sec:gaia}, I discuss how the Gaia satellite will transform our measurements of $\rhodm$. Finally, in \S\ref{sec:conclusions}, I present my conclusions. | \label{sec:conclusions} I have presented a review of nearly a century of measurements of the mean density of dark matter near the Sun: $\rhodm$. We are about to enter a golden age where such measurements become truly precise. Such accurate measures encode valuable dynamical information about our Galaxy, and are also of great importance for `direct detection' dark matter experiments. I have reviewed theoretical expectations for $\rhodm$, its laboratory extrapolation $\rhodmlab$ and the local velocity distribution function of dark matter $f({\bf v})$ (that is important for direct detection experiments). I presented the key theory behind measurements of $\rhodm$ in the Milky Way, and I collated both historical and modern measures. Finally, I looked ahead to what will soon be possible with the Gaia satellite. My key conclusions are as follows: \paragraph{Numerical simulations of $\rhodm$} \begin{itemize} \item State of the art Dark Matter Only (DMO) cosmological simulations make accurate predictions for the local phase space distribution function of dark matter (its mean density $\rhodm$ and velocity distribution function $f({\bf v})$) on scales of $\simgt 20$\,pc. Unresolved structure on smaller scales is unlikely to affect the conclusions of these simulations. \item Although unresolved structures in the simulations are not likely important, baryonic processes are. Gas cooling, star formation and stellar feedback during galaxy formation likely rearrange the dark matter distribution in galaxies, even if the dark matter and baryons interact only via gravity. Baryons act to make halos oblate and aligned with the central disc, at least out to $\sim 10$ disc scale lengths; to transform central dense dark matter cusps into cores (if stellar/black hole feedback is strong enough); and -- through biased accretion -- to lead to the formation of an accreted dark matter disc. Each of these processes affects the expectation values of $\rhodm$ and $f({\bf v})$ near the Sun. \end{itemize} \paragraph{Measurements of $\rhodm$} \begin{itemize} \item A key source of uncertainty on $\rhodm$ is the baryonic contribution to the local dynamical mass: $\Sigma_b$. I have compiled a new measurement from literature data: $\Sigma_b = 54.2 \pm 4.9 \Msunpctw$, where the dominant source of uncertainty is in the \HI\ gas contribution. Improving our determination of $\Sigma_b$ warrants renewed attention. \item Homogenising $\Sigma_b$ across different studies (using the above value), I find excellent agreement between different groups. In Table \ref{tab:measurements}, I have compiled a list of recent measures of both $\rhodm$ (calculated locally) and $\rhodmext$ (extrapolated from the rotation curve assuming spherical symmetry). Each of these studies is complementary. One -- G12 -- uses a very clean dataset with a simple selection function, but poorer sampling ($\sim 2000$ stars). Three -- S12, Z13, and BR13 -- use SDSS data with significantly improved sampling ($\sim 10,000$ stars), but with a significantly more complex data selection function. The latter studies have smaller formal errors, but present a greater challenge when estimating systematic errors. \item Comparing the above measures of $\rhodm$ with spherical extrapolations from the Milky Way's rotation curve ($\rhodmext = 0.005 - 0.015 \Msunpctw$; $0.2 - 0.56$\,GeV\,cm$^{-3}$), the Milky Way is consistent with having a spherical dark matter halo at $R_0 \sim 8$\,kpc. The latest measurements of $\rhodm$ from SDSS appear to favour little halo flattening in the disc plane, suggesting that the Galaxy has little or no accreted dark matter disc and a correspondingly quiescent merger history (see Figure \ref{fig:darkdisc}). I caution, however, that this result hinges on there being no large systematics that remain to be uncovered in the SDSS data, and on the local baryonic surface density being $\Sigma_b \sim 55 \Msunpctw$. \item There is a continuing need for detailed tests of our methodologies on dynamically realistic mock data. I illustrated this using both simple 1D tests and full 6D mock data based on an $N$-body simulation of the Milky Way. This latter reveals the surprising result that seemingly sensible assumptions about the distribution function of tracer stars in the disc can lead to significant systematic biases on $\rhodm$. Such model systematics will likely become a dominant source of uncertainty on $\rhodm$ in the Gaia era. \item Two groups have recently found evidence for disequilibria in the Milky Way in the form of vertical density/velocity waves in the Milky Way disc stars. I showed that, at the currently quoted wave amplitudes, these contribute a systematic error on $\rhodm$ of order $\sim 10$\%. This is not likely to be the dominant source of uncertainty on $\rhodm$ even with Gaia quality data. However, if such oscillatory modes persist as the data continue to improve, they will provide us with a brand new probe of Galactic structure. \end{itemize} | 14 | 4 | 1404.1938 |
1404 | 1404.1109_arXiv.txt | {Stellar shells, which form axially symmetric systems of arcs in some elliptical galaxies, are most likely remnants of radial minor mergers. They are observed up a radius of $\sim$100\,kpc. The stars in them oscillate in radial orbits. The radius of a shell depends on the free-fall time at the position of the shell and on the time since the merger. We previously verified the consistency of shell radii in the elliptical galaxy NGC\,3923 with its most probable MOND potential. Our results implied that an as~yet undiscovered shell exists at the outskirts of the galaxy.} {We here extend our study by assuming more general models for the gravitational potential to verify the prediction of the new shell and to estimate its position.} {We tested the consistency of the shell radial distribution observed in NGC\,3923 with a wide variety of MOND potentials of the galaxy. The potentials differed in the mass-to-light ratio and in distance to the galaxy. We considered different MOND interpolation functions, values of the acceleration constant $a_0$, and density profiles of the galaxy. We verified the functionality of our code on a Newtonian self-consistent simulation of the formation of a~shell galaxy.} {Our method reliably predicts that exactly one new outermost shell exists at a galactocentric radius of about 1900$^{\prime\prime}$ ($\sim$210\,kpc) on the southwestern side of the galaxy. Its estimated surface brightness is about 28\,mag\,arcsec$^{-2}$ in $B$ -- a value accessible by current instruments. This prediction enables a rare test of MOND in an elliptical down to an acceleration of $a_0/10$. The predictive power of our method is verified by reconstructing the position of the largest known shell from the distribution of the remaining shells. } {} | \label{sec:intro} Modified Newtonian dynamics (MOND) and its implications has been successfully tested in all types of disk and dwarf galaxies, and its numerous aspects have been even verified in interacting galaxies \citep{famaey12}. However, tests of MOND in ellipticals are still rare. Ellipticals typically lack kinematics tracers up to large enough radii, where the gravitational acceleration drops substantially below the MOND acceleration constant $a_0 = 1.2\times10^{-10}$m\,s$^{-2}$, at which the MOND effects emerge. Apart from a~few exceptions, there are no objects in known orbits, similar to the gas clouds in spiral galaxies, which would enable a direct measurement of the gravitational acceleration. Jeans analysis of dynamics of stars or planetary nebulae can be used to measure the gravitational field, but its results are ambiguous since the anisotropic parameter is unknown. Gravitational lensing is not able to probe the gravitational field in the low-acceleration regime (see Sect.~1 of \citealp{milg12} for more details and a~recent review of tests of MOND in ellipticals). Stellar shells, which are observed in many ellipticals, offer an interesting alternative to established methods to measure the gravitational field in this type of galaxies. They appear as glowing sharp-edged arcs centered on the center of the galaxy. Shells occur in about 10\% of early-type galaxies in the local Universe \citep{malin83,schweisei88,tal09,atkinson13}. In special cases, and we consider only these examples of shell galaxies hereafter, shells form an axially symmetric structure -- these are so-called Type\,I shell systems \citep{prieur90, wilkinson87}, see our Fig.~\ref{fig:N3923}. Approximately every third shell galaxy is of this type \citep{prieur90}. Several formation scenarios have been proposed, but the most accepted one today is the scenario of an almost radial minor merger \citep{quinn84}. When a~small galaxy (the secondary) reaches the center of a~bigger and more massive galaxy (the primary), the secondary is disrupted by tidal forces. Its stars begin to behave as test particles and oscillate in the potential well of the primary. When they reach their apocenters, they slow down and create kinematic density waves that are observed as the shells. However, the core of the secondary can survive the first passage. If it loses enough kinetic energy by dynamical friction, it becomes trapped in the potential well of the primary and begins to oscillate as well. During each passage through the center of the primary, the surviving part of the secondary is peeled off again and again, so that several generations of shells can be formed from one secondary. We judge that the mass ratio of colliding galaxies is about 1:10, because the total luminosity of shells usually accounts for a~few percent of the total luminosity of their host galaxy \citep{carter82,malin83-2,DC86,prieur88}. As we explain in Sect.~\ref{sec:shell_prop}, the radius of a~shell in a~Type\,I shell galaxy is only a~function of the shape of the galactic gravitational potential and the time elapsed since the merger. Therefore, if we know the radii of shells, we can test whether they are consistent with a~given potential. This is a~very convenient way for testing MOND, which predicts the dynamics only on the basis of the distribution of the baryonic matter. The three-dimensional density profile of the galaxy, needed to build its MOND potential, can be constrained for a shell elliptical galaxy from the morphology of its shells \citep{DC86}. Shells often extend very far from the center of their host galaxy. The elliptical NGC\,3923 (Fig.~\ref{fig:N3923}), which is the main subject of this paper, is decorated by the biggest known shell in the Universe. Its radius is more than 100\,kpc (Table~\ref{tab:shpos}) and, according to the MONDian model of the galaxy NGC\,3923 from \citet{bil13}, it is exposed to a gravitational acceleration of $a_0/5$ from the host galaxy. In this work, we~theoretically predict a~new -- currently not yet observed -- shell at a distance of about 220\,kpc, which would extend to the acceleration of $a_0/10$. The modified dynamics in individual ellipticals at such a~low acceleration has been tested only in two cases -- in NGC\,720 and NGC\,1521 \citep{milg12}. Type\,I shell galaxies are interesting from the point of view of MOND for another reason as well. The modified dynamics has been tested only in systems whose constituents move in nearly circular orbits (like disk galaxies, \citealp{thingsmond, rotcurv1, rotcurv2}), randomly distributed orbits (dwarf galaxies, \citealp{anddwarf}, elliptical galaxies, \citealp{sanders2010}) and ellipse-like orbits (polar rings, \citealp{lughausen13}). To our knowledge, MOND has never been tested for particles in radial trajectories. Since MOND was originally inspired by disk galaxies \citep{milg83a}, it is important to test it also for strongly noncircular orbits. It is not known whether MOND should be interpreted as a~modified gravity theory or as a~modification of the law of inertia (or as a~combination of both). In the first case, the kinematic acceleration of a~test particle only depends on the vector of gravitational acceleration at the immediate position of the particle; in the latter, the kinematic acceleration can generally depend on the whole trajectory of the particle since the beginning of the Universe. In the case of modified inertia, the MOND algebraic relation $a\mu(a/a_0) = a_\mathrm{N}$ (see Sect.~\ref{sec:grid}), deduced for particles in circular orbits, is not necessarily valid for particles that oscillate along a~line. Furthermore, in many cases the stars that constitute the shells periodically travel between the Newtonian ($a\gg a_0$) and deep-MOND ($a\ll a_0$) region of their host galaxy, unlike the stars in disk galaxies, which continue to be exposed to a gravitational field of nearly constant magnitude. \begin{figure} \sidecaption \resizebox{\hsize}{!}{\includegraphics{N3923.eps}} % \caption{Type\,I shell elliptical galaxy NGC\,3923. Courtesy of David Malin, Australian Astronomical Observatory.} \label{fig:N3923} \end{figure} The paper is organized as follows: in Sect.~\ref{sec:pospot}, we explain the equations for shell radii evolution and describe the method we use to constrain the gravitational potential of a~shell galaxy from the radial distribution of its shells. After presenting the observational data in Sect.~\ref{sec:obs_data} and our code for shell identification in Sect.~\ref{sec:aut_id}, we describe the results of the automated shell identification in Sect.~\ref{sec:res}, among which is the prediction of an as~yet undiscovered shell. The results are discussed in Sect.~\ref{sec:resdis}. In Sect.~\ref{sec:predictive_power}, we demonstrate the predictive ability of our method by reconstructing the position of a~known shell on the basis of the positions of the remaining shells. The functionality of the shell identification code is verified on a~Newtonian self-consistent simulation in Sect.~\ref{sec:newton}. The limitation and possible shortcomings of the method are discussed in Sect.~\ref{sec:unexpl}. The paper is summarized in Sect.~\ref{sec:summary}. | \label{sec:disc} \subsection{Discussion of the results} \label{sec:resdis} In Sects.~\ref{sec:grid}--\ref{sec:2sh} we varied some of the free parameters of the problem of shell identification in NGC\,3923. Here we summarize and discuss the results. In all the potentials we have explored and that are compatible with the observed shell radial distribution, it is possible to identify the four outermost shells ($a$, $b$, $c$ and $d$) as shells number 2, 3, 4, and 5 from the first generation. Moreover, the identification of the three outermost shells cannot be different. This leads us to expect the existence of shell number 1. However, it may be very faint. As we said in the Introduction (Sect.~\ref{sec:intro}), the shells disappear when they become too old and big because their surface brightness decreases under the detection limit. The surface brightness depends, among others, on the energy spectrum of the stars released from the secondary during its passage through the center of the primary. At the moment, we can only make the following rough estimate: if we assume that the new predicted shell constitutes the same number of stars as shell $a$, and the radius of the former is approximately twice as large as the latter, its surface brightness must be four times lower. The surface brightness of shell $a$ is about 26.5\,mag\,arcsec$^{-2}$ in the B band, which means that the new shell should have about 28\,mag\,arcsec$^{-2}$. This value is in the reach of existing instruments. All the identifications have the common feature that the observed shell distribution of NGC\,3923 can be explained in MOND only if the shell system was created in at least three generations (if a~shell distribution is compatible with the formation in $N$ generations, then it is evidently compatible with any number of generations higher than $N$). The three generations are sufficient to account for 25 out of 27 shells. The innermost two shells probably originate from the fourth generation, but the secondary remainder could have decayed before it reached the center of the primary for the fourth time. In simulations, each passage of the secondary through the primary center is accompanied by the formation of one stellar tail. Therefore three tails could be present in NGC\,3923, but their surface brightness can be low. Since all the identifications imply that the secondary had to impact NGC\,3923 along the southwestern major semi-axis at their first collision, two of the tails should point to the northeast and one to the southwest. In Table~\ref{tab:possh1} we can see the influence of the individual free parameters on the position of the predicted shell. The choice of the interpolation function has a similar influence on its radius as the variations of $M/L_{3.6}$ and $d$. Moreover, $M/L_{3.6}$ and $d$ were intentionally left to vary beyond the observational constraints. On the other hand, the choice of $a_0$ affects the radius of the expected shell much less than the choice of the interpolation function. Substituting the real galaxy by a point mass seems to be a severe modification that does not produce a meaningful prediction of the shell position. However, we can learn from this example that substituting a~potential for a~more concentrated one leads to an inward shift of the position of the predicted shell (Table~\ref{tab:possh1}). In contrast, the twice-expanded mass distribution is not as meaningless. If NGC\,3923 is not viewed perpendicularly to its major axis, the galaxy is more elongated than we have assumed. If it is the case, the predicted shell can be expected at a larger radius. The most probable radius of the predicted shell is the radius derived for the most probable combination of the mass profile, mass-to-light ratio, and galaxy distance from Earth, which are those derived in \citet{bil13}. This radius is +1874$\arcsec$ for the ``simple'' interpolation function, and +1940$\arcsec$ for the ``standard'' interpolation function. The ages of the generations are quite sensitive to the choice of the free parameters. For example, for the basic grid, the age of the first generation ranges from 2 to 4\,Gyr, the age of the second from 400 to 2200\,Myr, and that of the third generation even from 100 to 1000\,Myr. For the potential and the shell identification used in \citep{bil13}, the ages of the first, second, and third generation are derived as 2688, 631 and 364\,Myr, respectively. We did not designate shell $e$ as shell number 8 from the first generation (as suggested by Fig.~\ref{fig:idtab_basgrid}) and did not search for shell number 1 of the second generation. This may be related. We hesitated to consider shell $e$ as shell 8 of the first generation because it is clearly visible in the images of the galaxy, but shells number 6 and 7 are not. This situation never occurred in our simulations of shell galaxy formation (see, e.g., \citealp{ebrova12}), but we have experience only with exactly radial mergers and spherical primaries. Maybe this is not a~serious problem, because the surface brightness of individual shells in photographs of NGC\,3923 shows no radial trend and it is rather random. The other disturbing fact is that shell $f$, which is almost always classified as shell number 2 of the second generation, is very bright, but a~shell with a radius compatible with that of shell number 1 of the second generation has never been reported. This shell should lie at a radius of about +450$\arcsec$. Possibly, shell $e$ is shell 1 of the second generation, which was shifted inward by some effect. The shift can be easily explained if the material that formed the shell was released before the secondary reached the primary's center. We searched for a~photograph of the galaxy that would map the region of the expected occurrence of shell 1 of the second generation, but we were not able find one. We did not even find an~image that clearly showed shell $d$. The region of the galactocentric distances 400 and 600$\arcsec$ has probably never been properly explored. This region lies between the area covered by the modern narrow field-of-view CCD observations that show the central part of the galaxy and of the older wide-field images taken on photographic plates, which were processed to show the two faint outermost shells at the expense of saturating the center of the galaxy. \begin{figure}[b!] \sidecaption \resizebox{\hsize}{!}{\includegraphics{allidtab11b2.eps}} % \caption{Test of the predictive power of our method. Shell $a$ was omitted from the set of shell radii we used elsewhere in this paper and the procedure from the Sect.~\ref{sec:grid} was repeated. The meaning of this figure is analogous to that of Fig.~\ref{fig:idtab_basgrid}. For all the potentials from the basic grid, shells $b$, $c$ and $d$ can be identified as shells number 3, 4 and 5 from the first generation. If we did not know about the existence of the shell $a$, the method would suggest that this shell should exist. In this case we would be left with some doubt, because another identification of shells $b$, $c$ and $d$ is possible for a~small fraction of potentials, which gives them shell numbers 2, 3, and 4.} \label{fig:idtab_test} \end{figure} \subsection{Predictive power of the identification method} \label{sec:predictive_power} To test the predictive ability of our method, we tried to ``rediscover'' the outermost already known shell $a$, which lies at 1170$\arcsec$ from the center of NGC\,3923. We excluded it from the set of shells that we feed into our identification code. We repeated the work described in Sects.~\ref{sec:grid} and \ref{sec:interpol} (two different choices of the interpolation function) with this reduced set of shell radii. The result of the identification for the basic grid of potentials is shown in Fig.~\ref{fig:idtab_test}, which is analogous to Fig.~\ref{fig:idtab_basgrid}. The three outermost shells of this reduced set have $n=3$, 4, and 5 for all potentials compatible with the reduced set of shell radii of NGC\,3923 and for both interpolation functions, implying that two new shells must exist. If we assume that the correct interpolation function is the ``simple'' function, the predicted median radius of shell number 2 is located at +1168$\arcsec$ or +1210$\arcsec$ for the case of the ``standard'' function. The statistics of the predicted radius of shell number 2 are listed in Table~\ref{tab:possh2}. For the most probable free parameters of the potential (those from \citealp{bil13}), we derive +1149$\arcsec$ for the ``simple'' interpolation function and +1171$\arcsec$ for the ``standard'' interpolation function. If we had relied on the average value of these two most probable values, +1160$\arcsec$, we would have missed the correct value by only 1\%. However, for a~small but not negligible part of the tested potentials (for both cases of interpolation functions), an alternative identification of the three shells ($b$, $c$, $d$) is possible. It assignes them shell numbers 2, 3, and 4 and classifies them into the first generation. This makes the reconstruction of the radius of the excluded shell $a$ ambiguous. If we tried to predict the radius of shell 1 and shell $a$ had been discovered, its radius would be substantially different from the predicted value. Nevertheless, we are in a better situation in reality -- we already know the radius of the shell $a$. With this additional information the prediction of the position of the new shell is unambiguous. \begin{table} \centering \caption{Statistics of the predicted radius of shell number 2.} \begin{tabular}{lcccc}\hline\hline & $ r_{1,\mathrm{median}}$ & RMS & $r_{1,\mathrm{min}}$ & $r_{1,\mathrm{max}}$\\\hline basic grid & 1169 & 21 & 1139 & 1224\\ ``standard'' $\mu$ & 1210 & 28 & 1625 & 1254\\\hline \end{tabular} \tablefoot{``Rediscovering'' the outermost known shell $a$ at 1170$\arcsec$. All quantities are in arcseconds and their meaning is the same as in Table~\ref{tab:possh1}.} \label{tab:possh2} \end{table} \subsection{Newtonian self-consistent simulation} \label{sec:newton} Many simplifying assumptions were made when deriving the analytical formulas (\ref{eq:pos1})\,--\,(\ref{eq:pos2}) to computate the shell radii. To test their precision, we applied our code to the results of a~Newtonian self-consistent simulation of a~shell galaxy formation using GADGET-2 \citep{springel05}. The simulation was an enhanced version of that presented in \citet{bartoskovaselfcon}. The primary galaxy was modeled as a~composite of two Plummer spheres corresponding to stellar and dark matter components. The secondary was modeled by a~single Plummer sphere. The collision was exactly radial. The specifications of the mass profiles and initial conditions are listed in Table~\ref{tab:gadget}. Two generations of shells formed before the secondary was completely disrupted. We made snapshots of the simulation at three different times. We measured the shell positions in each of them as we would in the image of a~real galaxy. Then we entered the shell radii into our identification code (along with the known Newtonian potential of the simulated primary). In this case, we had the privilege to know, in any snapshot, in how many generations the shells were formed (i.e., we knew $N_\mathrm{max}$, see Sect.~\ref{sec:aut_id}). The code indeed found the correct identification for each snapshot. In a~few cases, we were even led by the code to look at the images more carefully because it suggested that other shells should exist and they really showed up to be present, although faint. The correct identification was always found for the lowest possible value of the parameter $\Delta$ -- for lower values of $\Delta$ no satisfactory identification exists. In none of the three snapshots the relative difference of the modeled and measured shells exceeded 4\%. We were able to see five shells in the snapshot in which only the first generation of shells was created, and seven and ten shells in the two snapshots in which two shell generations were already created. This simulation supports the claim that the one-generation scenario is unable to explain the high number of shells observed in some galaxies. \begin{table}[t] \centering \caption{Parameters of the Newtonian self-consistent simulation of the~shell galaxy formation.} \begin{tabular}{lccc} \hline \hline component & $M$ & $b$ & $N_\mathrm{p}$ \\ & $10^{10}$\,$M_{\sun}$ & kpc & $10^6$\\ \hline primary dark halo & 800 & 20 & 1.6\\ primary luminous matter & 20 & 8 & 0.4\\ secondary & 2 & 2 & 5\\ \hline \hline init. primary-secondary separation & 200 & kpc & \\ init. relative velocity & 102 & km$/$s & \\ \hline \end{tabular} \tablefoot{$M$ -- the total mass of a~Plummer sphere, $b$ -- Plummer radius, $N_\mathrm{p}$ -- number of particles} \label{tab:gadget} \end{table} \subsection{Limitations of our method} \label{sec:unexpl} The Newtonian self-consistent simulation gives us an idea, at least for one particular simulation, of the magnitude of influence of phenomena such as the noninstant disruption of the secondary, its nonzero size, and the self-gravity of its material. These phenomena were not taken into account when deriving the key relations Eqs.~(\ref{eq:pos1})\,--\,(\ref{eq:pos2}) for the time evolution of the shell radii. However, the simulation was still somewhat idealized and it was not MONDian. Here we try to list some of the remaining possible shortcomings of our model and of our conclusions. 1) \textit{Nonradiality of the merger and the ellipticity of the potential.} The merger that produced the shells in NGC\,3923 was hardly exactly radial. The simulations of \citet{hq87} and \citet{DC86} demonstrated the focusing effect of the host ellipticity on shells -- the higher the ellipticity of the potential, the narrower the angular extent of the shell system. The focusing effect probably also helps to create an axisymmetric shell system, even if the merger is not exactly radial. In this case, the orbits of stars would deviate more from the radial trajectories and Eqs.~(\ref{eq:pos1})\,--\,(\ref{eq:pos2}), which are the basis of our identification code, would lose precision. 2) \textit{Faster disruption of the secondary because of the external field effect (EFE).} It has been known for a long time that the galactic interactions in MOND are more complicated than in the Newtonian dynamics because of the nonlinearity of MOND equations. In MOND, the dynamics of a~system is affected by the presence of an external field, even if the external field is homogeneous (i.e., the strong equivalence principle is violated). The process of satellite disruption in a~highly elliptical orbit was discussed in detail by \citet{satelliteefe}. The external field effect causes an expansion of the satellite, so that it becomes more vulnerable to tides. In the era when the one-generation shell formation scenario was accepted, \citet{milgsh} suggested that when a~shell galaxy is formed, the secondary becomes gradually disrupted sooner than it reaches the center of the primary because of the EFE. This would mean that two of the assumptions of Eq.~(\ref{eq:pos1}) are incorrect. The question is how important this effect was in the case of NGC\,3923. Since the radial range of shells is so large, the shell system probably had to be formed in several generations. Since the mass-loss of the secondary due to tidal forces is strongest near the center of the primary, most of the material that forms shells was probably released at the center, as our model expects. If much material was released before the secondary reached the center, then the radii of the shells made of this material could, indeed, deviate substantially from our model. 3) \textit{Influence of the galactic neighbors.} The galaxy NGC\,3923 is the largest member of a~small galactic group. A~nearby small elliptical galaxy NGC\,3904 is seen ~2200$\arcsec$ northwest from NGC\,3923. This is very close to the expected position of the predicted shell. The distance of NGC\,3904 has been measured by the method of the surface brightness fluctuations. There are three individual measurements in the NASA/IPAC Extragalactic Database ranging from 28.3 to 29.8\,Mpc. This means that the galaxy is at least 5\,Mpc farther away from Earth than NGC\,3923. The apparent V magnitude is lower by 1 than that of NGC\,3923, therefore the stellar mass of NGC\,3904 is about 1.7\,$\times$\,lower than that of NGC\,3923, if their mass-to-light ratio are approximately equal. Therefore its MONDian acceleration is $3\times 10^{-3}a_0$ at a distance of 5\,Mpc. Thus the effect of NGC\,3904 on the position of the predicted shell is negligible because it is subject to acceleration of $0.1a_0$ from NGC\,3923. 4) \textit{Formation of shells from several minor mergers.} The shell system could, of course, be created by accretion of several secondaries, not only by a single one as our method assumes. However, this is highly improbable. Type~I shell galaxies constitute about 3\% of all early-type galaxies \citep{prieur90}. From this number, we can easily deduce that the probability that the shell system in a~randomly chosen Type\,I shell galaxy was formed by accretion of $k$ independent secondaries is $33/34^k$, that is, only 3\% of all Type\,I shell systems come from more than one secondary. Furthermore, the actual probability is even lower because the two or more independent shell systems would have to share a common symmetry axis when viewed from Earth. 5) \textit{Other formation scenarios of shell galaxies exist.} We assumed a minor-merger origin of the shell system in NGC\,3923. However, other scenarios of shell formation also exist, but they are even less explored than the minor merger model. The merger scenario is favored in the case of NGC\,3923 because the galaxy contains nonthermalized dust clouds \citep{sikkema07}. The so-called weak interaction model of the formation of shell galaxies requires a~rotationally supported thick stellar disk \citep{wim90,wim91}. For a~Type\,I shell galaxy, the thick disk has to lie in the plane of symmetry of the shell system, but a minor axis rotation of NGC\,3923 is observed \citep{minrot}. This rules out the weak interaction model. \citet{majorm} claimed that the result of a~merger of two identical spiral galaxies formed in their simulation resembled NGC\,3923. In such a~merger, our model of shell radii evolution is not applicable. 6) \textit{What is the radius of a~shell?} In our simplified model, where the stars are all released simultaneously from a~single point, the shell edges are discontinuities in the surface density. In simulations, and even more so in observed galaxies, the shell edges are blurred. What should then be considered as the shell radius? The radius of the highest surface brightness of the shell, or the radius of its steepest gradient? These two radii can differ by several percent. For now, we included this observation uncertainty, jointly with the systematic errors caused by the inaccuracy of our model of shell propagation, into the tolerance parameter $\Delta$. 7) \textit{Arbitrariness of the identification criteria.} We deliberately chose a wide range of parameters to test whether the identification of the four outermost shells was unique. However, the criteria were still arbitrary, but it will be possible to set the criteria more correctly when more work has been done. We can learn about the tolerance parameter $\Delta$ from self-consistent simulations. These simulations will have to include nonradial mergers, elliptical primaries, different secondary morphologies, etc. The best measure of the deviation of the modeled from the observed shell radii may be different from the relative difference we used here. We can imagine that the best measure can be defined, for example, as $\left|r_{\lambda}-r_\mathrm{model}\right|<C$ or $\left|r_{\lambda}-r_\mathrm{model}\right|<C\sqrt{r_{\lambda}}$ instead of $\left|r_{\lambda}-r_\mathrm{model}\right|/\left|r_{\lambda}\right|<\Delta$. The self-consistent simulations will also indicate the largest possible number of shell generations present in the system. This number will probably be connected with the values of the gravitational potential at the positions of the innermost and outermost observable shells. The possible number of missing shells can be constrained from observations. \begin{figure} \sidecaption \resizebox{\hsize}{!}{\includegraphics{predsh.eps}} % \caption{Position of the predicted shell in NGC\,3923. The middle thick arc is the most probable position of the predicted shell (calculated for the mass distribution used in \citealp{bil13}). The inner and the outer arcs present the error range deduced as the lowest and highest values in Table~\ref{tab:shpos} excluding the point mass potentials. The data for the underlying image are taken from the Digitized Sky Survey.} \label{fig:pred} \end{figure} The elliptical galaxy NGC\,3923 is a well-studied case of a~shell galaxy with many exceptional properties. According to our method, it is necessary in MOND for the four outermost known shells (labels $a$, $b$, $c$, and $d$ in Table~\ref{tab:shpos}) to have shell numbers 2, 3, 4, and 5. This implies that shell number 1 must exist. The position of the predicted shell depends on the free parameters of the potential, see Table~\ref{tab:shpos}. Most probably, the shell lies in an angular distance of about 1900$\arcsec$ (Fig.~\ref{fig:pred}, Sect.~\ref{sec:resdis}) from the galaxy center to the southwest. The shell could be observable by existing instruments. In addition to the shell, up to three stellar tails could be discovered -- two pointing at the northeastern side of the galaxy and one pointing at the southwestern side. We verified that this conclusion does not change when several uncertain assumptions are modified. We varied the mass-to-light ratio, the distance of the galaxy from Earth, the interpolation function, the value of the acceleration constant $a_0$, the density profile of the galaxy, and the treatment of a~problematic shell $i$. These results were achieved using our code for shell identification (identification means assigning two orbital quantities -- the shell and the generation number -- to each of the 25 outermost observed shells of NGC\,3923). The code tests whether the set of observed shell radii is consistent with a~given gravitational potential (that means that it is possible to find an identification of the shell set, so that the criteria described in Sect.~\ref{sec:aut_id} are satisfied). The identification criteria are forced by the minor-merger model of shell formation. The code uses analytical expressions to evolve the shell radii in time in a~given potential, Eq.~(\ref{eq:pos2}). The functionality of the code (and of the analytical equations) was successfully tested on a~self-consistent Newtonian simulation of a shell galaxy formation. In this simulation, the shell radii deviate from the analytical model by less than 4\%. To test the predictive ability of the method, we excluded the outermost known shell and tried to reconstruct its radius from the positions of the remaining shells. Using the same procedure as for the prediction of the new shell, we derived a radius of 1160$\arcsec$. The correct value is 1170$\arcsec$ (1\% deviation). If the identification of the four outermost shells is correct, the accreted galaxy originally arrived at NGC\,3923 from the southwestern side. For the potentials from the basic grid (Sect.~\ref{sec:grid}), the age of the oldest shells in the system must be between 2 and 4\,Gyr. We refrained from identifying shells with a radius smaller than 400$\arcsec$, since their identification is not unique. Their unique identification would be possible if we were sure that our model of the evolution of shell radii is sufficiently precise. This would require performing many MONDian self-consistent simulations. The prediction of the new outermost shell is valid provided that the radii of the real shells do not deviate from our analytical model by more than 10\%. The discovery of the new shell at the predicted position would evidently support MOND. If no new shell is discovered, it would give no information about the validity of MOND because the surface brightness of the predicted shell might simply be below our detection limit. However, if a new shell is discovered at a substantially different position than we predict, or if two or more new shells are detected, it might be a problem for MOND. We will perform a similar analysis for the dark matter theory in a next paper. We expect that the prediction of the new shell will be more ambiguous than in MOND because the potential is not as tightly constrained in dark matter theory. | 14 | 4 | 1404.1109 |
1404 | 1404.6173_arXiv.txt | We develop new hyperon equation of state (EoS) tables for core-collapse supernova simulations and neutron stars. These EoS tables are based on a density-dependent relativistic hadron field theory where baryon-baryon interaction is mediated by mesons, using the parameter set DD2 from \citet{typ10} for nucleons. Furthermore, light and heavy nuclei along with the interacting nucleons are treated in the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich which includes excluded volume effects. Of all possible hyperons, we consider only the contribution of $\Lambda$s. We have developed two variants of hyperonic EoS tables: in the np$\Lambda \phi$ case the repulsive hyperon-hyperon interaction mediated by the strange $\phi$ meson is taken into account, and in the np$\Lambda$ case it is not. The EoS tables for the two cases encompass wide range of density ($10^{-12}$ to $\sim$ 1 fm$^{-3}$), temperature (0.1 to 158.48 MeV), and proton fraction (0.01 to 0.60). The effects of $\Lambda$ hyperons on thermodynamic quantities such as free energy per baryon, pressure, or entropy per baryon are investigated and found to be significant at higher densities. The cold, $\beta$-equilibrated EoS (with the crust included self-consistently) results in a 2.1 M$_{\odot}$ maximum mass neutron star for the np$\Lambda \phi$ whereas that for the np$\Lambda$ case is 1.95 M$_{\odot}$. The np$\Lambda \phi$ EoS represents the first supernova EoS table involving hyperons that is directly compatible with the recently measured 2 M$_{\odot}$ neutron stars. | Compact astrophysical objects are born in the aftermath of massive stars ($>$ 8 M$_{\odot}$) through core-collapse supernova (CCSN) explosions in the penultimate stage of their evolution \citep{Bet}. In the CCSN mechanism, the gravitational collapse of the iron core begins as the core exceeds the Chandrasekhar mass. The subsequent core bounce occurs when the core density reaches beyond normal nuclear matter density and a hydrodynamic shock is generated. If the shock wave is strong enough, this might lead to a prompt supernova explosion, which, however, is not found in recent state-of-the-art computer simulations. The hot and neutrino-trapped protoneutron star (PNS) settles into hydrostatic equilibrium immediately after the core bounce. The PNS could evolve either into a neutron star or into a black hole within a few seconds after the emission of neutrinos. Though the CCSN explosion mechanism has been explored for the past five decades, a complete understanding of this phenomenon is still beyond our reach. In most CCSN simulations, the shock stalls after traveling a few hundred kilometers. The revival of the shock by neutrino heating \citep{wil} or the generation of a second shock due to a first order hadron-quark phase transition \citep{irina} could trigger a delayed CCSN explosion. Regarding the latter, until now this mechanism was only shown to be working for equations of state (EoS) that are not compatible with the latest neutron star mass measurements such as those from \citet{anto}. Besides the dimensionality of the problem \citep{nord} and neutrino reaction rates, the EoS of matter plays a tremendous role in a successful CCSN explosion \citep{janka12}. The first nuclear EoS table suitable for CCSN simulations was formulated by \citet{wolf} followed by the Lattimer and Swesty (LS) EoS \citep{ls} and the Shen EoS \citep{shen}. The last two EoS tables describe all possible compositions of matter depending on wide ranges of density, temperature, and proton fraction such as free nucleons, light nuclei in coexistence with nucleons, the ideal gas of nuclei, and uniform nuclear matter. The LS EoS table is based on Skyrme interaction for uniform matter and a compressible liquid drop model for non-uniform matter. On the other hand, for the first time, the Shen EoS table was constructed using the relativistic field theory for low- and high-density uniform matter. Non-uniform matter was described by the Thomas-Fermi model. Both of these two approaches, LS and Shen, employed the single nucleus approximation and neglected shell effects. The LS and Shen EoS tables have been used extensively for CCSN simulations over the years. Recently, several new EoS were developed, keeping in pace with updated knowledge from nuclear structure, experimental data, or neutron star observations, aiming at an improved underlying description and with possibly new particle degrees of freedom taken into account \citep{hs1,raduta10,horo,horo1,horo2,fis1,bli,hs2,stei,fis2,buyu,toga}. One such notable nuclear EoS called the HS EoS was formulated within the framework of the nuclear statistical equilibrium (NSE) model \citep{hs1}. The HS EoS table treated the ensemble of nuclei and nucleons in the NSE model using the relativistic mean field model for interacting nucleons, incorporated excluded volume effects in the thermodynamically consistent manner, considered excited states of nuclei and matched the low density matter with uniform matter at high density \citep{hs1}. A new nuclear EoS table was generated adopting the virial expansion for a non-ideal gas of nucleons and nuclei by \citet{horo}. The statistical model by \citet{botvina04,botvina10,buyu}, is based onthe multifragmentation of nuclei in heavy-ion collisions. In \citet{buyu_compare}, it was compared with some of the other aforementioned approaches. For the first time, the EoS has been constructed in a variational calculation using bare nuclear forces such as Argonne v18 (AV18) and Urbana IX (UIX) by \citet{toga,const}, which, however, does not yet include the case of non-uniform matter. The EoS described above would not only influence the supernova dynamics but also the formation of neutron stars and their structures. Neutron star observations could provide important inputs in the construction of EoS tables for CCSN simulations. The first supernova EoS table directly based on measured masses and radii of neutron stars was developed by Steiner and collaborators \citep{stei}. Unlike radii, neutron star masses have been estimated to a very high degree of accuracy. This has been possible because post-Keplerian parameters, such as orbital decay, periastron advance, Shapiro delay, and time dilation have been measured in many pulsars. Currently, the accurately measured highest neutron star mass is 2.01$\pm 0.04$ M$_{\odot}$ \citep{anto}. This puts a strong constraint on the $\beta$-equilibrated EoS. Most of the nuclear EoS mentioned above result in 2 M$_{\odot}$ neutron stars. Observed neutron star masses are also probes of compositions of dense matter. It has long been debated whether or not novel phases of matter such as hyperons, Bose-Einstein condensates of kaons, and quarks may exist in neutron star interior. It may happen that the phase transition from nuclear matter to exotic matter could occur in the early post-bounce phase of a CCSN. Strange degrees of freedom would be crucial for the long-term evolution of the PNS. It is to be noted that strange matter typically makes the EoS softer resulting in a smaller maximum mass neutron star than that of the nuclear EoS \citep{glen}. \citet{vandalen14} showed that the observed high masses of neutron stars in combination with hypernuclear data put tight constraints on the interactions of hyperons in neutron star matter. Note that there is also an interesting interplay between the strangeness content and the symmetry energy on properties of neutron stars, which was recently discussed by \citet{provi2013} for the case of hyperonic EoS. Several EoS including quark and hyperon matter were developed for and applied to supernova simulations \citep{ishi,naka08,irina,sumi,shen11,naka,oertel12,peres,sb}. None of the EoS tables with exotic matter were directly compatible with the 2 M$_{\odot}$ neutron star or they were just barely acceptable. On the other hand, many model calculations including exotic matter such as hyperons showed that the EoS of $\beta$-equilibrated matter may lead to 2 M$_{\odot}$ or more massive neutron stars \citep{weis1,weis2,last,colu,lopes,gus,vandalen14}. Recently, \citet{fis2} published an quark-hadron hybrid EoS with a maximum mass above 2 M$_\odot$, which, however, did not lead to a phase-transition-induced explosion. The limited number of realistic supernova EoS with exotic degrees of freedom motivates us to construct a hyperon EoS in the relativistic mean field theory with density-dependent couplings that is compatible with a 2 M$_{\odot}$ mass neutron star. The paper is organized as follows. Section 2 describes the methodology for the calculation of EoS tables including $\Lambda$ hyperons. The results of hyperon EoS tables are discussed in Section 3. Section 4 gives a summary and conclusions. In the Appendix, we give detailed information about the definition of the various quantities stored in the final EoS tables and discuss their accuracy and consistency. | We have constructed hyperon EoS tables including $\Lambda$ hyperons for supernova simulations and neutron stars in a density dependent relativistic mean field model. We also take into account the $\Lambda$-$\Lambda$ interaction mediated by $\phi$ mesons in this calculation. The nuclear statistical equilibrium model of \citet{hs1} is adopted for the description of matter made of light and heavy nuclei coexisting with unbound nucleons below saturation densities and temperatures up to 50~MeV. We have denoted the calculation including $\Lambda$ hyperons without $\phi$ mesons as the np$\Lambda$ case and that of the $\Lambda$ hyperons with $\phi$ mesons as the np$\Lambda \phi$ case. The DD2 parameter set \citet{typ10} has been used in this calculation for the nucleons. The vector meson - $\Lambda$ hyperon couplings are obtained from the SU(6) symmetry relations of the quark model, whereas the scalar meson - $\Lambda$ hyperon coupling is determined from the potential depth of the $\Lambda$ hyperon in nuclear matter at the saturation density of $-30$ MeV which is extracted from the experimental binding energies of $\Lambda$ hypernuclei. The system is populated with $\Lambda$s using the equilibrium condition $\mu_n = \mu_{\Lambda}$. The contribution of $\Lambda$s is considered in our calculation when its corresponding EoS gives a lower free energy than the EoS of only nuclei and nucleons and when the $\Lambda$ mass fraction exceeds $10^{-5}$ at the same time. It is noted that the fraction of $\Lambda$ hyperons is negligible at low-density and low-temperature domains. The population of $\Lambda$ hyperons grows in uniform matter at the cost of neutrons at high density. A significant fraction of thermal $\Lambda$ hyperons is populated in the system at higher temperatures. The free energy of the system including $\Lambda$ hyperons is lower compared to that of the nuclear matter case. However, $\Lambda$ hyperon matter involving $\phi$ mesons has higher free energy than that of the $\Lambda$ hyperon matter without $\phi$ mesons. Regarding the entropy per baryon, one notices that it is higher than in the case of nuclear matter when more degrees of freedom in the form of $\Lambda$ hyperons appear in the system. This indicates different thermal properties of the EoS, which are known to be important for neutron-star mergers \citep{bauswein13,kaplan13} and black hole formation \citep{hs2}. We observe that the EoS (pressure versus baryon mass density) of the $\Lambda$ hyperon matter with and without $\phi$ mesons is softer than the nuclear EoS. Furthermore, the repulsive interaction of $\phi$ mesons makes the EoS of the np$\Lambda \phi$ case stiffer than that of the np$\Lambda$ case. It is important to note that the pressure grows smoothly with baryon density even after the appearance of $\Lambda$ hyperons. We did not find any indication for a first-order phase transition connected with the appearance of hyperons, as discussed, e.g., by \citet{schaffner02,gulmi2012,gulmi2013}. We have generated two $\Lambda$ hyperon EoS tables with (BHB$\Lambda \phi$) and without (BHB$\Lambda$) $\phi$ mesons covering temperatures (0.1 -- 158.48 MeV), proton fractions (0.01 -- 0.6), and baryon density ($10^{-12}$ -- $\simeq$1 fm$^{-3}$). The EoS tables are written in two different formats: the first format is similar to the one used by \citet{shen}, and the second one corresponds to extended tables including electrons, positrons and photons in a binary format. Tables {\ref{table3}} - {\ref{table6}} illustrate certain parts of the main tables. Finally, we impose the charge neutrality and $\beta$-equilibrium in our $\Lambda$ hyperon EoS tables and calculate mass-radius relationship of the neutron star sequence at $T=0.1$ MeV. We obtain maximum neutron star masses 2.1 M$_{\odot}$ and 1.95 M$_{\odot}$ corresponding to the $\Lambda$ hyperon EoS with and without $\phi$ mesons, respectively. The maximum neutron star mass of $\Lambda$ hyperon matter including $\phi$ mesons is compatible with the recently measured 2.01$\pm$0.04 M$_{\odot}$ neutron star. We shall perform supernova simulations with new hyperon EoS tables and publish those results separately in the future. New hyperon EoS tables will be also useful for neutron star merger calculations. | 14 | 4 | 1404.6173 |
1404 | 1404.1086_arXiv.txt | Using data from STEREO and SOHO spacecraft, we show that temporal organization of energy release events in the quiet solar corona is close to random, in contrast to the clustered behavior of flaring times in solar active regions. The locations of the quiet-Sun events follow the meso- and supergranulation pattern of the underling photosphere. Together with earlier reports of the scale-free event size statistics, our findings suggest that quiet solar regions responsible for bulk coronal heating operate in a driven self-organized critical state, possibly involving long-range Alfv\'{e}nic interactions. | 14 | 4 | 1404.1086 |
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1404 | 1404.4176_arXiv.txt | We present results of 3-D numerical simulations of a fast magnetic twister excited above a foot-point of the potential solar coronal arcade that is embedded in the solar atmosphere with the initial VAL-IIIC temperature profile, which is smoothly extended into the solar corona. With the use of the FLASH code, we solve 3-D ideal magnetohydrodynamic equations by specifying a twist in the azimuthal component of magnetic field in the solar chromosphere. The imposed perturbation generates torsional Alfv\'en waves as well as plasma swirls that reach the other foot-point of the arcade and partially reflect back from the transition region. The two vortex channels are evident in the generated twisted flux-tube with a fragmentation near its apex that results from the initial twist as well as from the morphology of the tube. The numerical results are compared to observational data of plasma motions in a solar prominence. The comparison shows that the numerical results and the data qualitatively agree even though the observed plasma motions occur over comparatively large spatio-temporal scales in the prominence. | Vortex and swirling plasma motions are ubiquitous in the solar atmosphere. At small spatio-temporal scales the chromospheric swirling motions were discovered as super-tornadoes providing an alternative mechanism for channeling energy up to the inner solar corona (Wedemeyer-B{\"o}hm et al. 2012, 2013). Just after this novel observation, Su et al. (2013) reported the large-scale but slowly rotating coronal tornadoes. They studied the rotating vertical magnetic structures most likely driven by the underlying vortex flows in the photosphere that existed in a group with prominences. In case of such large-scale and slowly rotating tornadoes, which are long living magnetic structures, several other observational findings were made using recent space-borne observations (e.g., Panesar et al. 2013; Yan et al. 2013; Wedemeyer-B{\"o}hm et al. 2013; and references therein). However, recently the findings of Panasenco et al. (2014) poses a challenge to the large-scale coronal tornado detections. In the observational data they analyzed and found that the coronal tornado-like appearance usually associated with the prominences is mainly an illusion due to projection effects. The fact that the projection effects can significantly distort the interpretation of such observations of coronal tornadoes is known. Similar effects could become important in interpretation of the solar observations of various localized plasma motions, such as plasma cyclones, swirls and tornadoes, which are ubiquitous in the solar corona, and whose origin, nature, morphology, life-time and driving mechanisms are difficult to observationally determine. Our numerical studies of magnetic twisters in solar coronal arcades presented in this paper are designed to address some of these currently unsolved problems. The exact physical mechanisms responsible for the origin of long-lived coronal tornadoes are not fully known. Moreover, the relationship between the short-lived chromospheric tornadoes and the long-lived coronal tornadoes is also not well established. Shukla (2013) developed a generalized theory, which implies that the modified-kinetic Alfv\'en waves (m-KAWs) in a magnetized plasma can propagate in the form of tornadoes, characterized by the plasma whirls or magnetic flux ropes carrying orbital angular momentum. Now, in the lower solar atmosphere, the small-scale chromospheric tornadoes may be caused by the photospheric vortices (e.g., Bonet et al. 2008; Shelyag et al. 2011; Murawski et al. 2013a,b, and references therein). Moreover, various types of these vortex motions could be associated with the different eddies and waves depending on the localized plasma and magnetic conditions as well as on the nature of the drivers/perturbations (Fedun et al. 2011; Murawski et al. 2013b). Therefore, it is important to understand the nature and generation of such swirling plasma motions in the different layers of the solar atmosphere, where various topologies of solar magnetic fields occur. As far as the large-scale solar tornadoes are concerned, they are mostly observed in the association with the prominence legs (Su et al. 2012; Wedemeyer-B{\"o}hm et al. 2013), and are most likely related to the response of the photospheric vortices activated near the foot-points. These vortex flows exhibit spiral motions both upwards and downwards with speeds comparable to the values found for such tornado rotations in the form of prominence barbs (Wedemeyer-B{\"o}hm et al. 2012, Su et al. 2012). However, they are long-lived (on the time-scale of $12-24$ hours) but slow rotators. There is another kind of interesting twisting and then swirl of the plasma around the core prominence magnetic field that may have the same origin due to rotation near the prominences' foot-point but entirely different when compared to the long-lived slow tornadoes. We call it a fast magnetic twister and associate it with a coronal arcade. This paper is devoted to numerical studies of such a phenomenon. It must be pointed out that the fast magnetic twisters, which live on the time-scale of minutes, are seldomly observed in the solar atmosphere. Recently, Joshi et al. (2014) investigated a fast twisting prominence system in the context of its stability and reformation that is significant for space-weather prediction. However, their aim was certainly not to understand the possible driver responsible for the evolution of fast magnetic twister and plasma swirl in the filament system that was initially bipolar in nature. It should also be noted that Shelyag et al. (2013) studied solar photospheric vortices by using MHD simulations with non-gray radiative transport and a non-ideal equation of state. The main difference between these two studies is that only the former takes into account variation of the local velocity field on time. As a result, the photospheric vortices (tornado-like motions) do not exist but instead torsional Alfv\'en waves are generated. We discuss this finding after we present the results of our numerical simulations. In the present paper, we perform 3-D numerical simulations of the evolution of right-handed clock-wise twist and its responses in form of the torsional Alfv\'en and plasma perturbations in an initial potential field configuration of a magnetic flux-tube mimicking the observed prominence system. We call the magneto-plasma motions that evolved in our model "fast magnetic twisters". Since 3-D numerical simulations in realistic atmosphere would be extremely computationally expensive to model the observed prominence flux-tube and its associated dynamics, we rescale the realistic very large spatio-temporal scales characteristic for the observational domain to a much smaller 3-D numerical simulation domain. Nevertheless, our simulation results match qualitatively the observed magnetic field and plasma dynamics as it is shown in our comparison between the numerical results and some recent solar observations. This paper is organized as follows. In Sec.~\ref{sec:num_model}, we present the numerical simulation model. We outline the results of numerical simulations in the context of its physical significance in Sec.~3. In Sec.~4, we compare the numerical results with the relevant solar observational data. In the last section, we present discussion and concluding remarks. | We investigated numerically physical implications of the activation of the magnetic twists in a potential coronal magnetic flux-tube embedded in the solar atmosphere with a realistic temperature distribution. Our numerical results reveal the evolution of right-handed magnetic twists, double vortex channels, fragmentation and fast propagating perturbations, all evident in our coronal arcade model in which variable twists in the azimuthal component of the magnetic field were initially imposed. The result is a fast magnetic twister whose existence is reported here for the first time. The initial perturbations imposed in our coronal arcade model generate torsional Alfv\'en waves as well as plasma swirls that reach the other foot-point of the arcade and partially reflect back from the transition region. The two vortex channels are evident in the generated twisted flux-tube with a fragmentation near its apex that results from the initial twist as well as from the morphology of the tube. This highly depends upon the initial magnetic field configuration, plasma properties, and nature of perturbations, which all determine how the vortices, associated waves and plasma motions are formed. There were some previous studies of vortex motions at various spatio-temporal scales (e.g., Bonet et al. 2008; Shelyag et al. 2011; however, in none of them the fast magnetic twister was identified. Moreover, Shelyag et al. (2013) reported no vortices (tornado-like motions) in their numerical simulations but only torsional Alfv\'en waves. We do see both fast magnetic twisters and torsional Alfv\'en waves. The difference between their approach and ours is in temporal scales, which in their approach are much shorter than in ours. Based on our results, we conclude that a tornado needs a long lasting twist in order to be sustained for time scales of the order of 12 hours or longer. Our numerical results were compared to the observational data of plasma motions in a solar prominence, whose rare observation showed the evidence for the existence of a fast twister. Interestingly enough, the general properties of this twister are similar to those seen in our numerical simulations. However, we could only show that are numerical results and the data agreed only qualitatively because significant differences in the spatio-temporal scales between the observations and our numerical simulations prevented us from making a more direct comparison. In the future, more observations are needed to establish validity of our coronal arcade model at various spatio-temporal scales, and to examine if the double vortex system, plasma swirling, and fast torsional perturbations, all exist in a single prominence system before its eruption. \clearpage | 14 | 4 | 1404.4176 |
1404 | 1404.7496_arXiv.txt | N-flation is a radiatively stable scenario for chaotic inflation in which the displacements of $N \gg 1$ axions with decay constants $f_1 \le \ldots \le f_N < M_P$ lead to a super-Planckian effective displacement equal to the Pythagorean sum $f_{\rm{Py}}$ of the $f_i$. We show that mixing in the axion kinetic term generically leads to the phenomenon of kinetic alignment, allowing for effective displacements as large as $\sqrt{N} f_{N} \ge f_{\rm{Py}}$, even if $f_1, \ldots, f_{N-1}$ are arbitrarily small. At the level of kinematics, the necessary alignment occurs with very high probability, because of eigenvector delocalization. We present conditions under which inflation can take place along an aligned direction. Our construction sharply reduces the challenge of realizing N-flation in string theory. | Inflationary scenarios producing detectable primordial gravitational waves are extraordinarily sensitive to Planck-scale physics, motivating the understanding of these models in string theory. The recent observation of B-mode polarization at degree angular scales by the BICEP2 collaboration \cite{Ade:2014xna} provides the prospect of direct experimental study of large-field inflation, if the signal is established as primordial in origin. Among the best-motivated scenarios for large-field inflation in string theory are axion inflation models, including string-theoretic variants of natural inflation \cite{Freese:1990rb}, in which shift symmetries protect the inflaton potential (for a recent review, see \cite{Pajer:2013fsa}). In the effective field theory description, axionic shift symmetries with large periodicities, i.e.~with decay constants $f \gg M_P$, can ensure radiative stability of large-field inflation, but whether such symmetries admit completions in quantum gravity is a delicate question that requires knowledge of the ultraviolet theory. By embedding axion inflation in string theory one can address this problem through well-defined computations. A general finding about axions in presently-understood string vacua is that the decay constants $f$ are small, $f \ll M_P$, in all regions in which the perturbative and nonperturbative corrections to the effective action are under parametric control \cite{Banks:2003sx}. At the same time, axions are very numerous, with ${\cal O}(10^2)-{\cal O}(10^3)$ independent axions appearing in typical compactifications. To achieve large-field inflation in string theory, one could therefore consider a collective excitation of $N \gg 1$ axions $\phi_i$, $i=1,\ldots, N$, with effective displacement $\Delta\Phi$ larger than the displacements $\Delta\phi_i$ of the individual fields. This proposal, known as {\it{N-flation}} \cite{Dimopoulos:2005ac}, builds on the idea of assisted inflation \cite{Liddle:1998jc}. If the fields $\phi_i$ are canonically-normalized axions with periodicity $2\pi f_i$ then the diameter of the field space is \begin{equation} {\rm{Diam}} = 2\pi \sqrt{\sum f_i^2} \equiv 2\pi f_{{\rm{Py}}}\, , \end{equation} where $f_{{\rm{Py}}}$ denotes the Pythagorean sum of the $f_i$. In an inflationary model involving small displacements of each axion around the minimum of the potential, so that a quadratic approximation to the potential remains valid, the maximum collective displacement is $\Delta\Phi \lesssim c_D\cdot{\rm{Diam}} \approx f_{{\rm{Py}}}$ for some constant $c_D \sim {\cal O}(0.1)$. Finding string compactifications containing $N \gg 1$ axions with $f_N\ge\ldots \ge f_1 \gtrsim 0.1 M_P$ appears difficult. In this Letter we show that given specific well-motivated assumptions about the axion kinetic terms, one can achieve a large effective displacement $\Delta \Phi \approx \sqrt{N} f_N$ even if $f_1,\ldots,f_{N-1}$ are very small. \begin{figure} \centering \includegraphics[width=.3\textwidth]{illustration2.pdf} \caption{\small N-flation with and without alignment, for $N=2$. The outer box shows a fundamental domain in the dimensionless $\theta$ coordinates with period $2\pi$. The shaded rhombus and rectangle depict the physical size of the fundamental domain with and without alignment, respectively. The green and red vectors show the semidiameters in the aligned and unaligned cases. The inset is not to scale.}\label{fig:illustration} \end{figure} | We considered a theory containing $N$ axions with decay constants $f_1 \le \ldots \le f_N$, and asked whether the maximum collective displacement $\Delta\Phi$ can exceed the Pythagorean sum $f_{{\rm{Py}}}$ of the $f_i$ (in the absence of fine-tuning of the relative sizes of the $f_i$, as in \cite{Kim:2004rp,Choi:2014rja,Tye:2014tja}). The allowed region of field space is defined by the fundamental periodicities of the dimensionless axions; without loss of generality, this region can be taken to be a hypercube in $\mathbb{R}^N$. To convert dimensionless displacements to physical displacements requires the use of the metric on field space. If the metric on field space has eigenvectors that align with the edges of the hypercube then the diameter is $2\pi f_{{\rm{Py}}}$, and $\Delta\Phi \approx f_{{\rm{Py}}}$. But if instead the eigenvector of the metric with largest eigenvalue $f_N^2$ is aligned with a (long) diagonal of the hypercube, the diameter is $2\pi \sqrt{N} f_{N}$, so that $\Delta\Phi \approx \sqrt{N} f_{N}$, which is considerably larger than $f_{{\rm{Py}}}$ in the generic case in which the $f_i$ are distinct. We referred to this situation as {\it{kinetic alignment}}. Approximate kinetic alignment is equivalent to the phenomenon of eigenvector delocalization in random matrix theory, which has been proved to hold in a number of relevant cases, in particular if $K_{ij}$ is a Wishart matrix \cite{TaoVu}. At the level of kinematics, kinetic alignment is almost inevitable in a system with $N \gg 1$ axions and a general kinetic term. Although our arguments did not rely on string theory, and hold in an effective field theory with generic axion kinetic mixing, the necessary structures are readily obtained in compactifications of string theory. We then argued that the axion potential (\ref{vcos}) can be compatible with large-field inflation along an aligned direction. As an example, if $K_{ij}$ is a Wishart matrix and $P \le N$ of the dynamically-generated scales $\Lambda_i^4$ fall within a range of size $\sim 2$, then $P$ fields participate in the alignment, and the effective range is $\sqrt{P}f_N$. Alignment is possible for more general potentials, but we leave a systematic analysis for the future. Arranging for $N \gg 1$ axions to have decay constants $f_i$ as large as ${\cal{O}}(0.1) M_P$ is a serious challenge for the construction of models of N-flation in string theory (cf.~e.g.~\cite{Dimopoulos:2005ac,Easther:2005zr,Kallosh:2007cc,Grimm:2007hs}): perturbative control of the $g_{\rm{s}}$ and $\alpha^{\prime}$ expansions generally enforces $f_i \ll M_P$ \cite{Banks:2003sx}, and while accidental cancellations may permit a few of the $f_i$ to be larger, points in moduli space with many $f_i$ large are not presently computable. Kinetic alignment allows for successful large-field inflation even if only {\it{one}} axion has large (but sub-Planckian) decay constant, dramatically reducing the difficulty of embedding N-flation in string theory. The signatures of aligned N-flation are very similar to those of single-field $m^2\phi^2$ chaotic inflation \cite{Linde:1983gd}, even though the underlying symmetry structure is distinctive. | 14 | 4 | 1404.7496 |
1404 | 1404.5170_arXiv.txt | % Tadpole Galaxies look like a star forming head with a tail structure to the side. They are also named cometaries. In a series of recent works we have discovered a number of issues that lead us to consider them extremely interesting targets. First, from images, they are disks with a lopsided starburst. This result is firmly established with long slit spectroscopy in a nearby representative sample. They rotate with the head following the rotation pattern but displaced from the rotation center. Moreover, in a search for extremely metal poor (XMP) galaxies, we identified tadpoles as the dominant shapes in the sample -- nearly 80\% of the local XMP galaxies have a tadpole morphology. In addition, the spatially resolved analysis of the metallicity shows the remarkable result that there is a metallicity drop right at the position of the head. This is contrary to what intuition would say and difficult to explain if star formation has happened from gas processed in the disk. The result could however be understood if the star formation is driven by pristine gas falling into the galaxy disk. If confirmed, we could be unveiling, for the first time, cool flows in action in our nearby world. The tadpole class is relatively frequent at high redshift -- 10\% of resolvable galaxies in the Hubble UDF but less than 1\% in the local Universe. They are systems that could track cool flows and test models of galaxy formation. | Elongated galaxies with bright clumps at one end are visible in deep field images taken with HST or from the ground; van der Bergh et al., 1996 called them ``tadpole'' galaxies". Figure 1 in Elmegreen et al. (2005) shows different morphologies of galaxies observed with the Hubble Ultra Deep Field (UDF). The fourth row presents images of Tadpoles. This asymmetric morphology is rather common at high redshift but rare in the local universe. For example, tadpoles constitute 10\% of all galaxies larger than 10 pixels in the UDF (Elmegreen et al. 2007; Elmegreen \& Elmegreen, 2010), and they represent 6\% of the UDF galaxies identified by Straughn et al. (2006) and Windshorst et al. (2006) using automated search algorithms. In contrast, Elmegreen et al. (2012; hereafter Paper I), find only 0.2\%\ tadpoles among the uv-bright local galaxies of the Kiso survey by Miyauchi-Isobe et al. (2010). This decrease suggests that the tadpole morphology represents a common but transition phase during the assembly of some galaxies. Since local tadpole galaxies are very low mass objects compared to their high redshift analogues, this phase must be already over for the local descendants of high redshift tadpoles. The tadpole structure has inspired several explanations, such as ram pressure stripping that triggers star formation at the leading edge, to mergers (see S\'anchez~Almeida et al. 2013 for an extensive review). The explanation that we propose, based on observational evidence summarized here, is that the starburst head may result from the accretion of an external flow of pristine gas that penetrates the dark matter halo and hits and heats a pre-existing disk, which is viewed to the side as the tail. We will briefly present a summary of recent results showing, first that the local Tadpoles share the properties of their higher redshift and higher mass counterparts (section 2), that they belong to the extremely metal poor (XMP) sample of the Blue Compact Dwarfs family (section 3), they are rotating discs (section 4) and, finally, that the starbursts (heads) show a drop in the already low metallicity that can only be understood if fresh metal-poor gas is falling onto the galaxy (section 5). We finish with a brief summary and future actions. | 14 | 4 | 1404.5170 |
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1404 | 1404.5807_arXiv.txt | We report the discovery of 59 globular clusters (GCs) and two candidate GCs in a search of the halo of M31, primarily via visual inspection of CHFT/MegaCam imagery from the Pan-Andromeda Archaeological Survey (PAndAS). The superior quality of these data also allow us to check the classification of remote objects in the Revised Bologna Catalogue (RBC), plus a subset of GC candidates drawn from SDSS imaging. We identify three additional new GCs from the RBC, and confirm the GC nature of 11 SDSS objects (8 of which appear independently in our remote halo catalogue); the remaining $188$ candidates across both lists are either foreground stars or background galaxies. Our new catalogue represents the first uniform census of GCs across the M31 halo -- we find clusters to the limit of the PAndAS survey area at projected radii of up to $R_{\rm proj} \sim 150$ kpc. Tests using artificial clusters reveal that detection incompleteness cuts in at luminosities below $M_V = -6.0$; our 50\% completeness limit is $M_V \approx -4.1$. We construct a uniform set of PAndAS photometric measurements for all known GCs outside $R_{\rm proj} = 25$ kpc, and any new GCs within this radius. With these data we update results from \citet{Huxoretal11}, investigating the luminosity function (LF), colours and effective radii of M31 GCs with a particular focus on the remote halo. We find that the GCLF is clearly bimodal in the outer halo ($R_{\rm proj} > 30$ kpc), with the secondary peak at $M_V \sim -5.5$. We argue that the GCs in this peak have most likely been accreted along with their host dwarf galaxies. Notwithstanding, we also find, as in previous surveys, a substantial number of GCs with above-average luminosity in the outer M31 halo -- a population with no clear counterpart in the Milky Way. | Globular cluster (GC) systems are thought to trace both major star-formation episodes and accretion events. As such they have proven to be valuable tools for the study of their host galaxies \citep{Georgievetal12} -- from the seminal Milky Way (MW) work of \citet{SearleZinn78} to recent studies of more distant galaxies \citep{forteetal12,forbesetal11,ChiesSantosetal11}. The GC system of M31 has naturally been the focus of particular interest, providing (as a massive spiral galaxy) an excellent comparison to our own Milky Way. Moreover, the proximity of M31 (at $\sim 780$ kpc)\footnote{Throughout this paper we use the distance to M31 from \citet{McConnachieetal05}; see also \citet{Connetal12}.} allows for detailed investigation of its GC populations, which have been extensively studied (e.g. \citealt{Cramptonetal85,Battistinietal87,Elson88,Huchraetal91,Barmbyetal00,Perrettetal02,Fanetal08,galleti:09,Caldwelletal09,Fanetal10,Caldwelletal11}). Most of these studies have dealt with the regions comparatively close to the centre of M31, typically within $20-25$ kpc in projection. This is because the relative proximity of M31 also poses a problem in that the full extent of its stellar halo subtends a substantial angle on the sky ($\ga 20\degr$ in diameter) which is difficult to search uniformly for GCs, especially those with low luminosities and/or surface brightnesses. The Pan-Andromeda Archaeological Survey \citep[PAndAS;][]{McConnachieetal09} almost completely obviates these issues: its imaging spans a very wide area, typically reaching a projected distance $R_{\rm proj} \sim 150$ kpc from M31\footnote{Although this is still some distance short of the likely virial radius of M31.} -- and is yet sufficiently deep to allow the identification of even faint GCs. With high quality wide-field imaging such as that obtained for PAndAS, M31 halo GCs are much more easily located than those in more central regions where the background and crowding due to the M31 disk hinders reliable identification of star clusters in ground-based data. Halo GCs also offer the opportunity to study regions with very long dynamical time-scales that can preserve evidence of past events. If formed {\it in-situ}, remote halo GCs will have been much less affected by tidal forces than those towards the centre; if accreted along with dwarf satellite galaxies, their properties may reflect the nature of the original hosts. This paper continues and extends earlier investigations of the GC population of M31 by our group. In particular, it provides the final catalogue of halo GCs from PAndAS, greatly extending our previous surveys and results -- specifically those of \citet{Huxoretal08} (hereafter, Hux08) and \citet{Huxoretal11} (hereafter, Hux11). In Hux08 we presented 40 new GCs from a precursor survey to PAndAS conducted using the Wide-Field Camera (WFC) on the Isaac Newton Telescope (INT) along with some early imaging from MegaCam on the Canada-France-Hawaii Telescope (CFHT), and updated the classifications of many entries in the Revised Bologna Catalog (RBC)\footnote{http://www.bo.astro.it/M31/} -- the most complete catalogue of M31 GCs, and widely used by the community\footnote{Note that at that time we worked with Version 3.0 of the RBC; for the present work we refer to Version 5 from August 2012}. Hux11 explored the ``ensemble" properties of the updated M31 GC sample from Hux08. In the present paper we exploit the full, final PAndAS data, searching for new GCs, investigating candidate GCs from the RBC, and updating many of the results from Hux11 with a particular focus on the properties of the GCs in the halo. In addition to M31, the PAndAS data (and its preceding INT/WFC survey) also extend to M33, and our work on the GCs in this galaxy is published elsewhere \citep{Huxoretal09, Cockcroftetal11}. We have also used PAndAS imaging to discover new GCs in the M31 dwarf elliptical (dE) satellites NGC 147 and NGC 185 (three GCs and one GC respectively), as described in \citet{Veljanoskietal13b}. Although, strictly speaking, these clusters reside within the halo of M31, we do not include them in the present paper as they possess clearly identified (and intact) host galaxies. The GCs listed in our previous catalogue (Hux08) provided targets for follow-up observations and analysis, both by our own group and by others. In particular, our {\it Hubble Space Telescope} ({\it HST}) observations of many of the halo GCs led to a number of studies of their colour-magnitude diagrams (CMDs) and structural properties \citep{Mackeyetal07,Perinaetal09,Perinaetal11,Tanviretal12,Federicietal12,Perinaetal12,WangMa12}. Many of those GCs were also observed spectroscopically with ground-based facilities -- for example, \citet{AlvesBritoetal09} observed several at high resolution with the Keck Telescope. Similarly, \citet{Ma12} used optical and 2MASS photometry of many of our GCs to estimate their ages, masses and metallicities. The present paper is the first of a series of works in which we use our catalogue to shed new light on the outer regions of the M31 halo. In an accompanying paper \citep{Veljanoskietal14} we investigate the kinematics of the remote GC system, while in two forthcoming works we will explore the relationship between the GCs and the underlying field halo, and the resolved properties of the GCs through {\it HST} imaging (Mackey et al. in prep). This paper proceeds as follows: in \S \ref{data_and_search} we describe the CFHT/MegaCam dataset we employed, and the strategy used to locate new GCs. The newly discovered GCs are then presented in \S \ref{new_clusters}. In addition to discovering new GCs, we also used the same imaging data to clean previous samples of published M31 GCs and GC candidates, and the results of this undertaking are given in \S \ref{other_catalogue_updates}. The photometry of our new clusters, and all other GCs with a galactocentric distance of greater than 25 kpc, is described and tabulated in \S \ref{photometry}. Next we assess the completeness of our sample, critical to proper exploitation of the catalogue, in \S \ref{completeness}. Finally, in \S \ref{analysis}, we analyse the ensemble photometric properties of the M31 outer halo GC system, using our enlarged and improved catalogue. | In this paper we present the final catalogue of M31 halo GCs from the PAndAS survey. Of these, 57 were identified by our usual method of visually searching the new image data, and one further cluster was found by a code searching for faint dwarf galaxies. Our catalogue represents the first detailed and uniform census of GCs across nearly the full extent of the M31 halo. We find numerous clusters with very large projected galactocentric radii ($R_{\rm proj} \ga 100$ kpc), reflecting the huge spatial extent of the M31 GC system. We located a few additional GCs by revisiting outer halo candidates listed in the RBC. We found that three such candidates are indeed GCs, while one is a H{\sc ii} region with a possible embedded young cluster; and we also located one further new discovery that serendipitously falls near a star that was the source of the RBC entry. In addition, we found that three ``definite" outer halo GCs listed in the RBC are not clusters after all. Finally, we confirm that ten of the 17 ``high-confidence" SDSS clusters listed by \citet{dtz:13} are indeed GCs, based on our higher-quality PAndAS imaging. However, only one of their 42 ``candidate" objects that we were able to examine was found to be a cluster. Experiments with artificial clusters suggest that our GC survey is complete down to a cluster luminosity of $M_{V} = -6.0$, and has 50\% completeness limit at roughly $M_{V} \approx -4.1$ . Our analysis indicates that an additional $\sim 3 - 5$ clusters may lie undiscovered within the area covered by PAndAS imaging (i.e., within $\approx 150$ kpc of M31), due to small gaps in the survey coverage. We cannot rule out that there may also be many very faint clusters with $M_{V} \ga -4$ that we are unable to detect using PAndAS. We used the PAndAS imaging to measure luminosities, colours and sizes for all known M31 GCs outside $ R_{\rm proj} = 25$ kpc. The results of this process confirm most of the findings from Hux11 with a much larger sample. The bimodality of the luminosity function constructed using M31 halo GCs with $R_{\rm proj} > 30$ kpc is perhaps the most notable feature. This bimodality is not seen in the LF constructed using more central clusters, and we suggest it may be a consequence of the dwarf galaxy accretion history of the outer M31 halo. The colours of the halo GCs show only a marginally significant shallow gradient with projected radius, while the distribution of half-light radii for the M31 halo GCs reveals an apparently continuous spread of cluster sizes, rather than the bimodality suggested by previous studies that used much smaller samples and shallower imaging. Many of the new GCs described here have already been followed up by the PAndAS collaboration. For example, a large fraction of these objects is included in the studies of \citet{Veljanoskietal13a} and the companion paper to the present work by \citet{Veljanoskietal14}, where radial velocities have been used to explore the kinematics of the M31 outer halo GC system. Individual clusters have also proved of interest. In \citet{Mackeyetal13b} we investigated two of the new PAndAS GCs (PA-7 and PA-8), which are almost certainly associated with a prominent halo substructure known as the South-West Cloud \citep[see][]{Lewisetal13,Bateetal14}. These objects appear to be at least 2 Gyr younger than the oldest MW GCs, and thus fit with the trends identified by \citet{Perinaetal12}, and show strong similarities to the supposedly-accreted ``young halo" clusters in the MW \citep{MackeyvandenBergh05}. Our new clusters also provide a substantial number of GCs which exhibit properties unlike those studied in the MW. Examples include the few very most extended clusters, and the luminous, compact clusters found in the far halo of M31. Some of the new GCs may be of major interest. For example, PA-48 has a structure and ellipticity that may be more akin to a very faint dwarf galaxy than a typical globular cluster \citep[see][]{Mackeyetal13a}. {\it HST} imaging reaches to below the horizontal branch at the distance of M31 in a just a couple of orbits -- although it is a challenge to go much deeper. \citet{Brownetal04} required a total of 3.5 days of exposure time to reach to 1.5 mag below the old main sequence turn-off of the M31 globular cluster SKHB 312. However, this situation will change with the launch of {\em JWST}, which should be able to reach the main sequence turn-off for M31 GCs with manageable exposure times, allowing us to investigate the GC system of M31 in a manner comparable to our current understanding of the Galactic GC system. With low contaminating backgrounds, the GCs presented here will be ideal targets for such studies. | 14 | 4 | 1404.5807 |
1404 | 1404.3176_arXiv.txt | A novel model of particle acceleration in the magnetospheres of rotating active galactic nuclei (AGN) is constructed.The particle energies may be boosted up to $10^{21}$eV in a two step mechanism: In the first stage, the Langmuir waves are centrifugally excited and amplified by means of a parametric process that efficiently pumps rotational energy to excite electrostatic fields. In the second stage, the electrostatic energy is transferred to particle kinetic energy via Landau damping made possible by rapid "Langmuir collapse". The time-scale for parametric pumping of Langmuir waves turns out to be small compared to the kinematic time-scale, indicating high efficiency of the first process. The second process of "Langmuir collapse" - the creation of caverns or low density regions - also happens rapidly for the characteristic parameters of the AGN magnetosphere. The Langmuir collapse creates appropriate conditions for transferring electric energy to boost up already high particle energies to much higher values. It is further shown that various energy loss mechanism are relatively weak, and do not impose any significant constraints on maximum achievable energies. | New observations confirming a strong correlation of ultra-high energy cosmic ray protons with the active galactic nuclei (AGN) \citep{corel1} has stimulated the search for a possible mechanism that could accelerate protons up to tens of EeV and higher energies. In this paper we will explore energy transfer via the relativistic centrifugal force in the rotating magnetospheres of compact objects as a mechanism for boosting proton energies to such enormous levels. In general, this is not a new idea, \cite{bogoval1} and \cite{bogoval2} have considered the role of magnetocentrifugal effects in astrophysical outflows and nonaxisymmetric magnetospheres. Based on a rather different approach the mechanism of centrifugal acceleration was applied to explain the observed high and very high energy emission pattern \citep{osm7,newast} in some astrophysical settings. Relativistic centrifugal force turns out to be a crucial physical element governing particle acceleration, particularly, in astrophysical objects endowed with rotating magnetospheres, where magnetic energy density is larger than that of the plasma. The plasma particles are, thus, forced to follow the field lines, which in turn are corotating. Consequently, the particles, sliding along these magnetic field lines, experience centrifugal force and gain energy. The time-varying centrifugal force can also parametrically excite electrostatic modes providing an additional channel for transferring energy from the rotator to the electromagnetic waves and , then, possibly to the particles; this channel may be particularly relevant to the enormously energetic AGN magnetosphere \citep{incr,incr3}. The energy pumping mechanism has already been applied to both pulsars \citep{incr} and the AGN \citep{incr3}. In the AGN magnetosphere, the centrifugally excited electrostatic waves are found to be unstable; the growth rates, exceeding the corresponding rate of the accretion disc evolution, indicate the possibility of an efficient instability \citep{incr3}. Till now, our most extensive exploration of the parametrically driven Langmuir waves and their role in accelerating particles has been in the context of the Crab nebula \citep{incr,screp}. We showed that the process of generation of the centrifugally driven Langmuir waves is rather efficient, and for the Crab pulsar magnetosphere, energy gain of electrostatic modes might be in a reasonable coincidence with its observed slow down rate. These waves, sustained by the main electron-positron (magnetospheric) plasma, were shown to Landau damp effectively on the primary electron beam ( much less density than the main plasma), imparting large per particle energy to the already fast particles. We have argued that the Crab pulsar, with its extremely high rate of rotation, may guarantee acceleration of electrons to hundreds of TeV and even higher. In this paper, we go back to reexamine the problem begun in \citep{incr3}; we will investigate the efficiency of centrifugally driven electrostatic waves in the AGN magnetosphere, and determine if these waves can be a conduit for transferring energy towards particle acceleration. In contrast to the pulsars, the AGN atmosphere contains a quasi-neutral plasmas composed of protons and electrons, Consequently the mass dependent centrifugal force acting will produce an initial charge separation on electrons and protons, leading, perhaps, by means of the parametric instability, to extremely efficient energy pumping from the rotating magnetosphere. In addition to demonstrating the existence of unstable Langmuir waves , we also explore a mechanism that might be responsible for particle acceleration. It will be helpful to remember that the Langmuir turbulence inevitably leads to (nonlinear) instability, creating caverns-low density regions \citep{zakharov} . According to the investigation, the high frequency contribution of pressure inside the cavern pulls the particles from this area, provoking an explosive collapse of the cavern, efficiently transferring energy from the electrostatic waves to the particles pushed from the collapsing regions. Dynamics of collapse was studied in detail in \citep{galeev} and numerically investigated by \cite{degtiarev}. \cite{galeev} considered a theory of three dimensional problem and investigated the corresponding spectra of Langmuir turbulence, studying the role of absorption mechanisms for short wavelength plasmons. \cite{degtiarev} analysed the dynamics of modulational instability for long-wavelength electrostatic oscillations and numerically studied the role of Langmuir damping in the termination of collapse. After spelling out our theoretical model in Sec.2, we work out in Sec.3 the details of the particle acceleration mechanism for typical parameters of AGN magnetospheres. In Sec. 4, we discuss and summarize our results. \section[]{Theoretical model} Transferring the approach of \cite{screp} to the AGN atmosphere, we divide the problem into two subtasks: (a) generation of electrostatic waves, and (b) Particle acceleration which, in this case, happens through the Langmuir collapse. \subsection[]{Centrifugal excitation of Langmuir waves} For the mode calculations of this paper, the magnetic field lines are almost straight and co-rotate with the supermassive black hole. For a typical AGN with mass $M\sim 10^8\times M_{\odot}$, the angular velocity of rotation is given by \begin{equation} \label{rotat} \Omega\approx\frac{a c^3}{GM}\approx 10^{-3}\frac{a}{M_8}rad/s^2, \end{equation} where $M_8\equiv M/(10^8M_{\odot})$ and $0<a\leq 1$ is a dimensionless parameter characterizing the rate of rotation of the black hole. The magnetic field may be estimated by assuming that the magnetic energy density is of the order of radiation energy density of the AGN (equipartition) \citep{osm7}, \begin{equation} \label{mag} B\approx\sqrt{\frac{2L}{r^2c}}\approx 27.5\times\left(\frac{L}{10^{42}erg/s}\right)^{1/2}\times\frac{R_{lc}}{r}G, \end{equation} where $L$ is the bolometric luminosity of AGN, $R_{lc}=c/\Omega$ is the light cylinder radius and $r$ is the distance from the black hole. With these fields, the protons with high Lorentz factors, $\gamma\sim 10^{4-5}$, will have gyroradii much smaller than the kinematic length-scale ($R_{lc}$) of particles in the magnetosphere. Such particles will, clearly, follow and co-rotate with the magnetic field lines. The protons will, therefore, inevitably accelerate centrifugally, but as it is explained in detail by \cite{osm7}, this process is strongly limited by two major factors. In due course of motion protons gain energy, but this process lasts until the energy gain is balanced by energy losses due to the inverse Compton scattering.The maximum attainable proton Lorentz factor is, then, estimated as \citep{osm7} \begin{equation} \label{gic} \gamma_{_{IC}}\approx\left(\frac{6\pi m_pc^4}{\sigma_T L\Omega}\right)^2\approx 1.5\times 10^{11}\left(\frac{10^{42}erg/s}{L}\right)^2, \end{equation} where $m_p\approx 1.67\times 10^{-24}$g is proton's mass and $\sigma_T\approx 6.65\times 10^{-25}$cm$^{-2}$ is the Thomson cross-section. We have taken into account that the Black hole rotates with $10\%$ of its maximum rate ($a = 0.1$). This estimate, however, turns out to be a bit too optimistic. A more restrictive limit is set by the proton dynamics as it moves under the combined influence of the Coriolis and Lorentz forces. This limiting mechanism, called, for want of a better name, "breakdown of the bead on the wire (BBW) approximation \citep{rm00}", yields a more moderate gamma (see \citep{osm7} for details) \begin{equation} \label{gfb} \gamma_{_{BBW}}\approx\frac{1}{c}\left(\frac{e^2L}{2m_p}\right)^{1/3}\approx 1.4\times 10^{5}\left(\frac{L}{10^{42}erg/s}\right)^{1/3}, \end{equation} From Eqs. (\ref{gic},\ref{gfb}), it is clear that $\gamma_{_{BBW}}\ll\gamma_{_{IC}}$. BWW, thus, sets the theoretical upper limit on the Lorentz factor $\sim 1.4\times 10^5$. Via centrifugal acceleration, the energy is pumped from the rotating magnetosphere. Although the centrifugally accelerated protons are strongly limited in energy, the centrifugal mechanism of energy pumping is very much in action. To study the generation of extremely unstable Langmuir waves, we follow the method developed in \citep{incr,incr3}. Throughout the paper, we assume that the magnetic field lines are almost straight and lie in the equatorial plane. Then, in the $1+1$ formalism \citep{membran}, the Euler equation in the corotating frame can be written as \begin{equation} \label{eul1} \frac{d{\bf p}_{\beta}}{d\tau}= \gamma_{\beta}{\bf g}+\frac{e_{\beta}}{m_\beta}\left({\bf E}+ \frac{1}{c}\bf v_{\beta}\times\bf B\right), \end{equation} ${\beta}$ denotes the species index ( electrons and protons), ${\bf p}_{\beta}$ and ${\bf V}_{\beta}$ are, respectively, the dimensionless momentum (${\bf p}_{\beta}\rightarrow {\bf p}_{\beta}/m_\beta$) and velocity, ${\bf g}\equiv -{\bf\nabla}\xi/\xi$ is the gravitational potential (a crucial component of the model), $e_{\beta}(m_{\beta})$ is the charge(mass) of the corresponding particle, $d\tau\equiv\xi dt$, $\xi\equiv\left(1-\Omega^2r^2/c^2\right)^{1/2}$ and $\gamma_{\beta}\equiv\left(1-{\bf V}_{\beta}^2/c^2\right)^{-1/2}$ is the Lorentz factor. Transition to the laboratory frame (LF) is accomplished through the identity $d/d\tau\equiv\partial/(\xi\partial t)+\left({\bf v_{\beta}\nabla}\right)$, and the relation $\gamma=\xi\gamma'$ connecting the corotating and LFs of reference ( the prime denotes the quantity in the LF). The LF equation of motion \begin{eqnarray} \label{eul2} \frac{\partial{\bf p}_{\beta}}{\partial t}+({\bf v_{\beta}\cdot\nabla)p}_{\beta}= \nonumber \\ =-c^2\gamma_{\beta}\xi{\bf\nabla}\xi+\frac{e_{\beta}}{m_\beta}\left({\bf E}+ \frac{1}{c}\bf v_{\beta}\times\bf B\right), \end{eqnarray} coupled with the continuity \begin{equation} \label{cont} \frac{\partial n_{\beta}}{\partial t}+{\bf \nabla}\cdot\left(n_{\beta}{\bf v_{\beta}}\right)=0, \end{equation} and the Poisson equation, \begin{equation} \label{pois} {\bf \nabla\cdot E}=4\pi\sum_{\beta}e_{\beta}n_{\beta}. \end{equation} completes the system. In the equilibrium, the plasma is assumed to obey the frozen-in condition ${\bf E_0 + \frac{1}{c}v_{0\beta}\times B_0 = 0}$. The corresponding trajectory of the centrifugally accelerated particles, calculated by the standard single particle approach, turns out to be: $r_\beta(t) \approx \frac{V_{0\beta}}{\Omega}\sin\left(\Omega t + \phi_{\beta}\right)$ (see Appendix, Eq. (\ref{rtrel})) and $\upsilon_{0\beta}(t) \approx V_{0\beta}\cos\left(\Omega t + \phi_{\beta}\right)$, where we have taken into account the specific initial phases of particles, $\phi_{\beta}$. It is worth noting that in spite of the aforementioned behaviour of the radial coordinate, it does not mean that the particle will oscillate. As we will see later, the instability becomes so efficient that the corresponding time-scale of energy conversion will be less than the rotation period. Since different species experience different forces, the Euler equation will lead to spacial separation of charges, which in turn, generates a electrostatic field via the Poisson equation; under certain conditions, these fields may grow in time. For studying the development of Langmuir waves, we expand all physical quantities around this equilibrium state (keeping up to linear terms in perturbations): \begin{equation} \label{exp} \Psi\approx\Psi^0+\Psi^1, \end{equation} where $\Psi = \{n,{\bf v},{\bf p},{\bf E},{\bf B}\}$. Fourier decomposing the perturbations, \begin{equation} \label{pert} \Psi^1(t,{\bf r})\propto\Psi^1(t)exp[i{\bf kr}], \end{equation} one obtains the linearized system of equations (\ref{eul2}-\ref{cont}) \begin{equation} \label{eul3} \frac{\partial p_{\beta}}{\partial t}+ik\upsilon_{\beta0}p_{\beta}= \upsilon_{\beta0}\Omega^2r_{\beta}p_{\beta}+\frac{e_{\beta}}{m_{\beta}}E, \end{equation} \begin{equation} \label{cont1} \frac{\partial n_{\beta}}{\partial t}+ik\upsilon_{{\beta}0}n_{\beta}, + ikn_{{\beta}0}\upsilon_{\beta}=0 \end{equation} \begin{equation} \label{pois1} ikE=4\pi\sum_{\beta}n_{\beta0}e_{\beta}, \end{equation} describing the evolution of the electrostatic field. In terms of an effective density, defined by \begin{equation} \label{ansatz} n_{\beta}=N_{\beta}e^{-\frac{iV_{\beta}k}{\Omega}\sin\left(\Omega t + \phi_{\beta}\right)}, \end{equation} one can derive, after straightforward algebra, the following set of non-autonomous "Mode" equations \citep{screp} \begin{equation} \label{ME1} \frac{d^2N_p}{dt^2}+{\omega_p}^2 N_p= -{\omega_p}^2 N_e e^{i \chi}, \end{equation} \begin{equation} \label{ME2} \frac{d^2N_e}{dt^2}+{\omega_e}^2 N_e= -{\omega_e}^2 N_p e^{-i \chi}, \end{equation} where $\chi = b\cos\left(\Omega t+\phi_{+}\right)$, $b = \frac{2ck}{\Omega}\sin\phi_{-}$, $2\phi_{\pm} = \phi_p\pm\phi_e$ and $\omega_{e,p}\equiv\sqrt{4\pi e^2n_{e,p}/m\gamma_{e,p}^3}$ and $\gamma_{e,p}$ are the relativistic plasma frequencies and the Lorentz factors for the stream components. Note that for simplicity, we have assumed the particle population to consist of only two streams with initial phases $\phi_{\pm}$. After Fourier transforming Eqs. (\ref{ME1},\ref{ME2}) in time, we derive the "dispersion relation" of the corresponding modes \begin{equation} \label{disp} \omega^2 -\omega_e^2 - \omega_p^2 J_0^2(b)= \omega_p^2 \sum_{\mu} J_{\mu}^{2}(b) \frac{\omega^2}{(\omega-\mu\Omega)^2}, \end{equation} where $J_{\mu}(x)$ is the Bessel function. Referring the reader to \citep{screp} for details, we just state here that this system may undergo an instability when the real part of the frequency satisfies the resonance condition, $\omega_r = \mu_{res}\Omega$. After expressing the frequency, $\omega = \omega_r+\Delta$ one can straightforwardly reduce the above equation \begin{equation} \label{disp1} \Delta^3=\frac{\omega_r {\omega_p}^2 {J_{\mu_{res}}(b)}^2}{2}, \end{equation} that has a pair of complex solutions implying a growth rate ( imaginary part of $\Delta$) \begin{equation} \label{grow} \Gamma= \frac{\sqrt3}{2}\left (\frac{\omega_e {\omega_p}^2}{2}\right)^{\frac{1}{3}} {J_{\mu_{res}}(b)}^{\frac{2}{3}}, \end{equation} where $\omega_r = \omega_e$. The time dependent centrifugal force that parametrically drives the electrostatic waves is different for the two species- so are their Lorentz factors. Due to the presence of the Bessel function, which for large values of the index( $\mu_{res}=\omega_r/\Omega\gg1$ tends to be nonzero only when the argument $b$ is of the order of the index, the growth rate will peak when $b= {2ck}\sin\phi_{-}/ {\Omega}=\mu_{res}=\omega_r/\Omega$. For these most unstable modes, the phase velocity $\upsilon_{ph} \equiv\omega/k=2c\sin(\varphi_{-})$ will exceed the speed of light for certain values of $\varphi_{-}$. Since there no particles with such velocities, such waves will not Landau damp on the particles. However, if there is a process that can enhance the wave vector, Landau damping might be restored. it is in this context that we discuss, in the next subsection, the possibility of Langmuir collapse. The length scale of a "cavern" might significantly decrease, leading to a decrease of phase velocity, so that there are enough resonant particles for drawing energy from the electrostatic field. \subsection[]{Acceleration mechanism} It is worth noting that due to a small initial amplitude of the Langmuir wave, the high frequency pressure increases, pushing out the particles from the perturbed zone. The resulting polarization creates an additional electrostatic field which causes a further decrease density in this region, creating what are termed as "caverns". Simultaneously, the plasmons (quasiparticles) accelerate towards these cavities, enter them and enlarge their depth even more. The boosted high-frequency pressure induces an auto modulation instability of the spatial distribution of plasmons. For the purpose of this paper, we will consider a kinematically relativistic fluid with non-relativistic temperatures. In the rest frame, it has been shown that the fluid obeys the nonlinear set of hydrodynamic equations \citep{zakharov}, \begin{equation} \label{z1} \frac{\partial}{\partial t}\delta n+n_0 \nabla{\bf v_e} = 0, \end{equation} \begin{equation} \label{z2} \frac{\partial}{\partial t}{\bf v_e}+\frac{e}{m}\nabla{\varphi_e}+\frac{3}{2}\frac{T_e}{2mn_0}\nabla{\delta n} = 0, \end{equation} reduces to \begin{equation} \label{ez1} \left[\frac{\partial^2}{\partial t^2}-3\lambda_D^2\omega_p^2\frac{\partial^2}{\partial x^2}-\omega_p^2\right]E = \frac{\delta n}{n_0}\omega_p^2E, \end{equation} \begin{equation} \label{ez2} \left[\frac{\partial^2}{\partial t^2}-\lambda_D^2\omega_p^2\frac{\partial^2}{\partial x^2}\right]\delta n=\frac{1}{16\pi m_p}\frac{\partial^2E^2}{\partial x^2}, \end{equation} where $\delta n$ is the electron density perturbation, ${\bf v_e}$ is the corresponding velocity perturbation, $n_0$ is the unperturbed ion number density, $T_e$ is the electron temperature, $\varphi_e$ is the high frequency part of the electrostatic potential and $\lambda_D\equiv \sqrt{T_e/(4\pi n_0e^2)}$ is the Debye length scale. We assume that the plasma is quasi neutral. It has been shown that this system, generalized for higher dimensions, describing the Langmuir collapse, exhibits explosive behaviour, i.e, the initial growth rate of the instability \citep{arcimovich} \begin{equation} \label{incrcol} \Gamma_{LC}=Im(\omega)\approx\frac{1}{\gamma_p}\left[\frac{\langle E^2\rangle e^2m_p}{4k_BT}\right]^{1/2}, \end{equation} since it scales with the field intensity, will naturally increase with time. In deriving (\ref{incrcol}), we have taken into account the Lorentz boosting. According to the standard approach developed by \cite{zakharov}, kinetic and potential energies of the plasmons caught by the caverns are of the same order of magnitude \begin{equation} \label{k} k^2\lambda_D^2\sim\frac{\mid\delta n\mid}{n_0}. \end{equation} Thus the characteristic length-scale of the cavern $L_c$, defined by the wavelength of the plasmon($1/k$), scales inversely with density perturbation, i.e, $L_c~ 1/\sqrt{\delta n}$. Since the high frequency pressure, $P_{hf}=-|E|^2\delta n/(24k^2\lambda_D^2n_0)$ \citep{arcimovich} with $|\delta n|$, the greater the pressure the lesser the cavern width. This is precisely the recipe for an explosive instability leading to a smaller and smaller $L_c$. During this process, energy density of oscillations drastically increases accelerating the collapse. What happens later depends strongly on dimensionality of the process. If the collapse continues so that the $L_c=1/k$ when the wavelength of plasmons is of the order of the Debye scale, the resonance Landau damping becomes important, resulting in particle acceleration. More discussion follows in the next section. | In this section we consider the implications of the theoretical framework developed in the last section (instability of centrifugally induced electrostatic waves, and the expected Langmuir collapse) for particle acceleration in a typical AGN setting. It has been assumed that the magnetic field are so strong that inside the light cylinder zone the AGN magnetospheric plasma co-rotates rigidly. Therefore, in this area the plasma number density might be well approximated by the Goldreich-Julian density \begin{equation} \label{gj} n_0 = \frac{\Omega B}{2\pi ec}. \end{equation} If we assume that the maximum electron Lorentz factor is controlled by the same mechanism as protons ($\gamma_p\sim 1.4\times 10^5$), then their lighter mass will allow $\gamma_e\approx\gamma_p(m_p/m_e)^{1/3}\sim 1.6\times 10^6$ (see equation (\ref{gfb})) to be an order of magnitude larger. Considering two representative streams with Lorentz factors $\gamma_1\sim 1.6\times 10^6$ and $\gamma_2\sim 10^3$ and tempera ture $T\sim 10^4$K, one estimates that the instability time-scale, $1/\Gamma$, is less than the kinematic time-scale, $\sim 2\pi/\Omega$, implying a rather efficient process of pumping rotation energy into Langmuir waves. These waves will, then, accelerate particles by Landau damping aided by a possible Langmuir collapse. Since the perturbation of density modulation usually is small, $\delta n\ll n_0$, the change of frequency of plasmons is negligible, $\delta\omega\ll\omega$. One may assume, then, that the corresponding energy is constant \citep{arcimovich} \begin{equation} \label{E2a} \int d^q{\bf r}\mid E\mid^2 = const. \end{equation} implying the scaling \begin{equation} \label{E2} \mid E\mid^2\propto\frac{1}{l^q}, \end{equation} where $q$ equals $\{1,2,3\}$ depending on the dimension of the space. Inside the magnetosphere the magnetic field is strong enough to force particles to move along the field lines. The relevant geometry, thus, is 1 D and the high frequency pressure, $P\propto\mid E\mid^2$ scales as $1/l$ \citep{arcimovich}. On the other hand, the thermal pressure, $P_{th}=k_BT\delta n$, behaving as $1/l^2$ (see equation (\ref{k})) increases faster than the high frequency pressure. This means that inside the magnetosphere the centrifugally induced Langmuir waves do not collapse and only propagate towards the outer region of the magnetosphere. Outside the magnetosphere, the plasma kinematics are no longer governed by rotation. in this region, the density is controlled by the accretion processes. To estimate the density let us assume a spherically symmetric accretion. The expected accretion rate of particles per unit time and unit area is of the order of $n\upsilon$, where $n$ is the accretion particle number density and $\upsilon = \sqrt{GM_{_{BH}}/R_{lc}}$. The estimated density, then, is \begin{equation} \label{n} n=\frac{L}{4\eta\pi m_pc^2\upsilon R_{lc}^2}\approx 6.3\times 10^5\times \left(\frac{L}{10^{42}erg/s}\right) cm^{-3}. \end{equation} We have assumed that only $10\%$ of the rest energy of accretion matter ($\eta=0.1$) transforms to emission. For such dense matter the corresponding plasma frequency, $\omega_p=\sqrt{4\pi e^2n/m_p}$ exceeds the cyclotron frequency for protons $\omega_B=eB_{lc}/(m_pc)$, which means that the particles in the region outside the magnetosphere are no longer bound by the magnetic field and consequently $d = 3$. This in turn means that the high frequency pressure behaving as $1/l^3$, increases much faster than the thermal pressure, behaving as $1/l^2$ and correspondingly the collapse of the Langmuir waves becomes inevitable. During the collapse the density perturbation satisfies the approximate equation (Eqs. (\ref{ez1},\ref{k})) \begin{equation} \label{dnt} \frac{\partial^2\delta n}{\partial t^2}\approx\frac{\delta n\mid E\mid^2}{16\pi nm_p\lambda_D^2}, \end{equation} where the thermal pressure has been neglected. After complementing this equation with already discussed relations, $\mid E\mid^2\sim 1/l^3$ and $\delta n\sim 1/l^2$, one obtains \citep{zakharov} \begin{equation} \label{E2} \mid E\mid^2\approx \mid E_0\mid^2\left(\frac{t_0}{t_0-t}\right)^2 \end{equation} \begin{equation} \label{l} l\approx l_0\left(\frac{t_0}{t_0-t}\right)^{-2/3}, \end{equation} where $t_0$ is the time when the cavern collapses completely. It is worth noting that the initial Langmuir waves have been efficiently amplified in the very vicinity of the light cylinder surface. The corresponding lengthscale can be obtained by a simple approximate expression $\Delta r\approx\gamma/(d\gamma/dr)$, leading to \begin{equation} \label{dr} \Delta r\approx\frac{\gamma_0}{2\gamma}R_{lc}, \end{equation} where we have taken into account the radial behaviour of Lorentz factors of centrifugally accelerated particles \citep{rm00} \begin{equation} \label{gr} \gamma(r)=\frac{\gamma_0}{1-\frac{r^2}{R_{lc}^2}}. \end{equation} As we have already discussed the electrostatic field appears and amplifies by means of the separation of charges in the mentioned zone. Therefore, the electrostatic field is approximated by the Poisson equation \begin{equation} \label{E0} E_0\approx 4\pi ne\Delta r, \end{equation} which due to the Langmuir collapse will be boosted by the factor of $\left(\Delta r/l\right)^{3/2}$ (see Eqs.(\ref{E2},\ref{l})) where $l\approx 2\pi\lambda_D$ is the dissipation lengthscale \citep{arcimovich}. It is clear that at the final stage, energy of the amplified electrostatic field will transfer to the particles inside the cavern resulting in protons with extremely high energies: \begin{equation} \label{energy} \epsilon_p\approx\frac{E^2}{8\pi n}=\frac{ne^2}{4\pi^2\lambda_D^3}\Delta r^5. \end{equation} For a proton beam with $\gamma_p\sim 10^2$, one can easily calculate that even the initial instability time-scale measured in the lab frame $\sim 1/\Gamma_{LC}\sim 0.2$s is several orders of magnitude less than the kinematic time-scale. This difference will significantly increase, because the collapse has an explosive character and the electric field amplifies faster than the linear exponential increase. The Langmuir collapse is strong enough to guarantee efficient acceleration of particles to ultra high energies. In particular, from equation (\ref{energy}), one obtains \begin{equation} \label{energy1} \epsilon_p\left(eV\right)\approx 6.4\times 10^{17}\times\left(\frac{f}{10^{-3}}\right)^3\times\left(\frac{10^2}{\gamma_2}\right)^5 \times M_8^{-5/2}\times L_{42}^{5/2}, \end{equation} where $f = \delta n/n_0$ is the initial dimensionless density perturbation, $a = 0.1$, $\eta = 0.1$, $L_{42}\equiv L/10^{42}$erg/s and we have assumed $T\sim 10^4$K. As it is evident from this expression for a convenient set of parameters one can achieve enormous energies of the order of $10^{21}$eV. To achieve such energies, the required electrostatic fields must exceed the background magnetic field by many orders of magnitude (see Eqs. (\ref{mag},\ref{E0},\ref{energy})). This is possible because the origin of the electrostatic field is different from that of the background magnetic field; the magnetospheric rotation energy is almost a limitless and continuous source, and can readily feed electric fields of such enormous magnitude. For the parameters corresponding to the maximum attainable energy $10^{21}$eV, the length-scale of the cavern is of the order of $10^{12}$cm (see equation \ref{dr}). Again such a large scale structure of the electrostatic field can be maintained only because the available energy budget that is transferred to the Langmuir modes, is huge. It should also be stressed that the equilibrium frozen in condition (a condition relating the large scale equilibrium fields $E_0$ and $B_0$) is not affected by the much shorter scale electric fields associated with the Langmuir wave. During the acceleration phase, the particles might lose energy due to several mechanisms that, potentially, might reduce the overall efficiency of acceleration. Via the highly efficient synchrotron mechanism, for example, the particles may rapidly lose their perpendicular momentum, transit to the ground Landau level and slide along the magnetic field lines. This mechanism, thus, does not influence particle acceleration. The Inverse Compton scattering is also found to be little significance to the acceleration process. For such high energies, the relevant regime is Klein-Nishina, and the corresponding cooling time-scale goes as $t_{_{IC}}=\epsilon_p/P_{KN}\propto\epsilon_p$ \citep{or09}, where $P_{KN}$ is the power emitted per unit time; $P_{KN}$ is not sensitive to $\epsilon_p$ \citep{Blumenthal}. Since $t_{_{IC}}$ is a continuously increasing function of $\epsilon_p$, the inverse Compton process does not impose any constraints on achievable particle energies. Another mechanism is the curvature radiation, characterized by the cooling time-scale $t_{cur}=\epsilon_p/P_{cur}$, where $P_{cur} = 2e^2\epsilon_p^4/(3m_p^4c^3\rho)$ is the energy loss rate and $\rho$ is the curvature radius of the trajectory of particles. Acceleration is efficient until the acceleration time-scale, which is the collapse time-scale, is less than the cooling time-scale. Maximum energy is achieved when the following condition $t_{col}\approx t_{cur}$ is satisfied. If one takes into account the gyro radius, $R_{p}$, of relativistic protons and assumes $\rho\sim R_p$, one can obtain $\epsilon_{max}\approx 4\times 10^{24}\xi$ (eV), where $\xi\gg 1$ and characterizes the fact that the growth rate is much higher than the initial increment (see equation (\ref{incrcol})). Therefore, the curvature emission is also negligible and cannot impose notable constraints on the maximum energies of particles. Although we see that the present mechanism, in principle, might create primary cosmic ray (proton) energies in the ZeV range, the actual energies may be limited due to the interaction of these particles with the isotropic microwave cosmic radiation. This interaction could significantly reduce the proton energy to the so called GZK limit $4\times 10^{19}$eV \citep{gzk1,gzk2}. There is, however, ample observational evidence of cosmic rays with energies above the GZK limit \citep{overgzk}. This can happen, for instance, if there is not enough time for the background radiation to slow down the more energetic particles - that is- the source of highly energetic particles lies within what may be called the the GZK radius, $\sim 100$Mpc \citep{corel1}- the typical distance needed for significant energy loss on the cosmic microwave photons. In the context of this paper it is worth noting that, the strong correlation of AGN with cosmic rays is actively discussed by \cite{corel1}, who consider the possibility that a subclass of AGN, might be responsible for ultra-high energy cosmic rays. | 14 | 4 | 1404.3176 |
1404 | 1404.6086_arXiv.txt | So far, numerical studies of double-diffusive layering in turbulent convective flows have neglected the effects of rotation. We undertake a first step into that direction by investigating how Coriolis forces affect a double-diffusive layer inside a rotating spherical shell. For this purpose we have run simulations in a parameter regime where these layers are expected to form and successively increased the rate of rotation with the result that fast rotation is found to have a similar stabilising effect on the overall convective flux as an increase of the stability ratio $R_\rho$ has in a non-rotating setup. We have also studied to what extent the regimes of rotational constraints suggested by \citet{king2013} for rotation in the case of Rayleigh-B\'enard convection are influenced by double-diffusive convection: their classification could also be applicable to the case of double-diffusive convection in a spherical shell if it is extended to be also a function of the stability ratio $R_\rho$. Furthermore, we examined the ratio of saline and thermal Nusselt numbers and compared our results with models of \citet{spruit_theory_2013}, \citet{Rosenblum2011} and \citet{wood_2013}. We find our data to be fitted best by Spruit's model. Our result that fast rotation further decreases the convective transport, which is already lowered by double-diffusive convection, could play a major role for e.g. the modeling of the interior of some rapidly rotating giant planets, as gaseous giant planets have recently been proposed to be influenced by double-diffusive convection. | The physical process known as double-diffusive convection was first described in the 1950's by \citet{stommel1956} who observed the effect in an experiment. Shortly afterwards, it was also found in astrophysics when the first detailed stellar models were computed and \citet{schwarzschild_haerm_1958} found irregularities in their calculations concerning whether or not a zone with a gradient in molecular weight was stable according to the Ledoux criterion or the Schwarzschild criterion. But even more than fifty years after its discovery, the field is still actively researched which is due to two reasons: on the one hand it lacked immediate practical incentives that have accelerated the development of other branches of fluid mechanics. On the other hand, numerical simulations were not possible for a long time because of the considerable computational expenses they demand. For a summary of the historical development of the area see the paper by \citet{huppert_1981}, for a recent physical review about semiconvection see \citet{zaussinger_kupka_muthsam_2012}. \\ Double-diffusive convection occurs in situations where the effect of a thermal gradient on stability and the effect of a molecular weight gradient on stability compete with each other: if the temperature gradient stabilises the system and the molecular weight gradient destabilises it, thermohaline convection can occur. Its distinguishing property is the appearance of flow structures known as salt-fingers (thus also the name salt-fingering convection). In the opposite case (temperature gradient unstable and molecular weight gradient stable) layering convection/semiconvection can occur. Note that we used the term ``can occur''. Whether thermohaline/layering convection really does occur depends on the ratio of the molecular weight buoyancy frequency to the thermal buoyancy frequency, the so called stability ratio $R_\rho=-N^2_{\mu}/N^2_{T}$. In the incompressible case it is equivalent to the ratio of the Rayleigh numbers associated with the thermal instability and the instability caused by the molecular weight. In this paper, our focus will be on layering convection. Situations where this process occurs on earth include the convection in the arctic ocean where cool and fresh melt water from above leads to a destabilising negative temperature gradient and a stabilising negative molecular gradient in salt \citep{turner2010}. Other examples are East-African rift lakes which are heated from below by volcanic activity. This leads to a temperature gradient (unstable) and causes dissolved gases like methane and carbon dioxide to be introduced into the system, thus causing a stabilising molecular weight gradient \citep{Schmid2010225}. But not only systems on earth are prone to double-diffusive convection: it can also occur in astrophysical systems like in icy satellites, giant planets and massive stars. Very recently, \citet{ORourke2014} have investigated the effects of a stabilising compositional gradient and the resulting double-diffusive convection in Titan. The role of semiconvection for the interior of giant planets has been discussed by \citet{stevenson1982a} and recently by \citet{chabrier2007} who suggested that it might be responsible for the radius anomalies of some hot Jupiters. This thought is further developed by \citet{Leconte2012}; they investigated the effect of semiconvection on the interior structure of planets and showed that it could explain the luminosity anomaly of Saturn \citep{Leconte2013}. They also point out: ``Determining the solute transport properties in the regime of layered convection more precisely, however, will be central to evolutionary calculations. 3D hydrodynamical simulations in a realistic parameter range are thus strongly needed.'' \citep{Leconte2012}. However, numerical simulations of double-diffusive systems in a realistic astrophysical parameter range pose a serious challenge (and are, in fact, still impossible in the stellar regime with today's computers) because of the huge spread of length and time scales of which the smallest length scale --- the size of the diffusive boundary layer --- needs to be resolved. For example, the ratio of the diffusivities of temperature and solute (the Lewis number) for the plasma in the interior of a semiconvective region of a star is $ \Le \approx 10^{-9}$ \citep{zaussinger_diss}. This would require an impossible spatial resolution if one were to attempt a DNS of such a zone \citep[also][]{zaussinger_diss}. While simulations are nowhere near the realistic parameter range for stellar astrophysical conditions yet, the parameter regime of giant planets has become feasible with today's computers since their Prandtl and Lewis numbers are much more moderate: the Prandtl number ranges from $\Pran = 10^{-2}$ to $1$, the Lewis number is about $\Le = 0.01$ \citep{chabrier2007}. For idealised microphysics, there are a number of simulations in two dimensions \citep[e.g.][]{zaussinger_scn_2013} and in three dimensions \citep[e.g.][]{wood_2013} in this parameter regime. Recently, a simulation in a realistic parameter range for the Atlantic Ocean that correctly reproduces measurements has been conducted by \citet{Flanagan20132466}. However, all of the mentioned studies have neglected the effect of rotation on the development of double-diffusive convection. While this may be justifiable in the case of thin layers as they are occuring in the Arctic ocean (layer thickness 1 to 5 m, see \citealt{Timmermanns2008}) or in lake Kivu (average thickness of the mixed layers 0.48 m, see \citealt{Schmid2010225}), it might not be negligible for large layers that could be forming in global convection zones on rapidly rotating giant planets and stars. It might even prove to be essential if trying to determine if layered convection is indeed occurring in giant planets and stars and what its precise influences on the transport properties are. Our work is a first step in the direction of investigating the effects of rotation on semiconvective layers. We note that while \citet{Net2012} did study thermosolutial convection in rotating spherical shells, they investigated a different parameter regime than the one where layers are expected to form so their work gives us no lead as to how semiconvective \textit{layers} are influenced by rotation. We want to give a remark on nomenclature here: in oceans the molecular weight gradient is caused by dissolved salt. That is why salinity gradient is another common term for the molecular weight gradient, particularly in oceanography. We will use the term salinity in this papers as well because it is handier than molecular weight of second species. We assume salinity to be the concentration of the solute, no matter what exactly the solute is. The publication is structured as follows: in chapter \ref{sec:model_description} we present the physical model and the underlying equations. We introduce the governing dimensionless numbers and the boundary conditions. In chapter \ref{sec:numerical_implementation} we discuss the numerical setup. In chapter \ref{sec:results} we present the results of our simulations. First, we show the results for a run with one set of parameters without rotation to have a reference framework to which we can compare the following runs (chapter \ref{sec:nonrotating}). Next, we present the results of the simulations with rotation (chapter \ref{sec:rotation}) and highlight some differences before investigating the influence of a change of the Prandtl number $\Pran$ and the density ratio $R_\rho$ chapter \ref{sec:modifying_pr_and_rrho}. This is followed by a discussion in chapter \ref{sec:discussion} and conclusions in chapter \ref{sec:conclusion}. | \label{sec:discussion} \subsection{Rotational Constraints} \subsubsection{Characterisation through $\Ra$ and $\Ta$} As we have seen, it also depends on the Taylor number whether heat and salt are transported by convection or diffusion only. \citet{king2013} have recently suggested that a power law constructed from the product of Ekman and Rayleigh number can be used to describe how strong rotation affects convection. Although they have studied Rayleigh-B\'enard convection we think it is interesting to compare their results with ours. They have found three important convection regimes: rotationally constrained convection occurs for $\Ra E^{3/2} \lesssim 10$, weakly rotating convection for $10 \lesssim \Ra E^{3/2} < \infty$ and non-rotating convection for $E^{-1} = 0$. $E$ is the Ekman number $E = \nu / (2 \Omega L^2)$, which is closely related to the Taylor number we used: $E = 1/ \sqrt{\Ta}$. Transferred to our studies, the limiting value is given by \begin{equation} \frac{\Ra}{\Ta^{3/4}} \label{eq:lim_value} \end{equation} and the three regimes are non-rotating convection for $\Ta = 0$, weakly rotating convection for $10 \lesssim \Ra / \Ta^{3/4} < \infty $ and rotationally constrained convection for $\Ra / \Ta^{3/4} \lesssim 10 $. Which regimes our Taylor numbers belong to is seen in table \ref{tab:rot_constraint}; and indeed, the three regimes coincide very nicely with our results: convection is effectively prevented for $\Ta = 1.11 \cdot 10^8$ and $\Ta = 1 \cdot 10^9$ which correspond to the regime of rotationally constrained convection of $\Ra / \Ta^{3/4} \lesssim 10 $. However, the proposed regimes have to be expanded for the case of semiconvection. We have added an overview of the effect of a change of the density ratio $R_\rho$ on convection to table \ref{tab:rot_constraint}. We see that for $\Ta = 4 \cdot 10^7$ it crucially depends on $R_\rho$ if a global convective layer forms or if diffusion is the only transport mechanism of heat and salinity. Although the system should actually be only weakly influenced by rotation since $\Ra / \Ta^{3/4} = 19.9 > 10$, convection is completely subdued by rotation when $R_\rho = 1.5$. This suggests that the stability ratio $R_\rho$ has to enter (\ref{eq:lim_value}) in a way that a higher $R_\rho$ leads to a reduced value (because rotation has a stronger influence): \begin{equation} \frac{\Ra}{\Ta^{3/4}} \cdot f( {R_{\rho}}) \label{eq:rrho_lim_value} \end{equation} This is an interesting result and worth to be studied in greater detail. In this paper, however, we restrict ourselves to the short remark that the convective regimes that \citet{king2013} proposed could also be applicable to the case of semiconvection in a spherical shell if extended to be also a function of $R_\rho$. \begin{table} \begin{center} \begin{tabular}{ccccc} & & \multicolumn{2}{c}{Convection for} \\ $\Ta $ \quad &$\Ro_{\pi / 6}$ & $\Ra / \Ta^{3/4}$ & $R_\rho = 1.3$ & $R_\rho = 1.5$ \\[3pt]\hline $0 $ & $\infty$ & $\infty$ & y & y \\ $1 \cdot 10^5$ & 20 & 1780 & y & y \\ $4 \cdot 10^5$ & 10 & 629 & y & y \\ $1 \cdot 10^6$ & 6.0 & 292 & y & y \\ \hline $1 \cdot 10^7$ & 2.0 & 56.2& y & y \\ $4 \cdot 10^7$ & 1.0 & 19.9 & y & n \\ \hline $1 \cdot 10^8$ & 0.6 & 9.2 & n & n \\ $1 \cdot 10^9$ & 0.2 & 1.78& n & n \end{tabular} \end{center} \caption{ Taylor numbers, Rossby numbers at colatitude $\Lambda=\pi /6$ and corresponding values of the convective regime following \cite{king2013}. The two right columns indicate if convection occurred in our simulations with the indicated value for the density ratio $R_\rho$. The horizontal lines divide the table into rotationally non constrained (upper part), weakly constrained (middle part) and strongly constrained (lower part) regimes for $R_\rho=1.3$. For all simulations: $\Pran=1,\Le=0.1,\Ra = 10^7$. } \label{tab:rot_constraint} \end{table} \subsubsection{Characterisation through $\Ro$} As we have seen in the course of this paper, for $\Pran=1,\Le=0.1,R_\rho=1.3$ we have strongly constrained convection for Taylor numbers $\Ta \in \{10^8,10^9 \}$, weakly constrained convection for $\Ta \in \{ 10^7, 4 \cdot 10^7\}$ and non constrained convection for $\Ta \in \{0, 10^5, 4 \cdot 10^5, 10^6 \}$. This is indicated by the horizontal lines in table \ref{tab:rot_constraint}. It is interesting to compare the Rossby numbers from table \ref{tab:taylor_rossby} to the constraint that rotation exerts on the flow in our simulations. For the stability ratio $R_{\rho} = 1.3$, we get the result that if $\Ro<0.5$ in the bulk of the shell (indicated by the Rossby number at colatitude $\Lambda=\pi /6$ in table \ref{tab:rot_constraint}), we have the case of rotationally strongly constrained convection. The weakly constrained (or transition) cases correspond to $0.5 < \Ro < 2$ while the non constrained cases correspond to $\Ro > 2$. It is interesting to note that the Reynold stress correlations investigated in \citet{chan2001} and the structure of the temperature field shown in \citet{chan2007}, both times for so-called f-box simulations of rotating convection with uniform composition and a fully compressible flow, show a similar transition region at Coriolis numbers (which are defined as $1/\Ro$) that correspond to exactly the same regime of Rossby numbers as in our case with $R_{\rho}=1.3$: a transition region for $0.5< \Ro<1$ and a rotation dominated flow for $\Ro < 0.5$, at equatorial co-latitude respectively. However, as in the case of King et al.'s model, the Rossby number alone seems to be insufficient for figuring out the effect of rotation on semiconvection. Again, $R_\rho$ presents itself to be a crucial factor. For $R_\rho = 1.5$ we have a higher influence of rotation than for $R_\rho=1.3$. An increase to $R_\rho=1.5$ seems to shift the Rossby numbers by a factor of about $0.5$, meaning that the effective Rossby number for $\Ta=4 \cdot 10^7$ would be $\Roeff=0.5$. With this value, it enters the rotationally strongly constrained regime. And indeed, for $\Ta=4 \cdot 10^7$ and $R_{\rho}=1.5$ we have no convection (see figure \ref{fig:nusselt}). So the stability ratio also affects the Rossby number in a way that a higher $R_\rho$ leads to a lower effective Rossby number \Roeff: \begin{equation} \Roeff = \frac{\Ro}{f(R_\rho)}. \end{equation} \subsection{The relationship between $\Nus$ and $\Nut$} \subsubsection{The relationship between $\Nus$ and $\Nut$ for $\Ta=0$} There exist different models for the relationship between the thermal and saline Nusselt number. According to \citet{spruit_theory_2013} they are related via \begin{equation} \Nus - 1 = \frac{q}{\Le^{1/2} R_\rho} (\Nut - 1) \label{eq:spruit_nusselt_theory} \end{equation} for $R_\rho < \Le^{-1/2}$. $q$ is a fit parameter. According to (32) of \citet{Rosenblum2011} the relationship is \begin{equation} \Nus - 1 \approx \frac{1}{\Le R_\rho } (\Nut - 1), \label{eq:rosenblums_theory} \end{equation} which is especially for very low Lewis numbers in strong contrast to theoretical results from the linear stability theory. According to (42) and (43) of \citet{wood_2013}, the relation is given by \begin{equation} \Nus - 1 = \frac{B}{A} \frac{\Pran^{1/12}}{\Le} \Rat^{0.37-1/3} (\Nut - 1). \label{eq:woods_theory} \end{equation} The latter is given for $\Pran \ll 1$ which is not the case in our simulations, so a deviation can be expected. Typical values for $A$ and $B$ are given as $A\approx 0.1$ and $B \approx 0.03$, so $B/A \approx 0.3$. These three models are tested here against our results of average thermal and saline Nusselt numbers. The result for the simulation without rotation is seen in figure \ref{fig:theory_data}. \begin{figure} \begin{center} \begin{minipage}[]{0.7\linewidth} \includegraphics[width=\textwidth]{./Function_nusselts_t0_rrho13_pr1_onet0_upto_dts04_q095.png} \end{minipage} \caption{Average saline Nusselt number vs. average thermal Nusselt number for $\Ta=0$. The black dots are data points from our simulation, the (red) solid line is a plot of (\ref{eq:spruit_nusselt_theory}) with $q=0.95$, the (green) dotted line is a plot of (\ref{eq:rosenblums_theory}), the (blue) dash-dotted line is a plot of (\ref{eq:woods_theory}) with $B/A=0.3$, the (black) dashed line a plot of (\ref{eq:woods_theory}) with $B/A=0.128$.} \label{fig:theory_data} \end{center} \end{figure} We see that Spruit's theoretical prediction (solid line in figure \ref{fig:theory_data}) lies in the vicinity of the data points but does not exactly reproduce them except in one area where there is a big amount of data points at $\Nut \approx 6$. This area of abundant data represents the system, when it has reached the statistically stable end state. The line of data points, on the other hand, represents the system while it is relaxing to its end state. Rosenblum et al.'s model (dotted line in figure \ref{fig:theory_data}) does not fit our data. Since it does not have a fitting parameter, it cannot be adjusted to fit the data, either. Wood et al.'s model does not fit our data with their proposed values for $A$ and $B$. It does, however, fit the data equally good as Spruit's model does when adjusting $A$ and $B$ accordingly. We can therefore conclude that Spruit's model and the adjusted version of Wood et al.'s model both make successful predictions for the ratio of saline and thermal Nusselt numbers in the parameter range that we simulated in the non-rotating case. Albeit, they do so only after the system has reached its equilibrium state. Taking Spruit's model as a starting point, we calculate the interval that $\Nus/\Nut$ has to lie in. Starting from (\ref{eq:spruit_nusselt_theory}) after a few elementary transformations we get \begin{equation} \frac{\Nus}{\Nut} = \frac{q}{\Le^{1/2} R_\rho} - \frac{1}{\Nut} \left( \frac{q}{Le^{1/2} R_\rho} - 1 \right) \equiv g(\Nut) \end{equation} The smallest possible value of $\Nut$ is one, which corresponds to the case of pure diffusion: \begin{equation} g(1) = \frac{q}{\Le^{1/2} R_\rho} - \frac{q}{Le^{1/2} R_\rho} + 1 = 1. \end{equation} In the limit of $\Nut \rightarrow \infty$ we get \begin{equation} \mathrm{lim}_{\Nut \rightarrow \infty} g(\Nut) = \frac{q}{Le^{1/2} R_\rho}. \end{equation} Provided that $q \ge \Le^{1/2}R_\rho$ the ratio of Nusselt numbers $g(\Nut)$ is therefore bounded by \begin{equation} 1 \le \frac{\Nus}{\Nut} \le \frac{q}{Le^{1/2} R_\rho}. \end{equation} In our reference case, where $Le=0.1$ and $R_\rho=1.3$ this gives \begin{equation} 1 \le \frac{\Nus}{\Nut} \le 2.43 \, q. \end{equation} Setting the fit parameter $q=0.95$, which is the value that fits the data in figure \ref{fig:theory_data}, we end up with \begin{equation} 1 \le \frac{\Nus}{\Nut} \le 2.31 \end{equation} Our data confirms this for all times except for the initial plume phase, as can be observed from figures \ref{fig:thrice_taylor0} and \ref{fig:ratio_of_nusselts}. The maximal value of $\overline{\Nus}/\overline{\Nut}$ is $\approx 2.25$. \begin{figure} \begin{minipage}{0.5\linewidth} \begin{center} \includegraphics[width=\textwidth]{./Ratio_nusselts_t0_rrho13_pr1_onet0_upto_dts01.png} \end{center} \end{minipage} \begin{minipage}{0.5\linewidth} \begin{center} \includegraphics[width=\textwidth]{./Ratio_nusselts_t0_rrho13_pr1_onet0_upto_dts04.png} \end{center} \end{minipage} \caption{Ratio of average saline and thermal Nusselt number vs. simulation time for up to $t=0.1$ (left) and $t=0.4$ for $\Ta=0$. The state of the system can be separated into different regions of sharply rising and slowly declining ratio of Nusselt numbers that correspond to states of layered convection, boundary layer creation and overturning convection.} \label{fig:ratio_of_nusselts} \end{figure} The plots show another interesting result. It appears that the ratio of Nusselt numbers is a good classification for the state of the flow. After the plumes have broken, a convective layer is established (at $t\approx 0.013$ in figure \ref{fig:ratio_of_nusselts}). The thickness of the layer $d_s$ increases with time until the top of the layer reaches the upper boundary of the shell (at $t\approx 0.034$ ). Then, thermal and saline diffusive boundary layers at the shell boundary are established. This is indicated by a rise of $\overline{\Nus} / \overline{\Nut}$. We suspect that if we had a second layer on top, these would then start to merge at this point. But since we have imposed boundary conditions there, the state of the system relaxes to a homogeneous convective layer embedded between diffusive transition ranges at both top and bottom, a state that is reached at $t \approx 0.2$ . We note here that during layer formation and extension $q$ and, likewise, $A$ and $B$ in the models of Spruit and Wood et al., respectively, may not remain constant and their values may not be the same for differently sized stacks of layers or during a ``merging process'' or for different boundary conditions. If and which influence rotation and a change of $\Pran$ and $R_\rho$ have on $\overline{\Nus} / \overline{\Nut}$ will be investigated next. \subsubsection{Influence of rotation on the relationship between $\Nus$ and $\Nut$}\label{sss:ratio_nusselts_rotation} The first row of figure \ref{fig:nusselt_relation} shows $\overline{\Nus} / \overline{\Nut}$ against the simulation time for different rotation rates up to $t=0.2$ (left) and up to $t=1$ (right). \begin{figure} \begin{minipage}{0.5\linewidth} \begin{center} \includegraphics[width=\textwidth]{./Relation_nusselt_rrho13_pr1_bunt_disruptedline_bis_dts02.png} \end{center} \end{minipage} \begin{minipage}{0.5\linewidth} \begin{center} \includegraphics[width=\textwidth]{./Relation_nusselt_rrho13_pr1_bunt_disruptedline.png} \end{center} \end{minipage} \begin{minipage}{0.5\linewidth} \begin{center} \includegraphics[width=\textwidth]{./Relation_nusselt_rrho13_pr05_bunt_disruptedline_bis_dts02.png} \end{center} \end{minipage} \begin{minipage}{0.5\linewidth} \begin{center} \includegraphics[width=\textwidth]{./Relation_nusselt_rrho13_pr05_bunt_disruptedline_bis_dts1.png} \end{center} \end{minipage} \begin{minipage}{0.5\linewidth} \begin{center} \includegraphics[width=\textwidth]{./Relation_nusselt_rrho15_pr1_bunt_disruptedline_bis_dts02.png} \end{center} \end{minipage} \begin{minipage}{0.5\linewidth} \begin{center} \includegraphics[width=\textwidth]{./Relation_nusselt_rrho15_pr1_bunt_disruptedline_bis_dts1.png} \end{center} \end{minipage} \caption{The ratio of saline and thermal Nusselt numbers for the three parameter pairs $(\Pran=1, R_\rho=1.3)$ (upper row), $(\Pran=0.5, R_\rho=1.3)$ (middle row) and $(\Pran=1, R_\rho=1.5)$ (lower row) for simulation times up to $t=0.02$ (left column) and $t=1$ (right column).} \label{fig:nusselt_relation} \end{figure} For no rotation, at low simulation times, the ratio of saline and thermal Nusselt numbers rises monotonously with a high slope until it relaxes to a slightly falling ``plateau of (slowly growing) layered convection'' only to sharply rise again and relax to a statistically continuous value. Rotation seems to stretch the plateau which exists while the thickness $d_s$ of the layer grows and turns it into more of a sink and makes it much wider for higher rotation rates. For the highest rotation rates, the ones where the final state is one of diffusion, there is no plateau/sink at all, the ratio of Nusselt numbers falls monotonously and approaches one. The maximum value for $\overline{\Nus} / \overline{\Nut}$ does not change for $\Ta \le 1.11 \cdot 10^6$. For $\Ta=10^7$ it decreases from $\approx 2.25$ obtained for all lower Taylor numbers to $\approx 2$. For $Ta=4 \cdot 10^7$ it decreases further to $\approx 1.8$. For $\Ta=1.11 \cdot 10^8$ the ratio of Nusselt numbers does not reach its global maximum after $t\approx 0.05$ but before. This is before the system is in statistic equilibrium. When it reaches the equilibrium state, convection is suppressed and both Nusselt numbers tend to one. The same is true for $\Ta=10^9$. \\ Since fast rotation does have a significant effect on the ratio of Nusselt numbers and hence the flux ratio, a measure of the rate of rotation has to enter the theoretical prediction (\ref{eq:spruit_nusselt_theory}) or the fit formula (\ref{eq:woods_theory}). \subsubsection{Modifying $\Pran$ and $R_\rho$} Looking at the middle and last row of figure \ref{fig:nusselt_relation} we get the same result that was seen in chapters \ref{sec:modifying_pr_and_rrho} to \ref{sec:modifying_pr_and_rrho_at_higher_rotation_rates}. Lowering the Prandtl number decreases the influence that a higher rotation rate has on the stability of semiconvection. While for $\Ta=4\cdot 10^7$ the asymptotic state of the ratio of Nusselt numbers occurs at $t \approx 0.7$, for a Prandtl number half as high, the corresponding case with $\Ta=8\cdot 10^7$ reaches the asymptotic state already at $t \approx 0.35$. So the phases of layered convection and the creation of a diffusive boundary layer happen on a shorter time scale for lower Prandtl numbers. Likewise, increasing $R_{\rho}$ to $1.5$ on the other hand slows down the time development for $\Ta = 10^7$ and turns $\Ta = 10^7$ into a diffusive case where $\Nus/\Nut$ drops to 1 after an early maximum value. The saturation of $\Nus/\Nut$ for the non-diffusive cases occurs at the same time as for $\Nus$. \subsection{The influence of rotation on the lifetime of a layer} Next, we take note of the time at which the thermal Nusselt number reaches the asymptotic value. We chose the thermal Nusselt number because it has the sharpest kink when reaching the statistically stable state. The results are summarised in table \ref{tab:asymptotic_times}. The times were taken from figure \ref{fig:dts01udts1}. \begin{table} \begin{center} \begin{tabular}{rccc} $\Ta \cdot \Pran$ \quad & \multicolumn{3}{c}{$t_{\mathrm{asymptotic}}$} \\[3pt]\hline & \multicolumn{1}{l}{ $\quad \Pran = 1, R_\rho = 1.3 \quad $} & $\Pran = 1, R_\rho = 1.5$ \quad & $\Pran = 0.5, R_\rho = 1.3$ \quad \\ \hline \multicolumn{1}{r}{0} & 0.056 & n/a & n/a \\ $1 \cdot 10^5$ & 0.056 & n/a & n/a \\ $4 \cdot 10^5$ & 0.059 & \multicolumn{1}{c}{0.110} & \multicolumn{1}{c}{0.046} \\ $1.11 \cdot 10^6$ & 0.060 & \multicolumn{1}{c}{0.124} & \multicolumn{1}{c}{0.048} \\ $1 \cdot 10^7$ & 0.132 & \multicolumn{1}{c}{0.428} & \multicolumn{1}{c}{0.106} \\ $4 \cdot 10^7$ & 0.724 & $\infty$ & \multicolumn{1}{c}{0.328} \\ $1.11 \cdot 10^8$ & \multicolumn{1}{c}{$\infty$} & $\infty$ & $\infty$ \\ $1 \cdot 10^9$ & \multicolumn{1}{c}{$\infty$} & $\infty$ & $\infty$ \\ \end{tabular} \end{center} \caption{Time in thermal diffusion time scales when thermal Nusselt number reaches the statistically stable asymptotic state. n/a means that we did not run simulations for these parameters. $\infty$ means that there is no statistically stable convective state for these parameters.} \label{tab:asymptotic_times} \end{table} Obviously, increasing $R_{\rho}$ delays the time development of $\Nut$ while lowering $\Pran$ accelerates it. But since these are far too few data points to make a sound assumption about an underlying law we restrict ourselves to just listing them. | 14 | 4 | 1404.6086 |
1404 | 1404.7049_arXiv.txt | {Stellar activity, and in particular convection-related surface structures, potentially cause bias in the planet detection and characterisation. In the latter, interferometry can help to disentangle the signal of the transiting planet.} {We used realistic three-dimensional (3D) radiative hydrodynamical (RHD) simulations from the \textsc{Stagger}-grid and synthetic images computed with the radiative transfer code {{\sc Optim3D}} to provide interferometric observables to extract the signature of stellar granulation and transiting planets.} {We computed intensity maps from RHD simulations and produced synthetic stellar disk images as a nearby observer would see accounting for the centre-to-limb variations. We did this for twelve interferometric instruments covering wavelengths ranging from optical to infrared. We chose an arbitrary date and arbitrary star with coordinates that ensures observability throughout the night. This optimization of observability allows for a broad coverage of spatial frequencies. The stellar surface asymmetries in the brightness distribution, either due to convection-related structures or a faint companion mostly affect closure phases. We then computed closure phases for all images and compared the system star with a transiting planet and the star alone. We considered the impact of magnetic spots constructing a hypothetical starspots image and compared the resulting closure phases with the system star with a transiting planet.} {We analyzed the impact of convection at different wavelengths. All the simulations show departure from the axisymmetric case (closure phases not equal to 0 or $\pm\pi$) at all wavelengths. The levels of asymmetry and inhomogeneity of stellar disk images reach high values with stronger effects from 3rd visibility lobe on. We presented two possible targets (Beta Com and Procyon) either in the visible and in the infrared and found that departures up to 16$^\circ$ can be detected on the 3rd lobe and higher. In particular, MIRC is the most appropriate instrument because it combines good UV coverage and long baselines. Moreover, we explored the impact of convection on interferometric planet signature for three prototypes of planets with sizes corresponding to one hot Jupiter, one hot Neptune, and a terrestrial planet. The signature of the transiting planet on closure phase is mixed with the signal due to the convection-related surface structures, but it is possible to disentangle it at particular wavelengths (either in the infrared or in the optical) by comparing the closure phases of the star at difference phases of the planetary transit. It must be noted that starspots caused by the magnetic field may pollute the granulation and the transiting planet signals. However, it is possible to differentiate the transiting planet signal because the time-scale of a planet crossing the stellar disk is much smaller than the typical rotational modulation of a star.} {The detection and characterisation of planets must be based on a comprehensive knowledge of the host star; this includes the detailed study of the stellar surface convection with interferometric techniques. In this context, RHD simulations are crucial to reach this aim. We emphasize that interferometric observations should be pushed at high spatial frequencies by accumulating observations on closure phases at short and long baselines. } | \begin{table*} \centering \begin{minipage}[t]{\textwidth} \caption{3D simulations from \textsc{Stagger}-grid used in this work.} % \label{simus} % \centering % \renewcommand{\footnoterule}{} \begin{tabular}{c c c c c c c c} % \hline\hline % $<T_{\rm{eff}}>$\footnote{Horizontally and temporal average of the emergent effective temperatures from \cite{2013A&A...557A..26M}} & [Fe/H] & $\log g$ & $x,y,z$-dimensions & $x,y,z$-resolution & $\rm{M}_{\star}$ & $\rm{R}_{\star}$ & Number of tiles \\ $[\rm{K}]$ & & [cgs] & [Mm] & [grid points] & [$\rm{M}_\odot$] & [$\rm{R}_\odot$] & over the diameter\\ \hline 5768.51 (Sun) & 0.0 & 4.4 & 3.33$\times$3.33$\times$2.16 & 240$\times$240$\times$240 & 1.0 & 1.0 & 286\\ 5764.13 & -1.0 & 4.4 & 3.12$\times$3.12$\times$1.63 & 240$\times$240$\times$240 & 1.0 & 1.0 & 305\\ 5781.04 & -2.0 & 4.4 & 2.75$\times$2.75$\times$1.67 & 240$\times$240$\times$240 & 1.0 & 1.0 & 347\\ 5780.06 & -3.0 & 4.4 & 3.00$\times$3.00$\times$1.61 & 240$\times$240$\times$240 & 1.0 & 1.0 & 318\\ 4569.23 & 0.0 & 2.0 & 1000$\times$1000$\times$1288 & 240$\times$240$\times$240 & 1.3 \footnote{Averaged value from Fig.~4 of \cite{2012A&A...537A..30M}} & 18.9 & 17\\ 5001.35 & 0.0 & 3.5 & 27.08$\times$27.08$\times$24.49 & 240$\times$240$\times$240 & 1.15 \footnote{Averaged value from Fig.~2 of \cite{2011ApJ...740L...2S}} & 3.1 & 121\\ 5993.42 & 0.0 & 4.0 & 10.83$\times$10.83$\times$5.66 & 240$\times$240$\times$240 & 1.0 $^{c}$ & 1.6 & 266\\ 5998.93 & 0.0 & 4.5 & 2.92$\times$2.92$\times$1.76 & 240$\times$240$\times$240 & 1.15 $^{c}$& 0.99 & 312\\ \hline\hline % \end{tabular} \end{minipage} \end{table*} Two very successful methods for finding exoplanets orbiting around stars are the transiting and radial velocity methods. The transit happens when a planet passes between the exoplanet and its host star. The planet then blocks some of the star-light during the transit and creates a periodic dip in the brightness of the star. Observations taken during both the primary and secondary transit can be used to deduce the composition of the planet's atmosphere. \\ As the star moves in the small orbit resulting from the pull of the exoplanet, it will move towards the planet and then away as it completes an orbit. Regular periodic changes in the star's radial velocity (i.e., the velocity of the star along the line of sight of an observer on Earth) depend on the planet's mass and the inclination of its orbit to our line of sight. Measurements on the Doppler-shifted spectra give a minimum value for the mass of the planet. However, a potential complication to planet detection may be posed by stellar surface inhomogeneities (due to the presence of stellar granulation, magnetic spots, dust, etc.) of the host star. In this article we investigate in particular problem of stellar granulation. It was first observed on the Sun by \cite{1801RSPT...91..265H} and today modern telescopes provide direct observations \citep[e.g., ][]{2004ApJ...610L.137C}. However, the best observational evidence comes from unresolved spectral line in terms of widths, shapes, and strengths that, when combined with numerical models of convection, allow quite robust results to be extracted from the simulations \citep{2009LRSP....6....2N,2000A&A...359..669A}. For this purpose, large efforts have been made in recent decades to use theoretical modeling of stellar atmospheres to solve multidimensional radiative hydrodynamic equations in which convection emerges naturally. These simulations take into account surface inhomogeneities (i.e., granulation pattern) and velocity fields. The widths of spectral lines are heavily influenced by the amplitude of the convective velocity field, which overshoots into the stable layers of the photosphere where the lines are formed. This results in characteristic asymmetries of spectral lines as well as net blueshifts \citep[e.g.][]{dravins87}. The observation and interpretation of unresolved stellar granulation is not limited to the Sun \citep{2009LRSP....6....2N} because numerical simulations cover a substantial portion of the Hertzsprung-Russell diagram \citep{2013A&A...557A..26M,2013ApJ...769...18T,2009MmSAI..80..711L}, including the evolutionary phases from the main-sequence over the turnoff up to the red-giant branch for low-mass stars. Since the discovery of 51 Peg \citep{1995Natur.378..355M}, various studies have looked at starspots. For instance, \cite{1998ApJ...498L.153S} proposed the first quantitative impact of starspots on radial-velocity measurements. The authors studied the impact of these surface structures on the bisector (i.e., measure of the spectral line asymmetries) global slope and found that convection leads to bisector variations up to a few tens ms$^{-1}$. \cite{1997ApJ...485..319S} pointed out they can lead to even larger radial-velocity variations for G2V-type stars. It should be expected that, in the case of F dwarfs or K giants, the velocity fields would be even larger. \cite{2004AJ....127.3579P} measured star-to-star variations of 50 $ms^{-1}$ due to stellar activity in a sample of Hyades dwarfs. \cite{2007A&A...473..983D} discussed the possibility that, in F-K type stars, radial-velocity variations may be due to either spots or planets. \cite{2011ApJ...743...61S} showed that the transit data of a super-Neptune planet exhibit numerous anomalies that they interpret as passages over dark spots. The role of long-baseline interferometric observations in planet hunting is a complement to the radial velocity and adaptive optics surveys. Thanks to the higher angular resolution, interferometry is the ideal tool for exploring separations in the range 1 to 50 mas \citep{2012A&A...541A..89L}. This is achieved by observing the closure phase measurements directly associated with the asymmetries in the brightness distribution, and, as a consequence, off-axis detection of a companion. Long-baseline interferometry bridges the gap between the use of direct imaging, which finds wide companions, and the use of RV measurements, which detect close companions \citep{2012A&A...541A..89L}. Several attempts and discussions regarding prospective ideas towards this end have already been carried out. In particular for hot Jupiter planets, with the MIRC instrument at CHARA telescope \cite[e.g., ][]{2008SPIE.7013E..45Z,2008PASP..120..617V,2011PASP..123..964Z} or the AMBER, MIDI, PIONIER instruments at VLTI \citep[e.g., ][]{2010A&A...515A..69M,2011A&A...535A..68A,2012A&A...540A...5C,2013MNRAS.435.2501L}. However, the extraction of the planetary signal from the interferometric observables is a difficult task that requires very accurate precision levels, possible only with proportionate increase of the data signal to noise. In this work, we present interferometric predictions obtained from three-dimensional surface convection simulations run for stars spanning different effective temperatures, surface gravities, and metallicities. Further, we present results from a study of the impact of granulation on the detection of transiting planet for three prototypes of planets of different sizes corresponding to a hot Jupiter, a hot Neptune, and a terrestrial planet. \begin{figure*} \centering \begin{tabular}{c} \includegraphics[width=0.99\hsize]{intensity_maps_all.eps}\\ \end{tabular} \caption{Synthetic stellar disk images of the RHD simulations of Table~\ref{simus} (columns). The images correspond to a representative wavelength for each interferometric instruments of Table~\ref{instruments} from the optical (top row) to the far infrared (bottom row). The averaged intensity ($\times10^5$\,erg\,cm$^{-2}$\,s$^{-1}$\,{\AA}$^{-1}$) is reported in the lower left corner of each image.} \label{images} \end{figure*} | We presented an application of the \textsc{Stagger}-grid of realistic, state-of-the-art, time-dependent, radiative-hydrodynamic stellar atmosphere. We used the simulations to provide synthetic images from the optical to the infrared and extract interferometric observables aimed to study stellar convection as well as its impact on planet detection and characterisation. RHD simulations are essential for a proper quantitative analysis of interferometric observations and crucial for the extraction of the signal. We analysed the impact of convection at different wavelengths using the closure phases. Closure phase is the interferometric observable with intrinsic and unaltered information about the stellar surface asymmetries in the brightness distribution, either due to convection-related structures or a faint companion. We made our predictions as real as possible using actual interferometric instruments and configurations. All the simulations show departure from the axisymmetric case (closure phases not equal to 0 or $\pm\pi$) for all the wavelengths, but, at least for the chosen configurations, it is difficult to determine clear differences among the stellar parameters and, in particular, for the different metallicities of the solar simulations. The levels of asymmetry and inhomogeneity of stellar disk images reach very high values of several tens of degrees with stronger effects from 3rd visibility lobe on. We explored the possibility of detecting the granulation pattern on two real targets (Beta Com and Procyon). We found that the detection on the 2nd lobe is possible either in the visible or in the near infrared with closure phase departures of less than 1$^\circ$; detections on the 3rd, 4th, 5th, 6th lobes (with departures up to 16$^\circ$) are possible using CHARA's instruments, and, in particular, MIRC is the most appropriate instrument because it combines good UV coverage and long baselines. In general, interferometers probing optical and near infrared wavelengths are more adapted to reach higher spatial frequencies as the 3rd visibility lobe can be probed with baseline lengths less than 400 meters for stellar sizes larger than 2 mas. It is more complicated for the mid-infrared wavelengths where the baselines become kilometric. We emphasise that stars should be observed at high spatial frequencies by accumulating observations on closure phases at short and long baselines. We explored the impact of convection on interferometric planet signature for three prototypes of planets with sizes corresponding to one hot Jupiter, one hot Neptune, and a terrestrial one. Considering three particular planet transition phases, we compared the closure phases of the star with the transiting planet and the star alone. The signature of the transiting planet on the closure phase is mixed with the signal due to the convection-related surface structure but it is possible to disentangle it at particular wavelength (either in the infrared or in the optical). It can be achieved by measuring the closure phases for the star at different phases of the transit. Starspots caused by the magnetic field of the star may masquerade as planets for interferometric observations. We showed that the starspot signal on closure phases can be of the same order as the transiting planet signal (at least in the example configuration we considered). However, it should be possible to differentiate between them because the time-scale of a planet crossing the stellar disk is much smaller than the typical rotational modulation of the star. It is, however, important to note that when probing high spatial frequencies, the signal to noise ratio of the measurements would be very low due to low fringe visibilities, greatly deteriorating the closure phase precision and affecting the instrument capability. Moreover, this would influence the capability and sensitivity of detecting the signatures of granulation and disentangling the planetary signal. The detection and characterisation of planets must be based on a comprehensive knowledge of the host star, and this includes the detailed study of the stellar surface convection. In this context, RHD simulations are crucial to reach this aim. | 14 | 4 | 1404.7049 |
1404 | 1404.7425_arXiv.txt | ~\par An analytical framework is presented to understand the effects of a fluctuating intensity of the cosmic ionising background on the correlations of the \lya forest transmission fraction measured in quasar spectra. In the absence of intensity fluctuations, the \lya power spectrum should have the expected cold dark matter power spectrum with redshift distortions in the linear regime, with a bias factor $b_\delta$ and a redshift distortion parameter $\beta$ that depend on redshift but are independent of scale. The intensity fluctuations introduce a scale dependence in both $b_\delta$ and $\beta$, but keeping their product $b_\delta \beta$ fixed. Observations of the \lya correlations and cross-correlations with radiation sources like those being done at present in the BOSS survey of SDSS-III \citep{Busca2013,Slosar2013,Font14} have the potential to measure this scale dependence, which reflects the biasing properties of the sources and absorbers of the ionising background. We also compute a second term affecting the \lya spectrum, due to shot noise in the sources of radiation. This term is very large if luminous quasars are assumed to produce the ionising background and to emit isotropically with a constant luminosity, but should be reduced by a contribution from galaxies, and by the finite lifetime and anisotropic emission of quasars. | ~\par The \lya forest absorption measured in spectra of high-redshift quasars has now been established as a powerful tracer of large-scale structure. Assuming that the intrinsic continuum spectrum of the observed quasar can be accurately modelled, then the observed flux divided by the fitted continuum yields the transmitted fraction, $F=e^{-\tau}$ (where $\tau$ is the optical depth), at every wavelength pixel. This one-dimensional map that is obtained from the spectrum of every observed source is related (neglecting the contamination by metal lines) to the gas density, temperature and peculiar velocity of the hydrogen gas in the intergalactic medium that is intercepted by the line of sight. ~\par After the initial measurements of the \lya power spectrum along the line of sight from individual spectra \citep{Croft1998,Croft1999,McDonald2000,Croft2002,McDonald2006}, the first determination of the power spectrum of the \lya forest in three-dimensional redshift space came with the BOSS survey of SDSS-III \citep{Eisenstein2011,Dawson2013}. Analysis of the first 14000 quasars led to the detection of redshift space distortions \citep{Slosar2011}, as expected in a simple biased linear theory where the \lya power spectrum follows that of the dark matter with two bias parameters, reflecting the large-scale variation of the mean \lya transmission with the fluctuation in the mean mass density and peculiar velocity gradient. ~\par However, large-scale fluctuations in the \lya forest can also be affected by variations in the intensity of the ionising background radiation, as well as the imprint that reionisation may have left on the gas temperature distribution as a function of gas density. These effects have been studied and discussed by several authors in the past. Analytic models of randomly distributed sources were considered by \cite{Zuo1992}, and numerical realizations of random sources to compute the fluctuation properties of the ionising background were used in several subsequent papers \citep{Croft1999,Croft2004,Meiksin2004,McDonald2005,Ho09,White2010}. The impact of these ionising background fluctuations on the \lya forest were found to be generally small compared to the intrinsic \lya forest fluctuations due to the large-scale structure of the mass distribution. However, as pointed out in the early work of \cite{Croft1999}, the long mean free path of ionising radiation in the intergalactic medium at $z \sim 3$ implies that the fluctuations induced by the ionising background can become relatively more important in the limit of very large scales. These large scales are now becoming highly relevant with the recent detections of the BAO peak in the \lya forest \citep{Busca2013,Slosar2013,Font14,Delubac2014}. ~\par In this paper we reanalyse with an analytic method the impact of large-scale fluctuations in the ionising radiation intensity and the gas temperature-density relation on the observable redshift space \lya power spectrum. There are two independent effects on the power spectrum. The first arises from the clustering of sources and absorbers of radiation, which are assumed to trace the large-scale mass density fluctuations, each with their own bias factor. This clustering term is independent of the luminosity function, variability and anisotropic emission of the sources, as well as the size or other geometric properties of the absorbers: it depends only on how the density of sources and absorbers follow the underlying large-scale structure. The second effect is due to the fluctuations in the radiation intensity that arises from shot noise in the number of sources. This second term is independent of the source clustering, but depends on other source characteristics like the luminosity function. An analytical framework to treat these contributions to the \lya power spectrum is described in section 2, and results for simple illustrating models are presented in section 3, with a discussion and conclusions in section 4. We use a Cold Dark matter cosmological model with parameter values that are consistent with the \cite{Planck}: $H_0=67.3$ $\kms\mpc^{-1}$, baryon density $\Omega_{b}h^2=0.02205$, $\Omega_m=0.315$, $n_s=0.96$ and $\sigma_8=0.856$. ~\par As this paper was being finalized, we became aware of the work by Pontzen (2014), presenting very similar ideas as here. We mention in section 4 the similarities and differences between the two papers. | ~\par The first observational determination of the large-scale \lya power spectrum in redshift space by \cite{Slosar2011} showed a remarkably good agreement with the simple linear theory of redshift space distortions with the Cold Dark Matter power spectrum. The same conclusion was reached from measurements of the cross-correlations with damped \lya systems and quasars \citep{Font12,Font13}. However, the ionising intensity fluctuations should have an impact on these correlations. We have presented an analytical framework in this paper to model these effects in the \lya autocorrelation, which can also be easily generalised to the cross-correlation with quasars or other objects, assuming they contribute as sources of the ionising background. Our conclusion from the results obtained in a few illustrating cases is that both the clustering term that measures how sources and absorbers of the ionising background trace the mass density fluctuations, and the shot noise term that depends on the luminosity function and other properties of the sources, have an important and measurable effect on the monopole and quadrupole of the \lya autocorrelation. A substantial broadband term is added as a contamination to this autocorrelation, which is being marginalised over in present studies that are focused on inferring the scale of the Baryon Acoustic Oscillation peak \citep{Busca2013,Slosar2013}. As the modeling of the spectral calibration and quasar continua and the accuracy of the \lya correlation measurements in BOSS and upcoming surveys improve in the future, we can look forward to a detection of the broadband terms induced by radiation fluctuations discussed in this paper. ~\par There are several parameters that are important in determining how the \lya correlation is modified by intensity fluctuations. These are the quantities appearing in equation (\ref{eq:bias}) for the effective \lya bias factor, and the mean free path of ionising photons. The additional shot noise term is also dependent on many characteristics of the sources: the luminosity function, luminosity history and emission anisotropy. Disentangling all these effects from a detailed measurement and model fit to the redshift-space autocorrelations and cross-correlations will probably be a difficult challenge. However, if the emission properties and typical luminosity histories of quasars can be well understood from an accurate determination of the quasar-\lya cross-correlation, it should be possible to model the shot-noise contribution to the autocorrelation and to infer from the observations some constraints on the biasing terms that affect the source clustering term. It is also worth noting that in the \lya power spectrum, the term proportional to $\mu_k^4$ is affected by neither the source clustering nor shot noise effects, and the other two terms proportional to $\mu_k^2$ and independent of $\mu_k$ can in principle be used to separate the influence of the source clustering and shot noise effects (the term proportional to $\mu_k^2$ is not affected by shot noise for constant and isotropic sources, but would acquire a contribution for anisotropic and variable sources). The three-dimensional \lya power spectrum therefore provides a way of separating the radiation influences by separating the multipole terms, which are predicted to have the specific features near the scale of the mean free path shown in Figure \ref{pfig} can then be compared to constraints obtained from cross-correlations. ~\par The conclusions of our work are in agreement with those of Pontzen (2014), who has presented very similar ideas with a somewhat different mathematical treatment. There are a few differences in the way that absorbers are treated, and our incorporation of the redshift distortion effects allows us to predict the different behavior of the monopole and quadrupole terms in the \lya power spectrum, but the basic conclusions of the two papers are similar. ~\par While the radiation intensity fluctuations make the large-scale \lya forest correlations substantially more difficult to interpret as a tracer of the primordial fluctuations in the universe, these complications practically do not affect the measurement of the Baryon Acoustic Oscillation scale, and they should constitute a new motivation for studying the evolution of the source and absorber population of the ionising background. | 14 | 4 | 1404.7425 |
1404 | 1404.4677.txt | Data for a number of OH maser lines have been collected from surveys. The positions are compared to recent mid-infrared (MIR) surveys such as \emph{Spitzer}-GLIMPSE and \emph{WISE}, restricting the comparison to point sources. The colors and intensities of the IR sources are compared. There are many 18 cm OH masers, but far fewer in lines arising from higher energy levels. We also make a comparison with the 5 cm Class II methanol masers. We have divided the results into 3 subsamples: those associated with OH masers only, those associated with OH masers and Class II methanol masers, and those only associated with Class II methanol masers. There are no obvious differences in the color-color or color-magnitude results for the GLIMPSE point sources. However, according to the results from the \emph{WISE} 22 $\mu{}m$ survey, the sources associated with OH masers are brighter than those associated with methanol masers. We interpret the presence of OH and methanol masers mark the locations of regions where stars are forming. The OH masers are located on the borders of sharp features found in the IR. These are referred to as ¡°bubbles¡±. If the OH masers mark the positions of protostars, the result provides indirect evidence for triggered star formation caused by the expansion of the bubbles. | Interstellar Hydroxyl (OH) masers are an important tool for probing the environment of massive star-forming regions (SFRs). The maser phase is contemporaneous with the evolution of an ultra-compact (UC) H{\sc ii} region around the star (\cite{Re2002}), but dies out rapidly when the H{\sc ii} region has enlarged to a size greater than 30 milliparsec (mpc) (\cite{Ca2001}). Thus the masers offer a means to discover the star at its early stage when it is hidden from the dust in the surrounding molecular clouds. Some recent interferometric observations, e.g. \cite{Mie2005}, \cite{Fie2007}, \cite{HC2007}, \cite{Bae2008}, and \cite{Sle2010}, provide high spectral resolutions and high positional accuracies, which are used to study the origins of the maser flares, maser velocity structures, and measure the magnetic strength in the SFRs. These studies shed new light on small-scale maser process and help us to understand the physical environment of the SFRs. OH maser emission from the ground-state transitions ($^{2}\Pi_{3/2}$, $J = 3/2$ state) was firstly found toward several galactic H{\sc ii} regions (e.g. W3(OH)) by \cite{Wee1965} and \cite{Gu1965}. The 1665/1667 MHz ground-state transitions in SFRs are usually the strongest OH masers. They are generally accompanied by the weaker OH masers of other transitions, e.g. at excited transitions of $^{2}\Pi_{1/2}$, $J = 1/2$ and $^{2}\Pi_{3/2}$, $J = 5/2$. The excited state of OH ($^{2}\Pi_{1/2}$, $J = 1/2$ state) at 4765 MHz was firstly detected in the source W3(OH) and W49N (\cite{Zue1968}). The first detection of the excited state of OH ($^{2}\Pi_{3/2}$, $J = 5/2$ state) at 5 cm wavelength (6035 MHz) was made by \cite{Yee1969} toward W3. The highly excited state of OH ($^{2}\Pi_{3/2}$, $J = 7/2$ state) at 13441.417 MHz ($F = 4-4$) was discovered by \cite{Tue1970} in the W3(OH). The line radiation of excited OH (e.g. $^{2}\Pi_{1/2}$, $J = 1/2$ state; $^{2}\Pi_{3/2}$, $J = 5/2$ state; $^{2}\Pi_{3/2}$, $J = 7/2$ state) is particularly helpful in complementing the ground-state observations to understand the maser pumping process and interpret the physical conditions that are implied by the presence of the masers (\cite{Ca2001}). Extensive OH maser searches have been carried out toward color-selected infrared (IR) sources, or known SFRs associated with CH$_{3}$OH masers (e.g. Cohen et al. 1991; Cohen et al. 1995; Edris et al. 2007). These observations resulted in detections of hundreds of interstellar OH masers and supply an important tool for studies of maser pumping and physical conditions of their host SFRs (e.g. Szymczak et al. 2000; Szymczak \& G\'{e}rard 2004). However, until now there are no complete catalogues of all detected interstellar OH masers at each of the detected transitions. \cite{Mue2010} collected 3249 OH maser sources at 18 cm wavelength from the literature published up to April 2007, but the majority of the sources are stellar OH masers. Therefore, we performed an extensive literature search and compiled a complete catalogue of the detected interstellar OH masers so far. The evolutionary phase that the interstellar OH masers trace the evolutionary sequence for different species of masers is still unclear now. \cite{El2006} examined the mid-infrared (MIR) properties of methanol masers with or without associated OH masers using the \emph{Spitzer} Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE) point source data. He proposed that OH masers may be generally associated with a later evolutionary phase or the stellar mass range associated with OH masers extends to higher masses than for methanol masers. However, because of the small numbers in each sample in \cite{El2006}, more data and investigations are needed to give firm conclusions. From this consideration, we make use of the GLIMPSE point source data to extensively study the MIR environment of the interstellar OH masers from larger size samples of OH and methanol masers. GLIMPSE is a legacy science program of the \emph{Spitzer} Space Telescope which covered the inner Galactic plane ($|l| \leq 65 ^{\circ}$) at 3.6, 4.5, 5.8, 8.0 $\mu{}m$ MIR wavelength bands with 1.4\arcsec-1.9\arcsec\ resolutions, with the Infrared Array Camera (IRAC; \cite{Bee2003}). As such, it offers us the best opportunity to study the MIR environment of interstellar OH masers and compare them with other sources. In addition, we also investigate the MIR environment of interstellar OH masers with the data from Wide-field Infrared Survey Explorer (\emph{WISE}) survey which mapped the full sky at 3.4, 4.6, 12 and 22 $\mu{}m$ with an angular resolution of 6.1\arcsec, 6.4\arcsec, 6.5\arcsec, 12\arcsec\ in the four bands, respectively (\cite{Wre2010}). \emph{WISE} can provide more information about the MIR environment of interstellar OH masers at longer MIR wavelengths which are complementary and important for our study. The \emph{Spitzer}-GLIMPSE images at 8.0 $\mu{}m$ revealed ``a bubbling Galactic disk" (\cite{Che2006}; \cite{Che2007}). MIR bubbles are important and widespread morphological features in the interstellar medium (ISM). Bubbles could trigger the massive-star formation. During the expansion of the bubbles, neutral material accumulates on the border of bubbles, and becomes very massive with time. A new generation of stars may form in the collected layer (\cite{Dee2010}). In this case, OH masers are possibly associated with bubbles and might be found on the boarders of bubbles. Therefore, we investigate the relationship between OH masers and bubbles. This paper is organised as follows. In Section 2, we introduce the data description. In Section 3, we describe the catalogues and present the relationship of flux densities between 18 cm OH masers and 5 cm OH masers. In Section 4, we discuss the IR environment of the interstellar OH masers, followed by a summary in Section 5. | \subsection{GLIMPSE color} We have plotted color-color and color-magnitude diagrams for the GLIMPSE point sources associated with the interstellar OH masers which have better position accuracies with ATCA or VLA observations. For comparison, we choose the GLIMPSE sources within 30\arcmin\ radius of $l=320.0^{\circ}$, $b=0.0^{\circ}$. The comparison sample from the GLIMPSE point source catalogue includes 101,615 sources and provides enough information to investigate the color and magnitude difference between maser-associated GLIMPSE sources and normal GLIMPSE sources. The interstellar OH masers are from C98 with ATCA observations and A2000 with VLA observations. The former sample includes 206 interstellar OH masers and the latter sample contains 91 interstellar OH masers. Then we associate the positions of these two samples taking 2\arcsec\ as the separation criterion and obtain 266 interstellar OH masers. The positional accuracy of these 266 interstellar OH masers is about 0.4\arcsec. Among these 266 interstellar OH masers, 219 OH masers are in the GLIMPSE survey region ($|l| \leq 65 ^{\circ}$), and 113 OH masers are associated with GLIMPSE point sources within a 2\arcsec radius. The maser-associated GLIMPSE sources are obviously offset from the majority of the comparison sources in the color-color and color-magnitude diagrams and have much redder colors. The conclusion can be easily drawn from Fig. \ref{fig:fig2}, which is a plot of the [5.8]-[8.0] versus [3.6]-[4.5] colors, showing that the maser-associated sources mostly lie above the vast majority of the comparison sources. This result is similar to the color-color diagram of methanol masers (see Figure 15 of Ellingsen 2006). % fig2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} %\begin{center} \includegraphics[height=0.38\textwidth,width=0.48\textwidth, angle=0]{34_45-vs-58_80-OH-all-compare.ps} %\end{center} \caption{\sffamily Color-color diagram constructed from GLIMPSE point source catalogue. The OH masers with GLIMPSE counterparts are represented with solid circles. Sources within 30\arcmin\ radius of $l=320.0^{\circ}, b=0.0^{\circ}$ are represented with dots. Only sources for which there is flux density information for all four IRAC bands have been included in the plot, that is, 54 of 113 OH masers with a GLIMPSE point source within 2\arcsec\, and 20018 of 101615 of the comparison sample. \label{fig:fig2}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The sources associated with interstellar OH masers lie in a distinctive region of GLIMPSE color-color diagrams and occupy the same area as methanol masers. This result is interesting, but what can we derive from it? As discussed by \cite{El2006}, polycyclic aromatic hydrocarbon (PAH) emission and silicate absorption lines can complicate the problem and affect some of IRAC bands (see \cite{Dr2003} for a detailed discussion). But the actual influence of PAH emission and silicate absorption on the observed IRAC colors needs to be confirmed and measured by MIR spectroscopy. For this reason the interpretation of GLIMPSE colors of maser-associated sources is uncertain to a large degree. Nevertheless, it is still meaningful to make the comparison between the GLIMPSE point sources with and without OH masers, because they all suffer the same effects and limitations with the same instrument. % fig3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} %\begin{center} \includegraphics[height=0.38\textwidth,width=0.48\textwidth, angle=0]{36_80-vs-36_58-color.ps} %\end{center} \caption{\sffamily GLIMPSE [3.6]-[8.0] vs. [3.6]-[5.8] color-color diagram. The OH masers with associated GLIMPSE point sources are represented with solid circles if they don't have associated methanol multibeam (MMB) masers, as solid triangles if they have. The solid squares represent the methanol masers with associated GLIMPSE point sources but without associated OH masers, and these methanol masers are from Ellingsen (2006). Sources within 30\arcmin\ radius of $l=320.0^{\circ}, b=0.0^{\circ}$ are represented with dots. \label{fig:fig3}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % fig4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} %\begin{center} \includegraphics[height=0.38\textwidth,width=0.48\textwidth, angle=0]{36_45-vs-80mag-color.ps} %\end{center} \caption{\sffamily GLIMPSE [3.6]-[4.5] vs. 8.0 $\mu{}m$ color-magnitude diagram. The OH masers with associated GLIMPSE point sources are represented with solid circles if they don't have associated methanol multibeam (MMB) masers, as solid triangles if they have. The solid squares represent the methanol masers with associated GLIMPSE point sources but without associated OH masers, and these methanol masers are from Ellingsen (2006). Sources within 30\arcmin\ radius of $l=320.0^{\circ}, b=0.0^{\circ}$ are represented with dots. \label{fig:fig4}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The modeling of \cite{Whe2003} shows that Class 0 objects lie in the same area in the GLIMPSE [5.8]-[8.0] versus [3.6]-[4.5] color-color diagram as the interstellar OH masers and the methanol masers. It is interesting to see whether or not OH masers trace the same evolutionary stage as methanol masers. The methanol multibeam (MMB) survey is a blind survey with longitudes from $186^{\circ}$ to $20^{\circ}$ and includes 707 6.7 GHz Class II methanol masers in total (\cite{Cae2010}; \cite{Gre2010}; \cite{Cae2011}; \cite{Gre2012}). We cross-match the positions of 707 MMB masers and 113 interstellar OH masers which are associated with GLIMPSE point sources within 2\arcsec. Finally we obtain 79 OH masers which are also associated with methanol masers and 25 OH masers which are not associated with methanol masers (solitary OH masers for short). Besides we collect 35 methanol masers without an associated OH maser (solitary methanol masers for short) from Table 1 of Ellingsen's (2006) paper. The sample of his paper is a statistically complete sample detected in the Mt.Pleasant survey (\cite{Ele1996}) and includes 56 methanol masers. Among the 35 solitary methanol masers, only 17 methanol masers have GLIMPSE counterparts. We construct color-color and color-magnitude diagrams for these three samples. Fig. \ref{fig:fig3} plots a [3.6]-[8.0] versus [3.6]-[5.8] color-color diagram, using different symbols for the three samples of maser-associated GLIMPSE sources. The comparison sources are also shown with dots. Fig. \ref{fig:fig3} shows that the colors of the solitary methanol masers tend to be little bluer than that of the solitary OH masers, but not obviously, and the OH masers with an associated methanol maser lie between them. Fig. \ref{fig:fig4} shows the [3.6]-[4.5] color and 8.0 $\mu{}m$ magnitude diagram. There is no obvious difference among the solitary methanol masers, the OH masers with an associated methanol maser and the solitary OH masers. This result suggests that these two masers are possibly tracing closely evolutionary stage and cannot be clearly distinguished from the GLIMPSE color-color and color-magnitude diagrams, which is different from Figure 19 of \cite{El2006} which shows that methanol masers with associated OH masers are generally brighter at 8.0 $\mu{}m$ than those without. Perhaps the data is not large enough to reveal the color and magnitude difference between the two species of masers. Thus it is still necessary and interesting to compare the MIR properties of the GLIMPSE sources associated with OH masers and methanol masers in a larger and more complete sample in order to investigate maser evolutionary sequence. \subsection{\emph{WISE} colors} Since \emph{WISE} has lower angular resolution than GLIMPSE, we take 6\arcsec\ as the criterion to search for the \emph{WISE} counterparts for 266 interstellar OH masers. Among 266 OH masers, 205 OH masers have \emph{WISE} counterparts. After cross-matching them with 707 MMB masers, we obtain 32 OH masers without an associated methanol maser (solitary OH masers), which also lie in the MMB survey region. We get 139 OH masers which have associated methanol masers. We also search for the \emph{WISE} counterparts for the 35 methanol masers without an associated OH maser (solitary methanol masers) from Table 1 of Ellingsen's paper (2006), and we find 23 \emph{WISE} counterparts within 6\arcsec. For comparison, we select the \emph{WISE} sources within 20\arcmin\ radius of $l=300^{\circ}$, $b=0^{\circ}$. The comparison sample includes 7729 sources and has enough color and magnitude information for detailed MIR environment study. Then we construct the color-color and color-magnitude diagrams for these four samples including comparison sample to investigate the MIR environment of masers. The maser-associated \emph{WISE} sources are clearly offset from the vast majority of the comparison sources in most of the color-color and color-magnitude diagrams, and their colors are much redder. These features are the same as their GLIMPSE features. This can be clearly seen in Fig. \ref{fig:fig5}, which plots the [12] - [22] versus [3.4] - [4.6] color-color diagram, showing the deviation between the maser-associated \emph{WISE} sources and the comparison sources. % fig5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} %\begin{center} \includegraphics[height=0.38\textwidth,width=0.48\textwidth, angle=0]{34_46-vs-12-22-all-OH.ps} %\end{center} \caption{\sffamily Color-color diagram constructed from \emph{WISE} point source catalogue. The OH masers with \emph{WISE} counterparts are represented with solid circles. Sources within 20\arcmin\ radius of $l=300^{\circ}, b=0^{\circ}$ are represented with dots. Only sources for which there is flux density information for all four bands have been included in the plot, that is, 181 of 205 OH masers with a \emph{WISE} point source within 6\arcsec\, and 7728 of 7729 of the comparison sample. \label{fig:fig5}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % fig6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} %\begin{center} \includegraphics[height=0.38\textwidth,width=0.48\textwidth, angle=0]{34_46-vs-22mag-color.ps} %\end{center} \caption{\sffamily \emph{WISE} [3.4]-[4.6] vs. 22 $\mu{}m$ color-magnitude diagram. The OH masers with associated \emph{WISE} point sources are represented with solid circles if they do not have associated methanol multibeam (MMB) masers. And the methanol masers with associated \emph{WISE} point sources are represented with solid squares if they don't have associated OH masers. \emph{WISE} point sources within 20\arcmin\ radius of $l=300^{\circ}, b=0^{\circ}$ are represented with dots. \label{fig:fig6}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % fig7 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} %\begin{center} \includegraphics[height=0.38\textwidth,width=0.48\textwidth, angle=0]{hist-22mag.ps} %\end{center} \caption{\sffamily The distribution of 22 $\mu{}m$ magnitude. The dashed curve shows the distribution of the methanol masers without associated OH masers, and the solid curve is that of the OH masers without associated methanol masers. \label{fig:fig7}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % fig8 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} %\begin{center} \includegraphics[height=0.38\textwidth,width=0.48\textwidth, angle=0]{34_46-vs-22mag-all-OH.ps} %\end{center} \caption{\sffamily \emph{WISE} [3.4]-[4.6] vs. 22 $\mu{}m$ color-magnitude diagram for the OH masers same as Fig. \ref{fig:fig5}. The OH masers with \emph{WISE} counterparts are represented with solid circles. Sources within 20\arcmin\ radius of $l=300^{\circ}, b=0^{\circ}$ are represented with dots. \label{fig:fig8}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % fig9 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} %\begin{center} \includegraphics[height=0.38\textwidth,width=0.48\textwidth, angle=0]{plot_01.ps} %\end{center} \caption{\sffamily \emph{WISE} [3.4]-[4.6] color vs. Detection Rate/Efficiency diagram (22 $\mu{}m$ magnitude $<3$). The Detection Rate is represented with the solid line. And the Efficiency is represented with the dashed line. \label{fig:fig9}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fig. \ref{fig:fig6} plots the color-magnitude diagram of [3.4] - [4.6] color versus 22 $\mu{}m$ magnitude, which shows that the solitary OH masers have a brighter MIR source counterpart at 22 $\mu{}m$, compared to the solitary methanol masers. We also plot the histograms of the four bands for the \emph{WISE} sources associated with solitary OH masers and solitary methanol masers. We find that at 4.6, 12, 22 $\mu{}m$, there is a trend that the \emph{WISE} sources associated with solitary OH masers are brighter than the \emph{WISE} sources associated with solitary methanol masers, and it is most obvious at 22 $\mu{}m$ band (shown in Fig. \ref{fig:fig7}). This result may have a bias because the 22 $\mu{}m$ magnitude depends on the distance. However, the \emph{WISE} sources associated with these two kinds of masers all suffer from the same effect, and the obvious tendency could still illustrate some problems. The 22 $\mu{}m$ band should trace the same dust emission components as the 24 $\mu{}m$ band, which likely comes from very small grains (VSGs) out of thermal equilibrium, or a combination of emission from VSGs and from a larger grain population whose temperature is closer to 25 K (\cite{Ane2012}). The OH masers with the brighter 22 $\mu{}m$ emission may trace a later evolutionary stage of the central star than the methanol masers because of the higher dust temperature. \cite{Cre2002} found that the gas-phase molecular abundance is the key determinant of maser activity for both CH$_{3}$OH and OH masers. A large CH$_{3}$OH column density can be easily reached in SFRs due to a high abundance of methanol ice on grain mantles (\cite{Dae1999}). OH abundance can be enhanced by the photodissociation or ion-molecule process after the H$_{2}$O molecules are injected into the gas phase. Charnley et al. (1992, 1995) predicted that a maximum of methanol abundance appears before a peak of OH abundance. If these models are confirmed by further chemical modeling, this would support the proposed evolutionary sequence mentioned above. Alternatively, the stellar mass range associated with OH masers may extend to higher masses than that for methanol masers as revealed by \cite{El2006}. The distinctive color-color and color-magnitude properties of the \emph{WISE} sources associated with OH masers provide an opportunity to create a \emph{WISE}-selected target sample for future OH maser searches. Fig. \ref{fig:fig8} is the [3.4]-[4.6] vs. 22 $\mu{}m$ color-magnitude diagram, showing that the majority ($\sim$80\%) of the \emph{WISE} sources associated with known OH masers locate in a domain of $[3.4]-[4.6]>2$ and 22 $\mu{}m$ magnitude $<3$, while nearly null sources in the comparison field locate in this domain. On the other hand, it is possible to estimate the detection rate and efficiency of an OH maser search targeted toward \emph{WISE} point sources by comparing with one blind or untargeted OH maser survey. One untargeted survey with the Parkes by Caswell et al. (1980) had detected 19 interstellar OH masers in the region of $l=330^{\circ}-340^{\circ}$, $b=-0.3^{\circ}$ to $0.3^{\circ}$ at a sensitivity of $\sim$0.1 Jy. For a search with a single dish, any targets that lie within half the FWHM beam could be searched only once in a single pointing. Considering the spatial coverage of the Parkes beam ( $\sim$10 \arcmin\ at 1.66 GHz), the actual targeted \emph{WISE} sources could be deduced. Based on these, we plot the dependence of the detection rate and efficiency with the [3.4]-[4.6] color (under 22 $\mu{}m$ magnitude $<3$) in Figure 9, using the \emph{WISE} sources and the OH maser data in the Caswell et al. (1980) surveyed region. From this figure, for the \emph{WISE} sources satisfying the criteria of $[3.4]-[4.6]>2$ and 22 $\mu{}m$ magnitude $<3$, 84\% (16/19) of known OH masers in the blind survey would be expected to detect, this detection rate/percent is consistent with that (80\%) shown in Fig. \ref{fig:fig8} for all known OH masers. Therefore, this also suggests that it is more reasonable to estimate a detection efficiency of OH maser searches using the criteria of $[3.4]-[4.6]>2$ and 22 $\mu{}m$ magnitude $<3$, under which a detection efficiency of $\sim$10\% would be achieved. We searched for the \emph{WISE} All-sky Data Release and found about 7559 point sources satisfying the criteria. These \emph{WISE} sources would provide a potential target sample for the further OH maser searches, especially with the newly-built 65 meter radio telescope in Shanghai. It should be noted that this new telescope has a similar beamsize to the Parkes dish. As a simple estimation, considering the beam coverage of the Shanghai 65 meter or Parkes telescope, the target pointing positions are reduced to 5209 towards these \emph{WISE}-selected sources, thus $\sim$500 ground-state interstellar OH masers would be expected to detect. The expected total number of ground-state interstellar OH masers would be $\sim$600 in our Galaxy after considering that 84\% of all OH masers would be detected from the above statistics. \subsection{Bubble-Like structures} \begin{table*} \leftline{\textbf{Table 6. }Maser-associated bubbles.} \label{tab:tab6} \vspace{8pt} % \begin{center} % \begin{minipage}{105mm} \begin{tabular}{lrrcccccll} \hline \hline \scriptsize Catalogue No. & $l$ & $b$ & $R_{out}$ & Eccentricity & $\langle{R}\rangle$ & $\langle{T}\rangle$ & Morphology Flags & Name (OH) &Name (CH3OH)\\ & (deg) & (deg) & (arcmin) & & (arcmin) & (arcmin) & && \\ \hline N2 & 10.747 & -0.468 & 8.31 & 0.56 & 6.95 & 1.23 & B & G10.623-0.383 & \\ N65 & 35.000 & 0.332 & 2.59 & 0.49 & 2.15 & 0.54 & C & G35.024+0.350 & \\ N68 & 35.654 & -0.062 & 6.06 & 0.72 & 4.68 & 0.74 & C,CC & G35.577-0.029 & \\ S36 & 337.971 & -0.474 & 3.56 & 0.66 & 2.73 & 0.69 & C & G337.916-0.477 & \\ S62 & 331.316 & -0.359 & 2.50 & 0.58 & 2.02 & 0.45 & B & G331.342-0.346 & G331.342-0.346 \\ S66 & 330.781 & -0.414 & 7.42 & 0.69 & 5.63 & 1.37 & B,CC,MB & G330.878-0.367 & \\ & & & & & & & & G330.878-0.367 & \\ S110 & 316.809 & -0.031 & 1.82 & 0.63 & 1.42 & 0.36 & C,TP & G316.811-0.057 & G316.811-0.057 \\ S122 & 313.418 & 0.128 & 8.69 & 0.78 & 6.22 & 1.31 & C & G313.469+0.190 & G313.469+0.190 \\ S169 & 301.122 & -0.152 & 4.06 & 0.34 & 3.40 & 1.07 & B & G301.136-0.226 & G301.136-0.226 \\ CN15 & 0.562 & -0.843 & 1.03 & 0.73 & 0.71 & 0.27 & B, BC & G0.546-0.852 & \\ CN71 & 5.894 & -0.463 & 6.17 & 0.38 & 5.45 & 0.96 & B, FL, Y & G5.886-0.393 & \\ & & & & & & & & G5.885-0.392 & \\ CN135 & 9.612 & 0.196 & 0.48 & 0.69 & 0.34 & 0.13 & C, BC & G9.619+0.193 & G09.619+0.193 \\ & & & & & & & & G9.620+0.194 & \\ & & & & & & & & G9.621+0.196 & G09.621+0.196 \\ CS1 & 359.965 & -0.502 & 2.74 & 0.67 & 2.15 & 0.42 & B, Y & G359.970-0.457 & G359.970-0.457 \\ CS43 & 354.715 & 0.297 & 0.51 & 0.70 & 0.38 & 0.11 & C, Y & G354.724+0.300 & G354.724+0.300 \\ CS46 & 354.619 & 0.492 & 1.25 & 0.50 & 1.04 & 0.24 & C, BC, Y & G354.615+0.472 & G354.615+0.472 \\ CS55 & 353.417 & -0.375 & 1.34 & 0.91 & 0.78 & 0.15 & B & G353.410-0.360 & G353.410-0.360 \\ CS73 & 352.174 & 0.297 & 6.80 & 0.62 & 5.52 & 1.02 & B & G352.161+0.200 & \\ CS106 & 350.327 & 0.096 & 1.02 & 0.75 & 0.74 & 0.18 & B, CS & G350.329+0.100 & \\ \hline \end{tabular} % \end{minipage} %\end{center} \end{table*} % fig10 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} %\begin{center} \includegraphics*[height=0.5\textwidth,viewport=320 20 900 650]{CN135new.eps} %\end{center} \caption{\sffamily The three-color (4.5 $\mu{}m$: blue; 5.8 $\mu{}m$: green; 8.0 $\mu{}m$: red) image of the bubble CN135 from CH07 catalogue, with three OH masers (plus) located on the border of the bubble and two methanol masers (cross) sharing the same sites with their associated OH masers. \label{fig:fig10}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % fig11 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} \begin{center} \includegraphics*[height=0.5\textwidth,viewport=300 20 900 650]{N65new.eps} \end{center} \caption{\sffamily Same as Fig. \ref{fig:fig10}, but for the bubble N65 from CH06 catalogue. Notably only one OH maser (plus) is located on the border of the bubble. \label{fig:fig11}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The \emph{Spitzer}-GLIMPSE images revealed a large number of full or partial ring-like structures, which were referred to as bubbles (\cite{Che2006}; \cite{Che2007}). Bubbles are a common phenomenon in the ISM. Most of them may be produced by newly formed massive stars and clusters, which excite PAHs in the swept up shell, and the PAHs are strong emitters at 8 $\mu{}m$ in the photo-dissociation regions (PDRs) surrounding the H{\sc ii} region (\cite{Dee2010}). Churchwell et al. (2006, 2007) (hereafter CH06, CH07) have catalogued about 600 ring structures traced mainly by 8.0 $\mu{}m$ emission between Galactic longitudes $-65^{\circ}$ to $65^{\circ}$ by inspecting the GLIMPSE I/II mosaic visually. Deharveng et al. (2010) studied a gallery of bubbles mainly from Churchwell et al. (2006), finding that 86\% of their bubbles enclose H{\sc ii} regions. Good correlation of MIR bubbles with known H{\sc ii} regions or radio-continuum emission at 20 cm, and relatively low contamination from asymptotic giant brunch (AGB) star bubbles, supernova remnants (SNRs) and planetary nebulae (PNe) reported in the literature, indicates that bubbles are a good tracer of star formation activity (\cite{Che2006}; \cite{Dee2010}). Deharveng et al. (2010) also concluded that more than a quarter of the bubbles may have triggered the formation of massive objects. The majority studies into triggered star formation by the expansion of bubbles take advantage of multiwavelength data sets (typically with near-, mid-, far-infrared, millimeter and radio wavelengths) to estimate the mass, age, and luminosity of triggering and triggered sources, and compare the kinematic properties of the young stars with the surrounding ISM. The evidence of triggered star formation has thus been reported in several known H{\sc ii} regions and bubbles, e.g. Sh2-212 (\cite{Dee2008}), W51a (\cite{Kae2009}), RCW120 (\cite{Zae2010}), S51 (\cite{Zhe2012}), N4 (\cite{Lie2013}), and G52L (\cite{Gue2013}). Although these studies provide reasonable evidence of triggered star formation, they always conclude with uncertainties and open questions such as the uncertainties of the association between YSOs and the collected material (\cite{Kae2009}) and the age uncertainties of stars in the condensation regions (\cite{Zae2010}). \cite{Kee2012} took a statistical approach to investigate the association of bubbles with massive star formation and found a strong positional correlation of massive young stellar objects (MYSOs) and bubbles. However, it is yet not clear whether the expansion of bubbles could cause the following generation of stars. Interstellar OH masers trace the massive star formation, thus, the association study between interstellar OH masers and bubbles may obtain the indirect evidence supporting the triggered star formation by the expansion of bubbles. We use the catalogue made by Churchwell et al. (2006, 2007) which contains 591 bubbles to study the association between bubbles and 219 interstellar OH masers mentioned above. Churchwell et al. (2006, 2007) measured the bubbles' parameters such as their semimajor ($R_{out}$) and semiminor ($r_{out}$) axes of the outer ellipse. We use $1.2R_{out}$ as the criterion to cross-match the OH maser positions and the bubble center positions. The criteria is larger than $R_{out}$ because the definition of $R_{out}$ is subjective. We find that 18 bubbles are associated with 22 OH masers. Among them, one bubble (CN135) is associated with three OH masers, and two bubbles (CN71, S66) are associated with two OH masers, respectively. These associations may be caused by merely geometric effects, but still need to be investigated. Here we assume all the masers are associated with bubbles. Then we cross-match these 22 OH masers with 707 MMB masers taking 2\arcsec\ criterion. The result is that ten methanol masers are associated with ten OH masers and nine bubbles. The basic information about 18 maser-associated bubbles and the names of the associated OH masers and methanol masers are also listed in Table 6. The low association between bubbles and interstellar OH masers may be due to the maser sample we used. The 219 OH masers as described above are mainly from targeted surveys. Therefore, many bubbles may not have been searched for OH masers on the boarders. In addition, the low association may suggest that the young stars on the boarders of the majority of the bubbles are at an early stage and have not developed the physical conditions suitable for the pumping of OH masers. Besides, the result may simply imply that the majority of the bubbles have not yet triggered the star formation on the borders, or the triggered star formation is inefficient on the borders of bubbles. We display the false color images of the bubbles (4.5 $\mu{}m$: blue; 5.8 $\mu{}m$: green; 8.0 $\mu{}m$: red) using the display program ds9\footnote{See http://hea-www.harvard.edu/RD/ds9/ref} and point out the positions of OH masers and methanol masers in the bubble infrared images. As examples, Fig. \ref{fig:fig10} shows the three-color image of the bubble CN135. It shows that three OH masers are located on the border of the bubble and two methanol masers share the same sites with OH masers. Fig. \ref{fig:fig11} is the three-color image of the bubble N65. It only has one OH maser on the boarder of the bubble. The remaining sixteen bubbles have the same maser distribution as CN135 or N65, and many masers are associated with bright emission at 8.0 $\mu{}m$. The 6.7 GHz Class II methanol masers and interstellar OH masers are the tracers of massive star formation. This result confirms that the massive star formation is ongoing on the border of bubbles and the bubbles may trigger the massive star formation by their outward expansion. % fig12 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure} %\begin{center} \includegraphics[height=0.3\textwidth,width=0.5\textwidth, angle=0]{hist-1.ps} %\end{center} \caption{\sffamily Observed distributions of average bubble angular diameters ($2\langle{R}\rangle$), average bubble thickness (angular measure $\langle{T}\rangle$) and bubble thickness relative to average outer radius ($\langle{T}\rangle/\langle{R_{out}}\rangle$). The dot dashed curves show the distributions of 18 maser-associated bubbles, and the solid curves are those of the 591 bubbles. The solid circles are the medians of 18 maser-associated bubbles, while the solid triangles are the medians of the 591 bubbles. \label{fig:fig12}} \end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % fig13 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\begin{figure} %\begin{center} % \includegraphics[height=0.38\textwidth,width=0.48\textwidth, angle=0]{hist-2.ps} % %\end{center} % \caption{\sffamily %Distribution of average bubble thickness (angular measure $\langle{T}\rangle$). The dashed curve shows the distribution of 18 maser-associated bubbles, and the solid curve is that of the 591 bubbles. % \label{fig:fig13}} %\end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % fig14 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\begin{figure} %\begin{center} % \includegraphics[height=0.38\textwidth,width=0.48\textwidth, angle=0]{hist-3.ps} %\end{center} % \caption{\sffamily %The distribution of bubble thickness relative to average outer radius ($\langle{T}\rangle/\langle{R_{out}}\rangle$). The dashed curve shows the distribution of 18 maser-associated bubbles, and the solid curve is that of the 591 bubbles. % \label{fig:fig14}} %\end{figure} %\efi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Beyond that, we study the properties of maser-associated bubbles. The left figure in Fig. \ref{fig:fig12} is the average angular diameter ($2\langle{R}\rangle$) distribution of 591 bubbles and 18 maser-associated bubbles. We can see from it that the average angular diameters of 18 maser-associated bubbles are slightly larger than that of 591 bubbles. The middle figure in Fig. \ref{fig:fig12} shows that there is a deviation of the average angular thickness ($\langle{T}\rangle$) between 18 maser-associated bubbles and 591 bubbles. From the right figure in Fig. \ref{fig:fig12}, we can see that the ratio of average thickness to average outer radius ($\langle{T}\rangle/\langle{R_{out}}\rangle$) is smaller than 0.3 for 18 maser-associated bubbles. The $2\langle{R}\rangle$, $\langle{T}\rangle$, and $\langle{T}\rangle/\langle{R_{out}}\rangle$ medians for 591 bubbles and 18 maser-associated bubbles are labeled in Fig. \ref{fig:fig12}. The $2\langle{R}\rangle$, and $\langle{T}\rangle$ medians of 18 maser-associated bubbles are 4.30\arcmin\ and 0.50\arcmin, which are larger than 1.82\arcmin\ and 0.25\arcmin\ for 591 bubbles; The $\langle{T}\rangle/\langle{R_{out}}\rangle$ medians for 18 maser-associated bubbles and 591 bubbles are 0.182 and 0.228, respectively. Deharveng et al. (2010) suggest that the large size of bubbles correspond to an older age or evolution in the ISM with low densities. Churchwell et al. (2006) concluded that bubble shell thickness increases approximately linearly with shell radius. The measurements of larger average bubble angular diameter ($2\langle{R}\rangle$) and smaller thickness relative to average outer radius ($\langle{T}\rangle/\langle{R_{out}}\rangle$) of 18 maser-associated bubbles may suggest that the maser-associated bubbles are generally older than normal bubbles. However, these results may be simply due to the artifacts of small number statistics and need further studies. | 14 | 4 | 1404.4677 |
1404 | 1404.5434_arXiv.txt | We present the results of a detailed investigation of the Galactic supernova remnant RCW 86 using the {\it XMM-Newton} X-ray telescope. RCW 86 is the probable remnant of SN 185 A.D, a supernova that likely exploded inside a wind-blown cavity. We use the {\it XMM-Newton} Reflection Grating Spectrometer (RGS) to derive precise temperatures and ionization ages of the plasma, which are an indication of the interaction history of the remnant with the presumed cavity. We find that the spectra are well fitted by two non-equilibrium ionization models, which enables us to constrain the properties of the ejecta and interstellar matter plasma. Furthermore, we performed a principal component analysis on EPIC MOS and pn data to find regions with particular spectral properties. We present evidence that the shocked ejecta, emitting Fe-K and Si line emission, are confined to a shell of approximately 2 pc width with an oblate spheroidal morphology. Using detailed hydrodynamical simulations, we show that general dynamical and emission properties at different portions of the remnant can be well-reproduced by a type Ia supernova that exploded in a non-spherically symmetric wind-blown cavity. We also show that this cavity can be created using general wind properties for a single degenerate system. Our data and simulations provide further evidence that RCW 86 is indeed the remnant of SN 185, and is the likely result of a type Ia explosion of single degenerate origin. | Supernovae (SNe) chemically enrich and energise the interstellar medium (ISM). Part of their explosion energy is used in the supernova remnant phase to accelerate particles and in fact, SNRs are thought to be the main contributor to Galactic cosmic rays with energies up to the knee in the cosmic ray spectrum ($\approx10^{15}$ eV). Type Ia SNe are of interest as cosmological standard candles, and have been essential for the discovery that the Universe is accelerating \citep{riessetal1998,perlmutteretal1999}. However, the progenitor systems of Type Ia supernovae are still a matter of debate \citep[e.g.][]{maozmanucci2012}. Both the topic of particle acceleration in supernova remnants (SNRs) and the nature of type Ia supernovae make the SNR RCW 86 (also known as G315.4-2.3 or MSH 14-6{\it 3}) a very interesting object. Although the name RCW 86 originally referred to the optically bright southwestern region, it is now also associated with the total remnant and we will therefore use it throughout this paper. It has been suggested that it is the remnant of an event recored by Chinese astronomers in the year 185 A.D. \citep{clarkandstephenson1975}, although this is still a matter of debate \citep[see e.g.][]{dickeletal2001, smith1997, vinketal2006}. Located at a distance of $2.5 \pm 0.5$~kpc \citep[][]{helderetal2013}\footnote{ For a long time it was unclear whether RCW 86 is located at a distance of $\sim 2.5$~kpc \citep{westerlund1969,rosadoetal1996}, or much more nearby at $\sim 1$~kpc \citep{longblair1990,bocchinoetal2000}. The recent proper motion measurements of \citet{helderetal2013}, combined with plasma temperature measurements based on the broadline H$\alpha$ emission, now clearly indicates that RCW 86 is at a distance of 2.5~kpc, or even further if the plasma temperature is quenched due to cosmic-ray acceleration. }, RCW 86 is a shell-type SNR with an angular diameter of approximately 40 armin, making it unusually large (R $\approx 15d_{2.5}$ pc) for its age, if it is indeed the remnant of SN 185. For the remnant to have reached this size in 1830 years, it must have been expanding with a mean velocity of around 7800 km~s$^{-1}$. This high velocity, but also several other characteristics, have led to the suggestion that the SNR has been expanding in a low density, wind-blown cavity \citep*[]{vinketal1997}. The measured expansion velocities of 500-900 km s$^{-1}$ in the SW and NW \citep{longblair1990,ghavamianetal2001}, and the $\approx$1200~km~s$^{-1}$ measured in the NE and SE portions of the remnant \citep{helderetal2013} suggest that different parts of the remnant are in different stages of interaction with the dense surroundings of the wind cavity. X-ray images of RCW 86 reveal a non-spherically symmetric shell with different morphologies in the soft (0.5-2 keV) and hard (2-5 keV) X-ray bands \citep*{vinketal1997}, as illustrated in Fig. \ref{fig:rgb}. \citet{rhoetal2002} found, using Chandra data, that the hard X-ray emission in the south western part of the remnant is close to an Fe-K line emitting region. They suggest that the hard X-ray continuum is synchrotron radiation coming from electrons accelerated at the reverse shock of the remnant. Besides the non-thermal emission in the SW, there is also synchrotron emission present in the NE (\citet*{bambaetal2000}, \citet{vinketal2006}) and, somewhat fainter, in the NW \citep{yamaguchietal2011, williamsetal2011, castroetal2013}. X-ray synchrotron radiation requires the presence of 10-100 TeV electrons, the presence of which has been corroborated since then by the detection of TeV gamma-ray emission from this remnant \citep{aharonianetal2009,rcw86cosmicrayconstraints}. In addition, the amplification as observed by \citet{vinketal2006} and \citet{castroetal2013} also suggests efficient particle acceleration at the shock of RCW 86. The measured shock velocities in the optical of 600--1500 km s$^{-1}$, however, are too low to explain the occurrence of X-ray synchrotron emission \citep[e.g.][]{Zirakashviliaharonian2007}. In this regard, RCW 86 differs from the other young Galactic SNRs Cas A, Kepler, Tycho and SN 1006, for which X-ray synchrotron emission is accompanied by measured shock velocities in the range of 3000--5400 km s$^{-1}$. \citet{helderetal2013} argued for the NE region that either the shock velocity was much higher in the recent past (and the shock slowed down on a timescale much shorter than the synchrotron cooling time of the electrons), or, as also argued by \citet{castroetal2013}, the shock velocity measured in Balmer line emitting shocks are lower than those of synchrotron emitting shocks. This is supported by the higher shock velocity measurement in X-rays for the northeastern part of the SNR ($V_s = 6000$ km s$^{-1}$ \citet{helderetal2009}). The latter possibility could arise if the cavity wall exists of clumpy material, and the H-alpha shocks arise from parts of the forward shock which are moving more slowly, in higher density regions. \citet{uenoetal2007} used the Suzaku telescope to map the Fe-K emission in the southwestern part of the remnant. They found that the distribution of the Fe-K line emission anti-correlates with the hard X-ray continuum (3.0-6.0 eV), but that in fact the Fe-K emission correlates well with the radio synchrotron emission. Since radio synchrotron emission originates from regions somewhat downstream of the forward shock, they conclude that the Fe-K emission must come from shocked ejecta. In addition, they measured an intrinsic line broadening in this ejecta component of $\approx50$ eV. \citet*{yamaguchietal2011} used additional Suzaku observations to take a more detailed look at the Fe-K emission in the whole of RCW 86. They confirmed that the line centroid suggests a low ionization state of Fe and suggest a type Ia progenitor based on the amount of Fe present in the remnant. The question of what the type of supernova is that led to the formation of RCW 86 is still open. The remnant is located in close vicinity to several B-type stars, which suggests RCW 86 is the result of a core-collapse supernova \citep{westerlund1969}. Recently, however, \citet{williamsetal2011} argued strongly that it is the remnant of a type Ia explosion, pointing to 1) the all-around presence of Balmer filaments \citep{smith1997}, 2) the high Fe mass found in the interior of the remnant, 3) the lack of a pulsar wind nebula or neutron star in the SNR, and 4) the lack of high abundance O emitting regions. They also show, using hydrodynamical simulations, that if RCW 86 is indeed the remnant of SN 185 A.D., the currently observed ambient medium densities, expansion velocities and size can only be explained if the remnant expanded in a low-density cavity. If RCW 86 is the remnant of a type Ia explosion, a cavity can be created by a high velocity accretion-wind \citep*{hachisuetal1996, badenesetal2007}, which requires a white dwarf that accretes material in a rate higher than the critical rate for stable hydrogen burning. A confirmation of the SN explosion type for RCW 86 would therefore not only be a confirmation that type Ia supernovae can arise through the single degenerate channel, but also that these progenitor systems can actively modify their environment. In this work we aim to investigate the issues outlined above using the {\it XMM-Newton} X-ray telescope. We use the high spectral resolution of the RGS instrument to investigate the interaction history of the remnant with the cavity wall, and the imaging and spectral capabilities of the EPIC CCDs to have a more detailed look at the presence of Fe-K and other ejecta emission close to the forward shock. In addition, we use the principal component analysis (PCA) technique to highlight regions of interest, which we then further investigate using the EPIC instrument. Finally, we use hydro-simulations to show that the size, the dynamics and the emission properties of RCW 86 can be well-reproduced by a single degenerate wind-blown cavity scenario. \begin{table} \caption{List of {\it XMM-Newton} observations of RCW 86.} \label{tab:po} \begin{center} \begin{tabular}{lllrr} OBSID & RA & DEC & time [s] & orbit \\ \hline 0110011301 & 220.56 & -62.37 & 19566 & 126 \\ 0110011401 & 220.51 & -62.22 & 18677 & 126 \\ 0110010701 & 220.73 & -62.63 & 23314 & 126 \\ 0110010501 & 220.14 & -62.60 & 16097 & 309 \\ 0110012501 & 220.24 & -62.72 & 12232 & 592 \\ 0208000101 & 221.26 & -62.30 & 59992 & 757 \\ 0504810101 & 221.57 & -62.30 & 116782 & 1398 \\ 0504810601 & 221.57 & -62.30 & 36347 & 1399 \\ 0504810201 & 221.40 & -62.47 & 75216 & 1406 \\ 0504810401 & 220.15 & -62.60 & 72762 & 1411 \\ 0504810301 & 220.50 & -62.22 & 72381 & 1412 \\ \hline \end{tabular} \end{center} \end{table} | We presented the most complete X-ray view of RCW 86 so far, using all {\it XMM-Newton} pointings currently available. We fitted the combined RGS and MOS spectra of four quadrants of the remnant, thus obtaining detailed plasma parameters of both the shocked ambient medium and ejecta plasma components for a large part of the remnant. The large differences in ionization ages between the shocked ejecta and shocked ISM are most naturally explained by a supernova exploding in a wind-blown cavity, where the reverse shock has been close to the forward shock for a large part of the lifetime of the remnant so that the ejecta have substantially lower ionization ages compared to the shocked ISM. From the ambient medium ionization ages, we can construct an interaction history of the forward shock with the cavity wall, for which we find that the SW has been shocked earliest, followed by the NW, SE and finally the NE. The NE part of the remnant may have just started to interact with the cavity wall, which could explain the presence of synchrotron emission at he FW shock in this region while the H$\alpha$ shock velocity is $\approx1200$ km s$^{-1}$. Using principal component analysis, we obtained the highest resolution map of the location of ejecta emission (most prominently Fe-K), thus far. The ejecta seem located in an oblate spherical shell, close to the forward shock. We obtain an Fe mass of around $1~ (f_{0.1})^{0.5}$ M$_{\odot}$, consistent with a type Ia progenitor. In addition, we used hydrodynamical simulations to show that the current size and dynamical and spectral parameters of RCW 86 can be well-reproduced by a white dwarf exploding in a wind-blown cavity, as suggested by \citet{badenesetal2007, williamsetal2011}. Our work further strengthens the notion that RCW 86 had a single degenerate progenitor system, which actively modified its environment. | 14 | 4 | 1404.5434 |
1404 | 1404.7741_arXiv.txt | { We further explore a scenario in which the recently observed 3.55 keV photon line arises from dark matter decay to an axion-like particle (ALP) of energy 3.55 keV, which then converts to a photon in astrophysical magnetic fields. This ALP scenario is well-motivated by the observed morphology of the 3.55 keV flux. For this scenario we study the expected flux from dark matter decay in the galactic halos of both the Milky Way and Andromeda (M31). The Milky Way magnetic field is asymmetric about the galactic centre, and so the resulting 3.55 keV flux morphology differs significantly from the case of direct dark matter decay to photons. However the Milky Way magnetic field is not large enough to generate an observable signal, even with ASTRO-H. In contrast, M31 has optimal conditions for $a \to \gamma$ conversion and the intrinsic signal from M31 becomes two orders of magnitude larger than for the Milky Way, comparable to that from clusters and consistent with observations. } | 14 | 4 | 1404.7741 |
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1404 | 1404.5058_arXiv.txt | We establish a new model of coupling between a cosmic dark fluid and electrodynamic systems, based on an analogy with effects of electric and magnetic striction, piezo-electricity and piezo-magnetism, pyro-electricity and pyro-magnetism, which appear in classical electrodynamics of continuous media. Extended master equations for electromagnetic and gravitational fields are derived using Lagrange formalism. A cosmological application of the model is considered, and it is shown that a striction-type interaction between the dark energy (the main constituent of the dark fluid) and electrodynamic system provides the universe history to include the so-called unlighted epochs, during which electromagnetic waves can not propagate and thus can not scan the universe interior. | Dark fluid composed of a dark energy and a dark matter is considered nowadays as a key constitutive element of modern cosmological models (see, e.g., \cite{DE1,DE2,DE3,DM1,DM2,DM3,DMDE,DEcosmo,DE2011,DEmodified,DF1,DF2,DF3,DF4,DF99}). Both the dark energy and dark matter are assumed to consist of electrically neutral particles and thus the dark fluid does not interact with an electromagnetic field {\it directly}. That is why, we would like, first of all, to explain the terminological context, which allows us to speak about electrodynamic phenomena induced by the dark fluid. Let us imagine a hierarchical cosmological system, in which the dark fluid (energetically dominating substrate with a modern contribution about $95\%$) is considered to be the guiding element, and an electrodynamic subsystem (as a part of baryonic matter with its modern contribution about $5\%$) to be the subordinate element. In this context the electrodynamic subsystem plays the role of a {\it marker}, which signalizes about the variations in the state of dark fluid, the energetic reservoir, into which this marker is immersed. We are interested to answer the question: what mechanisms might be responsible for a (possible) transmission of information about the dark fluid state to the electrodynamic system. Since electrodynamic systems form the basis for the most important channel of information about the universe structure, one could try to reconstruct features of the dark fluid evolution by tracking down specific fine details of the spectrum of observed electromagnetic waves, of their phase and group velocities. The most known {\it marker-effect} of such type is the polarization rotation of electromagnetic waves travelling through the axionic dark matter \cite{PR1,PR2,PR3,PR5}. Let us remind a few details of this phenomenon. From the physical point of view, the corresponding mechanism is connected with magneto-electric cross-effect \cite{Dell,HehlObukhov}, which is generated in the medium by the pseudoscalar field associated with dark matter axions. From the mathematical point of view, this mechanism is described by inserting a special term into the Lagrangian, $\frac14 \phi F^*_{mn}F^{mn}$, which is linear in the pseudoscalar (axion) field $\phi$ and is proportional to the pseudo-invariant of the electromagnetic field quadratic in the Maxwell tensor \cite{ax1}. The model of this axion-photon coupling was extended for the non-stationary state of the dark matter (see, e.g., \cite{BBT1,BBT2}), and for the states, for which nonminimal effects linear in the space-time curvature are significant (see, e.g., \cite{BNi}). Availability of the example of the coupling of photons with the dark matter axions encourages us to search for marker-effects related to the interaction of electrodynamic system with the dark energy, the main constituent of the dark fluid. We assume that electrodynamic systems can be influenced by the pressure of the dark energy in analogy with mechanical stresses, which are known to control the response in electric and magnetic materials in industry and technique. To be more precise, we can search for dark fluid analogies with the following classical effects. First, we mean the analogy with the classical piezo-electric effect (the appearance of an electric polarization in the medium influenced by mechanical stress and vice-versa), and with the classical piezo-magnetic effect (appearance of a magnetization under stress)(see, e.g., \cite{Nye,SSh,LL,Mauginbook}). Second, we would like to consider an analogy with the inverse electrostriction effect (a combination of external pressure and electric field generates the electric polarization in the medium), and an analogy with the inverse magnetostriction effect (a combination of external pressure and magnetic field generates the magnetization in the medium), as well as, an analogy with the magneto-electric cross-effect displayed by the external stress. Based on results of classical electrodynamics of continuous media, we can expect that piezo-effects will be visualized, when the dark fluid is anisotropic (e.g., in the early universe). The striction effects due to their symmetries are expected to be available in the isotropic universe also. In addition to piezo- and striction- effects induced by the dark fluid pressure we can expect the appearance of marker-signals similar to pyro-electric and pyro-magnetic responses of the medium, in which the temperature changes with time \cite{Nye,SSh,LL} (pyro-effect also is hidden, when the dark fluid is isotropic). One of the important characteristic of the dark fluid is its macroscopic velocity four-vector and covariant derivative of this four-vector. When we focus on the influence of the dark fluid non-uniform motion on the properties of electrodynamic system, we, in fact, search for analogs of dynamo-optical phenomena \cite{LL}; we hope to consider these phenomena in detail in the next paper. In principle, we could consider an analogy with the so-called thermo-electric and thermo-magnetic effects, induced by heat-fluxes in the medium, but this sector of physical modeling is out of scope of this paper. Also, in this paper we do not consider magneto-electric cross-effects induced by the combination of the dark energy pressure and of the axionic dark matter. Effects of this type are worthy of special consideration. We have to emphasize that mathematical theory of pyro-, piezo- and striction- effects is developed in detail for classical electrodynamics of continuous media, and below we consider a general relativistic extension of that theory for the case of dark fluid action on the electrodynamic system. In this sense, we take the mathematical scheme of the description of such interactions, which is well-tested, has clear interpretation and is based on the Lagrange formalism, and then we construct its general relativistic analog, using this scheme in the context of dark fluid electrodynamics. This paper is organized as follows. In Section II we remind the terminology and introduce the Lagrangian and master equations for the model of electromagnetically inactive dark fluid. Section III contains detailed description of the extended model: in Section III.A we extend the Lagrangian by the terms, which describe interactions of the pyro-, piezo- and striction- types between dark energy and electrodynamic system; in Section III.B we derive extended electrodynamic equations and discuss the structure of tensor coefficients describing pyro- (III.B.1), piezo- (III.B.2) and striction-(III.B.3) coefficients associated with the coupling to dark energy; in Section III.C we obtain the extended gravity field equations in general form. In Section III.D we write the equation for a axion field attributed to the dark matter. In Section IV we reduce the derived master equations to the case, when the medium is spatially isotropic: Section IV.A contains details of reduced electrodynamic equations; in Section IV.B we collect details of modified gravity field equations; in Section IV.C we consider an example of extended model with hidden magnetic and/or electric anisotropy. In Section V we consider a cosmological application of the established model to the problem of description of the so-called unlighted epochs in the universe history, and their relations to the striction-type interactions of electrodynamic systems with the cosmic dark energy. In Section VI we summarize the results. Appendix includes working formulas for the extended variation procedure. | 1. A new model of coupling between a cosmic dark fluid and electrodynamic systems is established, i.e., the extended Lagrangian is introduced and the extended master equations are derived for electromagnetic and gravitational fields. What is the novelty of this model from the mathematical point of view? First, we introduced four cross-terms into the Lagrangian, which contain the Maxwell tensor up to the second order, on the one hand, and contain the pressure tensor of the dark energy and the convective derivative of its energy-density scalar, on the other hand. Thus, a modified Lagrangian is not of pure field-type, since these cross-terms are the products of pure field-type elements ($F_{ik}$) and of quantities defined algebraically (see (\ref{fluid}), (\ref{1fluid}) for the definitions of $U^i$, $W$, ${\cal P}_{pq}$). Second, we described a modified procedure of variation with respect to the metric, which happened to be necessary for these new cross-terms defined algebraically. This modified procedure is based on the rule of variation of the macroscopic velocity four-vector (\ref{11T1}) taken from the works \cite{2007A,2007B}; on the rule of algebraic decomposition of the second variation of the dark energy Lagrangian (\ref{S2})-(\ref{sym3}), and on the ansatz about the structure of this decomposition in the case of spatially isotropic medium (see (\ref{DE6})-(\ref{DE8})). \vspace{1mm} \noindent 2. What is the physical motivation of the Lagrangian extension, which we made? Since we follow the mathematical scheme, which is well-known in the relativistic electrodynamics of continuous media, we indicate the new cross-terms in the extended Lagrangian (\ref{actmin}) using the similar terminology: as (dark energy inspired) analogs of terms describing electric and magnetic striction, piezo-electricity and piezo-magnetism, pyro-electricity and pyro-magnetism. This analogy allowed us to interpret new coupling constants as (dark energy induced) pyro-, piezo- and striction coefficients, respectively. \vspace{1mm} \noindent 3. First cosmological application of the model shows that a striction-type interaction between the dark energy and test electrodynamic system provides the phase and group velocities of electromagnetic waves to become sophisticated functions of cosmological time. In the asymptotic regime, at $t \to \infty$, these functions tend to the speed of light in vacuum, i.e., $V_{({\rm ph})} \to c$ and $V_{({\rm gr})} \to c$. However, during the universe evolution the so-called unlighted epochs can appear, for which the effective refraction index of the cosmic medium is an imaginary quantity. At the boundary points of these unlighted epochs the group velocity of the electromagnetic waves takes zero value, so the electromagnetic energy transfer stops. \vspace{1mm} \noindent 4. The last unlighted epoch (if such epochs have ever existed in the real Universe) should finish before the so-called recombination era, as far as, cosmic microwave background composed of relic photons traveling freely is observable. In our terms this means that the characteristic time $t_{(\rm last UE)}{=}t^{*}{+}\Delta_2$ is less than $t_{({\rm rec})} \simeq 10^{13} {\rm sec}$. Using (\ref{pi4}), (\ref{un2}), (\ref{pi3}) at $t_0{=}t_{({\rm rec})}$ and the condition $t_{(\rm last UE)}< t_{({\rm rec})}$, we obtain a cosmological constraint $\Pi(t_{({\rm rec})})<\frac{n^2(t_{({\rm rec})})}{\alpha}$ linking the phenomenological parameter of a striction-type coupling $\alpha$, the value of the refraction index $n(t_{({\rm rec})})$ at the end of the recombination era, and the value of the dark energy pressure $\Pi(t_{({\rm rec})})$ at that moment. It is only one example of constraints appearing in this model; we intend to discuss other constraints in a special note. \vspace{1mm} \noindent 5. The criteria of existence of the unlighted epochs are very sensitive to the choice of the scalar field potential, which one uses for modeling of the dark energy. We have illustrated this sentence on the example of the anti-Gaussian model. In particular, taking into account one-loop corrections to the dark energy scalar field potential, one can show, that scalar fluctuations are able to avoid the unlighted epoch formation. \vspace{1mm} \noindent 6. We expect that the established model can provide new interesting results in application to the anisotropic Bianchi-I cosmological model, since in this period of the universe evolution pyro-magnetic and piezo-magnetic effects can appear in addition to the magneto- striction effect admissible both on the anisotropic and isotropic stages of the universe expansion. \vspace{3mm} \noindent {\bf Acknowledgments} \noindent This work is supported by the Russian Foundation for Basic Research (Grant No. 14-02-00598). | 14 | 4 | 1404.5058 |
1404 | 1404.6092_arXiv.txt | {\textit{Context.} X-ray observations of sdO stars are a useful tool to investigate their properties, but so far only two sdO stars were detected at X-rays.\\ \textit{Aims.} We aimed to perform the first systematic search for X-ray emission from sdO stars to characterize the X-ray emission from single and binary sdO stars.\\ \textit{Method.} We observed a complete flux-limited sample of 19 sdO stars with the \Chandra\ HRC-I camera to measure the count rate of the detected sources or to set a tight upper limit on it for the undetected sources.\\ \textit{Results.} We obtained a robust detection of \BDtwo\ and Feige 34 and a marginal detection of \BDthree. The estimated luminosity of \BDtwo\ is above $10^{31}$ erg s$^{-1}$, which is high enough to suggest the possible presence of an accreting compact companion. This possibility is unlikely for all the other targets (both detected and undetected), since in their case $L_{\rm X} \lsim 10^{30}$ erg s$^{-1}$. On the other hand, for all 19 targets the estimated value of $L_{\rm X}$ (or its upper limit) implies an X-ray/bolometric flux ratio that agrees with log($L_{\rm X}/L_{\rm bol}$) = --6.7 $\pm$ 0.5, which is the range of values typical of main-sequence and giant O stars.\\ \textit{Conclusions.} The observing campaign performed by \Chandra\ has discovered three new X-ray emitting sdO stars; for one of them the observed X-ray flux might be emitted by an accreting compact companion, while for the other two stars it is most probably due to intrinsic emission. The same is possibile for the 16 undetected stars.\\ | \label{sec:1} Hot subdwarf (sd) stars are blue low-mass stars, commonly located at high Galactic latitudes, which are at an advanced evolutionary phase; they have already lost most of their hydrogen envelope and are now burning their helium core \citep[see ][ for a review]{Heber09}. Based on their spectral properties, hot sd stars are classified into two different types: the cooler B-type subdwarfs (sdB), which have T$_{\rm eff}<$ 40,000 K and usually display no or weak helium lines in their spectra, and the hotter O-type subdwarfs (sdO), which have T$_{\rm eff}>$ 40,000 K and, in most cases, are helium rich \citep{Hirsch+08}. While the sdB stars form a rather homogeneous group, the class of sdO stars is very heterogeneus: they cover a wide range of effective temperatures (T$_{\rm eff}$ = 40--100 kK), surface gravities (log($g$) = 4--6.5), and helium abundances \citep{HeberJeffery92,Heber+06}. Therefore, sdO stars can be subdivided into He-poor and He-rich, according to the atmospheric abundances, and into `luminous' and `compact', depending on their low or high values of log($g$), respectively \citep{Napiwotzki08b}. The two classes of sd stars are very different also with respect to their origin. The sdB stars belong to the extreme horizontal branch (EHB) stars \citep{Heber86}: unlike normal HB stars, they evolve directly to the white-dwarf cooling sequence after the core helium exhaustion, without ascending the asymptotic giant branch (AGB), since their hydrogen envelope is too thin to sustain hydrogen burning. The origin of sdO stars is more complex. The luminous He-poor stars are low-mass post-AGB stars, while the compact ones are post-EHB stars and very probably are descendant of sdB stars. It is more difficult to explain the origin of the He-rich sdO stars. The luminous ones are on the post-AGB track, while the compact ones cannot evolve from sdB stars: in their case the most probable formation mechanism is either the merging of two He-core or C/O-core white dwarfs \citep{Iben90,SaioJeffery00,SaioJeffery02} or the so-called \textit{late hot-flasher} scenario \citep{Brown+01}. Radial velocity surveys of sd stars have shown that a high percentage ($>$ 40 \%) of the cool sdB stars occur in close binary systems \citep{Maxted+01,Napiwotzki+04, Morales-Rueda+06}, while the binary fraction of sdO stars is much lower \citep{Napiwotzki08a}: therefore, binary evolution can play an important role in the formation of subdwarf stars, particularly in that of sdBs. Three mechanisms have been identified to form subdwarf stars, starting from systems with stellar components \citep{Han+02,Han+03}: 1) one or two phases of common-envelope and spiral-in evolution; 2) one or two phases of stable Roche-lobe overflow; and (3) the merger of two helium-core white dwarfs. Moreover, a common-envelope phase involving a substellar companion has been suggested as a possible formation scenario \citep{Soker98,Charpinet+11}. In some cases the final outcome is the formation of a binary system with a subdwarf star and a compact companion; usually, the compact companion of the hot subdwarf is expected to be a white dwarf (WD), but if the mass of the original stars is large enough, a neutron star (NS) or black hole (BH) companion can be formed. The observation of hot subdwarfs at X-ray wavelengths can be a very useful tool to investigate their properties. First of all, they can be characterized by intrinsic X-ray emission. In fact, main-sequence, giant and supergiant early-type (O and B) stars are a well-known class of soft X-ray sources, with $L_{\rm X} \sim 10^{31}-10^{32}$ erg s$^{-1}$. Their X-ray emission is attributed to turbulence and shocks in their strong winds \citep{LucyWhite80}, and the X-ray and the bolometric luminosities are linked by the canonical relation $L_{\rm X} \sim 10^{-7} \times L_{\rm bol}$ \citep{Pallavicini+81,Sciortino+90,GuedelNaze09}. Although the hot subdwarfs are characterized by lower luminosities (log($L_{\rm bol}/L_{\odot}$) $\lsim$ 4 instead of 5--6), they can have winds with mass losses of up to 10$^{-8}$ and 10$^{-10}$ M$_{\odot}$ y$^{-1}$ for sdO and sdB stars, respectively \citep{Hamann10,JefferyHamann10}. Therefore, hot sd stars might also be X-ray emitters of the same type, and it is interesting to investigate whether the above average relation extends to such low luminosities as well. In addition, the observation of X-ray emission could indicate the presence of a compact companion that accretes matter from the subdwarf wind: in this case the measured X-ray luminosity can provide useful information on the binary orbit and the mass-loss rate from the subdwarf star. A Swift/XRT search for X-ray emission from candidate sdB+WD/NS binaries, selected from optical spectroscopy and photometry \citep{Geier+10}, gave negative results \citep{Mereghetti+11}, probably because of the weak winds of sdB stars, which are unable to provide a high enough accretion rate. On the other hand, the only two sdO stars for which pointed X-ray observations are available both showed a clear X-ray emission. The first case is \HD, which is the brightest (V = 8) sdO star and is known since 1970 as a single-lined spectroscopic binary \citep{Thackeray70,SticklandLloyd94}. The compact nature of its companion, undetected in the optical/UV, was indicated by the presence of soft X-ray emission with a periodicity of 13.18 s \citep{Israel+97}. A long \XMM\ observation allowed us to constrain the orbital parameters and the X-ray spectrum and luminosity ($L_{\rm X} \simeq 3\times10^{31}$($d$/650 pc)$^{2}$ erg s$^{-1}$) and to establish that the most likely companion is a WD \citep{Mereghetti+09}. The X-ray flux from \HD\ does not disappear completely when the X-ray pulsar is eclipsed by the sdO star. The spectrum observed during the eclipse shows emission lines of H- and He-like nitrogen, an overabundant element in \HD. This emission could result from reprocessing of the accretion-powered X-rays in the sdO wind, but also from \HD\ iteself \citep{Mereghetti+13}. Its value of $L_{\rm X}/L_{\rm bol} \sim 10^{-7}$ agrees with the average value found in main-sequence early-type stars. The second sdO star detected in X-rays is the bright He-rich star \BDone, which has stellar parameters very similar to those of \HD. Like \HD, it shows P-Cygni UV line profiles indicating wind mass-loss at a rate of $\sim3\times10^{-9}$ $M_{\odot}$ yr$^{-1}$ \citep{JefferyHamann10}, but no evidence of binary nature was reported from optical/UV photometry and spectroscopy. We recently observed it with \textit{XMM-Newton} and discovered soft X-ray emission, with a spectrum similar to that of \HD, and pulsations at 19.16 s, indicating that \BDone\ is also a binary with a NS or WD companion \citep{LaPalombara+12}. The luminosity is in the range $10^{32}-10^{35}$ erg s$^{-1}$ (for a source distance of 2 kpc), consistent with wind accretion onto a WD or, more likely, onto a NS. However, optical observations show no variations in the radial velocity of \BDone\ and, hence, there is no dynamical evidence for the existence of a compact companion yet \citep{Heber+14}. Prompted by our results on \HD\ and \BDone, we planned a survey with \Chandra\ HRC-I of a complete flux-limited sample of sdO stars. Our aim was to perform the first systematic search for X-ray emission from this type of stars to characterize the X-ray emission from single and binary sdO stars. In \S\ref{sec:2} we present the sample of the selected sources and the adopted observing strategy; in \S\ref{sec:3} we describe the observations, the data reduction, and the results; finally, in \S\ref{sec:4} we briefly discuss these results and compare them with those obtained for \HD\ and \BDone. | \label{sec:5} We have carried out the first systematic X-ray survey of all the sdO stars brighter than V=12 using the \Chandra\ satellite. The upper limits for the 16 undetected sources do not exclude that the average relation between X-ray and bolometric luminosity derived for more luminous O stars also extends to the subdwarfs class. Thanks to the detection of \BDtwo, Feige 34, and possibly \BDthree, we more than doubled the number of sdO stars seen in the X-ray band. \BDtwo\ belongs to the subclass of luminous He-rich sdO, like the only two previously known X-ray emitting sdO, and, like these, it might have a compact companion. Feige 34 and \BDthree\ are instead compact sdO stars, the first of this kind to be detected in the X-ray band. Deeper X-ray observations are required to assess whether these three sdO stars contain compact accreting objects, or if their X-ray emission is intrinsic and due to shock-heating processes in the wind as is typical of more luminous early-type stars. In addition, more optical/IR studies are also required to exclude the presence of late-type companions that might contribute to the observed X-ray flux. | 14 | 4 | 1404.6092 |
1404 | 1404.4432_arXiv.txt | We investigate effects of cosmic-rays on the linear growth of the Kelvin-Helmholtz instability. Cosmic-rays are treated as an adiabatic gas and allowed to diffuse along magnetic field lines. We calculated the dispersion relation of the instability for various sets of two free parameters, the ratio of the cosmic-ray pressure to the thermal gas pressure and the diffusion coefficient. Including cosmic-ray effects, a shear layer is more destabilized and the growth rates can be enhanced in comparison with the ideal magnetohydrodynamical case. Whether the growth rate is effectively enhanced or not depends on the diffusion coefficient of cosmic-rays. We obtain the criterion for effective enhancement by comparing the growing time scale of the instability with the diffusion time scale of cosmic-rays. These results can be applied to various astrophysical phenomena where a velocity shear is present, such as outflows from star-forming galaxies, AGN jet, channel flows resulting from the nonlinear development of the magnetorotational instability, and galactic disks. | } Cosmic-rays, thermal gases, and magnetic fields are ubiquitous in the universe and indispensable components of astrophysical objects in various scales. How they interact with each other and how they exchange their energies are thought to key ingredients to understand various astrophysical phenomena. However, current understanding of the interaction between these components is not sufficient. There are numerous works considering how cosmic-rays affect thermal gas and magnetic fields in different ways. Some treat interactions between cosmic-rays and magnetohydrodynamics (MHD) waves in kinetic approach and others use the cosmic-ray transport equation in the diffusion limit \citep{1971ApJ...170..265S,1975MNRAS.172..557S}. Among them, one of the most convenient ways is to regard cosmic-rays as a gas composed of relativistic particles and allow the gas diffuse in the ISM with a specific diffusion coefficient \citep{1985A&A...151..151S}. Especially, in the presence of an ordered magnetic field, cosmic-rays diffuse along the magnetic field line since the gyration of cosmic-ray particles around the magnetic field line prevents efficient exchanges of energies between cosmic-ray particles \citep{1999ApJ...520..204G}. In this simplified manner, a lot of works have been done on the purpose of revealing how cosmic-ray pressure affects the dynamical evolution of the ISM. Cosmic-rays are considered to be one of major components of the interstellar medium(ISM). The energy density of cosmic-rays in the interstellar space is known to be comparable to those of thermal gas and magnetic fields. The considerably high energy density means that we should take into account effects of cosmic-rays on thermal gas and magnetic fields when we consider the dynamical evolution of the ISM. Also, in hot plasmas trapped in the gravitational potential of clusters of galaxies, i.e., the intra-cluster medium (ICM), cosmic-rays are considered to play important roles in transporting energy from AGN jets to surrounding materials. For example, \cite{2003ApJ...589..338R} carried out the linear analysis of the Parker instability \citep{1966ApJ...145..811P,1992ApJ...401..137P} for various sets of the diffusion coefficient and the ratio of the cosmic-ray gas pressure to the thermal gas pressure. \cite{2003A&A...412..331H} and \cite{2004ApJ...607..828K} developed numerical codes solving MHD equations coupled with cosmic-ray pressure and investigated the linear and nonlinear development of the Parker instability in the presence of cosmic-rays. Later, simulations of the Galactic disk were performed by \cite{2004ApJ...605L..33H,2009A&A...498..335H} to reveal roles of cosmic-rays in driving the magnetohydrodynamical dynamo. Furthermore, effects of cosmic-rays on the linear growth of magnetorotational instability \citep{Velikhov1959,1960PNAS...46..253C,1991ApJ...376..214B} have been investigated by \cite{2012Ap&SS.337..247K}. Cosmic-rays possibly affect growth of the thermal instability \citep{1965ApJ...142..531F}. There are some studies on linear analysis of the instability \citep{1994ApJ...431..689B,2005A&A...430..567W,2009MNRAS.397.1521S}. In \cite{2010ApJ...720..652S}, linear analysis and numerical simulations on the thermal instability with anisotropic conduction and cosmic-ray gas transport are applied to the ICM. In these systems, velocity shears would be naturally formed, suggesting development of Kelvin-Helmholtz(KH) instability. The KH instability is a fundamental process of hydrodynamical instability and thus is greatly paid attention in astrophysics \cite[e.g.,][]{1961hhs..book.....C}. For example, in a cluster of galaxies, member galaxies of the cluster move in the surrounding hot plasma. Therefore, the contact surface exists between the ICM and the ISM of each galaxy. At the contact surface, the KH instability can develop and the ISM may be stripped from the galaxy. The vortex acts as an amplifier of magnetic fields \citep{2007ApJ...663..816A,2013ApJ...768..175S}. Shear flows can also be found in outflows in the ISM, the inter-galactic medium, and the ICM. The difference in the velocities of the jet and the ambient medium leads to the development of the KH instability. As a result, the jet material and the ambient medium are expected to be efficiently mixed up. Another example at which the KH instability plays important role is the accretion disks threaded by the magnetic fields. In such systems, gravitational energy of accreting gas is converted into the magnetic and kinetic energy through the MRI, resulting a formation of so-called channel flow. Although the channel flow structure is a fully exact solution of non-linear MHD equations and MRI is expected to continue to grow exponentially, the channel flow is actually disrupted by the secondary KH instability \citep{1994ApJ...432..213G}. Then the disk becomes fully turbulent system. Thus, the saturation levels of MRI mode and rate of angular momentum transport would be strongly affected by the growth of the KH instability. Since saturation levels of MRI determines the amount of the magnetic energy transported into the disk corona, the growth of the KH instability would impact on the coronal heating \citep{2012arXiv1205.6537U}. Also we have to note that the KH instability is important to consider the disk wind from the turbulent accretion disks. The accretion disks threaded by the magnetic field can drive disk wind \citep{1982MNRAS.199..883B}. The disk winds driven from the turbulent accretion disks suffer from a kind of the KH instability \citep{2013A&A...550A..61L} and resulting in the formation of turbulent outflows \citep{2013A&A...552A..71F}. Cosmic-rays are thought to have a potential to drive outflows from star-forming galaxies, i.e., so-called cosmic-ray driven wind \citep{1975ApJ...196..107I}. In such galaxies, supernova remnants in star-forming regions are a plausible source of cosmic-rays. The presence of cosmic-rays in galactic winds from star-forming galaxies is observationally supported by detections of high-energy gamma-ray photons from starburst galaxies, such as, M82 and NGC 253 \citep{2009Sci...326.1080A,2009Natur.462..770V,2010ApJ...709L.152A} and the Galactic diffuse soft X-ray emission\citep[e.g.,][]{1997ApJ...485..125S}. These emission are a probe of interactions between cosmic-rays and the ISM or radiation fields in these galaxies. Many theoretical models of the cosmic-ray driven wind have been developed to account for the spatial distribution and the spectral properties of the Galactic diffuse X-ray emission \citep[e.g.,][]{1991A&A...245...79B,2002A&A...385..216B,2008ApJ...674..258E}. Although cosmic-rays could play important roles in such astrophysical situations, the development of the KH instability in the presence of cosmic-rays has not been paid attention. The linear analysis of the KH instability in magnetized fluid was done by \cite{1961hhs..book.....C} for the first time. In this work, the infinitesimal thickness of the sheared layer is assumed. Later, in \cite{1982JGR....87.7431M} (referred to as MP82, hereafter), the magnetized KH instability for a flow with sheared velocity profile with finite thickness was discussed. Then, in this paper, as a first step towards the understanding of effects of cosmic-rays on the KH instability, we extend the linear analysis of MHD equations in the presence of a sheared velocity field investigated by MP82 In other words, we perform a linear analysis of MHD equations with comic-ray effects in the same situation. In Section 2, our method to calculate growth rates of the KH instability is described in detail. We show results of the linear analysis in Section 3. Section 4 is devoted to summarize the results and explain how cosmic-ray pressure and diffusion affect the linear growth of the KH instability. Finally, Section 5 concludes this paper. In the following, physical variables with dimensions are denoted by letters with tilde, $\tilde{A}$, and the dimensionless counterparts are denoted by letters without tilde, $A$. | In this study, we investigate the linear growth of the KH instability in the presence of cosmic-ray gas. MHD equations incorporated with cosmic-ray pressure are linearized and then solved as an eigen-value problem to obtain growth rates in the linear phase. Our results show i) cosmic-ray pressure enhances the growth of the instability, and ii) cosmic-ray diffusion can suppress the enhancement in the magnetic field parallel to the flow. The suppression is more effective for perturbations with shorter wavelengths. Especially, when the cosmic-ray pressure dominates over the thermal gas pressure, the instability can develop even for large sonic and Alfv$\mathrm{\acute{e}}$n Mach numbers that stabilize the system without cosmic-ray effects. Therefore, cosmic-ray effects are prominent for the system with the flow velocity larger by a factor than the sound and the Aflv$\mathrm{\acute{e}}$n velocity, $M_\mathrm{s},M_\mathrm{a}>3$. \subsection{Values of the cosmic-ray pressure to the thermal gas pressure ratio $\alpha$} It is found that the parameter $\alpha$, the ratio of the cosmic-ray pressure to the thermal pressure, is crucial for the development of the KH instability. In star-forming galaxies, the value is expected to be similar to the Galactic value, $\alpha\sim 1$. \cite{2008ApJ...674..258E} developed a galactic outflow model including cosmic-rays based on the model originally presented in \cite{1991A&A...245...79B}. Their model implies that the cosmic-ray pressure is comparable to the thermal gas pressure. However, assuming that supernova remnants predominantly produce Galactic cosmic-rays, cosmic-ray energy density distribution in a star-forming galaxy obeys the spatial distribution of star-forming regions in the galaxy. It is naturally expected that some regions with large values of $\alpha$ exist locally while the value is globally unity. Furthermore, the value of $\alpha$ might be larger in starburst galaxies than that in the Galaxy inferred from the model of \cite{2008ApJ...674..258E}. It is known that starburst galaxies, such as, M82 and NGC 253, are known to be gamma-ray sources \citep[e.g.,][]{2009Sci...326.1080A,2009Natur.462..770V,2010ApJ...709L.152A}. These gamma-ray emission are a tracer of cosmic-rays in these galaxies, because they are thought to be emitted by the interaction between cosmic-rays and ISM gas or radiation fields in these galaxies. The cosmic-ray energy density at the nuclei of starburst galaxies is estimated to be several hundreds to thousands times higher than that of the Galactic value. This is supported by an independent estimation of the cosmic-ray energy density at the nuclei by ultraluminous infrared galaxies \citep{2010ApJ...720..226P} from infrared observations. \subsection{Possible sites of KH instability with cosmic-rays} The cosmic-ray effects considered in this paper may be important in the following astrophysical sites. \subsubsection{Outflows from star-forming galaxies} In the best-fit model of \cite{2008ApJ...674..258E}, the sonic and Alfv$\acute{\mathrm{e}}$n Mach numbers of the flow increase as the height from the disk increases and reaches to a few at the height of 10 kpc. The KH instability would not develop in the region without cosmic-rays because the flow is supersonic with $M_\mathrm{s},M_\mathrm{a}>2$-$3$. However, the cosmic-ray pressure is slightly larger than the thermal gas pressure in the region, suggesting the development of the instability supported by cosmic-ray pressure. For the adopted value of the cosmic-ray diffusion coefficient, $\tilde{\kappa}=3\times 10^{28}$ cm$^2$ s$^{-1}$ and the terminal velocity, $\sim 800$ km s$^{-1}$, of the outflow inferred from their model, the scale length $\tilde{a}$ is about $0.1$ kpc. If we consider the parallel case with $\alpha=1.0$ and $\kappa=1.0$ in Figure \ref{fig:para_b}, in which the wave number that gives the maximum growth rate is found to be $k_y\sim 0.3$, perturbations with scales of $\sim 0.3$ kpc are expected to grow efficiently. The growing time scale $\tilde{t}_\mathrm{grow}$ is estimated to be \begin{eqnarray} \tilde{t}_\mathrm{grow}=\frac{\tilde{a}}{\gamma_\mathrm{max}\tilde{U}_0} &=&2\times 10^{6}\ \mathrm{yr}\left(\frac{\tilde{a}}{0.1\ \mathrm{kpc}}\right) \nonumber\\ && \hspace{-2em}\times\left(\frac{\gamma_\mathrm{max}}{0.05}\right)^{-1} \left(\frac{\tilde{U}_0}{800\ \mathrm{km}\ \mathrm{s}^{-1}}\right)^{-1}, \end{eqnarray} where $\gamma_\mathrm{max}$ is the maximum growth rate. On the other hand, the time required for the gas moving at $800$ km s$^{-1}$ to travel $10$ kpc is about $10^7$ yr. Therefore, the KH instability supported by cosmic-rays can develop in the region. \begin{figure}[tbp] \begin{center} \includegraphics[scale=0.45]{./efunc.eps} \caption{Real and imaginary parts of eigen functions normalized so that the imaginary part is unity at $x=0$. Solid and dashed lines correspond to calculations with $\alpha=1$ and $\alpha=0$. Other parameters are set to be $M_\mathrm{s}=1.5$, $M_\mathrm{a}=4.0$, $k_y=0.4$, $k_z=0$, and $\kappa=1.0$.} \label{fig5} \end{center} \end{figure} \subsubsection{AGN jets} In order to explain high-energy emission produced by jets from active galactic nuclei(AGN), stratified jet models have been put forward. In such models, a jet is divided into two component, the material moving at relativistic speeds and the surrounding material moving at relatively low velocities. The latter component is realized as a result of the interaction between the jet and the ambient medium, which can be found in relativistic hydrodynamical simulations \citep[see, e.g.,][]{1999ApJ...523L.125A}. In such circumstances, a cocoon filled with cosmic-rays accelerated at the boundary between the components can form and give rise to non-thermal emission by synchrotron and inverse compton processes \citep{2000MNRAS.312..579O,2002ApJ...578..763S,2008ApJ...681.1725S}. The cosmic-rays are expected to accelerate via 2nd-order Fermi process in a tangled magnetic field produced by the KH instability at the boundary. If that is the case, the thus produced cosmic-rays enhance the development of the KH instability and the efficiency of the acceleration process. Recently, \cite{2011ApJ...728..121G} performed numerical simulations of the propagation of a cosmic-ray dominated AGN jet in the ICM. They found that the structure created in the ICM as a result of the injection of cosmic-ray dominated jet look similar to observed X-ray cavities in the ICM of some clusters of galaxies \citep[see, e.g.,][]{2007ARA&A..45..117M}, while kinetic energy dominated jets create relatively elongated cavity. In their calculations, cosmic-ray energy pressure is dominant over the thermal gas pressure in the inner region of the jet. Thus the value of $\alpha$ is considerably large in the region and cosmic-ray effects on the KH instability considered in this paper can be expected. \subsubsection{Channel flows as a result of magnetorotational instability} The third example is the magnetorotational instability in differentially rotating accretion disks \citep{1991ApJ...376..214B}. Numerical simulations of the instability have found that the instability results in the formation of channel flows \citep{1992ApJ...400..595H}. As the channel flows grow, the KH instability develops and then destroys the channel flow, which leads to the non-linear saturation of the magnetorotational instability \citep{1994ApJ...432..213G}. The KH instability would also be pronounced on the surface of the accretion disks. Due to the amplification of the magnetic field by MRI, the disk wind (outflow) is formed \citep{1982MNRAS.199..883B}. The outflow is unstable on the dynamical timescale, which is potentially due to the KH instability \citep{2013A&A...550A..61L}. This results in a formation of turbulent outflow. In the presence of cosmic-rays, the non-linear saturation process should be affected. \subsubsection{Galactic disks} Another possible site for the KH instability with cosmic-rays is galactic disks, where a gas flows in a spiral potential of the galaxy. \cite{2004MNRAS.349..270W} have studied stability of gas flows in several spiral potentials and found that clumps are formed in shear layers where gases are compressed by the spiral shock. They attribute the generation of clumps to the KH instability developing in the shear layer. For a galaxy with the physical scale of several kpc and the velocity of the rotation of 100 km s$^{-1}$, the product of the physical scale and the velocity, which is of the order of $10^{28}$ cm$^2$ s$^{-1}$, can be comparable to the the diffusion coefficient of galactic cosmic-rays and thus cosmic-rays may affect the development of the KH instability. \subsection{Some remarks} While we examined how cosmic-rays affect the linearly growing stage of the KH instability, their influence on the non-linear stage is also of great interest. In the non-linear stage of the instability, it is known that the instability destroys the shear flow and makes the fluid turbulent. Investigating effects of cosmic-rays on the creation of vortices in a turbulent fluid requires hydrodynamical simulations incorporated with cosmic-ray diffusion \citep{2004ApJ...605L..33H}. Such simulations are one of the future works. Furthermore, although we treat cosmic-rays as an adiabatic gas, it is also important to consider the KH instability in the presence of non-thermal particles with a particular energy spectrum. In order to tackle the problem, it is necessary to solve hydrodynamical equations with cosmic-ray transport in energy space, which is also a future work of special interests. | 14 | 4 | 1404.4432 |
1404 | 1404.1082.txt | {}{}{}{}{} % 5 {} token are mandatory \abstract % context heading (optional) % {} leave it empty if necessary {We study the kinematic properties of the ionised gas outflows and ambient interstellar medium (ISM) in a large and representative sample of local luminous and ultra-luminous infrared galaxies (U/LIRGs) (58 systems, 75 galaxies) at galactic and sub-galactic (i.e., star-forming clumps) scales, thanks to integral field spectroscopy (IFS)-based high signal-to-noise integrated spectra. The velocity dispersion of the ionized ISM in U/LIRGs ($<$$\sigma$$>$ $\sim$ 70 kms$^{-1}$ ) is larger than in lower luminosity local star-forming galaxies ($<$$\sigma$$>$ $\sim$ 25 kms$^{-1}$ ). While for isolated disc LIRGs star formation appears to sustain turbulence, gravitational energy release associated with interactions and mergers plays an important role in driving $\sigma$ in the U/LIRG range. We find that $\sigma$ has a dependency on the star formation rate density ($\Sigma_{SFR}$), which is weaker than expected if it were driven by the energy released by the starburst. The relatively small role of star formation (SF) driving the $\sigma$ in U/LIRGs is reinforced by the lack of an increase in $\sigma$ associated with high luminosity SF clumps. We also find that the impact of an active galactic nucleus (AGN) in ULIRGs is strong, increasing on average $\sigma$ by a factor 1.5. Low-z U/LIRGs cover a range of velocity dispersion ($\sigma$ $\sim$ 30 to 100 km s${^{-1}}$) and star formation rate density ($\Sigma_{SFR}$ $\sim$ 0.1 to 20 M$_{\odot} yr^{-1} kpc^{-2}$) similar to those of SFGs. Moreover, the observed weak dependency of $\sigma$ on $\Sigma_{SFR}$ for local U/LIRGs ($\sigma \propto \Sigma_{SFR}^{+0.06}$) is in very good agreement with that measured in some high-z samples. The presence of ionized gas outflows in U/LIRGs seems universal based on the detection of a broad, usually blueshifted, H$\alpha$ line. The observed dependency of the {\it maximum} velocity of the outflow (V$_{max}$) on the star formation rate (SFR) is of the type V$_{max}(non-AGN) \propto SFR (L_{IR})^{+0.24}$. We find that AGNs in U/LIRGs are able to generate faster ($\sim$ $\times$ 2) and more massive ($\sim \times$ 1.4) ionized gas outflows than pure starbursts. The derived ionized mass loading factors ($\eta$) are in general below 1, with only a few AGNs above this limit. The escaping gas fraction is low with only less massive (log(M$_{dyn}/ M_{\odot}) <$ 10.4) U/LIRGs having outflowing terminal velocities higher than their escape velocities, and more massive galaxies retaining the gas, even if they host an AGN. The observed average outflow properties in U/LIRGs are similar to high-z galaxies of comparable SFR. However, while high-z galaxies seem to require $\Sigma_{SFR} >$ 1 $M_{\odot} yr^{-1} kpc^{-2}$ for launching strong outflows, this threshold is not observed in low-z U/LIRGs even after correcting for the differential fraction of the gas content. In the bright SF clumps found in LIRGs, ionized gas outflows appear to be very common (detection rate over 80\%). Their observed properties are less extreme than those associated with the entire galaxy. The clumps in LIRGs follow the general size-L-$\sigma$ scaling relations found for low- and high-z clumps, though they are in general smaller, less luminous, and are characterized by lower $\sigma$ than at high-z. For a given observed (no internal extinction correction applied) star formation surface density, outflows in LIRG clumps would be about one to two orders of magnitude less energetic than the outflows launched by clumps in high-z SF galaxies. } | 14 | 4 | 1404.1082 |
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1404 | 1404.3212_arXiv.txt | Observations show a prevalence of high redshift galaxies with large stellar masses and predominantly passive stellar populations. A variety of processes have been suggested that could reduce the star formation in such galaxies to observed levels, including quasar mode feedback, virial shock heating, or galactic winds driven by stellar feedback. However, the main quenching mechanisms have yet to be identified. Here we study the origin of star formation quenching using Argo, a cosmological, \boldtext{hydrodynamical} zoom-in simulation that follows the evolution of a massive galaxy at $z\geq{}2$. This simulation adopts the same sub-grid recipes of the Eris simulations, which have been shown to form realistic disk galaxies, and, in one version, adopts also a mass and spatial resolution identical to Eris. The resulting galaxy has properties consistent with those of observed, massive ($M_*\sim{}10^{11}$ $M_\odot$) galaxies at $z\sim{}2$ and with abundance matching predictions. Our models do not include AGN feedback indicating that supermassive black holes likely play a subordinate role in determining masses and sizes of massive galaxies at high $z$. The specific star formation rate (sSFR) of the simulated galaxy matches the observed $M_*$ - sSFR relation at early times. This period of smooth stellar mass growth comes to a sudden halt at $z=3.5$ when the sSFR drops by almost an order of magnitude within a few hundred Myr. The suppression is initiated by a leveling off and a subsequent reduction of the cool gas accretion rate onto the galaxy, and not by feedback processes. This ``cosmological starvation'' occurs as the parent dark matter halo switches from a fast collapsing mode to a slow accretion mode. Additional mechanisms, such as perhaps radio mode feedback from an AGN, are needed to quench any residual star formation of the galaxy and to maintain a low sSFR until the present time. | \label{sect:Intro} A large number of massive galaxies at $z\sim{}2$ are dominated by a passively evolving stellar population with little ongoing star formation (e.g., \citealt{2003ApJ...587L..79F, 2004Natur.430..184C, 2004ApJ...616...40F, 2005ApJ...626..680D, 2006ApJ...638L..59V, 2007A&A...476..137A, 2007ApJ...655...51W, 2008ApJ...682..896K, 2008A&A...482...21C, 2009ApJ...691.1879W, 2009ApJ...706L.173B, 2010ApJ...708..202M, 2010ApJ...709..644I, 2012ApJ...755...26O, 2013ApJ...764L...8B, 2013ApJ...770L..39W, 2014ApJ...780...34L, 2014A&A...561A..86M}). The fraction of such galaxies is 20-30\% for galaxies with stellar masses $\sim{}2-5\times{}10^{10}$ $M_\odot$ and raises to $\sim{}50\%$ for galaxies with masses above $\sim{}10^{11}$ $M_\odot$ (e.g., \citealt{2011ApJ...735...86W, 2011ApJ...739...24B, 2013ApJ...777...18M, 2014arXiv1401.2984T}). \boldtext{These galaxies are called quiescent, a reference to their weak or absent star formation activity, although the actual operational definition is typically based on U-V and V-J restframe colors, see section \ref{sect:CompObs}}. So far, no consensus has been reached on the nature of the physical processes responsible for suppressing (``quenching'') star formation in massive galaxies at high redshift. Empirical studies show that out to at least $z\sim{}1$ the likelihood of a galaxy being quenched is correlated both with its stellar mass (``mass quenching'') and with the environmental density of neighboring galaxies (``environmental quenching''), see \cite{2010ApJ...721..193P}. The latter quenching channel is primarily affecting satellite galaxies (e.g., \citealt{2012ApJ...757....4P, 2013MNRAS.432..336W}), while the quiescent fraction of central galaxies appears to be not strongly correlated with current environmental overdensity (\citealt{2014MNRAS.438..717K} and references therein). Environmental quenching is likely related to processes preferentially occurring in galaxy groups and clusters, such as ram-pressure stripping of the interstellar medium (ISM; \citealt{1972ApJ...176....1G, 1999MNRAS.308..947A}), the reduction of gas accretion onto satellites (``starvation'', \citealt{1980ApJ...237..692L, 2000ApJ...540..113B, 2008ApJ...672L.103K, 2008MNRAS.383..593M, 2008MNRAS.387...79V, 2011ApJ...736...88F, 2013MNRAS.430.3017B}), or frequent galaxy interactions (``harassment'', \citealt{1981ApJ...243...32F, 1996Natur.379..613M}). Most mass quenching mechanisms discussed in the literature either prevent or decrease the accretion of gas onto galaxies or eject gas from galaxies. For instance, the growth of a stable virial shock in massive halos reduces the accretion of relatively cool, not strongly shock-heated, gas onto galaxies \citep{2003MNRAS.345..349B, 2005MNRAS.363....2K, 2006MNRAS.368....2D, 2006MNRAS.370.1651C}. In addition, cooling of shock-heated gas might be counteracted by gravitational heating from infalling satellite galaxies or gas clumps \citep{2008MNRAS.383..119D, 2008ApJ...680...54K, 2009ApJ...697L..38J, 2012ApJ...754..115J}. Other quenching channels are related to active galactic nuclei (AGN) and to star formation in galaxies. Major mergers of gas-rich disk galaxies at high redshift may ignite powerful starbursts \citep{1986ApJ...303...39D, 2005ApJ...618..569M} and result in quasar-activity \citep{1988ApJ...325...74S, 2004ApJ...608...62S, 2005MNRAS.361..776S, 2005ApJ...620L..79S, 2005Natur.433..604D, 2006ApJS..163....1H, 2011MNRAS.412.1965M} that may launch outflows and remove large amounts of gas from galaxies. AGNs can also operate in a jet-powered \emph{radio mode} in which they counteract the cooling of gas from the hot halo surrounding galaxies with low intensity mechanical heating (e.g., \citealt{2006MNRAS.365...11C, 2006MNRAS.370..645B, 2007MNRAS.380..877S}). Ejective feedback originating in quasar activity could explain why the entropy in galaxy clusters is close to the value needed to offset gas cooling \citep{2004ApJ...608...62S}. It also offers a physical basis for the co-evolution of black-hole mass and the bulge mass of the galaxy host \citep{1998AJ....115.2285M, 2003ApJ...589L..21M, 2004ApJ...604L..89H} and for the correlation between quasar activity and star formation \citep{1998MNRAS.293L..49B, 2003MNRAS.346.1055K}. However, it is still an open question whether quasar driven outflows triggered by galaxy interactions or mergers actually quench star formation in massive, high redshift galaxies (see \citealt{2012NewAR..56...93A} for a recent review). In fact, at high redshift there is little evidence for a link between merging and quasar activity \citep{2011ApJ...727L..31S, 2012ApJ...744..148K}, except at the highest quasar luminosities \citep{2012ApJ...758L..39T}, or between quasar activity and star formation \citep{2014ApJ...783...40G}. Galaxy evolution simulations that include quasar mode feedback have not yet converged on a conclusive answer either, primarily because there exists a variety of choices as to which physical processes are modeled and how they are implemented (e.g., \citealt{2010ApJ...722..642O, 2010MNRAS.406L..55D, 2011ApJ...737...26N, 2011MNRAS.412..269P, 2012MNRAS.425..605F, 2013MNRAS.434.3606N, 2013MNRAS.431.2513W, 2014arXiv1402.4482G}). Numerical simulations agree, however, that radio mode feedback can reduce the $z=0$ stellar masses of central galaxies in clusters, that it can result in more realistic galaxy colors and also better agreement with observed X-ray scaling relations \citep{2006MNRAS.366..397S, 2008ApJ...687L..53P, 2008MNRAS.387...13K, 2010MNRAS.406..822M, 2010MNRAS.409..985D, 2011MNRAS.417.1853D, 2011MNRAS.414..195T, 2013MNRAS.433.3297D, 2013MNRAS.436.1750R, 2014MNRAS.438..195P}. However, this feedback channel primarily affects the hot gas halo surrounding galaxies, and typically does not launch large scale winds involving the ISM of the galaxy. Hence, radio mode feedback appears to be an unlikely candidate for triggering a rapid star formation quenching in high redshift galaxies, but it may play an important role in maintaining low star formation activity in already quenched galaxies (e.g., \citealt{2005MNRAS.362...25B, 2006MNRAS.365...11C}). Hence, we are left with two related, but distinct, questions. First, why do high redshift galaxies leave the star forming sequence \citep{2007ApJ...660L..43N, 2007A&A...468...33E, 2007ApJ...670..156D, 2011A&A...533A.119E}? We will show that massive, high redshift galaxies can only remain on the star forming sequence for so long before the finite supply of gas limits their star formation activity. Specifically, during an early collapse phase, gas accretion rates and sSFRs are high and massive galaxies form and assemble much of their stellar mass. This is followed by a cosmological starvation phase in which accretion rates, and subsequently star formation activity, level off and eventually decline. Second, why do galaxies shut-down their star formation almost completely instead of maintaining a low, but non-negligible star formation activity? We will argue that a combination of stellar feedback and, potentially, AGN radio mode feedback, coupled with gravitational heating is required to complete the transition from the star forming sequence to the quiescent galaxy population. \begin{table*} \begin{center} \begin{tabular}{cccccccc} \tableline Run & $m_{\rm gas}$ & $m_{\rm star}$ & $m_{\rm DM}$ & $\epsilon_{\rm bar}$ & $\epsilon_{\rm DM}$ & $n_{\rm SF}$ & $z_{\rm end}$ \\ & ($M_\odot$ $h^{-1}$) & ($M_\odot$ $h^{-1}$) & ($M_\odot$ $h^{-1}$) & (pc $h^{-1}$) & (pc $h^{-1}$) & (m$_{\rm H}$ cm$^{-3}$) \\ \tableline LR* & $9.9\times{}10^5$ & $2.9\times{}10^5$ & $4.7\times{}10^6$ & 219 & 365 & 0.1 & 1 \\ MR1 & $1.2\times{}10^5$ & $3.7\times{}10^4$ & $5.8\times{}10^5$ & 109 & 183 & 0.1 & 2 \\ MR2 & $1.2\times{}10^5$ & $3.7\times{}10^4$ & $5.8\times{}10^5$ & 109 & 183 & 5 & 2 \\ HR & $1.5\times{}10^4$ & $4.6\times{}10^3$ & $5.8\times{}10^5$ & 88 & 183 & 5 & 3.4 \\ \tableline \end{tabular} \caption{Overview of the individual runs performed as part of the Argo project. The first four columns provide the label and the masses of gas, star, and DM particles in the zoom-in region of the run. The next two columns are the gravitational spline softening lengths of baryonic (i.e., gas and star) particles and of DM particles in proper units. The penultimate column shows the star formation threshold. The final column indicates the redshift at which the run is stopped. Runs MR1 and MR2 start from the same initial conditions and differ only in the adopted star formation threshold. \boldtext{*We carried out at this resolution: the default LR run with our fiducial physics model, the LR-noFB run without energetic feedback from supernovae, the LR-noFB(z$<$4) run without supernova feedback after $z=4$, and the LR-noML(z$<$3) run without stellar mass loss after $z=3$.}} \label{tab:Res} \end{center} \end{table*} Our results are based on a cosmological, zoom-in simulation of a massive, high redshift galaxy. The simulated galaxy resides at the center of a halo ($M_{\rm vir}\sim{}10^{13}$ $M_\odot$ at $z=0$) that should harbor common (i.e., of intermediate stellar mass $\sim{}1-3\times{}10^{11}$ $M_\odot$) quiescent galaxies in the local Universe. The halo is located in a typical, mildly over-dense region that does not contain a more massive halo. Hence, our findings likely apply to a majority of massive, quiescent, central galaxies. Despite their importance and ubiquity, galaxies in $\sim{}10^{13}$ $M_\odot$ halos have only recently been targeted by cosmological, zoom-in simulations \citep{2008ApJ...672L.103K, 2010ApJ...709..218F, 2011ApJ...736...88F, 2010ApJ...725.2312O, 2012ApJ...744...63O, 2014ApJ...781...38C}. One of the reasons is the numerical challenge of resolving galaxies in such massive halos. In addition, physical models are often tuned based on simulations of lower mass, star forming galaxies (e.g., \citealt{2006MNRAS.373.1074S}). Hence, it is not obvious that the same models are adequate to simulate massive, quiescent galaxies. Fortunately, we can gauge the realism of our numerical approach even before starting the Argo simulation. In particular, simulations run with the same code, with similar methodology, and at a comparable resolution produce dwarf galaxies \citep{2013arXiv1308.4131S}, Milky-Way like galaxies \boldtext{(e.g., the Eris simulation, \citealt{2011ApJ...742...76G})}, and massive galaxies \citep{2010ApJ...709..218F} with reasonably realistic properties. The same numerical approach is also able to reproduce the enrichment level of the circum-galactic gas around high redshift galaxies \citep{2013ApJ...765...89S}. The paper is organized as follows. We outline the set-up of the Argo simulation and the strategy of the data analysis in section \ref{sect:Sim}. We present our first results in section \ref{sect:CompObs} where we compare the properties of the simulated galaxy with those of observed high redshift galaxies. In section \ref{sect:LeavingSFS} we then analyze the star formation history of the simulated galaxy finding an onset of quenching at $z\sim{}3.5$. We identify cosmological starvation as the cause of the star formation suppression in section \ref{section:OriginQuenching}. We highlight potential caveats that may affect the conclusion drawn from our work in section \ref{sect:Caveats}. We compare our results to previous theoretical works in section \ref{sect:Discussion}. Finally, in section \ref{sect:Summary} we end this paper with a summary of our main findings and our conclusions. | \label{sect:Summary} One of the major unsolved problems in galaxy evolution is to identify the physical process, or the processes, regulating the transition of galaxies from the star forming to the quiescent population. The old ages of massive, quiescent galaxies in the local Universe place this quenching of star formation at an early time, likely before $z\sim{}2$ \citep{2010MNRAS.404.1775T}. Similarly, the ages of massive, quiescent galaxies at $z=2-4$ (e.g., \citealt{2013ApJ...770L..39W, 2014ApJ...783L..14S}) indicate that some galaxies reduce their SFRs to low levels at even higher redshift. In this paper we analyze the origin of star formation quenching in high redshift galaxies with the help of a state-of-the-art cosmological simulation of a massive galaxy. Our main findings are as follows. \begin{itemize} \item The global properties of the simulated galaxy are in good agreement with those of similarly massive galaxies observed at high redshift. Reproduced properties include the stellar-to-virial mass ratio, the size of the stellar component, and the sSFR while on the star forming sequence. \item The simulation includes thermal supernova feedback, but does not model feedback from AGN. This suggests that AGN feedback is not an essential ingredient to reproduce properties of massive, quiescent galaxies at high redshift. \item At $z\sim{}3.5$ the simulated galaxy leaves the star forming sequence and the sSFRs decrease by almost an order of magnitude within a few 100 Myr. The SFR declines approximately exponentially with a e-fold time of $\sim{}$ 100 Myr. By $z\sim{}2$ the colors and the stellar mass of the simulated galaxy agree with those of massive, quiescent galaxies present at those redshifts. \item The drop of the sSFR is not caused by feedback processes, but rather a consequence of a leveling off and subsequent decline in the cool gas accretion rate onto the halo of the galaxy. \item The decrease of the sSFR is somewhat faster and more pronounced in our higher resolution runs compared with the low resolution run. We attribute this difference to the diminished efficacy of the implemented stellar feedback scheme at low numerical resolution. Hence, feedback likely plays a crucial role in suppressing star formation to the very low levels (less than a few $M_\odot$ yr$^{-1}$) observed in a large fraction of massive, quiescent, high redshift galaxies. \end{itemize} Based on our findings we propose a novel picture for the suppression of star formation that differs from previous suggestions based on a halo mass threshold or on star formation quenching via feedback-driven outflows during major mergers. After a period of fast gas accretion and exponential growing SFRs, some massive galaxies at high redshift enter a period of cosmological starvation in which the gas and dark matter accretion rates onto their halos first stall and subsequently decrease. Affected galaxies leave the main sequence as the stalled gas accretion rates no longer support exponentially increasing SFRs. The cosmological starvation picture physically connects the sSFR of high redshift galaxies to the gas accretion rate onto their halos. It makes a number of testable predictions. Generally, we expect that central galaxies residing in unrelaxed, still collapsing large scale structures have larger sSFRs than central galaxies embedded in a relaxed, virialized environment. Specifically, we predict that at $z\geq{}2$ central galaxies of a given stellar mass are more likely to be still star forming if they reside in a higher density environments, e.g., are surrounded by a larger number of satellite galaxies. In fact, this reversal of the local star forming -- density relation, namely larger \emph{specific} star formation rates in denser regions, has been observed at $z\sim{}1$ \citep{2007A&A...468...33E}. Also, we expect the region of shock-heated gas to expand outward during a period of reduced gas accretion rate and, thus, lower density of the pre-shocked infalling gas (see equation 29 in \citealt{2003MNRAS.345..349B}). Hence, cosmological starvation might also be tested by inferring and comparing the size of the virial shock around massive, quiescent galaxies and around star forming galaxies of the same mass. At $z<1$ environmental processes related to the presence of a hot, dilute atmosphere of shock-heated gas affect satellite galaxies and help in suppressing their SFR (e.g., \citealt{2014MNRAS.438..717K}). Satellite galaxies around massive, high redshift galaxies may thus potentially be used to probe the extent of the virial shock. Finally, during the starvation phase the accretion of both gas and stellar material is reduced. Hence, we predict that recently quenched, high redshift galaxies have (on average) a different distribution of satellite galaxies (e.g., fewer satellites at large distances, fewer massive satellites) than star forming galaxies of the same stellar mass. Cosmological starvation highlights the importance of the recent halo accretion history for the evolution of galaxies. Abundance matching techniques show that the stellar mass of galaxies is primarily controlled by their halo mass. Here we demonstrate that the accretion rate onto halos acts as an additional lever that controls the star formation rate of central galaxies at high redshift. Accretion rates and masses are tightly coupled for halos with an average accretion history \citep{2008MNRAS.383..615N}, but differ for the large fraction of halos that deviate from pure exponential growth \citep{2009MNRAS.398.1858M}. The exploration of the large variety of halo accretion histories in future work may lead to a deeper understanding of the observed diversity of high redshift galaxies. | 14 | 4 | 1404.3212 |
1404 | 1404.1519.txt | We present 23 interferometric images of parsec-scale jet of the quasar PKS 1741--03 at 15, 24 and 43 GHz spanning about 13 yr. We model the images as a superposition of discrete two--dimensional elliptical Gaussian components, with parameters determined by the cross--entropy technique. All the images present a spatially unresolved component (core) and usually two or three components receding from it. The same components were found in simultaneous 24 and 43 GHz maps, showing the robustness of our model-fitting. The core-shift opacity effect between these frequencies is weak. We have identified seven components moving along straight lines at constant apparent superluminal speeds ($3.5\la\beta_\mathrm{obs}\la 6.1$), with different sky position angles ($-186\degr\la\eta\la-125\degr$). The core flux density tracks quite well the fluctuations seen in the historical single-dish light curve at 14.5 GHz, with no measurable delay. The total flux density from the moving jet components is delayed $\sim$2 yr in relation to the core light curve, roughly the same as the lag between the ejection epoch and the maximum flux density in the light curves of the jet components. We propose that there are three non-exclusive mechanisms for producing these delays. From the kinematics of the most robust jet components and the core brightness temperature, we determined the bulk Lorentz factor ($4.8\la\gamma\la 24.5$) and the jet viewing angle ($0\fdg 35 \la \theta \la 4\fdg 2$); these values agree with previous estimates from the spectral energy distribution of PKS 1741--03 and its radio variability. | The quasar PKS 1741--03 (OT 068) exhibits intense flux density fluctuations at radio wavelengths, and those that occur at shorter time-scales have been attributed to refractive interstellar scintillation phenomena \citep{qia95}. Located at redshift $z=1.054$ \citep{whi88}, PKS 1741--03 shows a core-like radio morphology at kiloparsec scales, meaning that its brightness distribution is compatible with an unresolved source \citep{kha10}. It is also relatively compact at parsec scales, presenting a core that exceeds the maximum expected brightness temperature of $10^{12}$ K \citep{waj00,kov05}, and an inconspicuous jet, in which a few discrete jet components have been identified \citep{laz00,waj00,lis09b,pin12}. Very few efforts have been made to study the kinematics of the components present in its parsec-scale jet. As far as we know, only \citet{pin12} have used interferometric-based work to estimate the kinematic parameters of the jet components. They identified three jet components at 8 GHz, one of which has presented quasi-ballistic motion\footnote{In the sense that each jet component moves approximately with constant speed and position angle on the plane of sky.} with an apparent speed of about 1.7$c$, where $c$ is the speed of light. In order to expand the kinematic study of PKS 1741--03, we present results obtained from the modelling of 23 interferometric images at 15, 24 and 43 GHz, using a very robust statistical technique known as cross--entropy (hereafter CE; \citealt{rubi97,cap11}). This paper is structured as follows. In Section 2, we present the observational data of PKS 1741--03 analysed in this work, as well as a description of our CE model-fitting code, and assumptions adopted in the modelling. The structural parameters of individual components and their kinematic parameters are given in Section 3, where we also present measurements of the core-shift opacity effect, the core flux density variability and its relation to the historical single-dish light curve. Some constraints on the energetics and geometrical orientation of the parsec-scale jet are provided in Section 4. We discuss the time evolution of the flux density of some jet components in Section 5, in terms of shock-in-jet models, freefree absorption and supermassive binary black hole systems. We present our conclusions in Section 6. We assume throughout this work a $\Lambda$CDM cosmology with $H_0=71$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_\rmn{M}=0.27$, and $\Omega_\rmn{\Lambda}=0.73$, which implies 1 mas = 8.14 pc and 1 mas yr$^{-1}$ = 26.56$c$ for PKS 1741--03. | In this paper, we have analysed 23 inteferometric images of the quasar PKS 1741--03, obtained between 1995 and 2008 at 15, 24 and 43 GHz (15, six and two maps, respectively). We have assumed that the brightness distribution on the parsec-scale jet can be modelled by discrete components described mathematically by two--dimensional elliptical Gaussian functions. The number of Gaussian components was varied from one to six for each epoch, with the values of the free structural parameters being determined through the statistically robust CE global optimization method \citep{rubi97,cap11}. Our results indicate the presence of a central component, identified as the parsec-scale core region (the most intense component in terms of flux density in all the 21 epochs and responsible for 56--95 per cent of the total flux density of PKS 1741--03), and two to five (usually two) jet components per image. These components recede ballistically from the core with superluminal apparent speeds (from 3.5 to 6.1$c$), as well as with approximately constant position angles for individual components (from $-186$\degr to $-125$\degr). The trajectory of the jet component C2 on the plane of sky seems to be substantially bent (probable because of acceleration perpendicular to the jet flow; \citealt{hom09}). However, we have maintained our tentative ballistic description for C2 because of the small number of available epochs to track its motion, the relatively long interval between consecutive epochs, and its relatively low flux density. Future interferometric observations are fundamental to check whether non-radial motions do exist in this source. The same components detected in the two 43-GHz images of PKS 1741--03 are seen in the respective simultaneous images at 24 GHz, reinforcing the robustness of our CE modelling. Using these maps, we estimated a mean absolute core-shift between 24 and 43 GHz of about 50$\pm$55 $\mu$as, which is in reasonable agreement with previous estimates made by \citet{pus12} at lower frequencies. Our core-shift estimates for PKS 1741--03 must be considered cautiously because they are based only on dual frequency data obtained at two different epochs. The parsec-scale core flux density variability tracks quite well the fluctuations seen in the historical single-dish light curve at 14.5 GHz, presenting a null DCF time delay. However, the total flux density from the moving jet components (not considering core's contribution) shows a DCF delay of about 2.1 yr, roughly the same as the lag between the ejection epoch and the maximum flux density in the light curves of the jet components C3, C5 and C7. We propose three non-exclusive mechanisms for producing these delays: evolution of relativistic shock waves and/or ram-pressure confined plasmoids (e.g., \citealt{ozsa69,blko79,koni81,mage85,turl11}), an optically thick medium (external to the relativistic jet) with a size smaller than $\sim$12 pc, which absorbs (via bremsstrahlung) part of the synchrotron emission from the jet components \citep{wal00,gal04}, and a supermassive binary black hole system in which ejection of the jet components is associated with the black hole that is not coincident with the VLBI core \citep{rol13}. Based on the kinematic properties of the fastest jet component (C7), we derived a lower limit of $6.2\pm 1.4$ for the jet bulk Lorentz factor, as well as a conservative upper limit of $9\fdg 3\pm 2\fdg 2$ for the jet viewing angle. The relationship between the size of the components and their distance from the core provides an additional constraint for the jet viewing angle, favouring $\theta \sim 3\degr$. Our estimates for $\gamma$ and $\theta$ are in agreement with those assumed in the modelling of the spectral energy distribution of PKS 1741--03 \citep{cegu08}. Considerations involving the relationship between the observed and intrinsic brightness temperature of the parsec-scale core of PKS 1741--03 suggest that the value of the Doppler boosting factor must lie approximately between 2 and 49, compatible with previous estimates based on variability at radio wavelengths and gamma-ray flux and brightness temperature of the core \citep{waj00,faca04,hov09,sav10}. Finally, more strict kinematic limits for the parsec-scale region of the quasar PKS 1741--03 have been derived using the apparent speeds of the most robust jet components and the derived range for the Doppler boosting factor: $4.8 \la \gamma \la 24.5$ and $0\fdg 35 \la \theta \la 4\fdg 2$. It is important to emphasize this work presents the first application of our CE model-fitting technique to interferometric radio images of an AGN jet. Its extension to galactic and extragalactic jets, in general, is straightforward and this will be pursued in future work. | 14 | 4 | 1404.1519 |
1404 | 1404.5508_arXiv.txt | {The Magnetism in Massive Stars (MiMeS) project aims at understanding the origin of the magnetic fields in massive stars as well as their impact on stellar internal structure, evolution, and circumstellar environment. } {One of the objectives of the MiMeS project is to provide stringent observational constraints on the magnetic fields of massive stars, however, identification of magnetic massive stars is challenging, as only a few percent of high-mass stars host strong fields detectable with the current instrumentation. Hence, one of the first objectives of the MiMeS project was to search for magnetic objects among a large sample of massive stars, and to build a sub-sample for in-depth follow-up studies required to test the models and theories of fossil field origins, magnetic wind confinement and magnetospheric properties, and magnetic star evolution.} {We obtained high-resolution spectropolarimetric observations of a large number of OB stars thanks to three large programs (LP) of observations that have been allocated on the high-resolution spectropolarimeters ESPaDOnS, Narval, and the polarimetric module HARPSpol of the HARPS spectrograph. We report here on the methods and first analysis of the HARPSpol magnetic detections. We identified the magnetic stars using a multi-line analysis technique. Then, when possible, we monitored the new discoveries to derive their rotation periods, which are critical for follow-up and magnetic mapping studies. We also performed a first-look analysis of their spectra and identified obvious spectral anomalies (e.g., surface abundance peculiarities, H$\alpha$ emission), which are also of interest for future studies. } {In this paper, we focus on eight of the 11 stars (from the HARPSpol LP sample) in which we discovered or confirmed a magnetic field from the HARPSpol LP sample (the remaining three were published in a previous paper). Seven of the stars were detected in early-type Bp stars, while the last star was detected in the Ap companion of a normal early B-type star. We report obvious spectral and multiplicity properties, as well as our measurements of their longitudinal field strengths, and their rotation periods when we are able to derive them. We also discuss the presence or absence of H$\alpha$ emission with respect to the theory of centrifugally-supported magnetospheres.} {} | The properties of the magnetic fields of the {intermediate mass stars (1.5 to 8~\msun) of spectral type A and late-B (B4 and later) on the main sequence (A/B stars hereafter) are now well established \citep[see the reviews of ][as well as references hereinafter]{landstreet92,donati09}}. They are found in { a small fraction} of these stars, exclusively among the chemically peculiar Ap/Bp stars {\citep{wolff68,shorlin02,bagnulo06,auriere10,kochukhov13}}. They are mainly dipolar or low-order multi-polar fields, with polar strengths ranging from 300 G to 30 kG, most having fields of order 1~kG {\citep[e.g.][]{landstreet78,landstreet89,bohlender87,bohlender93,mathys97,wade00a,wade06,kochukhov06b,elkin10,bailey12}}. These fields are stable over many years, and even decades {\citep[for stars with sufficient observations, e.g.][]{landstreet89,khokhlova97,silvester14}}. While the field strengths seem to show a statistical decrease with stellar age, the field incidence does not depend on the stellar age \citep{kochukhov06a,landstreet08}. Such stable and large scale fields are called fossil fields \citep[i.e. they are not continuously maintained from dissipation,][]{cowling45,cowling53,borra82} and are observed in intermediate-mass stars from the pre-main-sequence phase (in Herbig Ae/Be stars), throughout the main-sequence phase, and very likely even until the red giant phase of stellar evolution {\citep{auriere08,auriere11,alecian13}}. Fossil fields have very different properties compared to the magnetic fields of the Sun and other cool, low-mass stars, which indicate a different origin. While in low-mass stars, the presence of a deep sub-surface convective zone allows for a dynamo to occur and produce very complex and unstable magnetic fields as observed at the surface of the Sun, intermediate-mass stars lack such a convective zone to generate their fields. It is believed instead that the fossil fields are remnants from fields enhanced or accumulated during star formation \citep[e.g.][]{moss01}. Studies performed the last years have brought a variety of new evidence in favour of this theory and in the generation and history of the such fossil fields \citep{wade05,braithwaite06,wade07,folsom08,alecian08a,alecian08b,alecian09,duez10a,duez10b,alecian13}. {Massive stars (above 8 \msun) of spectral type O and early-B on the main sequence (OB stars hereafter), similarly to intermediate-mass stars, possess a large radiative envelope}. We therefore {assume} that the origin of the field is similar in both types of stars. The {OB} stars are however hotter than {A/B} stars, and can drive significant radiative winds \citep{castor75}. Magnetic interaction between the star and the environment could therefore be significant \citep{uddoula02}. It has also been proposed that magnetic fields can have a strong impact on the structure and evolution of massive stars \citep[e.g. via enhanced or suppressed mixing, surface velocity braking,][]{maeder00,uddoula09,briquet12}. Until recently, our knowledge of the magnetic properties of the OB stars was very poor. Fields were only detected in a few peculiar cases, such as in He-strong or He-weak stars, as well as in a few non-peculiar stars. Such a lack of observational constraints motivated a large consortium to start the Magnetism in Massive Stars (MiMeS) project, {to study the origin and physics of the magnetic fields in massive stars. One of the main objectives of the MiMeS consortium was to obtain stringent observational constraints on the magnetic properties of massive stars. With this aim, we have performed a high-resolution spectropolarimetric survey of about 360 OB stars selected in the field of the Galaxy and in young clusters or associations. A large sample was required to detect a number of magnetic stars large enough for compiling good statistics on the magnetic properties of the OB stars. To perform this survey}, three spectropolarimetric large programmes (LPs) were allocated between mid-2008 and early 2013, on ESPaDOnS installed on the Canada-France-Hawaii Telescope (CFHT, Hawaii), on Narval installed on the Telescope Bernard Lyot (TBL, Pic du Midi, France), and on HARPS accompanied with the polarimetric module HARPSpol installed on the ESO~3.6m telescope (La Silla, Chile). {The Narval and ESPaDOnS magnetic detections were published in separate papers \citep[e.g.][]{grunhut09,grunhut13,oksala10,briquet13}, and the whole ESPaDOnS, Narval and HARPSpol survey will be published in forthcoming papers (Wade et al., Grunhut et al., Petit et al., Neiner et al., Alecian et al., in prep.). The present paper focuses {on the magnetic detections} of the HARPSpol sample.} Within the HARPSpol survey, we detected nine new magnetic stars and confirmed the presence of the magnetic fields at the surface of two others - HD~105382 and HD~109026 - that had been previously reported \citep{briquet07,borra83}. The two new magnetic detections (HD~122451 and HD~130807) and the field confirmation in HD~105382 obtained during the first run (May 2011) of the LP have already been published in a Letter \citep{alecian11}. In this paper, we report seven new detections and one field confirmation in HD~109026 that were obtained during the four remaining runs (Dec. 2011, July 2012, Feb. 2013, June 2013). This paper is structured as follows. In Section 2, we describe the observations and reduction we performed. In Section 3, we describe the spectral properties of the new magnetic stars. In Section 4, we analyse the polarised spectra and interpret them to propose magnetic field geometries. In, Section 5 we discuss the magnetospheric signatures observed (or not) in H$\alpha$, and in Section 6, we present a summary of our results. | We report the discovery of magnetic fields at the surface of seven early-B stars, as well as confirming the magnetic field of HD~109026, from observations obtained within the MiMeS project with HARPSpol. We do not detect the magnetic field in the early-B primary component of HD~109026, we reject the primary as being a He-weak star, and we are able to associate the previously reported magnetic field with the secondary Ap component only. Taking into account the discoveries obtained during the first run \citep{alecian11}, the HARPSpol LP allowed us to discover a total of nine new magnetic B stars, and to confirm the magnetic fields in one (HD 105382) additional early-B star. This brings us to a total of $\sim40$ MiMeS magnetic discoveries, illustrating the important contribution of the HARPSpol LP to the MiMeS project. Our data also allowed us to analyse the spectral properties of the newly discovered magnetic early-B stars, which led to the discovery of one double-lined spectroscopic binary (HD~109026) and one triple-lined spectroscopic binary (HD~156324). For three of the new magnetic stars (HD~66765, HD~67621, HD~109026) we acquired enough data to derive their rotation period, which will facilitate future spectropolarimetric follow-up for magnetic mapping. All magnetic stars discussed in this paper show abundance peculiarities: six display He-strong peculiarities, two He-weak peculiarities, and it is not yet clear to what class of CP stars the magnetic secondary of HD~109026 belongs (He-weak, Ap Si or Ap SrCrEu). It appears that, as in intermediate-mass stars, magnetic fields in B-type stars in the temperature range $18000-22000$~K are preferentially detected in chemically peculiar stars. Variable H$\alpha$ emission is detected in four out of the eight stars discussed in this paper. We argue that their emissions are very likely coming from centrifugal magnetospheres as is the case for many other magnetic OB stars \citep{petit13}. We also note the absence of H$\alpha$ emission in the other stars, while the simplest form of the theory predicts that their magnetic fields are strong enough and their rotation fast enough to host centrifugal magnetospheres. The absence of emission in H$\alpha$ is not in contradiction with the theoretical predictions of centrifugal magnetospheres, but confirms the global complexity of the formation and dynamics of such magnetospheres, as discussed by \citet{petit13}. A full statistical analysis of the whole HARPSpol, ESPaDOnS, and Narval MiMeS sample is in progress and will treat in particular the relation between the magnetic fields properties in massive stars and the stellar parameters, chemical peculiarities, pulsations, rotation, and age (Wade et al., Grunhut et al., Petit et al., Neiner et al., Landstreet et al., Alecian et al., in prep.). Those studies will improve our knowledge of the impact of the magnetic fields on massive star formation, structure and evolution. | 14 | 4 | 1404.5508 |
1404 | 1404.2058_arXiv.txt | In this article we have solved an hypothetical problem related to the stability and gross properties of two dimensional self-gravitating stellar objects using Thomas-Fermi model. The formalism presented here is an extension of the standard three-dimensional problem discussed in the book on statistical physics, Part-I by Landau and Lifshitz. Further, the formalism presented in this article may be considered as class problem for post-graduate level students of physics or may be assigned as a part of their dissertation project. | The study of gross properties of bulk self-gravitating objects using Thomas-Fermi model has been discussed in a very lucid manner in the text book on Statistical Physics by Landau and Lifshitz \cite{LL}. In this book the model has also been extended for the bulk system with ultra-relativistic electrons as one of the constituents. Analogous to the conventional white dwarf model, these electrons in both non-relativistic and ultra-relativistic cases provide degeneracy pressure to make the bulk system stable against gravitational collapse. The results are therefore an alternative to Lane-Emden equation or Chandrasekhar equation \cite{ST,RQ}. The mathematical formalism along with the numerical estimates of various parameters, e.g., mass, radius, etc. for white dwarf stars may be taught as standard astrophysical problems in the master of science level classes for the students having astrophysics and cosmology as spacial paper. The standard version of Thomas-Fermi model has also been taught in the M.Sc level atomic physics and statistical mechanics general classes. More than two decades ago, Bhaduri et.al. \cite{AJP} have developed a formalism for Thomas-Fermi model for a two dimensional atom. The problem can also be given to the advanced level M.Sc. students in the quantum mechanics classes. The numerical evaluation of various quantities associated with the two dimensional atoms are also found to be useful for the` students to learn numerical techniques, computer programing along with the physics of the problem. The work of Bhaduri et.al. is an extension of standard Thomas-Fermi model for heavy atoms into two-dimensional scenario. A two-dimensional version of Thomas-Fermi model has also been used to study the stability and some of the gross properties of two-dimensional star cluster \cite{MAX}. In our opinion this is the first attempt to apply Thomas-Fermi model to two-dimensional gravitating object. However, to the best of our knowledge the two-dimensional generalization of Thomas-Fermi model to study gross properties of bulk self-gravitating objects, e.g., white dwarfs has not been reported earlier. This problem can also be treated as standard M.Sc level class problem for the advanced level students with Astrophysics and Cosmology as special paper. In this article we shall therefore develop a formalism for two dimensional version of Thomas-Fermi model to investigate some of the gross properties of two-dimensional hypothetical white dwarf stars. The work is essentially an extension of the standard three-dimensional problem which is discussed in the statistical physics book by Landau and Lifshitz \cite{LL}. The motivation of this work is to study Newtonian gravity in two-dimension. Analogous Coulomb problem with logarithmic type potential has been investigated in an extensive manner. However, the identical problem for gravitating objects has not been thoroughly studied (except in \cite{MAX}). One can use this two-dimensional gravitational picture as a model calculation to study the stability of giant molecular cloud during star formation and also in galaxy formation. The article is arranged in the following manner. In the next section we have developed the basic mathematical formalism for a two-dimensional hypothetical white dwarf star. In section-III, we have investigated the gross properties of white dwarf stars in two-dimension. In section-IV, the stability of two-dimensional white dwarfs with ultra-relativistic electrons as one of the constituents have been studied. Finally in the last section we have given the conclusion of this work. | In conclusion we would like to comment that although the formalism developed here is for a hypothetical stellar object, which is basically an extension of standard three dimensional problem discussed in the book by Landau \& Lifshitz, we strongly believe that it may be considered as interesting post-graduate level problem for the physics students, including its numerical part. this problem can also be treated as a part of dissertation project for post graduate physics students. The study of Thomas-Fermi model in two-dimension for self-gravitating objects may be used for model calculations of star formation and galaxy formation from giant gaseous cloud. Finally, we believe that the problem solved here has some academic interest. \noindent{\bf{Acknowledgment:}} We would like to thank the anonymous referee for constructive criticism and pointing out some of the usefull references. | 14 | 4 | 1404.2058 |
1404 | 1404.5487_arXiv.txt | {} {{\boldtext We revisit with new augmented accuracy the theoretical dynamics of basic isotope exchange reactions involved in the $^{12}$C/$^{13}$C, $^{16}$O/$^{18}$O, and $^{14}$N/$^{15}$N balance because these reactions have already been studied experimentally in great detail. } } {Electronic structure methods were employed to explore potential energy surfaces, full-dimensional rovibrational calculations to compute rovibrational energy levels that are numerically exact, and chemical network models to estimate the abundance ratios under interstellar conditions.} {New exothermicities, derived for HCO$^+$ reacting with CO, provide rate coefficients markedly different from previous theoretical values in particular at low temperatures, resulting in new abundance ratios relevant for carbon chemistry networks. {\boldtext In concrete terms, we obtain a reduction in the abundance of H$^{12}$C$^{18}$O$^+$ and an increase in the abundance of H$^{13}$C$^{16}$O$^+$ and D$^{13}$C$^{16}$O$^+$. } In all studied cases, the reaction of the ion with a neutral polarizable molecule proceeds through the intermediate proton-bound complex found to be very stable. {\boldtext For the complexes {OCH$^+\cdots$CO}, % {OCH$^+\cdots$OC}, {COHOC$^+$}, {N$_2 \cdots$HCO$^+$}, {N$_2$H$^+\cdots$OC}, and {N$_2$HN$_2^+$}, we also calculated vibrational frequencies and dissociation energies. } } {The linear proton-bound complexes possess sizeable dipole moments, which may facilitate their detection.} | \label{sec:intro} Isotopic fractionation reactions have already been invoked by \cite{watson76a} and \cite{dalgarno76} to explain the enrichment of heavy isotopes of molecules in dark cold interstellar cloud environments. The exothermicity involved in the isotopic exchange reaction directly depends on the difference of the zero-point energies (ZPE) between the two isotopes, if one assumes that the reaction proceeds in the ground-rovibrational states of both the reactant and product molecule. This assumption has been questioned for the reaction H$_3^+$+HD$\rightleftharpoons$H$_2$D$^+$+H$_2$, where some rotational excitation in H$_2$ may reduce the efficiency of the reverse reaction \citep{pagani92,hugo09}. In this paper we revisit some fractionation reactions involved in the $^{12}$C/$^{13}$C, $^{16}$O/$^{18}$O, and $^{14}$N/$^{15}$N balance by reinvestigating the potential energy surfaces involved in the isotopic exchange reactions. Within the Born-Oppenheimer approximation, a single nuclear-mass-independent potential energy surface (PES) is considered for all isotopic variants of molecules under consideration. The nuclear motions are introduced subsequently and isotopologues, molecules of different isotopic compositions and thus different masses, possess different rotational constants, different vibrational frequencies, and different ground-state (zero-point) vibrational energies, in other words, different thermodynamic properties \citep{urey47}. Differences in zero-point energies can become important under cool interstellar cloud conditions where molecules rather undergo isotopic exchange (fractionation) than react chemically. This thermodynamic effect may result in isotopologue abundance ratios (significantly) deviating from the elemental isotopic ratios. Knowledge of the abundance ratios may in return provide valuable information on molecular processes at low collision energies. As far as astrophysical models are concerned, $^{13}$C and $^{18}$O isotopic fractionation studies involving CO and HCO$^+$ \citep{lebourlot93,liszt07, roellig13, maret13} are based on the pionneering paper by \cite{langer84}, who referred to the experimental studies by \cite{smith80a} and used theoretical spectroscopic parameters for the isotopic variants of HCO$^+$ reported by \cite{henning77}. \cite{lohr98} derived the harmonic frequencies and equilibrium rotational constants for CO, HCO$^+$, and HOC$^+$ at the configuration interaction (including single and double excitations) level of theory (CISD/6-31G**) and tabulated reduced partition function ratios and isotope exchange equilibrium constants for various isotope exchange reactions between CO and HCO$^+$. Surprisingly, this paper has not received much attention in the astrophysical literature, and its conclusions have never been applied. The studies of \cite{langer84} and \cite{lohr98} led to qualitatively different conclusions regarding the following fractionation reaction: \begin{eqnarray} {^{13}\mathrm{C}}{^{16}\mathrm{O}} + \mathrm{H}^{12}\mathrm{C}{^{18}\mathrm{O}}^+ \rightarrow \mathrm{H}^{13}\mathrm{C}{^{16}\mathrm{O}}^+ + {^{12}\mathrm{C}}{^{18}\mathrm{O}} + \Delta E , ~~ \label{reaction_diff} \end{eqnarray} \noindent which was found to be endothermic with $\Delta E/k_{\mathrm{B}}=-5$ K by \cite{langer84} and exothermic with $\Delta E/k_{\mathrm{B}} = 12.5$ K by \cite{lohr98}, where $k_{\mathrm{B}}$ is the Boltzmann constant. To clear up this discrepancy, we carried out numerically exact calculations for the vibrational ground state of HCO$^+$ using a potential energy surface previously developed by \cite{mladenovic98b}. Our calculations gave $\Delta E/k_{\mathrm{B}} = 11.3$ K for reaction (\ref{reaction_diff}), in good agreement with the harmonic value of \cite{lohr98}. In addition, we noticed that the $\Delta E/k_{\mathrm{B}}$ values of \citet{henning77} for the reactions \begin{eqnarray} {^{13}\mathrm{C}}{^{16}\mathrm{O}} + \mathrm{H}^{12}\mathrm{C}{^{16}\mathrm{O}}^+ & \rightleftharpoons & \mathrm{H}^{13}\mathrm{C}{^{16}\mathrm{O}}^+ + {^{12}\mathrm{C}}{^{16}\mathrm{O}} ~~~~ \label{reaction2} \end{eqnarray} \noindent and \begin{eqnarray} {^{12}\mathrm{C}}{^{18}\mathrm{O}} + \mathrm{H}{^{12}\mathrm{C}}{^{16}\mathrm{O}}^+ & \rightleftharpoons & \mathrm{H}{^{12}\mathrm{C}}{^{18}\mathrm{O}}^+ + {^{12}\mathrm{C}}{^{16}\mathrm{O}} ~~~~ \label{reaction3} \end{eqnarray} \noindent were quoted as 17$\pm$1 K and 7$\pm$1 K by \cite{smith80a} and as 9 and 14 K by \cite{langer84}. Reconsidering the original values of \cite{henning77}, we found that \cite{langer84} permuted the zero-point energies for H$^{13}$C$^{16}$O$^+$ and H$^{12}$C$^{18}$O$^+$ in Table 2 of their paper. From the original spectroscopic parameters of \cite{henning77}, we derive $\Delta E/k_{\mathrm{B}} = 10.2$ K for reaction (\ref{reaction_diff}), in good agreement with our result and the result of \cite{lohr98}. The permutation of the zero-point vibrational energies of H$^{13}$C$^{16}$O$^+$ and H$^{12}$C$^{18}$O$^+$ affects the exothermicities and rate coefficients summarized in Table 1 and Table 3 of the paper by \cite{langer84}. These data are actually incorrect for all isotope fractionation reactions CO+HCO$^+$, except for \begin{eqnarray} {^{13}\mathrm{C}}{^{18}\mathrm{O}} + \mathrm{H}^{12}\mathrm{C}{^{16}\mathrm{O}}^+ & \rightleftharpoons & \mathrm{H}^{13}\mathrm{C}{^{18}\mathrm{O}}^+ + {^{12}\mathrm{C}}{^{16}\mathrm{O}} . ~~~~ \label{reaction_isto} \end{eqnarray} \noindent The rate coefficients reported by \cite{langer84} are still widely used when including isotopes such as $^{13}$C and $^{18}$O into chemical (molecular) networks \citep{maret13,roellig13}. With these points in mind, our goal is to provide reliable theoretical estimates for the zero-point vibrational energies first of H/DCO$^+$ and to derive proper rate coefficients for the related fractionation reactions. Our improved results for the exothermicities and rate coefficients are summarized in Tables \ref{table_kelvin} and \ref{table_rate}. \cite{henning77} also reported spectroscopic parameters for various isotopic variants of N$_2$H$^+$. This was our initial motivation to expand the present study to ion-molecule reactions between N$_2$H$^+$ and N$_2$. $^{15}$N fractionation in dense interstellar clouds has been first considered by \cite{terzieva00}, who referred to the experimental information of the selected ion flow-tube (SIFT) studies at low temperatures of \cite{adams81}. {\boldtext The reactions discussed in this paper, CO+HCO$^+$ and N$_2$+HN$_2^+$, are the most obvious candidates for isotopic fractionation. In addition, they have been studied in the laborataory, which allows a detailed discussion. A similar reaction has been invoked for CN \citep{milam09}, but no experimental and/or theoretical information is available there. } In the Langevin model, the long-range contribution to the intermolecular potential is described by the isotropic interaction between the charge of the ion and the induced dipole of the neutral. Theoretical approaches based on this standard assumption may qualitatively explain the behaviour of the association rates. However, they generally provide rate coefficients that are higher than experimental results \citep{langer84}. The rate coefficients for ion-molecule reactions are quite constant at higher temperatures but increase rapidly at lower temperatures. The latter feature is an indication of barrierless potential energy surfaces. The electrostatic forces are always attractive and can be experienced over large distances even at extremely low temperatures relevant for dark cloud enviroments. Short-range forces appear in closer encounters of interacting particles and may (prominently) influence the overall reaction rate. To explore the short-range effects we also undertake a study of linear proton-bound ionic complexes arising in the reactions involving HCO$^+$, HOC$^+$, and N$_2$H$^+$ with CO and N$_2$, which are common interstellar species. Our theoretical approach is described in Sect. \ref{sec:calculations}. The specific aspects of the fractionation reactions of HCO$^+$ and HOC$^+$ with CO are reanalysed in Sect. \ref{sec:hco+} and the fractionation reactions N$_2$H$^+$+N$_2$ in Sect. \ref{sec:nnh+}. We discuss the equilibrium constants and rate coefficients of CO+HCO$^+$/HOC$^+$ in Sect. \ref{sec_discussion:hco+}, providing the astrochemical implications of the new exothermicities in Sect. \ref{discussion:astro}. The isotope fractionation reactions N$_2$H$^+$+N$_2$ are considered including the nuclear spin angular momentum selection rules in Sect. \ref{sec_discussion:nnh+}. The linear proton-bound cluster ions are analysed in Sect. \ref{discussion:pes}. Our concluding remarks are given in Sect. \ref{sec:conclusion}. | 14 | 4 | 1404.5487 |
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1404 | 1404.3097_arXiv.txt | {K-means is a clustering algorithm that has been used to classify large datasets in astronomical databases. It is an unsupervised method, able to cope very different types of problems.} {We check whether a variant of the algorithm called single pass k-means can be used as a fast alternative to the traditional k-means. } { The execution time of the two algorithms are compared when classifying subsets drawn from the SDSS-DR7 catalog of galaxy spectra. } {Single-pass k-means turn out to be between 20\,\%\ and 40\,\% faster than k-means and provide statistically equivalent classifications. This conclusion can be scaled up to other larger databases because the execution time of both algorithms increases linearly with the number of objects. } { Single-pass k-means can be safely used as a fast alternative to k-means. } | The classification algorithm k-means has the potential to classify huge astronomical databases, such as those to be expected with the advent of new instruments and catalogs (see Sect.~\ref{intro}). We tested a variant of the original algorithm, called single pass k-means, which unifies the two main steps of k-means (Sect.~\ref{algorithms}). Single pass k-means turns out to be between 20\,\% and 40\,\% faster than k-means (Sect.~\ref{test1}), and it provides statistically equivalent classifications (Sect.~\ref{equivalence}). Saving 20\,\%\ to 40\,\%\ of the time may not look like a lot, however the actual gain when using single pass k-means depends very much on the specific application. Keep in mind that k-means (and so single pass k-means) is a tool with the potential of classifying gigantic datasets by bruteforce. The foreseeable applications may require long execution times and, therefore a 40\,\%\ saving may actually represent days or weeks of work. The tests were carried out using a particular catalog of galaxy spectra with limited data volumes (up to 20\,000 objects in 1637 dimensions). However, single pass k-means would outperform k-mean even for other larger datasets. That the computer time employed by the two alternative algorithms increases linearly with time implies that the gain should be constant even for significantly larger datasets. Moreover, k-means is a workhorse proven to converge in many very different contexts. The datasets we use are not special, therefore the properties inferred for them can probably be extrapolated to many other datasets. | 14 | 4 | 1404.3097 |
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1404 | 1404.4162_arXiv.txt | {{\it Planck}'s data acquired during the first 15.4 months of observations towards both the disk and halo of the M31 galaxy are analyzed. We confirm the existence of a temperature asymmetry, previously detected by using the 7-year WMAP data, along the direction of the M31 rotation, therefore indicative of a Doppler-induced effect. The asymmetry extends up to about $10\degr$ ($\simeq 130$ kpc) from the M31 center. We also investigate the recent issue raised in Rubin and Loeb (2014) about the kinetic Sunyaev-Zeldovich effect from the diffuse hot gas in the Local Group, predicted to generate a hot spot of a few degrees size in the CMB maps in the direction of M31, where the free electron optical depth gets the maximum value. We also consider the issue whether in the opposite direction with respect to the M31 galaxy the same effect induces a minimum in temperature in the Planck's maps of the sky. We find that the {\it Planck}'s data at 100 GHz show an effect even larger than that expected.} | Galactic disk rotation can be accurately investigated in the optical, infrared (IR) and radio bands and allows to infer important information, among others, about the dynamical mass content of galaxies (see e.g. \citealt{binney}). On the other hand, many ambiguities still exist about the main constituents of the galactic halos. The degree to which galactic halos rotate with respect to the disks is a particularly difficult task to be investigated, even for the closest galaxy to the Milky Way: M31 \citep{courteau}. A novel approach in the study of the rotation of either the disk and halo of nearby galaxies (particularly the M31 galaxy) has been discussed in \cite{depaolis2011}. By using the 7-year WMAP data, a possible temperature asymmetry was found both in the M31 disk and halo along the direction of the M31 rotation, therefore reminiscent of a Doppler-induced effect. By adopting the geometry described in Fig. 1 in \cite{depaolis2011}, and extending the analysis up to about $20 \degr$ ($\simeq 260$ kpc) around the M31 center, we found in the two opposite regions of the M31 disk a temperature difference of about $130$ $\mu$K, more or less the same in the W, V and Q WMAP bands. A similar effect was visible also towards the M31 halo up to about 120 kpc from the M31 center with a peak value of about $40$ $\mu$K. The robustness of that result was tested by considering 500 randomly distributed control fields and also simulating 500 sky map realizations from the best-fit power spectrum constrained with BAO and $H_0$ (see \citealt{depaolis2011} for details). It turned out that the probability that the detected temperature asymmetry towards the M31 disk is due to a random fluctuation of the CMB signal is below about $2\%$ while in the case of the M31 halo it is less than about $30\%$. Although the confidence level of the signal was not high with WMAP data, if estimated purely statistics, nevertheless we believed that the geometrical structure of the temperature asymmetry pointed towards a definite effect modulated by the rotation of the M31 disk and halo and suggested that with the {\it Planck} data it could be possible to definitely prove or disprove our conclusions. Indeed, the {\it Planck} satellite is about ten times more sensitive than the WMAP satellite and has an angular resolution about three times better: the {\it Planck} full width half maximum (FWHM) resolution ranges from $33.3 \arcmin$ to $4.3 \arcmin$ going from 30 GHz to 857 GHz, and its final sensitivity is in the range of $2-4.7$ $\mu$K/K in terms of $\delta T/T$ for the Low Frequency Instrument (LFI), that is in the range $30-70$ GHz, and of $2-14$ $\mu$K/K for the High Frequency Instrument (HFI) below 353 GHz (see e.g. \citealt{burigana2013} for a recent review on {\it Planck}'s results). The aim of the present paper is therefore to analyze in detail the {\it Planck} data acquired during the first 15.4 months of observations towards both the disk and halo of the M31 galaxy. In addition, we also take the opportunity of investigating in some detail the recent issue raised in \cite{rubinloeb} about the kinetic Sunyaev-Zel'dovich effect from the diffuse hot gas in the Local Group, which happens to show up as a hot spot of a few degrees in size in the direction of M31 (where the free electron optical depth gets the maximum value). We also investigate whether in the opposite direction with respect to the M31 galaxy, the same effect induces a minimum in temperature in the {\it Planck}'s maps of the sky. | Galactic halos are relatively less studied than galactic disks and there are still many ambiguities not only in the main halo constituents, but also with respect to the degree to which galactic halos rotates with respect to the disks \citep{courteau,deason}. Actually, the rotation of the galactic halos is clearly related to the formation scenario of galaxies. In the standard collapse model (see e.g. \citealt{eggen}) both the halo and disk derive from the same population and the rotation of the outer halo should be, in this case, aligned with the disk angular momentum. On the contrary, in a hierarchical formation scenario, structures reaching later the outer halo should be less connected to the disk. Therefore, it is evident that information on the galactic halo rotation provides key insights about the formation history of galaxies. It is also well known that the M31 disk rotates with a speed of about 250 km s$^{-1}$ and this has been clearly shown also by the velocity maps obtained from radio measurements \citep{Chemin,Corbelli}. These maps look very similar to what we find in the {\it Planck} data towards the M31 disk. In the previous Section we have also shown that {\it Planck}'s data show the existence of a temperature asymmetry with respect to the disk-halo rotation axis, up to a galactocentric distance of about 130 kpc and with a peak temperature contrast of about $40~\mu$K. We remark that, until now, the only evidence of the M31 halo rotation was put forward by the analysis of the dwarf galaxies orbiting M31 \citep{ibata}. In all generality, five possibilities may be considered in order to explain the effects discussed in Sections 2.1-2.3: ($i$) free-free emission; ($ii$) synchrotron emission; ($iii$) anomalous microwave emission (AME) from dust grains; ($iv$) kinetic Sunyaev-Zel'dovich (SZ) effect; ($v$) cold gas clouds populating the M31 halo. A detailed study of their contribution using all the {\it Planck}'s bands to constrain the model parameters and the relative weight of these five models will be published elsewhere. Here, we only note that effects $(i)-(iii)$ give a signal with a rather strong dependence on the wavelength, while $(iv)$ and $(v)$ are almost independent of the observation band in the microwave regime and to first approximation could provide the main contribution to the observed effect. Thus, our investigation shows the power of CMB to trace, along with the clusters of galaxies via Sunyaev-Zeldovich effect and the large scale voids (e.g. \citealt{G}), also the individual galactic halos. | 14 | 4 | 1404.4162 |
1404 | 1404.3742_arXiv.txt | We perform the first fit to the anisotropic clustering of SDSS-III CMASS DR10 galaxies on scales of $\sim 0.8 - 32$ $h^{-1}$ Mpc. A standard halo occupation distribution model evaluated near the best fit Planck $\Lambda$CDM cosmology provides a good fit to the observed anisotropic clustering, and implies a normalization for the peculiar velocity field of $M \sim 2 \times 10^{13}$ $h^{-1}$ $M_{\sun}$ halos of $f\sigma_8(z=0.57) = 0.450 \pm 0.011$. Since this constraint includes both quasi-linear and non-linear scales, it should severely constrain modified gravity models that enhance pairwise infall velocities on these scales. Though model dependent, our measurement represents a factor of 2.5 improvement in precision over the analysis of DR11 on large scales, $f\sigma_8(z=0.57) = 0.447 \pm 0.028$, and is the tightest single constraint on the growth rate of cosmic structure to date. Our measurement is consistent with the Planck $\Lambda$CDM prediction of $0.480 \pm 0.010$ at the $\sim 1.9\sigma$ level. Assuming a halo mass function evaluated at the best fit Planck cosmology, we also find that $10\%$ of CMASS galaxies are satellites in halos of mass $M \sim 6 \times 10^{13}$ $h^{-1}$ $M_{\sun}$. While none of our tests and model generalizations indicate systematic errors due to an insufficiently detailed model of the galaxy-halo connection, the precision of these first results warrant further investigation into the modeling uncertainties and degeneracies with cosmological parameters. | \label{sec:intro} The clustering of galaxies on small scales provides important constraints on the relationship between galaxies and the underlying dark matter distribution. This relation is of interest in itself as a constraint on galaxy formation and evolution, as well as for quantifying the impact of galaxy-formation scale physics on larger scale clustering measures used for cosmological parameter constraints. Modern approaches to modeling the relationship between galaxies and the underlying dark matter distribution rely on the basic tenet that galaxy formation requires a gravitationally-bound dark matter halo or sub-halo to accumulate and condense gas \citep{Peacock00,Seljak00,Benson00,White01,Berlind02,CooraySheth02,Yang03}. In their simplest form, such ``halo models'' contain one dominant variable that determines the probability that a (sub-)halo hosts a galaxy of interest. In the halo occupation distribution (HOD) formalism adopted in this paper, halo mass is the dominant variable and halos are permitted to host more than one galaxy. In the sub-halo abundance matching (``SHAM'') formalism, the maximum circular velocity at accretion is often used \citep{Marinoni02,Vale06,Conroy06}. The primary advantage of SHAM is that each sub-halo hosts only a single galaxy, thus requiring fewer free parameters to specify the model but assuming a specific but physically motivated relation between central and satellite galaxies. The practical disadvantage is that $N$-body simulations require higher resolution to resolve sub-halos. In principle both of these approaches could be generalized to include additional secondary variables such as halo formation time, with observable consequences \citep{Gao05,Wang13,Zentner13,Cohn13}. There are a host of observables available to constrain halo models as a function of galaxy properties: one-point statistics like number density or luminosity functions, two- or three-point galaxy clustering \citep{Zehavi11,Marin11}, marked statistics \citep{Sheth05,White09} and direct measurements the galaxy group multiplicity function \citep{Yang09,Reid09}. The most widely used observable is the projected correlation function, $w_p$, which removes sensitivity to redshift space distortions by integrating over the line-of-sight separation. While redshift space distortion effects are more difficult to model, they do provide complementary constraints both on the velocity distribution of galaxies relative to their host dark matter halos \citep{vdB05} and on cosmological parameters \citep{Yang04}. The primary goal of the present paper is to use the information in the anisotropy of the galaxy correlation function on scales $\sim 0.8 - 32$ $h^{-1}$ Mpc to simultaneously constrain the HOD and growth rate of cosmic structure through the pairwise infall of galaxies caused by their mutual gravitational attraction \citep{Kaiser87}. Constraints on gravitational infall on these scales is of particular interest in searching for signatures of modified gravity: for instance, an $f(R)$ model with $|f_{R0}| = 10^{-4}$ predicts a $\sim 25\%$ increase in the amplitude of pairwise infall velocities on scales of 10-30 Mpc \citep{Keisler13,Zu13,Lam12}. Alternatively, the non-linear regime is also a promising avenue for constraining dark sector coupling \citep{Piloyan14}. We can also use the constraints on the HOD to infer the nuisance parameter $\sigma^2_{\rm FOG}$ employed in our analysis on larger scales \citep{Reid12,Samushia13} to account for the velocity dispersions of galaxies relative to their host dark matter halos. See \citet{Hikage14} for a similar concept applied to the power spectrum multipoles. In this paper we focus on the CMASS sample from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS). This sample has thus far been the focus of several cosmological analyses, most recently providing a one per-cent absolute distance measurement using the baryon acoustic oscillation (BAO) standard ruler \citep{Anderson13} and a 6\% constraint on the growth rate of cosmic structure \citep{Samushia13,Beutler13,Sanchez13,Chuang13}. The projected correlation function of these galaxies has also been used to constrain halo models using both the HOD \citep{White11,Guo14} and SHAM \citep{Nuza13} formalisms; this work represents the first quantitative comparison to the small-scale anisotropic clustering of the CMASS galaxies. The layout of the paper is as follows. In Sec.~\ref{sec:pre} we describe the basic conceptual elements of our analysis. Sec.~\ref{sec:data} details our dataset, while Sec.~\ref{sec:FB} focuses on mitigating the impact of fiber collisions in our spectroscopic galaxy sample. Sec.~\ref{sec:meas} presents fiber-collision corrected measurements and uncertainties. Sec.~\ref{sec:HODmodel} presents the details of our $N$-body simulation based HOD model that we use to fit the observed anistropic CMASS galaxy clustering. The principal results of a simultaneous fit to the HOD parameters and $f\sigma_8$ are presented in Sec.~\ref{sec:results}. In Sec.~\ref{sec:modgrav} we discuss the implications of our results for constraining modified gravity models, and in Sec.~\ref{sec:conc} we discuss future prospects for this technique. | \label{sec:conc} We have made the most precise comparison to date between the observed anisotropic clustering of galaxies at relatively small separations ($\sim 0.8 - 32$ $h^{-1}$ Mpc) and the predictions of a standard halo model in the context of $\Lambda$CDM. We found good agreement between our simplified, redshift-independent HOD model and our measurements of both the projected and anistropic clustering on small scales. Our fits constrain the growth rate of cosmic structure at the effective redshift of our galaxy sample: $f\sigma_8(z_{\rm eff} = 0.57) = 0.450 \pm 0.011$. This constraint is consistent with but improves on our DR11 analysis of large scale anistropy \citep{Samushia13} by a factor of 2.5. Intriguingly, our result has the same statistical power but is $\sim 1.9\sigma$ low compared with Planck's $\Lambda$CDM prediction, $f\sigma_8 = 0.480 \pm 0.010$ \citep{PlanckXVI}. The competitive statistical precision of our measurement warrants a systematic evaluation of the observational and modeling systematics. For the former, we introduced a new anisotropic clustering statistic $\hat{\xi}_{0,2}$ that does not include information below the fiber collision scale, but approaches the usual multipoles on large scales. We carefully assessed the systematic and observational uncertainties from the angular upweighting method to correct fiber collisions to order to estimate the projected correlation function $w_p(r_{\sigma})$. We combined these measurements to obtain robust joint constraints on the halo occupation distribution and growth rate of cosmic structure probed by CMASS galaxies. To assess the robustness of our modeling assumptions, we investigated several generalizations to our HOD assumptions and particularly how we assign velocities to the mock galaxies from which we draw our theoretical predictions; the results are summarized in Table \ref{tab:hod}. The variations we examined caused at most $\sim 0.5\sigma$ shifts in the $f\sigma_8$ constraints. However, given the statistical precison of our reported constraint, further investigation with more sophisicated modeling of the galaxy-halo connection is warranted. Of the possibilities we explored, a model that relaxes the assumption that halos hosting satellite galaxies also host centrals (labelled ``cen/sat test'') improved the fit to our measurements by $\Delta \chi^2 = 10$ but did not shift $f\sigma_8$ constraints appreciably. Such a model is well-motivated by our target selection process -- both color cuts and photometric errors cause massive galaxies to scatter in and out of the sample. Alternatively, we can also improve the model fit by increasing the satellite galaxy velocity dispersion at fixed halo mass. At least within the cosmological parameter space we explored, we found that for two different definitions of the central galaxy velocity, the data prefer ${\bf v}_{\rm DENS}$, the motion of the densest $\sim 0.2r_{\rm vir}$ clump, over ${\bf v}_{\rm COMV}$, the halo center-of-mass velocity averaged over all particles within $\Delta_m = 200$. A comparison of these two velocity fields also indicates a possible shift of $\sim 1.5\%$ in the effective large scale $f\sigma_8$, and should therefore be considered when this level of precision is reached. While we have not tested any explicit modified gravity models, we have shown that the clustering of few $\times 10^{13}$ $h^{-1}$ Mpc halos are consistent with the expectations of $\Lambda$CDM and a simple picture of galaxy formation in which halo mass is the only relevant variable determining the probability of hosting a CMASS galaxy. To quantify the precision of this test, our best fit model matches the observed $\hat{\xi}_{0}$ at the 3 per-cent level from 0.8 - 32 $h^{-1}$ Mpc, and 15 to 5 per-cent level from 5 to 32 $h^{-1}$ Mpc for $\hat{\xi}_2$, with reasonable agreement compared to our uncertainties on smaller scales as well. As the example of $f(R)$ shows, modified gravity could potentially dramatically alter structure growth on these scales, and our analysis should be used to constrain such models. In addition to the $f\sigma_8$ constraint afforded by our measurements, more precise galaxy velocity bias predictions in $\Lambda$CDM would allow our joint constraints on $\gamma_{\rm IHV}$ and $b\sigma_8$ to be interpreted as an additional consistency test between the halo mass inferred from clustering amplitude $b\sigma_8$, and from the halo virial velocities probed by $\gamma_{\rm IHV}$. Finally, even ignoring the information of the small-scale clustering on $f\sigma_8$, our data tightly constrain the impact of the intra-halo motions of galaxies on clustering at relatively large scales. We derive a prior on the ``finger-of-god'' nuisance parameter that is tighter but consistent with the prior adopted in \citet{Reid12} and \citet{Samushia13}. Moreover, our detailed study of the clustering on small scales also allowed us to validate that $\sigma^2_{\rm FOG}$ as defined in those works can precisely describe the impact of intra-halo velocities of CMASS galaxies on quasi-linear scales. | 14 | 4 | 1404.3742 |
1404 | 1404.6398_arXiv.txt | The $\gamma$-ray flare of PKS 1222+216, observed in June 2010, is interpreted as an outcome of jet dynamics at recollimation zone. We obtained the $\gamma$-ray light-curves in three different energy bands, namely, 100--300 MeV, 300 MeV--1 GeV and 1--3 GeV from observations by the \emph{Fermi} Large Area Telescope (LAT). We also use the \emph{Swift}--XRT flux from 0.3--10 keV obtained from archival data. We supplement these with the 0.07--0.4 TeV observations with MAGIC telescope, available in the literature. The detection of source at very high energy (VHE, $E>100$ GeV) with a differential photon spectral index of $2.7\pm0.3$ and the rapid variability associated with it suggests that the emission arises from a compact region located beyond the broad line emitting region. The plausible $\gamma$-ray emission mechanism can then be inverse Compton scattering of IR photons from obscuring torus. Further, the decay time of LAT flare cannot be explained by considering simple radiative loss mechanisms. Hence, to interpret the LAT light curves, we develop a model where the broadband emission originates from a compact region, arising plausibly from the compression of jet matter at the recollimation zone. The flare is then expressed as an outcome of jet deceleration probably associated with this focusing effect. Based on this model, the rise of the LAT flare is attributed to the opening of emission cone followed by the decay resulting from jet deceleration. The parameters of the model are further constrained by reproducing the broadband spectral energy distribution of the source obtained during the flare episode. Our study suggests that the particle energy density exceeds magnetic energy density by a large factor which in turn may cause rapid expansion of the emission region. However, near equipartition can be achieved towards the end of LAT flare during which the compact emission region would have expanded to the size of jet cross-section. | \label{sec: I} Flat spectrum radio quasars (FSRQs) are radio loud active galactic nuclei (AGNs) with relativistic jet oriented close to the line of sight of the observer. Under the unification theory, they are classified along with BL Lacs as blazars \citep{1995PASP..107..803U}. Non-thermal emission extending from radio to $\gamma$-rays, rapid flux variability and high degree of polarization are some of the common properties observed in blazars \citep{2000AIPC..515...19S,2008PASJ...60..707F,2004NewAR..48..367K}. Their spectral energy distribution (SED) is characterized by a typical double-humped feature extending from radio to $\gamma$-ray energies \citep{1999ApJ...514..138K,1998ApJ...497..178W} and in a few cases, up to very high energies (VHEs, E$>$100 GeV) \citep{2008Sci...320.1752M, 2010HEAD...11.2706W, 2011ApJ...730L...8A}. The observed rapid flux variability suggests the emission to arise from a compact region located close to the central engine and moving down the jet at relativistic speed \citep{1995MNRAS.273..583D}. The low energy emission, extending from radio to UV/X-ray, is generally interpreted as synchrotron emission from a non-thermal population of electrons, while the high energy emission is believed to originate from inverse Compton scattering of low energy photons. The target photons for inverse Compton scattering can be the synchrotron photons from the jet themselves (SSC) \citep{1981ApJ...243..700K, 1985ApJ...298..114M, 1989ApJ...340..181G} or photons external to the jet (EC) \citep{1987ApJ...322..650B, 1989ApJ...340..162M, 1992A&A...256L..27D}. Simple emission models that consider only synchrotron and SSC processes, cannot explain the $\gamma$-ray emission from FSRQs and one needs to invoke EC emission to explain the SED satisfactorily \citep{2001ApJ...553..683H, 2009ApJ...703.1168B, 2012MNRAS.419.1660S}. A few plausible target photons for the EC process are photons from the accretion disk \citep{1993ApJ...416..458D, 1997A&A...326L..33B}, reprocessed accretion disk photons from the broad line emitting region (BLR) \citep{1994ApJ...421..153S, 1996MNRAS.280...67G} and/or infra-red (IR) photons from the dusty obscuring torus \citep{1994ApJ...421..153S, 2000ApJ...545..107B, 2008MNRAS.387.1669G}. PKS 1222+216 ($z=0.432$) is a flat spectrum radio quasar detected at VHE by the Major Atmospheric Gamma-ray Imaging Cherenkov Telescope \citep[\emph{MAGIC},][]{2010ATel.2684....1M,2011ApJ...730L...8A}. It is the third FSRQ detected at VHE after 3C 279 and PKS 1510-089 \citep{2008Sci...320.1752M, 2010HEAD...11.2706W}. PKS $1222+216$ has been active at LAT energies since September 2009, undergoing occasional brightness enhancements \citep{2011ApJ...733...19T}. Such flaring episodes were also detected in other observatories operating at different/similar wavebands \citep{2010ATel.2641....1B,2010ATel.2626....1C}. The source underwent two major flares of $\sim 10^{-5}$ph cm$^{2}$ s$^{-1}$ ($0.1-300$ GeV, $>10\sigma$) in April and June 2010 \citep{2011ApJ...733...19T}. The second flare in June was associated with a rapid VHE flare observed by the \emph{MAGIC} telescope (on June 17, 2010), with a flux doubling timescale of $\sim$ 10 min \citep{2010ATel.2684....1M,2011ApJ...730L...8A}. The \emph{Swift}--XRT did not cover the peak of the flares in April or June, but followed the source in the decaying part of the June flare \citep{2011A&A...534A..86T}. We have analysed the LAT data of PKS 1222+216 from June 16th to 22nd in three different energy bands and obtained the light-curves of the flare. We have also analysed the contemporaneous \emph{Swift}--XRT data to obtain a time-averaged broad-band spectrum (\S 2). The observed VHE spectrum with a differential photon spectral index of $2.7\pm0.3$, and the rapid variability introduces additional constraint on the location and the size of the emission region \citep{2012MNRAS.425.2519N}. The observed VHE spectral index suggests that the inverse Compton process happens in the Thomson regime as scattering in Klein-Nishina regime predicts a steeper spectrum \citep[$\sim 4$;][]{2009herb.book.....D}. This constraint rules out the possibility of EC scattering of BLR photons and hence demands the emission region to be located beyond the BLR \citep{2009MNRAS.397..985G, 2012MNRAS.425.2519N}. On the other hand, the rapid variability timescale of $\sim$10 min requires a smaller emission region compared to the jet cross-section at this distance. This led \citet{2011A&A...534A..86T} to propose a blob-in-jet model where the high energy emission originates from a compact region buried inside the jet along with the standard emission region covering the whole jet cross-section. They further argued that such a scenario is possible when an expanding jet interacts with the external medium resulting in a recollimation shock, which in turn compresses the matter towards the jet axis, giving rise to a compact emission region. The dynamics of the outflow at the recollimation zone have been studied by \citet{2009ApJ...699.1274B} following a semi analytical approach and they found that the focussing of jet due to the recollimation shock is also associated with the deceleration of jet flow. Similar result of jet deceleration at recollimation shock has also been seen in high resolution numerical simulations \citep{2007MNRAS.382..526P}. Deceleration of jet can be understood as a result of radiative losses \citep{1999APh....11...19M} and/or due to sweeping up of ambient/jet matter \citep{2007MNRAS.382..526P,2009ApJ...692.1374B,1999ApJ...512..699C}. If the jet axis is aligned close to the line of sight of the observer, then deceleration of jet will result in a time dependent Doppler boosting with an increase in the opening angle of the emission cone. In this paper, we interpret the $\gamma$-ray light curve of PKS 1222+216 during the flare on June 2010 as a result of jet dynamics happening at the recollimation zone. The kinetic equation describing the evolution of electron spectrum in the emission region is solved numerically. The resultant photon spectrum is obtained by convolving the time dependent electron distribution with single particle emissivity corresponding to various emission processes. The rise of photon flux during the flare results from an increase in the opening angle of the emission cone, while the fall is governed by the effects of jet deceleration. In the next section, we describe the data analysis procedures, and in \S \ref{sec:obs_con} we describe the constraints derived from the observations and the rationale behind the present model. In \S4, we present the details of the model and the underlying assumptions. Finally in \S \ref{sec:resndis}, we discuss the results obtained followed by conclusions in \S\ref{sec:conclude}. A cosmology with $\Omega_m = 0.3$, $\Omega_\Lambda = 0.7$ and $H_0 = 70\;km\;s^{-1}\;Mpc^{-1}$ is used in this work which corresponds to a luminosity distance $d_L$= $2.37$ Gpc for $z=0.432$. | \label{sec:conclude} Detection of VHE $\gamma$-rays with a variability timescale of $\sim 10$ min suggest a very compact emission region located beyond BLR. Existence of such compact emission region, on parsec scale, requires strong convergence of the jet flow, suggesting recollimation as one of the possible mechanism. In this paper, the variation in the $\gamma$-ray spectrum of PKS 1222+216, observed by {\emph Fermi}-LAT, is explained considering the jet dynamics at recollimation zone. Besides providing a compact emission region due to compression of jet matter by recollimation shock, study of jet dynamics at recollimation zone suggests deceleration of jet flow. We adapt this scenario to reproduce the daily binned $\gamma$-ray light-curves observed in three different energy bands. The parameters governing the model are further constrained by reproducing the simultaneous/contemporaneous broadband SED of the source during the flare. The inferred values of the bulk Lorentz factor ($\Gamma$) and Doppler factor ($\delta$) are consistent with the ones estimated through radio and $\gamma$-ray studies of LAT bright blazars \citep{2012IJMPS...8..163H}. Due to the lack of simultaneous observations at radio/optical (synchrotron) and X-ray (SSC) energies during the flare, the light-curves at these energies cannot be compared with the present model. Future simultaneous multi-wavelength observations of the source at energies covering from radio-to-$\gamma$-ray can verify the present model and can be used to impose more stringent constraints on the parameters involved. The spectral evolution of the source at these energies will also help us in studying the effect of magnetic field and the underlying particle distribution during a flare. For instance, variation of magnetic field in the emission region along with the bulk Lorentz factor during a flare will lead to additional increase/decrease in the synchrotron and SSC fluxes along with a shift in their peak frequencies. Similarly, a change in the spectral index can throw light on the basic particle acceleration mechanism. These in turn will help us in understanding the energetics and dynamics of the AGN jets. Authors thank the anonymous referees for their useful comments and suggestions. PK thanks K Nalewajko for clarification on some of the calculations in his paper \citep{2012MNRAS.425.2519N}. SS acknowledges Ranjeev Misra for useful discussions. This research has made use of data obtained from High Energy Astrophysics Science Archive Research Center (HEASARC), maintained by NASA's Goddard Space Flight Center and NASA/IPAC Extra-galactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the NASA. \begin{figure} \begin{center} \includegraphics[scale=1,angle=0]{pks1222_1d_lc.eps} \end{center} \caption{The daily binned \emph{Fermi}-LAT light-curves of PKS 1222+216 in three energy bands obtained during the flare along with the model light curves. The instantaneous jet power ($P_{jet}$) is shown in the bottom panel. Error bars are standard 1$\sigma$, statistical only. The estimated systematic uncertainties in the fluxes are 10\% at 100 MeV, and 5\% between 316 MeV to 10 GeV. The solid and dashed vertical line marks the epoch of VHE and XRT observation during the LAT flaring episode. Inverted triangles are LAT fluxes at the time of VHE detection by \emph{MAGIC}, extracted from a two hour integrated LAT data (see \S 2).} \label{fig:lc} \end{figure} \begin{figure} \begin{center} \includegraphics[scale=1]{pks1222_SED.eps} \end{center} \caption{ The broadband spectrum of PKS1222+216 at \emph{MAGIC} and XRT observation epoch. The VHE data (black solid circles) are obtained from \citet{2011ApJ...730L...8A} and the corresponding LAT fluxes are extracted from two hour (black squares) integrated LAT data. The grey data represents the XRT observation with corresponding LAT fluxes from six hour integrated LAT data.The dashed, double dashed and dotted lines represent the synchrotron, SSC and EC spectra at the time of VHE detection by \emph{MAGIC}. The solid black and grey lines represent the total emission from all spectral components at the two epoch respectively. The IR-optical-UV data are taken from literature and are reproduced by the torus emission at $1200$ K and multi temperature blackbody emission from accretion disk (see \S2 and \S \ref{sec:resndis}).} \label{fig:spec} \end{figure} | 14 | 4 | 1404.6398 |
1404 | 1404.1294.txt | We present an extensive optical and near-infrared photometric and spectroscopic campaign of the type IIP supernova SN 2012aw. The dataset densely covers the evolution of SN 2012aw shortly after the explosion up to the end of the photospheric phase, with two additional photometric observations collected during the nebular phase, to fit the radioactive tail and estimate the $^{56}$Ni mass. Also included in our analysis is the already published \textit{Swift} UV data, therefore providing a complete view of the ultraviolet-optical-infrared evolution of the photospheric phase. On the basis of our dataset, we estimate all the relevant physical parameters of SN 2012aw with our radiation-hydrodynamics code: envelope mass $M_{env} \sim 20 M_\odot$, progenitor radius $R \sim 3 \times 10^{13}$ cm ($ \sim 430 R_\odot$), explosion energy $E \sim 1.5$ foe, and initial $^{56}$Ni mass $\sim 0.06$ $M_\odot$. These mass and radius values are reasonably well supported by independent evolutionary models of the progenitor, and may suggest a progenitor mass higher than the observational limit of $16.5 \pm 1.5 M_\odot$ of the Type IIP events. | Type II supernova (SN) events are the product of the collapse of a moderately massive progenitor, with an initial mass between $8 M_\odot$ (e.g. \citealt{pumo09}) and $30$ $M_\odot $ (e.g. \citealt{walmswell12}). According to the classical classification scheme (see \citealt{filippenko97} for a review) their spectra show prominent Balmer lines, which means that at the time of the explosion they have still retained their hydrogen-rich envelope. ``Plateau" Type II SNe (Type IIP) show a nearly constant luminosity for $ \sim 80-120$ days \citep{barbon79}. The plateau is an optically thick phase, in which the release of the thermal energy deposited by the shock wave on the expanding ejecta is driven by the hydrogen recombination front, which gradually recedes in mass (e.g. \citealt{kasen09}, \citealt{pumo11}). When the recombination front reaches the base of the hydrogen envelope, the light curve sharply drops by several magnitudes in $\sim 30$ days (e.g. \citealt{kasen09}; \citealt{olivares10}). This transition phase is followed by the linear ``radioactive tail'', powered by the decay of $^{56}$Co to $^{56}$Fe, which depends on the amount of $^{56}$Ni synthesized in the explosion (e.g. \citealt{weaver80}). In a few cases, the progenitors have been identified in high-resolution archival images and found to be to red supergiants (RSGs) of initial masses between $\sim 8 M_\odot$ and $\sim 17 M_\odot$. Available data show an apparent lack of high-mass progenitors, and this fact has been dubbed as the ``RSG problem'' \citep{smartt09}. \citet{walmswell12} suggested that the dust produced in the RSG wind could increase the line of sight extinction, with the net effect of underestimating the luminosity and, as a consequence, the mass of the progenitor. However, \citet{kochanek12} pointed out that all work to date, including that of \citet{walmswell12} has incorrectly used interstellar extinction laws rather than a consistent physical treatment of circumstellar extinction, which may lead to overestimate the effect of extinction. Finally, we note that there is evidence that a minor fraction of Type II SNe results from the explosion of blue supergiant stars, the best example being SN 1987A \citep{arnett89}. These SNe show a significant variety in the explosion parameters, but they generally display a Type IIP behaviour. \citet{smartt_etal_09} and \citet{pastorello12} have suggested that less than $3-5\%$ of all Type II SNe are 1987A-like events. The interest in Type IIP SNe is twofold. Firstly, observations show that Type IIP SNe are the most common explosions in the nearby Universe (e.g. \citealt{cappellaro99}; \citealt{li11}). This means that, given their observed mass range, they can be used to trace the cosmic star formation history up to $z \sim 0.6$ (see \citealt{botticella12}; \citealt{dahlen12}). Secondly, it has been suggested that they can be used as cosmological distance indicators (see \citealt{hamuy02}; \citealt{nugent06}; \citealt{poznanski09}; \citealt{olivares10}). Despite their frequency and importance, only a fraction of Type IIP SNe has been extensively monitored, photometrically and spectroscopically from the epoch of explosion through the late nebular phase. This type of extensive and extended monitoring is only viable for the closest events (typically closer than $10-15$ Mpc), as spectroscopic observations become difficult even with $10$m-class telescopes, beyond $300$ days. Examples with Type IIP SNe with this sort of coverage are SN 1999em \citep{elmhamdi03}, SN 1999gi \citep{leonard02}, SN 2004et \citep{maguire10}, SN 2005cs \citep{pastorello09}, SN 2009md \citep{fraser11}, SN 2012A \citep{tomasella13}. Therefore, the occurrence of a nearby Type IIP SN offers us a unique opportunity to collect very high quality photometric, spectroscopic and polarimetric data from early stages up to the nebular phase. Through the analysis of pre-explosion images we also have the possibility to compare the progenitor parameters estimated with hydrodynamical explosion codes with the predictions of evolutionary models. SN 2012aw was discovered by \citet{fagotti12} in the spiral galaxy M95 (NGC 3351), at the coordinates $\alpha_{2000}=10^{\rm h}43^{\rm m}53^{\rm s}.76$, $\delta_{2000}=+11^{\rm o}40'17''.9$ on 2012 March $16.86$ UT. The magnitude at the discovery epoch was $R \sim 15$ mag and steeply rising ($R \sim 13$ mag, by J. Skvarc on March $17.90$ UT). The latest pre-discovery image was on March $15.86$ UT \citep{poznanski12atel}. These data allow us to constrain the explosion epoch to March $16.0 \pm 0.8$ UT, corresponding to the Julian Day (JD) 2,456,002.5 \citep{fraser12}. In the following, we will refer to this epoch as day $0$. The designation SN 2012aw was assigned after an early spectrum taken by \citet{munari12cbet} on 2012 March $17.77$ UT that showed a very hot continuum without obvious absorption or emission features, and subsequently spectroscopic confirmations independently obtained by \citet{itoh12} and by \citet{siviero12} that showed a clear H$_\alpha$ P Cygni profile, indicating a velocity of the ejecta of about $15000$ km s$^{-1}$ \citep{siviero12}. SN 2012aw was also observed in the X-rays with \textit{Swift} \citep{immler12} between 2012 March 19.7 and March 22.2 UT at a luminosity $L_X = 9.2 \pm 2.5 \times 10^{38}$ erg s$^{-1}$, and at the radio frequency of $20.8$ GHz on March $24.25$ UT \citep{stockdale12} at a flux density of $0.160 \pm 0.025$ mJy. A subsequent radio observation on March 30.1 UT at the frequency of $21.2$ GHz revealed a flux density of $0.315 \pm 0.018 $ mJy \citep{yadav12}, thus confirming a radio variability. Finally, spectropolarimetric observations with VLT+FORS2 suggested a significant intrinsic continuum polarization at early phases, a possible signature of a substantial asymmetry in the early ejecta \citep{leonard12}. A candidate progenitor was promptly identified as a RSG in archival Hubble Space Telescope data by \citet{eliasrosa_atel12} and by \citet{fraser_atel12}. Detailed pre-SN multi-band photometry was carried out on space (HST WFPC2 $F814W$) and ground based (VLT+ISAAC, NTT+SOFI) archival images by \citet{fraser12}. Adopting a solar metallicity, they estimated a luminosity in the range $10^5 - 10^{5.6} L_\odot$ and an effective temperature between $3300$ and $4500$ K, and a progenitor radius larger than $500$ $R_\odot$. Their comparison with stellar evolutionary tracks pointed toward a progenitor with an initial mass between $14$ and $26$ $M_\odot$. We note that the uncertainties in the \citet{fraser12} parameters are mostly due to the line of sight extinction estimate, which they estimated to be larger than $E(B-V)=0.4$ mag at the $ 2 \sigma$ level and larger than $E(B-V) = 0.8$ mag at the $1 \sigma$ level. \citet{vandyk12} conducted a similar analysis, where they carefully discussed the infrared photometric calibration and the subtle effects due to the progenitor \textit{pre-explosion} reddening (which they estimated as $E(B-V)=0.71$ mag) and the variability of the RSG. They found the spectral energy distribution (SED) to be consistent with an effective temperature of $3600$ K, a luminosity $L \sim 10^{5.21} L_\odot$, a radius $R=1040$ $R_\odot$ and an initial mass between $15$ and $20$ $M_\odot$. After interpolating their adopted tracks (taken from \citealt{ekstrom12}), they finally constrained the progenitor initial mass to be $\sim 17-18$ $M_\odot$, which is at the upper end of the initial masses for the Type IIP SNe progenitors detected to date, as suggested by \citet{smartt_etal_09}. Subsequently, \citet{kochanek12} suggested that the \citet{fraser12} and the \citet{vandyk12} progenitor luminosity (and mass) values may have been overestimated, since they adopted for the reddening the classical absorption-to-reddening ratio $R_V=3.1$, which is appropriate for a standard dust composition \citep{cardelli89}. \citet{kochanek12} pointed out that a massive RSG produces mostly silicates, for which a ratio of $R_V=2$ is more appropriate. Moreover, visual extinction may be overestimated, since the contribution of the scattered light in the interstellar extinction budget is neglected. In turn, they suggested a progenitor luminosity between $L=10^{4.8} L_\odot$ and $L=10^{5.0}L_\odot$ and a mass $M < 15$ $M_\odot$. Accurate $BVRI$ light curves of SN 2012aw were published by \citet{munari13}, who carefully discussed the problems related to the homogenization of photometric measurements obtained at different telescopes, producing an optimal light curve by means of their ``lightcurve merging method''. Moreover, extensive photometric and spectroscopic observations were presented by \citet{bose13}, covering a period from $4$ to $270$ days after explosion. \citet{bose13} measured the photospheric velocity, the temperature and the $^{56}$Ni mass of SN 2012aw; they estimated the explosion energy and the mass of the progenitor star by comparing their data with existing simulations. In this paper we present the results of our observational campaign, which include unpublished near-infrared data. We used our data for \textit{new} hydrodynamical simulations to estimate the relevant physical parameters. The same approach has been used for other two Type IIP SNe, namely SN 2012A \citep{tomasella13} and SN 2012ec (Barbarino et al. 2014, in prep.), thus providing a homogeneous analysis that can be used for consistent comparisons. The paper is organized as follows: in Section \ref{m95}, we list the relevant properties of the host galaxy M95; in Section \ref{reddening} we discuss the reddening estimate, both Galactic and host; in Section \ref{phot}, we present our photometric dataset and analyze the photometric time evolution; in Section \ref{spec}, we present the spectroscopic observations and discuss the time evolution of the spectral features; in Section \ref{phys} we discuss the physical parameters obtained from the photometric and spectroscopic data: the bolometric light curve, from which we give an estimate of the $^{56}$Ni mass, the expansion velocity of the ejecta, and and SED evolution. In Section \ref{model}, we present the results of our hydrodynamical modelling, computed to match the observational parameters of SN 2012aw. Conclusions are presented in Section \ref{conclusions}. | 14 | 4 | 1404.1294 |
|
1404 | 1404.6077_arXiv.txt | {} {Radio synchrotron polarization maps of the Galaxy can be used to infer the properties of interstellar turbulence in the diffuse magneto-ionic medium (MIM). In this paper, we investigate the normalized spatial gradient of linearly polarized synchrotron emission ($|\nabla \textbf{P}|/|\textbf{P}|$) as a tracer of turbulence, the relationship of the gradient to the sonic Mach number of the MIM, and changes in morphology of the gradient as a function of Galactic position in the southern sky.} {We used data from the S-band Polarization All Sky Survey (S-PASS) to image the normalized spatial gradient of the linearly polarized synchrotron emission ($|\nabla \textbf{P}|/|\textbf{P}|$) in the entire southern sky at $2.3$~GHz. The spatial gradient of linear polarization reveals rapid changes in the density and magnetic fluctuations in the MIM due to magnetic turbulence as a function of Galactic position. We made comparisons of these data to ideal MHD numerical simulations. To constrain the sonic Mach number ($M_{s}$), we applied a high-order moments analysis to the observations and to the simulated diffuse, isothermal ISM with ideal magneto-hydrodynamic turbulence.} {We find that polarization gradient maps reveal elongated structures, which we associate with turbulence in the MIM. Our analysis indicates that turbulent MIM is in a generally transonic regime. This result for the turbulent regime is more general than the ones deduced by the analysis of electron density variation data, because it is based on the stochastic imprints of the Faraday rotation effect, which is also sensitive to the magnetic field fluctuations. Filamentary structures are seen with typical widths down to the angular resolution, and the observed morphologies closely match numerical simulations and, in some cases, H$\alpha$ contours. The $|\nabla \textbf{P}|/|\textbf{P}|$ intensity is found to be approximately log-normal distributed. No systematic variations in the sonic Mach number are observed as a function of Galactic coordinates, which is consistent with turbulence in the WIM, as inferred by the analysis of H$\alpha$ data. We conclude that the sonic Mach number of the diffuse MIM appears to be spatially uniform towards the Galactic plane and the Sagittarius-Carina arm, but local variations induced by nearby extended objects are also found.} {} | \label{intro} Galactic magnetic fields and matter (i.e. atoms, ions and molecules) spread between the stars constitute a complex dynamic plasma, known asthe interstellar medium (ISM). The density and temperature of the particles and the magnitude of the fields are fundamental parameters that shape the structure of the interstellar environment and characterize its evolution. Earlier studies \citep[for a review see e.g.][]{Ferriere01,Cox05} have pointed out the presence of magnetohydrodynamic (MHD) turbulence in the ISM, which is responsible for the distribution and the dissipation of energy through a wide range of spatial scales. MHD turbulence is thought to play an essential role for many key interstellar processes \citep[for a review see e.g.][]{Elmegreen04}, including star formation \citep[see][]{KrumholzMcKee05,McKeeOstriker07}, cosmic ray propagation \citep[see][]{Schlickeiser11,Lazarian11} and magnetic reconnection \citep[see][]{LazarianVishniac99}. Additionally, astrophysical MHD turbulence is an integral part of the dynamics of the Galaxy, providing a significant pressure (and energy density) to support the diffuse ISM \citep{Boulares90}. Many efforts have been made over the past decades to characterize magnetic fields and turbulence in the ISM as well as their mutual dependence \citep[see review by][]{BurkhartLazarian12a}. The presence of a turbulent cascade in the ISM was obtained by tracing density variations in the warm ionized medium \citep{Armstrong95,ChepurnovLazarian10}. However, MHD turbulence is traced in the different phases of the ISM by several typical signatures, such as density, velocity \citep{Pogosyan09,Chepurnov10}, and synchrotron intensity \citep{LazarianPogosyan12,Iacobelli13} variations. Because observations of astrophysical MHD turbulence and magnetic fields are challenging, the fundamental parameters of ISM turbulence, such as the sonic and Alfv\'{e}nic Mach numbers, the magnetic field structure and strength, the Prandtl and Reynolds numbers, and the physical scale of energy injection are still poorly constrained. Therefore observational studies of MHD turbulence in the ISM, combined with analytic predictions and numerical simulations, are essential. Radio observations are a fundamental tool for gaining insight into magnetic fields, the density of the ionized gas, and their turbulent fluctuations. In particular, radio polarization maps constitute a useful diagnostic for studying turbulence and magnetic fields in the diffuse, ionized ISM \citep[see e.g.][]{Wieringa93,Gaensler01,Haverkorn04a,Haverkorn04b,Schnitzeler07}. Surveys covering a large part of the sky add information on the spatial dependence of these fields as well. Previous surveys of the southern sky are affected by several limitations such as incomplete sky coverage \citep[e.g. the survey at 2.4~GHz by][]{Duncan95,Duncan97}, the absence of polarimetric data \citep[e.g. the survey at 2.3~GHz by][]{Jonas85,Jonas98} as well as a limited angular resolution \citep[e.g. the survey at 1.4~GHz by][]{Testori08}. The S-band Polarization All Sky Survey (S-PASS) \citep{Carretti13} is a recent spectro-polarimetric survey of the entire southern sky carried out with the Parkes 64m telescope at 2.3~GHz to diminish depolarization effects with respect to 1.4~GHz surveys. The use of the spatial gradient of the polarization vector to image the small-scale structure associated with ISM turbulence has been recently discovered by \citet{Gaensler11} and exploited by \citet{Burkhart12}. They show how to map the magnetized turbulence in diffuse ionized gas from the gradient of the Stokes~Q and U pseudo-vectors. In a 18~deg$^{2}$ patch of the Galactic plane, they find an intricate filamentary network of discontinuities in gas density and magnetic field. In agreement with the result of \citep{Hill08} for the warm ionized medium, these authors find turbulence in the magneto-ionic medium (MIM) to be transonic, with a sonic Mach number $M_{s}\lesssim2$ and therefore weakly compressible. These results were partially derived from the ability of statistical moments to characterize the sonic Mach numbers from spatial gradient maps of linear polarization by testing the sensitivity of statistical methods to different regimes of turbulence. Analyses of \citet{Gaensler11} and \citet{Burkhart12} find correlations between the spatial morphology, the higher order moments of the distribution of the spatial gradients of polarized emission and the sonic and Alfv\'{e}nic Mach number. In this paper we present the first mapping of different regimes of turbulence in the diffuse, ionized ISM over the entire southern sky by applying the statistical moments analysis to several regions. In particular, by comparing the analysis of high order moments in both simulations of MHD turbulence and observations we search for spatial variations of the sonic Mach number. Galactic coordinates are used throughout the following sections. In Sect.~\ref{s:obs} we present an overview of both the data and the gradient method. In Sect.~\ref{s:imaging} we present the spatial gradient map of the polarization vector displaying an extended network of filaments, and in Sect.~\ref{s:regimes_turbulence} different regimes of MHD turbulence in the ISM are characterized from the moment map analysis. Finally, we discuss our results and present conclusions in Sect.~\ref{s:conclusion}. | \label{s:conclusion} Normalized spatial gradients of the polarization vectors have been used for the first time to map the entire southern sky. The large sky coverage allows the exploration of cases not treated by the previous studies of \citet{Gaensler11} and \citet{Burkhart12}. The S-PASS $|\nabla \textbf{P}|/|\textbf{P}|$ map displays a wealth of filamentary structures with typical widths down to the angular resolution. The emission is characterized by a polarization horizon of about 3~kpc, implying density and magnetic fluctuations down to a linear scale $<10$~pc given the angular size of the S-PASS beam. An extended and patchy pattern of $|\nabla \textbf{P}|/|\textbf{P}|$ intensity is found within the third and fourth Galactic quadrants at high ($b\lesssim -60^{\circ}$) latitudes towards the south Galactic pole. Two different morphologies (i.e. ``single'' or ``double'' jump profiles) corresponding to different MHD turbulence cases (i.e. low or high sonic Mach numbers) are observed, thus supporting the predictions of numerical simulations \citep{Burkhart12}. % Normalized spatial gradients of the polarization vector are effective tracers of extended and Faraday rotating features, such as \ion{H}{ii} regions and evolved SNRs. Indeed we clearly recognize the two known nearby and old SNRs Antlia and G\,353-34. In addition, by combining the information from both the $|\nabla \textbf{P}|/|\textbf{P}|$ and H$\alpha$ intensity maps we can highlight the presence of both electron density and magnetic structures, in agreement with simulations \citep{Burkhart12}. Although multiple scales of energy injection are expected in the ISM \citep{NotaKatgert10}, instabilities triggered by supernova events and Galactic shear in the ISM are expected to mainly generate and sustain interstellar MHD turbulence \citep[][]{MacLow04,Hill12}. Observational studies of turbulence in the warm and ionized ISM also indicate a spectral index matching that of the \citet{Goldreich&Sridhar95} theory of Alfv\'{e}nic turbulence, consistent with a weakly compressible medium. This is the case for transonic turbulence as shown by \citet{Hill08}, who estimated the sonic Mach number by comparing statistics of H$\alpha$ WHAM data with simulations. By applying a moment analysis to a number of fields, we extend it to the MIM and confirm the earlier result of these authors, finding lines of sight to be consistent with $M_{s} \lesssim 2$ (see Table~\ref{t:nonorm_regions}). The use of the spatial gradient of linear polarizations combined with a robust statistical analysis makes mapping of the sonic and Alfv\'{e}nic Mach numbers spatial variations in the MIM a feasible and mandatory aim of forthcoming radio observations at high angular resolution. These studies will allow us to gain complementary insight into the turbulence and shocks in the ionized ISM over a wide range of plasma $\beta$-parameter regimes. To gain a complete picture of Mach numbers and spatial variations in the MIM, complete sky coverage is needed, requiring a corresponding high resolution and sensitivity survey of the northern sky. | 14 | 4 | 1404.6077 |
1404 | 1404.4843_arXiv.txt | {Star formation efficiency (SFE) theories are currently based on statistical distributions of turbulent cloud structures and a simple model of star formation from cores. They remain poorly tested, especially at the highest densities.} {We investigate the effects of gas density on the SFE through measurements of the core formation efficiency (CFE). With a total mass of $\sim$2$\times 10^4~\msun$, the W43-MM1 ridge is one of the most convincing candidate precursor of Galactic starburst clusters and thus one of the best places to investigate star formation.} {We used high-angular resolution maps obtained at 3~mm and 1~mm within the W43-MM1 ridge with the IRAM Plateau de Bure Interferometer to reveal a cluster of 11 massive dense cores (MDCs), and, one of the most massive protostellar cores known. An \emph{Herschel} column density image provided the mass distribution of the cloud gas. We then measured the \lq instantaneous\rq~CFE and estimated the SFE and the star formation rate (SFR) within subregions of the W43-MM1 ridge.} {The high SFE found in the ridge ($\sim$6\% enclosed in $\sim$8 pc$^3$) confirms its ability to form a starburst cluster. There is however a clear lack of dense cores in the northern part of the ridge, which may be currently assembling. The CFE and the SFE are observed to increase with volume gas density while the SFR per free fall time steeply decreases with the virial parameter, $\alpha_{vir}$. Statistical models of the SFR may well describe the outskirts of the W43-MM1 ridge but struggle to reproduce its inner part, which corresponds to measurements at low $\alpha_{\rm vir}$. It may be that ridges do not follow the log-normal density distribution, Larson relations, and stationary conditions forced in the statistical SFR models.} {} | The formation of high-mass stars remains poorly understood but an emerging scenario suggests that they form in massive dense cores (MDCs: $\sim$0.1~pc and $>10^5~\cmc$ as defined in \citealt{motte07}, see also \citealt{wang14}) through dynamical processes such as colliding flows initiated by cloud formation \citep[e.g.][]{csengeri11a,quang13}. The \emph{Herschel} key program HOBYS \citep[see][]{motte10hobys,motte12hobys} identifies ridges as high-density filaments, above $10^{23}$~cm$^{-2}$ in column density, favorable to the formation of high-mass (OB-type, $\geq$8~\msun) stars \citep[see][]{hill11-vela,quang11-w48,martin12}. The most extreme of these ridges, W43-MM1, lies in the massive, highly concentrated and very dynamic W43 molecular complex located at 6 kpc \citep{quang11-w43,carlhoff13}. In its central region, W43-MM1 is thought to be experiencing a cloud collision (\citealt{quang13}), causing a remarkably efficient burst of high-mass star formation \citep{motte03}. The W43-MM1 ridge can be modeled by a 3.9~pc$\,\times\,2$~pc$\,\times\,$2~pc ellipsoid with a total mass of $\sim$2$\times 10^4$~M$_\odot$ and an average density of $\sim$4.3$\times10^4~\rm cm^{-3}$, physically large enough and massive enough to form a large cluster. Its fragmentation has been studied before, with a 0.2 pc resolution, by \cite{motte03}. Fragmentation, magnetic field, outflows, and hot core of the densest part of the W43-MM1 ridge has also been observed with high-angular resolution by \cite{cortes06} and \cite{sridharan14}. A handful of studies have been carried out to estimate the core formation efficiency (CFE) in high-mass star forming regions, and suggested that the stellar formation efficiency (SFE) increases with gas density (\citealt{bontemps10}, \citealt{palau13}). As for the stellar formation rates (SFRs), most statistical models directly relate it to the amount of gas above a given density threshold \citep[][]{krumholz05,padoan11,hennebelle11}. If this view agrees with the SFR measurements in low-mass star-forming clouds \citep{heiderman10}, which are found to be proportional to cloud masses \citep[Eq.~3 of][]{lada10,evans14}, they are not representative of typical Galactic clouds forming high-mass stars (\citealt{motte03}, \citealt{quang11-w48}). These observational differences cast doubt on the accuracy of extrapolating scaling laws observed in low-mass star-forming regions to describe star formation in clouds forming high-mass stars. MDCs hosting high-mass protostars can be used to investigate the fragmentation of ridges and measure the concentration of its gas into high-density seeds and then high-mass stars. In the present paper\footnote{ Based on observations carried out with the IRAM Plateau de Bure Interferometer. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). }, we investigate the CFE variations through the W43-MM1 ridge and compare the resulting SFE \& SFR estimates to predictions of star formation models. Section~\ref{s:obs} presents an interferometric imaging of W43-MM1 that reveals a cluster of MDCs characterized in Sect.~\ref{s:census}. Section~\ref{s:cfe} presents an analysis of the CFE in subregions of the ridge and discusses the CFE variations with cloud volume density. In Section~\ref{s:sfe-sfr} we present two methods to compute the SFEs and the SFRs from the observed CFEs in W43-MM1. Finally, the SFR measured in the different subregions of the ridge are compared to predictions of statistical models of star formation in Sect.~\ref{s:sfrff}. | \label{s:conclusion} We use the IRAM Plateau de Bure interferometer to image the W43-MM1 ridge at 3~mm and a zoom on its main MDC at 1~mm (see Fig.~\ref{oncont}). We compare the mass distribution observed throughout these maps with the column density image of W43-MM1 built from \emph{Herschel} data. Our main results and conclusions may be summarized as follows: \begin{itemize} \item The 3~mm mosaic reveals eleven $\sim$0.07~pc MDCs, labeled N1 to N11, across the W43-MM1 ridge. These MDCs range in mass between $\sim$50~$\msun$ and $\sim$2100~$\msun$; have mean densities between $n_{\rm H_2}$ $\sim 7\times10^6~\cmc$ and $\sim$1$\times10^8~\cmc$. The 1~mm snapshot identifies two $\sim$0.03--0.04~pc HMPCs within N1, the most massive of the MDCs sample (see Table~1). The N1a protostellar core, with its $\sim$1080~$\msun$ mass, is the most massive known 0.03~pc young stellar object ever observed in an early phase of evolution (see Fig. 2). It is expected to form a couple of $\sim$50~$\msun$ stars. \item We use the MDCs masses to estimate the concentration of the cloud gas toward high density (see Table 3), usually called the gas-to-core formation efficiency (CFE). The W43-MM1 ridge split into four exclusive subregions displays a clear correlation of the CFE with cloud volume density: \emph{CFE}~$\propto~<\nhtwo>_{\rm cloud}^{0.91}$ (see Fig.~\ref{cfe-density}). \item The CFE measurements are extrapolated to \lq instantaneous' stellar formation efficiencies (SFEs) following two approaches constraining the MDC to stellar cluster efficiency (see Table 3 and Fig. 4). The SFE values are also used to make estimate of 1) the `instantaneous' stellar formation rate (SFR) expected during the protostellar lifetime and 2) the dimensionless star formation rate per free-fall time theoreticians use: SFR$_{\rm ff}$. \item The SFEs obtained for the W43-MM1 ridge and its subregions A and B are large, SFEs$\,=3-11\%$, and their SFRs estimates are $4-11$ times larger than the values expected from their masses, following the equation proposed by \cite{lada13}. We propose it is due to a strong correlation of the CFE to the gas volume densities in W43-MM1. With its SFR absolute value, \emph{SFR}~$ = 6000~\msun$\,Myr$^{-1}$, W43-MM1 qualifies as a mini-starburst region. It may account, during one protostellar lifetime of $\sim$0.2~Myr, for as much as one twentieth of the total $\sim$1~\msun\,yr$^{-1}$ SFR of the Milky Way. \item The CFE of the eastern and western parts of the ridge are clearly unbalanced, leading to SFE values as different as 0.6\% and 10.2\%. It might be due to the eastern region currently assembling its mass along multiple filaments whose interaction could impede cloud fragmentation and star formation. \item Our observations lead to a SFR$_{\rm ff}$ relation with virial number which is steadily increasing when $\alpha_{\rm vir}$ is decreasing (see Fig. 5). While statistical SFR models display such a trend for high $\alpha_{\rm vir}$, they saturate for values close to those observed in the W43-MM1 ridge. Models with more realistic conditions are necessary to fully describe the complexity of this very dense, turbulent, non isothermal, and non stationary cloud structure. Higher resolution and deeper imaging are necessary to confirm current observational findings. \end{itemize} | 14 | 4 | 1404.4843 |
1404 | 1404.5597_arXiv.txt | {The role of magnetic fields in the star formation process is a contentious matter of debate. In particular, no clear observational proof exists of a general influence by magnetic fields during the initial collapse of molecular clouds.} {Our aim is to examine magnetic fields and their influence on a wide range of spatial scales in low-mass star-forming regions.} {We trace the large-scale magnetic field structure on scales of $10^3-10^5$~AU in the local environment of Bok globules through optical and near-infrared polarimetry and combine these measurements with existing submillimeter measurements, thereby characterizing the small-scale magnetic field structure on scales of $10^2-10^3$~AU.} {For the first time, we present polarimetric observations in the optical and near-infrared\thanks{Based on observations made with ESO telescopes at the La Silla Paranal Observatory under programme IDs 089.C-0846(A) and 090.C-0785(A).} of the three Bok globules B335, CB68, and CB54, combined with archival observations in the submillimeter and the optical. We find a significant polarization signal $\left(P\gtrsim2~\%,\ P/\sigma_{\rm{P}}>3\right)$ in the optical and near-infrared for all three globules. Additionally, we detect a connection between the structure on scales of $10^2-10^3$~AU to $10^3-10^4$~AU for both B335 and CB68. Furthermore, for CB54, we trace ordered polarization vectors on scales of $\sim10^5$~AU. We determine a magnetic field orientation that is aligned with the CO~outflow in the case of CB54, but nearly perpendicular to the CO~outflow for CB68. For B335 we find a change in the magnetic field oriented toward the outflow direction, from the inner core to the outer regions. } {We find strongly aligned polarization vectors that indicate dominant magnetic fields on a wide range of spatial scales.} | Magnetic fields are observed in a wide range of astronomical scales: from the entire galaxy and giant molecular clouds \citep{1996ARA&A..34..155B, 2001SSRv...99..243B}, to smaller molecular clouds with low-mass star formation and protostellar disks \citep[see, e.g., ][]{2008Ap&SS.313...87G, 2001ApJ...561..871H, 2004Ap&SS.292..239W}, to circumstellar disks where they drive outflows, jets, and the accretion onto the central star \citep[see, e.g.,][]{2007prpl.conf..277P, 2009ApJ...691L..49S, 1998ApJ...492..323G}. Magnetic fields have been discussed as playing an important role in star formation \citep[see, e.g.,][]{2009MmSAI..80...54G}. In general, they can influence the contraction timescale, the gas-dust coupling, and the shape of cloud fragments, and they host jets and outflows \citep[see, e.g.,][]{2007ARA&A..45..565M}.\\ In the dusty envelopes around young stellar objects, polarization of background starlight due to dichroic extinction and thermal emission by non-spherical dust grains is the most important signature of magnetic fields \citep[see, e.g.,][]{2000prpl.conf..247W, 2008Ap&SS.313...87G, 1999AAS...194.4714C}. The dust grains become partially aligned to the magnetic field, with their long axes perpendicular to the magnetic field lines \citep[see, e.g.,][]{2007JQSRT.106..225L}. The thermal emission of the dust grains thus becomes polarized, with a polarization direction perpendicular to the magnetic field, projected onto the plane of sky. Additionally, the light of background stars that shines through the star-forming region becomes polarized by dichroic absorption by the dust grains. Here, the resulting polarization maps directly trace the magnetic field lines, projected onto the plane of sky \citep[see, e.g.,][]{2000prpl.conf..247W}. Such polarization observations allow an assessment of the relative importance of uniform and tangled magnetic fields: A high level of polarization, uniform in direction, indicates a well-ordered field that is not significantly tangled on scales smaller than the beam size, i.e., a magnetic field that plays an important role in the evolution of the local density structure during the star formation. \\ A very good environment for studying the role of magnetic fields is given in low-mass star-forming regions, so-called Bok globules. These objects are less affected by large-scale turbulences and other nearby star-forming events. Bok globules are small in diameter ($0.1-2$~pc), simply structured, and are relatively isolated molecular clouds with masses of $2-100$~M$_\sun$ \citep{1991ApJS...75..877C, 1977PASP...89..597B, 1985prpl.conf..104L}.\\ Given the sensitivity of millimeter/submillimeter (sub-mm) telescopes that allow for polarimetric observations, the thermal emission of the dust grains, observable in the sub-mm, traces the densest, central part of a Bok globule. The less dense, outer parts are traced with polarized observations of background starlight that is dichroicly absorbed and observable in the near-infrared (near-IR)~/ optical. Thus, multiwavelength observations that combine sub-mm, near-IR, and optical polarization observations reveal the magnetic field geometry from the smallest to the largest scales of the Bok globule. So far, there have only been about two dozen sub-mm polarization observations of Bok globules, while only about half a dozen of these show ordered magnetic field structures \citep{2009ApJS..182..143M, 2010ApJS..186..406D}. The majority of the sub-mm polarization observations show tangled field patterns, an indicator for negligible magnetic fields. Contrary to that, the near-IR and optical observations of \citet{2011AJ....142...33A}, \citet{2013ApJ...769L..15S}, and \citet{2000A&AS..141..175S} revealed ordered field structures in the less dense, outer parts, indicating dominant magnetic fields in these parts of low-mass star-forming regions. Motivated by this, we performed a polarization study of Bok globules with two morphologically different globule types: B335 and CB68 are simply structured, small globules, whereas CB54 is a more complexly structured, larger Bok globule. In this work, we present polarization observations in the optical and near-IR of the three Bok globules B335, CB68, and CB54, combined with archival sub-mm and optical observations, for the first time.\\ We start with a description of the sources and the selection criteria in Section~\ref{sec:description}. In Section~\ref{sec:obs} we describe the observations, and in Section~\ref{sec:datared} the data reduction. In Section~\ref{sec:polmap} we analyze the polarization maps, and in Sects.~\ref{sec:Bfield} and~\ref{sec:CO} we discuss the magnetic field and the correlation between the magnetic field structure and the CO~outflows. In Section~\ref{sec:summary} we discuss the observability of the gap regions between the sub-mm and near-IR observations that we find and summarize our results. | \centering \begin{tabular}{l l c c c c c c c } \hline\hline Instrument & Object & $\alpha_{2000}$ & $\delta_{2000}$ & Type & P & $\gamma$ & Filter & Ref.\\ & & (hh:mm:ss.ss) & (dd:mm:ss.ss) & & (\%) & $\left(^\circ\right)$ & & \\ \hline ISAAC/VLT & EGGR118 & 16:17:55.26 & -15:35:51.93 & unpolarized & $<1.79$ & & J & 1 \\ & GJ1178 & 13:47:24.36 & +10:21:37.90 & unpolarized & $<1.08$ & & J & 1 \\ SOFI/NTT & CMa R1 No.24 & 07:04:47.36 & -10:56:17.44 & polarized & $2.1\pm0.05$ & $86\pm1$ & J & 2 \\ & HD64299 & 07:52:25.51 & -23:17:46.78 & unpolarized & $0.151\pm0.032$ & & B & 3 \\ & WD0310-688 & 03:10:31.02 & -68:36:03.39 & unpolarized & $0.051\pm0.09$ & & V & 4 \\ IFOSC/IGO & HD251204 & 06:05:05.67 & +23:23:38.54 & polarized & $4.04\pm0.066$ & 147 & V & 3 \\ & GD319 & 12:50:05.00 & +55:06:00.00 & unpolarized & $0.045\pm0.047$ & & B & 3 \\ & HD65583 & 08:00:32.12 & +29:12:44.40 & unpolarized & $0.013\pm0.02$ & $144.7\pm30$ & B & 5 \\ \hline \end{tabular} \tablebib{(1)~\citet{2008MNRAS.387..713R}; (2) \citet{1992ApJ...386..562W}; (3) \citet{1990AJ.....99.1243T}; (4) \citet{2007ASPC..364..503F}; (5) \citet{1981AJ.....86.1518C}.} \end{table*} \subsection{Near-IR observations} The near-IR observations were carried out in March-May 2012 and January 2013 at ESOs Very Large Telescope (VLT) and the New Technology Telescope (NTT). We observed with the instruments Infrared Spectrometer And Array Camera (ISAAC) and Son OF ISAAC (SOFI), which are mounted at the Nasmyth~A foci of the $8~$m VLT (UT3), respectively of the $3.58$~m NTT, both equipped with a $1024\times 1024$ Hawaii Rockwell array optimized for wavelengths of $1-2.5~\mu$m.\\ In both ISAAC/VLT and SOFI/NTT a single Wollaston prism is used for polarization observations. In this observing mode, the polarized flux is measured simultaneously at two different angles that differ by $90\degr$. To derive the linear polarization degree and orientation of an object, two observations must be performed at each pointing of the telescope with different orientations of the Wollaston prism, typically $0\degr$ and $45\degr$. For ISAAC/VLT and SOFI/NTT, this is realized by a rotation of the complete instrument. To avoid overlapping between different polarization images an aperture mask of three alternating opaque and transmitting strips of about $20''\times150''$ for ISAAC/VLT and $40''\times300''$ for SOFI/NTT is used.\\ We carried out Js-band polarization observations of five fields of B335 and CB68 with ISAAC/VLT and of four fields of CB54 with SOFI/NTT. \subsection{Optical observations} The optical observations in R~band were carried out in March 2012 at the $2~$m~IUCAA Girawali Observatory (IGO, India). The IUCAA Faint Object Spectrograph \& Camera (IFOSC), attached at IGOs Cassegrain focus, is equipped with an EEV~$2$K~$\times~2$K CCD camera optimized for a wavelength range of \mbox{$350-850$~nm} \citep[for details, see][]{2002BASI...30..785}.\\ IFOSC/IGOs polarimetry mode makes use of a single Wollaston prism combined with a half-wave plate. The linear polarization degree and orientation is derived through two observations with two different half-wave plate orientations. The field of view for the polarimetry mode is about $4'\times4'$. IFOSC/IGO does not use an aperture mask like ISAAC/VLT or SOFI/NTT. The unambiguous assignment of the observed point sources to the corresponding direction of polarization is done as part of the data reduction procedure.\\ We performed polarization observations of four fields of CB68 with IFOSC/IGO. \label{sec:summary} For the first time, we have obtained multiwavelength polarization maps that cover the extent of Bok globules over a range of $10^2-10^5$~AU, covering optically thin and optically thick regions. We observed the three globules B335, CB68, and CB54 in the near-IR and in the optical, and combined our observations with archival sub-mm and optical data. The major results follow. \begin{enumerate} \item The polarization degrees in the near-IR and in the optical amount to several percent $\left(2~\%\lesssim P\lesssim10~\%\right)$. \item In the case of B335 and CB68, two simple structured Bok globules, the orientation of the sub-mm polarization vectors in the dense inner part $(10^2-10^3~\text{AU})$ of the globules continue to the outer, less dense globule parts $(10^4-10^5~\text{AU})$. \item In the case of CB54, a globule with large-scale turbulences, the orientation of the polarization vectors in the near-IR is well-ordered on scales of $\sim10^4~$AU. \item In the case of B335, we found comparable magnetic field strengths in the globule parts traced by our near-IR observations and in the parts traced by sub-mm observations, by using the CF method. \item We do not find a general correlation between the magnetic field structure and the CO~outflow of the Bok globule. In CB54 we find a magnetic field orientation parallel to the CO~outflow, while B335 shows a change in the orientation of the magnetic field toward the outflow axis from the inner core to the outer regions. In CB68, we find a magnetic field orientation nearly perpendicular to the CO~outflow. \item The instrumental polarization of ISAAC/VLT depends significantly on the airmass of the observed object. For our unpolarized standard star, EGGR118, we determined the deviation of the polarization degree, $\Delta P\approx1.4~\%$. \end{enumerate} The well-ordered polarization vectors indicate dominant magnetic fields from scales of $10^2-10^3$~AU to scales of $10^4-10^5$~AU. In the particular case of CB54, the randomly oriented polarization pattern in the sub-mm can be explained by, e.g., a change in the orientation from the region south of the sub-mm map to the region north of the sub-mm map (see Fig.~\ref{fig:CB54_polmap}).\\ A gap remains with a width of about $1'-2'$ between the sub-mm observations done with SCUBA/JCMT and the near-IR observations performed with ISAAC/VLT and SOFI/NTT of B335, CB68, and CB54. \citet{2013A&A...551A..98L} derive typical hydrogen column densities for the region traced by the SCUBA/JCMT observations in Bok globules of $N_{\text{H}}\gtrsim10^{22}$~cm$^{-2}$, as well as $N_{\text{H}}\lesssim10^{21}$~cm$^{-2}$, for the regions observed with ISAAC/VLT and SOFI/NTT. To close the gap and, finally, spatially connect the magnetic field observations from the smallest to the largest scale, obvervations that trace the region of $10^{21}$~cm$^{-2}\lesssim N_{\text{H}}\lesssim10^{22}$~cm$^{-2}$ need to be done. Based on the flux level determined at the edges of the sub-mm map of B335 and CB54 observed with SCUBA/JCMT \citep{2003ApJ...592..233W, 2001ApJ...561..871H}, we estimate that these observations can be performed in less than one hour with ALMA since cycle$~2$. \\ The key to understanding the influence of magnetic fields on the low-mass star formation process is knowledge about the three-dimensional structures of the magnetic field and the object itself. Our observations, as well as all observations, suffer from projectional effects along the line of sight. Thus, it is necessary to do three-dimensional modeling of Bok globules, which includes a proper description of dust, dust grain alignment, gaseous outflows, and polarimetric radiative transfer, in addition to polarimetric observations. However, this type of analysis is beyond the scope of this study. \begin{appendix} | 14 | 4 | 1404.5597 |
1404 | 1404.2238_arXiv.txt | In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of a universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two-dimensionality and the shallower $k^2$ subinertial range spectrum of kinetic energy forcing the magnetic field with a $k^4$ subinertial range to attain larger-scale coherence. The inertial range shows a clear $k^{-2}$ spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling. | Initial conditions can be obtained either as a result of an earlier turbulence simulation driven by monochromatic driving or the fields can be synthesized with given power spectra and random phases. In the following, we describe and compare these different cases. \subsection{Via monochromatic driving} Our goal is to have an initial condition that quickly leads to self-similar decay. Earlier experience \cite{SM_kbtr10,SM_Tevzadze:2012kk,SM_Kahniashvili:2012uj} has shown that this is easily achieved by using a snapshot from a turbulence simulation that was driven with stochastic monochromatic forcing in the equation for the magnetic vector potential. The resulting initial condition used in our present work is shown in \Fig{pkt2304_hel_short2304pm1_kf60b_initial}. It shows approximate $k^2$ and $k^4$ subinertial ranges for kinetic and magnetic energy spectra, respectively. Both spectra are maintained also at later times in such a way that they gradually shift upward with time (see Fig.~1 of the Letter). \begin{figure}[h!] \includegraphics[width=\columnwidth]{pkt2304_hel_short2304pm1_kf60b_initial} \caption[]{ Magnetic (solid lines) and kinetic (dashed lines) energy spectra for the initial condition of Run~A. }\label{pkt2304_hel_short2304pm1_kf60b_initial} \end{figure} \begin{figure}[h!]\begin{center} \includegraphics[width=\columnwidth]{pkt1152_MKol1152a5} \end{center}\caption[]{ Like \Fig{pkt2304_hel_short2304pm1_kf60b_initial}, but with an initial $k^4$ spectrum for the magnetic energy using random phases. }\label{pkt1152_MKol1152a5}\end{figure} In the present simulations (Run~A of the Letter), both magnetic and kinetic energies show a slight uprise of power near the Nyquist wavenumber, $k_{\rm Ny}=\pi/\delta x$, where $\delta x$ is the mesh spacing. This indicates that the resolution is only marginal for the Reynolds number chosen here. However, during the subsequent decay calculation, after several Alfv\'en times, this excess power at $k_{\rm Ny}$ disappears, as is seen in Fig.~1 of the Letter. \subsection{Via random phases} An alternative mechanism of producing initial conditions is to generate a vector field in wavenumber space with a given spectrum and random phases. In \Fig{pkt1152_MKol1152a5} we show an example where we have for magnetic energy a $k^4$ spectrum for $k<k_0$ and $k^{-5/3}$ for $k>k_0$, but zero kinetic energy. Our initial velocity is zero and the initial vector potential in Fourier space is $\hat{A}_{j}(\kk)$ such that for all three components $j$ are given by \EQ k\hat{A}_{j}(\kk)=A_0{(k/k_0)^{n_1/4-1/2}\over [1+(k/k_0)^{n_1-n_2}]^{1/4}}\,e^{\ii\phi(\kk)}, \EN where $n_1=4$ and $n_2=-5/3$ are the exponents of the related magnetic energy spectrum, $\phi(\kk)$ are random phases, $A_0$ is the amplitude, and $k=|\kk|$. We choose $k_0/k_1=60$ and run with $\nu=5\times10^{-6}$ at $1152^3$ meshpoints, which is slightly more dissipative than the runs reported in the Letter with $\nu=2\times10^{-6}$ using $2304^3$ meshpoints. In \Fig{pkt1152_MKol1152a5} we show the times $t/\tauA=10$, 50, 200, and 900, where $\tauA=(\vAz k_0)^{-1}$ is the initial Alfv\'en time. At very early times ($t\approx\tauA$), a $k^4$ kinetic energy spectrum develops, which is consistent with the causality constraint, but after several hundred Alfv\'en times the spectrum becomes gradually shallower and approaches a $k^2$ subinertial range. However, unlike the initial condition shown in \Fig{pkt2304_hel_short2304pm1_kf60b_initial}, the magnetic field is continuously decaying and the integral scale is increasing, which is the reason why the $k^2$ subinertial range is less strongly developed in \Fig{pkt1152_MKol1152a5}. Nevertheless, the magnetic spectrum shows again clear inverse transfer, although it is initially somewhat slower, as can be expected given the time it takes to build up the $k^2$ velocity spectrum. \subsection{Steeper initial spectra} If we start with a magnetic energy spectrum steeper than $k^4$, the spectrum quickly changes into a $k^4$. This is demonstrated in \Fig{pkt1152_MKol1152_k6b}, where we start with an initial $k^6$ spectrum, followed by a $k^{-5/3}$ subrange. We show the times $t/\tauA=1$, 5, 20, 80, and 400, and see that already at $t/\tauA=20$ the subinertial range has nearly a $k^4$ subrange. \begin{figure}[h!]\begin{center} \includegraphics[width=\columnwidth]{pkt1152_MKol1152_k6b} \end{center}\caption[]{ Like \Fig{pkt1152_MKol1152a5}, but with an initial $k^6$ spectrum for the magnetic energy using random phases. }\label{pkt1152_MKol1152_k6b}\end{figure} | The decay of magnetically dominated MHD turbulence is a rich field, sharing several similarities with the case in which the magnetic field is dynamo-generated, for example the alignment properties with the eigenvectors of the rate-of-strain tensor. In the Letter, we have focussed on the inverse transfer properties that were previously only known for helical MHD turbulence. This is a new and exciting result that has now been confirmed by two additional independent groups \cite{SM_BL14,SM_Zra14}. The results presented in the Supplemental Material support the robustness of this result and suggest that the inverse transfer is not explained by other previously studied mechanisms. | 14 | 4 | 1404.2238 |
1404 | 1404.0521_arXiv.txt | The source \src\ was discovered in the hard X-ray band by \igr. A periodic X-ray modulation at $\sim$326~s was detected in its \swift\ light curves by our group (and subsequently confirmed by a \swift\ campaign). In this paper, we report on the analysis of all the \swift\ observations, which were collected between 2005 and 2011, and of an $\sim$20~ks \xmm\ pointing that was carried out in 2013 September. During the years covered by the \swift\ and \xmm\ observations, the 1--10~keV fluxes range from $\sim$1.5 to $4\times$10$^{-11}$~\flux. \src\ displays spectral variability as a function of the pulse phase and its light curves show at least one short (a few hundreds of seconds) dip, during which the flux dropped at 20--30\% of the average level. Overall, the timing and spectral characteristics of \src\ point to an accreting neutron star in a high-mass system but, while the pulse-phase spectral variability can be accounted for by assuming a variable local absorbing column density, the origin of the dip is unclear. We discuss different possible explanations for this feature, favouring a transition to an ineffective accretion regime, instead of an enhanced absorption along the line of sight. | The source \src\ \citep{revnivtsev04short,walter04short} was discovered in 2003 during a survey of the Galactic Centre region with \igr. The hard X-ray (18--60~keV) flux of \src\ was $\sim$1.6~mCrab, roughly corresponding to $1.4\times10^{-11}$~\flux. \citet{revnivtsev04short} and \citet{stephen05short} pointed out that this new \igr\ source was the counterpart of the soft X-ray \rst\ point source 1RXS\,J172006.1--311702. \citet{masetti06short} proposed an optical counterpart % with a narrow H$\alpha$ line and reddened continuum, suggesting a high-mass X-ray binary (HMXB) system. The association was fortified by \citet{tomsick08}, who obtained a refined \cxo\ X-ray position. More recently, our team reported on the discovery of a coherent modulation of the X-ray emission of \src\ at a period of $\sim$326~s \citep{nichelli11}. The signal was detected in a run of the \swift\ Automatic Timing ANAlysis of Serendipitous Sources at Brera And Roma astronomical observatories (SATANASS\,@\,BAR) project. SATANASS\,@\,BAR consists in a systematic Fourier-based search for new pulsators in the \swift\ X-ray data.\footnote{For our analogous \cxo\ project, the \cxo\ ACIS Timing Survey at Brera And Rome astronomical observatories (CATS\,@\,BAR), see \citet{eis13,eisrc13,eism13}.} So far, about 4000 X-ray Telescope (XRT) light curves of point sources with a sufficiently high number of photons ($\ga$150) were analysed and the effort yielded six previously unknown X-ray pulsators (including \src, two other new pulsators were reported in \citealt{nichelli09}). The original detection of the period of \src\ occurred in a couple of \swift\ consecutive observations performed in 2005 October 26--27. After that, more \swift\ observations were carried out between 2010 October and 2011 May to characterize better \src. The period measured during the new \swift\ campaign was slightly longer ($\sim$328~s; \citealt{nichelli11}, see also Section\,\ref{timingan}), indicating that the modulation reflects almost certainly the spin of a neutron star. Here we give more details on the \swift\ observations and we report on a 20-ks long \xmm\ observation of \src\ performed on 2013 September 19, where we discovered an evident dip (a flux drop). While in low mass X-ray binaries these features are usually due to obscuring matter located in the outer accretion disc (see e.g. \citealt{diaztrigo06} for a review), in HMXBs they are probably produced by a transition to a different accretion regime (see \citealt{drave13} and references therein). In Sections \ref{observations} and \ref{analysis}, we describe the X-ray observations used and present the results of our timing and spectral analysis. Discussion follows in Section\,\ref{discussion}, where we concentrate on the origin of a peculiar short off-state observed in \src\ with \xmm. | \label{discussion} We reported on an in-depth characterization at X-rays of the source \src, both from the temporal and the spectral point of view. Pulsations, originally discovered by our group in \swift\ data and reported by \citet{nichelli11}, have been recovered in an archival \cxo\ observation, and clearly observed in the new \xmm/EPIC data analysed in detail here, with a periodicity of $327.878\pm0.024$~s. Such a long pulse period is typical of a neutron star in an HMXB. In fact, an early-type companion is also indicated by optical studies \citep{masetti06short} and by the precise \cxo\ position \citep{tomsick08}. Both a Be (main sequence or giant) star and a blue supergiant are viable possibilities for the companion star of \src. Unfortunately, for \citet{masetti06short} it was not possible to derive significant information about the optical counterpart (spectral type, absorption and source distance), since a reliable photometry was missing. From the Corbet diagram of X-ray-pulsar spin period versus orbital period \citep{corbet86}, the observed pulse period suggests an orbital period of either $\sim$3--30~d or $\sim$100--200~d for an HMXB hosting either a supergiant donor or a Be, respectively. Strong pulse to pulse variations (usually produced by fluctuations in the wind accreted by the neutron star) and a pulse profile energy dependence are evident in \src, as it is often observed in accreting pulsars with massive donors. The hard \xmm\ spectrum (power-law photon index in the range 0.8--1.2) is in line with an HMXB origin for the X-ray emission. The presence of a soft component is indicated by the X-ray spectroscopy. The spectrum is well fit by a blackbody emission together with a hard power law. While both a colder ($kT\sim0.15$~keV) and a hotter ($kT\sim1.18$~keV) blackbody are valid deconvolution of the spectrum, we favour the hot solution, which is consistent in temperature and size ($R_{\mathrm{BB}}\approx0.3\,d_5$~km, where $d_5$ is the distance in units of 5~kpc) with an HMXB interpretation of the hot blackbody as produced in the polar cap region of the neutron star accretion column \citep{becker07}. The strong variability of the spin-phase-selected spectra (Fig.\,\ref{xmmfold}, bottom panel) can be accounted for by a variable absorbing column density along the spin cycle, probably mapping a different density of the local matter illuminated by the X-ray beam pattern. Significant variations (up to a factor of 4) in the absorbing column density are also present in the long-term X-ray light curve (Fig.\,\ref{xrtlc}). Variations in the local absorption are usual in HMXBs because the compact object is constantly embedded in an intense structured and clumpy wind. Moreover, in a few cases, large-scale structures have been observed in HMXBs (gas streams) and interpreted as the result of the disruption of the wind by the neutron star passage, which produce density perturbations that modulate the observed \nh\ along the orbital cycle \citep{blondin90,manousakis11}. We observed a remarkable feature in the EPIC light curve, a dip or a so-called off-state, characterized by a reduction in the source intensity down to $\sim$20--30\% of its normal level, and lasting for about one neutron star spin cycle. Similar features have been seen so far only in a few HMXB pulsars with supergiant companions and are potentially important to derive information on the accretion regime and the neutron star properties: \mbox{Vela\,X--1} (orbital period $P_{\mathrm{orb}}\simeq9$~d and spin period $P_{\mathrm{spin}}\simeq283$~s; \citealt{inoue84,kreykenbohm99,kreykenbohm08short}), 4U\,1907+09 ($P_{\mathrm{orb}}\simeq8.4$~d and $P_{\mathrm{spin}}\simeq437.5$~s; \citealt{dsdk12}), GX\,301--2 ($P_{\mathrm{orb}}\simeq41.5$~d and $P_{\mathrm{spin}}\simeq686$~s; \citealt*{gkb11}), and in the Supergiant Fast X-ray Transients IGR\,J16418--4532 ($P_{\mathrm{orb}}\simeq3.7$~d and $P_{\mathrm{spin}}\simeq1212$~s; \citealt{drave13}), and IGR\,J17544--2619 ($P_{\mathrm{orb}}\simeq4.9$~d and candidate $P_{\mathrm{spin}}\simeq71.5$~s; \citealt{drave14}). During these off-states, X-ray pulsations sometimes appear to be suppressed \citep{kreykenbohm99}, sometimes are still detected \citep*{doroshenko11}, and the X-ray spectrum softens. This implies that these dips are not caused by the obscuration by a dense wind clump passing our line of sight to the pulsar, but are due to a real flux drop. \citet{gkb11} suggested that softer X-rays during these dips are likely due to the suppression of the harder X-ray emission produced in the accretion column, leaving visible the soft X-rays coming from the underlying thermal mound at the bottom of the accretion column \citep{becker07}. The reason for a suppression (or cessation) of the hard X-rays produced in the accretion column is unclear. Aside from temporarily enhanced absorption along the line of sight, three main explanations for off-states have been proposed: a temporary transition to a centrifugal inhibition of the accretion (see e.g. \citealt{kreykenbohm08short} for Vela\,X--1), a Kelvin--Helmholtz (KH) instability \citep{dsdk12}, or an accretion regime change from a Compton cooling regime (producing a higher luminosity) to a radiative cooling regime (lower luminosity) in the equatorial plane of the neutron star magnetosphere, due to a switch from fan beam to pencil beam emission pattern \citep{shakura13}. Also in \src, the significantly softer spectrum during the off-state leads us to exclude the possibility of an obscuration of the central source by a wind structure (or clump), which would cause instead a spectral hardening. The small duration of the dip (a little more than a spin cycle) does not allow us to establish if the remaining fainter emission is pulsating, so a centrifugal barrier temporarily halting accretion, could be a possibility, although the short duration of the off-state makes it unlikely \citep{gkb11}. In \src, the spectrum during the dip cannot be completely accounted for {\em only} by an unvarying blackbody emission (this is ruled out by the marked spectral variability), and significant (power-law-like) hard X-ray emission is present, suggesting that in our case accretion is not suppressed in contrast, again, to what is expected with the onset of a propeller regime. \begin{figure} \centering \resizebox{\hsize}{!}{\includegraphics[angle=-90]{xrtspec.ps}} \caption{\label{xrtspec} Comparison of the \swift\ spectrum from observation 8003 with that obtained from the observations 8005, 8009, and 8010, which are very similar to each other, combined (red triangles). The solid lines show the best-fitting power-law models (same photon index, but different \nh\ and normalization). Bottom panel: residuals of the fit in units of standard deviations with error bars of size one.} \end{figure} \begin{figure} \centering \resizebox{\hsize}{!}{\includegraphics[angle=-90]{part1.ps}\hspace{-2.5cm}\includegraphics[angle=-90]{part2.ps}} \caption{\label{xrtlc} Top panels: \swift\ long-term light curve (the flux is in the 1--10 keV energy range and not corrected for the absorption). Note the time gap and the different time-scales. Bottom panels: corresponding absorption column as inferred from the spectral analysis.} \end{figure} A transition to accretion via KH instability is discussed by \citet{dsdk12} as a possible explanation of dips in the transient source 4U\,1907+09, following the theory of wind accretion in HMXBs surveyed by \citet*{bozzo08}. In the framework of the different accretion regimes discussed by \citet{bozzo08}, the magnetospheric boundary at the Alfv\'en radius, $R_{\mathrm A}$, can be KH unstable in two regimes: in the sub-Keplerian magnetic inhibition regime (where $R_{\mathrm{acc}} < R_{\mathrm{A}} < R_{\mathrm{cor}}$, where $R_{\mathrm{acc}}$ is the accretion radius, $R_{\mathrm{cor}}$ is the corotation radius, where the neutron star angular velocity is equal to the Keplerian angular velocity), and in the subsonic propeller regime (where $R_{\mathrm{A}} < R_{\mathrm{acc}} < R_{\mathrm{cor}}$). The spin period of $\sim$328~s implies a corotation radius, $R_{\mathrm{cor}}$, of $8\times 10^{9}$~cm. Thus, in both regimes, $R_{\mathrm{cor}}$ represents an upper limit to the value of the other two important radii involved. The relation $R_{\mathrm{acc}} < R_{\mathrm{cor}}$ ($R_{\mathrm{acc}}=2GM/v_{\mathrm{rel}}^2$, where $M$ is the neutron star mass, and $v_{\mathrm{rel}}$ is the relative velocity of the neutron star and the companion wind) translates into a lower limit for $v_{\mathrm{rel}}$ of $\sim$2200~km~s$^{-1}$, which is, on average, quite high in comparison with usual HMXBs, but it cannot be excluded, given the large variability expected in inhomogeneous winds of massive stars \citep*{oskinova12}. Adopting equation~21 in \citet{bozzo08} for the X-ray luminosity $L_{\rm KH}$ produced by matter entering the magnetosphere through KH instability in the subsonic propeller regime, all the parameters involved in this formula are basically unknown for \src, except for the neutron star spin period. However, we can derive an upper limit to $L_{\rm KH}$ by assuming the following: $R_{\mathrm{acc}} = R_{\mathrm{A}} = R_{\mathrm{cor}}$, an orbital period of 5~d (which is reasonable for an accreting pulsar with a supergiant companion and the observed spin period; \citealt{corbet86}) and a total mass for the binary system of 30~M$_{\odot}$ (implying $a_{\mathrm{10d}}=0.63$ in equation~21 in \citealt{bozzo08}), a relative velocity of 2200~km~s$^{-1}$ ($v_8=2.2$ in equation~21 in \citealt{bozzo08}), a wind mass-loss rate of $10^{-6}$~M$_{\odot}$~yr$^{-1}$, a density ratio $\rho_{\mathrm{i}}/\rho_{\mathrm{e}} = 1$ [where $\rho_{\mathrm{i}}$ and $\rho_{\mathrm{e}}$ are the internal (below $R_{\mathrm{A}}$) and the external densities (above $R_{\mathrm{A}}$)], and $\eta_{\rm KH}\sim0.1$ for the efficiency factor. This translates into $L_{\rm KH} < 1.5\times10^{35}$~\lum, which can easily be accounted for if one assumes a reasonable distance to the source (see below). Note that the upper limit to the Alfv\'en radius, $R_{\mathrm{A}} < R_{\mathrm{cor}}$, results in an upper limit to the dipolar magnetic field of $B<1.2\times10^{14}$~G ($\mu<6\times 10^{31}$~G~cm$^{3}$; equation~19 in \citealt{bozzo08}). Again, we caution that all these estimates rely on particular (though reasonable) assumptions on all other parameters involved in the system geometry and wind properties. Even larger uncertainties are involved in the estimate of the KH instability mass accretion rate across the magnetosphere in the sub-Keplerian magnetic inhibition regime, where also the shear velocity is involved. Assuming the same values as above for the parameters in equation~10 in \citet{bozzo08}, we derive $L_{\rm KH}\sim10^{34}$~\lum. A third possible explanation for off-states involves the application of the \citet{shakura12} model of subsonic quasi-spherical accretion on to moderately low luminosity ($<$$4\times10^{36}$~\lum) and slowly rotating neutron stars. Here, off-states are explained by transitions to an ineffective accretion regime, rather than with a cessation of the accretion. In this scenario, an off-state is the signature of a transition from a regime where the cooling of the gravitationally captured plasma entering the neutron star magnetosphere is dominated by Compton processes to a less efficient radiative cooling regime \citep*{shakura13}. This transition might be triggered by a change in the X-ray beam pattern, from a fan beam to a pencil beam, produced by a reduced optical depth in the accretion flow. Since matter enters the neutron star magnetosphere more easily from the equatorial region, a high lateral X-ray luminosity by a fan beam directly illuminating the equator, allows a more efficient Compton cooling, facilitating accretion and thus resulting in a higher luminosity. So, a transition from a fan to a pencil X-ray beam pattern increases the Compton cooling time, triggering a lower luminosity state (an off-state). The transition back to the normal X-ray luminosity can be triggered by an enhanced density above the magnetosphere, increasing the accretion rate. The transition to an off-state occurs at an X-ray luminosity of about $3\times 10^{35} \mu_{30}^{-3/10}$~\lum, where $\mu_{30}=\mu/[10^{30}$~G~cm$^3]$ is the neutron star dipole magnetic moment. The luminosity level in the off-state is about $10^{35} \mu_{30}^{7/33}$~\lum\ in the radiation cooling regime \citep{shakura13}. The average unabsorbed 1--10~keV flux of \src\ during the \xmm\ observation varies, depending on the adopted model (see Table\,\ref{specs}), from $\sim$$3\times10^{-11}$ to $\sim$$4\times10^{-11}$~\flux. Nothing is known about the distance of \src, which could be anywhere towards the edge of the Galaxy. At 5~kpc, the former flux translates into a luminosity of $9\times10^{34}d^2_5$~\lum, the latter into $1.2\times10^{35}d^2_5$~\lum\ (where $d_5$ is the distance in units of 5~kpc). Above $\approx$$4\times10^{36}$~\lum, the quasi-spherical shell cannot exist and supersonic (Bondi) accretion is more likely, but this would require a distance $d>28$~kpc. This implies that, for reasonable source distances in the range 5--10 kpc, the X-ray emission easily matches the X-ray luminosity needed to trigger the switch to an off-state, assuming a standard neutron star magnetic field of $\sim$$10^{12}$~G. To conclude, the observed spectral softening during the dip (which is common in similar off-states observed in other HMXBs) is more naturally explained by a transition to an ineffective accretion regime, instead of an obscuring dense clump in front of the X-ray source (which would have implied an hardening). However, given the unknown distance, the different possibilities for the transition to an inefficient accretion regime discussed above cannot be clearly disentangled. | 14 | 4 | 1404.0521 |
1404 | 1404.6527_arXiv.txt | We present a detailed analysis of dark matter halo shapes, studying how the distributions of ellipticity, prolateness and axial ratios evolve as a function of time and mass. With this purpose in mind, we analysed the results of three cosmological simulations, running an ellipsoidal halo finder to measure triaxial halo shapes. The simulations have different scales, mass limits and cosmological parameters, which allows us to ensure a good resolution and statistics in a wide mass range, and to investigate the dependence of halo properties on the cosmological model. We confirm the tendency of haloes to be prolate at all times, even if they become more triaxial going to higher redshifts. Regarding the dependence on mass, more massive haloes are also less spherical at all redshifts, since they are the most recent forming systems and so still retain memory of their original shape at the moment of collapse. We then propose a rescaling of the shape-mass relations, using the variable $\nu=\delta_{c}/\sigma$ to represent the mass, which absorbs the dependence on both cosmology and time, allowing to find universal relations between halo masses and shape parameters (ellipticity, prolateness and the axial ratios) which hold at any redshift. This may be very useful to determine prior distributions of halo shapes for observational studies. | Nowadays different observational campaigns agree on the standard cosmological model to explain and describe the structure formation in our Universe \citep{fu08,planckxx}. In this scenario, almost $95\%$ of the energy content on the Universe is in unknown forms of energy and matter, generally called dark energy and dark matter. The structure formation process occurs around the initial density peaks \citep{bardeen86,bond96,ludlow11,paranjape12,paranjape13} and proceeds hierarchically along the cosmic time: small systems collapse first, at high redshift, and then merge together forming more massive ones \citep{lacey93,lacey94,tormen98a}. Galaxy clusters are the largest virialized systems in the Universe and so the last to form: almost $80\%$ of their mass is attributed to dark matter, while the rest to baryons, divided in $hot$ (diffuse gas, $75\%$), $cold$ (stars, $7\%$) and other forms ($18\%$) \citep{ettori09}. They collapse as consequence of gravitational instability and grow as a result of different violent merging events \citep{tormen04}; many observations have captured them as characterised by multiple mass components \citep{postman12,zitrin13a}, elongated in the plane of the sky \citep{zitrin13b} or along the line-of-sight \citep{morandi11}. Galaxy clusters are also characterised by the presence of many substructures, which are the cores of progenitor haloes accreted during the formation history and may contain galaxy cluster members \citep{giocoli10}. The mass density distribution of relaxed haloes typically follows a well defined profile \citep{navarro96} that has a logarithmic slope of $-1$ in the inner part and $-3$ toward the outskirt. The distance from the center at which the logarithmic slope approaches $-2$ defines the scale radius $r_s$ from which we can define the concentration $c=R_{vir}/r_s$, where $R_{vir}$ represents the virialisation radius of the system. Galaxy clusters can be used as cosmological probes since they are expected to follow a well defined concentration-mass relation \citep{neto07,zhao09,prada11,giocoli12b} and their predicted abundance as a function of redshift is well portrayed \citep{sheth99b,jenkins01,tinker08}. These may then be combined with other analyses for example cosmic shear \citep{schrabback07,schrabback10}, CMB primordial density fluctuation \citep{planckxx}, Sunyaev Zel'dovich effect and X-ray data \citep{roncarelli07,roncarelli10}, two \citep{marulli12,marulli13} and three point correlation functions \citep{moresco13}. However, the use of galaxy clusters as cosmological probes depends on how well structural properties -- mass, concentration, triaxiality and subhalo abundance -- can be recovered combining different observations. Many studies have revealed that the possibility to correctly estimate the mass and the concentration of the clusters is an open problem for X-ray, SZ and also optical observations. For example, different lensing analyses on numerical and pseudo-analytical clusters have shown that the estimated mass is on average biased to be lower than the true one \citep{becker11,meneghetti10b}. This is due to the fact that the dark matter haloes in which the clusters are embedded are typically prolate \citep{giocoli12c}, while most of the works still uses spherical models: we have a large probability to see them elongated in the plane of the sky and this leads to underestimate the mass if we limit ourselves to spherical halo boundaries which will not capture the whole halo. On the other hand, when the major axis of the halo ellipsoid is elongated along the line-of-sight we tend to overestimate the mass. A correct modeling of the halo triaxiality is therefore important in order to reach a better understanding of these biases and how structural properties can be recovered from the observations. The triaxiality of the halo is also responsible for the amplification of the Einstein radius size (both when the cluster is very elongated in the plane of the sky and along the line-of-sight) and of the generation a possibile bias in the estimated concentration and in the measurement of the inner slope of the density profile \citep{giocoli14}. SZ and X-ray mass reconstructions tend to rely on the assumption that the systems are spherically symmetric and the hot gas is in hydrostatic equilibrium. \citet{rasia12} have shown that the X-ray mass are on average biased low by a large amount, highlighting both the presence of non-thermal pressure and temperature anisotropy in the inter cluster medium. In this context it is worth to notice that the discrepancy between X-ray, SZ and lensing mass appear not only when the cluster is not relaxed but also when its mass density distribution deviate from spherical symmetry. Combined multi-wavelength observations are thus important not only to understand the physical state of cosmic structures but also their shape. The interpretation of observations requires a comparison with the predictions coming from theory and simulations \citep{limousin13}. For this reason, it is becoming more and more important to model the results of simulations with as much detail as possible, even if this is computationally more expensive. Dark matter haloes are usually identified in simulations as spherical systems, since it is quite easy, computationally speaking, and it is also proven to be a good approximation when calculating the main properties of the halo population, such as the mass function, the concentration and so on. Moreover, even if their boundaries are spherical, obviously matter inside them is not isotropically distributed and so even from a spherical distribution it is possible to compute the axial ratios and other shape parameters. Nevertheless, it is clear that considering all systems as spheres is a bit rough and so many works claim the need of a more realistic model, such as triaxial ellipsoids \citep{warren92,jing02,allgood06,despali13}. Being more precise and allowing a greater variety of shapes, this method is particularly useful when one wants to study dark matter halo shapes and determine their influence on observable 2D projected quantities. A precise knowledge of the ellipticity and of the axial ratio distributions of galaxy cluster-size halos is fundamental also when observations from different bands are combined to recover the cluster mass \citep{morandi10,morandi12}. In this case the distribution priors can be used to constrain both the ellipticity on the plane of the sky and the elongation along the line-of-sight of the cluster ellipsoid \citep{sereno13}. Thus, the aim of this work is to study the shape of triaxial haloes and model its distribution, its evolution with redshift and the dependence on cosmology. In particular, we will analyse the distribution of the shape parameters (axial ratios, ellipticity and prolateness) as a function of halo mass and redshift; we will then present some universal relations and fitting formulae which may be used to retrieve the typical shape distribution at a certain time or for a certain mass bin, when a comparison with observations or a prediction is needed. The structure of this paper is as follows. In Section \ref{simulations} we present the numerical simulations used in this work and the post processing pipeline. Section \ref{results1} describes the results on shape parameters: we analyse the properties of the halo population at various redshifts of the simulations and show some universal fitting formulae for the shape parameters. In Section \ref{mergerzf} we describe the merger tree catalogues and how it is possible to relate the shape with the formation redshift of haloes. Finally in Section \ref{conclusions} we summarise and discuss our results. | To characterise how the distribution of halo shapes evolves in time, we analysed a set of three cosmological simulations -- GIF2, Baby and Flora, which cover a wide range of halo masses and allow to compare two different cosmologies. We presented the simulations and the post-processing pipeline used to identify the halo population and calculate the shape properties, using the EO halo finder, already described in \citet{despali13}. Then we discussed the resulting distributions and proposed some best fitting relations. The main result of this work is the existence of universal distributions of the shape parameters ($e$, $p$ and the axial ratios), when rescaling the mass to the universal variable $\nu=\delta_{c}/\sigma$. It allows to eliminate the dependences on cosmology and epoch, moving the distributions of all redshifts all on the same linear relations. Then we report and study other properties of halo shapes, which can be summarised as follows: \begin{itemize} \item at fixed mass, halo shapes become more elongated at high redshifts; the behavior is qualitative the same for both cosmologies, with a slight difference in the median values due to the difference in formation times of haloes; \item haloes of similar mass possess larger ellipticity and prolateness at higher redshifts: on average $e$ and $p$ from redshift $z=2$ to the present time change of about $40-50\%$; \item at any given time, the more massive is an halo, the less spherical it is: this is due to the fact that massive haloes still retain memory of their "original'' shape, which has not been yet contaminated or rounded by other events and which is related to the direction of filaments or of the last major merger; thus, at any given time, massive haloes show higher values both of $e$ and $p$ -- cleary the same trend is reflected in the axial ratios); \item another quasi-universal distribution is given by the relation between $p$ and $e$, which remains on average with a slight redshift dependence; \item halo ellipticity is a decreasing function of the generalized formation redshifts $z_f$ -- as the redshift when the main halo progenitor assembles a fration $f$ of its present-day mass, with no particular dependence on cosmology: both GIF2 and Baby cosmology lie on the same relation. \end{itemize} To conclude, halo triaxial properties show a dependence on cosmological parameters since related to the halo assemble histories. In this work we have presented how ellipticity, prolatness and axial ratios correlate with the universal variable $\nu$: in a way that these quantities are independent on halo mass, redshift and background cosmology. We find our results useful to be implemented in a Monte Carlo method to generate mock haloes with given triaxial properties, and in triaxial mass reconstruction methods that require priors for the axial ratio distributions. | 14 | 4 | 1404.6527 |
1404 | 1404.4652_arXiv.txt | We explore the application of Monte Carlo transport methods to solving coupled radiation-hydrodynamics problems. We use a time-dependent, frequency-dependent, 3-dimensional radiation transport code that is special relativistic and includes some detailed microphysical interactions such as resonant line scattering. We couple the transport code to two different 1-dimensional (non-relativistic) hydrodynamics solvers: a spherical Lagrangian scheme and a Eulerian Godunov solver. The gas-radiation energy coupling is treated implicitly, allowing us to take hydrodynamical time-steps that are much longer than the radiative cooling time. We validate the code and assess its performance using a suite of radiation hydrodynamical test problems, including ones in the radiation energy dominated regime. We also develop techniques that reduce the noise of the Monte Carlo estimated radiation force by using the spatial divergence of the radiation pressure tensor. The results suggest that Monte Carlo techniques hold promise for simulating the multi-dimensional radiation hydrodynamics of astrophysical systems. | The dynamical effects of radiation can be important in astrophysical contexts, so numerical simulations must often address the radiation transport problem. The radiation field, when treated fully, is a function of not only three spatial coordinates, but also of time, frequency and two direction angles. The high dimensionality of the problem makes it computationally very challenging, and approximate methods that ignore certain dependencies (e.g., on frequency and/or angle) are often employed. Recent efforts aim to relax these approximations and improve the accuracy of the transport scheme. Given the difficulty of the radiation-hydrodynamics (RHD) problem, and the critical importance of it in astrophysical simulation, a number of different numerical techniques should be explored. Ultimately, no single approach may prove ideal in every conceivable application, and the relevant tradeoffs in performance will need to be considered on a case by case basis. In this paper we explore the coupling of Monte Carlo radiative transfer (MCRT) to hydrodynamics. The Monte Carlo approach offer several advantages as compared to a deterministic solution of the radiative transfer equation. MCRT generalizes readily to arbitrary 3-dimensional geometries, and can naturally incorporate multi-frequency, multi-angle, and time-dependent transport effects. It is also straightforward to include complex physical interactions, such as anisotropic and inelastic scattering processes, polarization, and resonant line scattering. MCRT methods generally parallelize well (although not necessarily trivially for memory intensive problems \citep{Kasen2008}) and so can be run profitably on massively-parallel machines. This last consideration may ultimately prove to be the most significant, as the available computing power increases over time. The main disadvantage of MCRT methods is the presence of stochastic error, such that the computation of a large number of packet trajectories may be required. A number of variance reduction techniques exist to help limit the unwanted effects of noise, and certain acceleration techniques can alleviate the well known computational inefficiency of MCRT in regimes of high optical depth. The ultimate expense of MCRT relative to other transport methods is difficult to estimate, but generally as the dimensionality of the problem increases, the advantages of Monte Carlo methods become more apparent. This suggests that MCRT will be competitive in addressing the full 3-D multi-angle multi-frequency RHD problem. Here we present calculations using a MCRT code designed to handle the full-dimensionality of the Boltzmann transport problem -- i.e., the dependence on 3 spatial dimensions, time, frequency and angle. The code is special relativistic and includes some more complex physical interactions, such as resonant line scattering. It makes use of implicit techniques \citep{Fleck1971} in order to permit time-steps larger than the gas-radiation energy coupling time. For the sake of demonstrating the essential principles and assessing the viability of the approach, we restrict ourselves to coupling to a one-dimensional hydrodynamics solver; upcoming work will generalize to multi-dimensional RHD. In section \ref{Sec:LiteratureReview}, we review some of the existing literature on RHD in astrophysics, including previous efforts in MCRT. In section \ref{Sec:Equations} we outline the equations solved and the simplifying assumptions employed. Section \ref{Sec:MonteCarlo} describes the Monte Carlo implementation, while section \ref{Sec:Hydro} describes our numerical hydrodynamics scheme. Section \ref{Sec:ImplicitMC} describes the implicit Monte Carlo technique and its use in our code. Section \ref{Sec:RadiationTests} describes some radiation-only tests of our frequency-dependent transfer code. Section \ref{Sec:RadhydroTests}, the centerpiece of this paper, presents a suite of RHD test problems. Section \ref{Sec:RadiationForceComparsion} shows how Monte Carlo noise can be reduced by computing the radiation force via spatial derivatives of the Eddington tensor, rather than through a direct Monte Carlo force estimator. Section \ref{Sec:Performance} provides some brief considerations of the numerical performance of our code and the possibilities for improving it in the future. Finally, Section \ref{Sec:Conclusion} presents our conclusions. | \label{Sec:Conclusion} We have demonstrated that MCRT coupled to both Lagrangian and Eulerian hydrodynamics solvers can result in accurate, robust treatments of RHD problems, including those in which the radiation energy dominates. Although we have focused here on 1-dimensional test problems, our Eulerian code is multi-dimensional, and subsequent studies will address astrophysical problems in higher spatial dimensions. Our approach makes use of the implicit MCRT method to allow us to take hydrodynamical time-steps much larger than the gas cooling time. We also showed how to use Monte Carlo estimators to construct expressions for the radiation force four-vector $G^i$ that are accurate to all orders of $v/c$, although the hydrodynamics equations are only solved to order $v/c$. We compared simulations using our exact expression for $G^i$ to those using a more approximate expression based on the divergence of the radiation pressure tensor, which is valid when the radiation is in the diffusion regime. We found that the latter method can lead to a significant reduction in Monte Carlo noise in cases of coarse spatial resolution. In most of the problems studied here, the presence of stochastic noise did not introduce substantial error in the dynamics, however the effects of noise become a larger concern in problems where radiation energy is strongly dominated. Several additional refinements will be explored in the future. We will consider the use of a more sophisticated treatment of the radiative source terms in the Godunov scheme. Improvements in performance may be realized by incorporating the discrete diffusion technique. It is straightforward to incorporate the effects of more complicated radiation-matter interactions, including photoionization and anisotropic scattering processes such as Compton scattering with Klein-Nishina corrections. Possible applications of this technique include radiatively-launched winds from galaxies, tidal disruptions of stars, shock breakouts and ejecta-ISM interactions in supernovae. | 14 | 4 | 1404.4652 |
1404 | 1404.5462_arXiv.txt | The ubiquity of planets poses an interesting question: when first planets are formed in galaxies. We investigate this problem by adopting a theoretical model developed for understanding the statistical properties of exoplanets. Our model is constructed as the combination of planet traps with the standard core accretion scenario in which the efficiency of forming planetary cores directly relates to the dust density in disks or the metallicity ([Fe/H]). We statistically compute planet formation frequencies (PFFs) as well as the orbital radius ($\braket{R_{rapid}}$) within which gas accretion becomes efficient enough to form Jovian planets. The three characteristic planetary populations that are inferred from the accumulation of observed exoplanets are examined: hot Jupiters ($0.01 < r_p / \mbox{AU}< 0.5$, $30 < M_p/M_{\oplus} < 10^4$, where $r_p$ and $M_p$ are the semimajor axis and the mass of planets, respectively), exo-Jupiters ($0.5 < r_p / \mbox{AU}< 10$, $30 < M_p/M_{\oplus} < 10^4$), and low-mass planets such as super-Earths ($0.01 < r_p / \mbox{AU}< 0.5$, $1 < M_p/M_{\oplus} < 30$). We explore the behavior of the PFFs as well as $\braket{R_{rapid}}$ for the three different populations as a function of metallicity ($-2 \leq$[Fe/H]$\leq -0.6$). We show that the total PFFs (the sum of the PFFs for all the three populations) increase steadily with metallicity, which is the direct outcome of the core accretion picture. For the entire range of the metallicity considered here, the population of the low-mass planets dominates over the Jovian planets (i.e. the hot and the exo-Jupiters). The Jovian planets contribute to the PFFs above [Fe/H]$\simeq -1$. For the formation of two kinds of the Jovian planets, we find that the hot Jupiters form at lower metallcities than the exo-Jupiters. This arises from the radially inward transport of planetary cores by their host traps. Our results show that the transport becomes more effective for disks with lower metallicities due to the slower growth of the cores. The PFFs for the exo-Jupiters exceed those for the hot Jupiters around [Fe/H]$\simeq -0.7$. Finally, we show that the critical metallicity for forming Jovian planets is [Fe/H]$\simeq -1.2$, which is evaluated by comparing the values of $\braket{R_{rapid}}$ between the hot Jupiters and the low-mass planets. The comparison intrinsically links to the different gas accretion efficiency between these two types of planets. This study therefore implies that important physical processes in planet formation may be tested by examining exoplanets around metal-poor stars. | \label{intro} The unprecedented success in exoplanet observations has inferred that planet formation occurs in various environments \citep[e.g.,][]{us07,mml11,brb12}. The metallicity of host stars provides one of the major factors for discovering exoplanets \citep[e.g.,][]{sim04,sl11,blj12}. The observations suggest that massive planets like our Jupiters are observed preferentially around metal-rich stars whereas the detectability of low-mass planets such as super-Earths apparently does not correlate with stellar metallicity. The metallicity dependence is often referred to as the "planet-metallicity relation". Currently, the presence of exoplanets is confirmed around stars with a wide range of metallicities ([Fe/H]$\la 0.6$).\footnote{ The standard notation is adopted, so that [Fe/H] is a logarithmic metallicity normalized by the solar metallicity. In other words, [Fe/H]=0 for solar metallicity.} The lowest metallicity at which massive exoplanets are observed is so far [Fe/H]$\simeq -2$ \citep{skh10,srd12}, although these observations are currently a matter of debate. In fact, other observations show that the presence of planets for the same targets is very likely to be ruled out \citep{dsb13,mrh13,jj14}. Most observed massive and low-mass planets are confined well within [Fe/H]$\ga -0.6$. A successful theoretical framework to understand the exoplanet observations is the so-called core accretion scenario \citep[e.g.,][]{p96,il04i}. In this scenario, gas giants undergo sequential accretion of dust and gas: cores of gas giants form first via oligarchic growth by planetesimal collisions \citep[e.g.,][]{ki98,tdl03}, and then the cores accrete surrounding gas and form massive envelopes around them \citep[e.g.,][]{m80,ine00,lhdb09,mbp10}. Population synthesis calculations developed by this picture confirmed that massive planets within the orbital radius $r=10$ AU can be built within the disk lifetime \citep[$\sim 10^{6-7}$ yr, e.g.,][]{il04i,mab09,hp13a}. Furthermore, the calculations succeeded well in reproducing the planet-metallicity relation. This arises because the efficiency of forming planetary cores is directly linked to the number density of dust in disks in the model \citep[e.g.,][]{il04ii,mab12,hp14a}. One of the intriguing questions that remain to be addressed is whether or not we can extrapolate these results to metal-poor stars ([Fe/H]$< -0.6$). What is the critical metallicity for forming gas giants in the standard core accretion picture? In this paper, we explore the problem and quantify at what value of metallicity the formation of gas giants can proceed. To this end, we carry out a statistical analysis for planetary populations by using a semi-analytical model developed in a series of earlier papers \citep[hereafter, HP11, HP12, HP13, HP14]{hp11,hp12,hp13a,hp14a}. By computing planet formation and migration in evolving gaseous disks, we estimate the planet formation frequency (PFF) as well as the averaged value of $R_{rapid}$ (defined as $\braket{R_{rapid}}$) within which gas accretion onto the cores becomes rapid ($\sim 10^5$ yr). The analysis is applied for three different planetary populations that are suggested by the observations (see Table \ref{table1}): hot Jupiters ($0.01 < r_p / \mbox{AU}< 0.5$, $30 < M_p/M_{\oplus} < 10^4$, where $r_p$ and $M_p$ are the semimajor axis and the mass of planets, respectively), exo-Jupiters ($0.5 < r_p / \mbox{AU}< 10$, $30 < M_p/M_{\oplus} < 10^4$), and low-mass planets with short orbital periods such as super-Earths ($0.01 < r_p / \mbox{AU}< 0.5$, $1 < M_p/M_{\oplus} < 30$). \begin{table*} \begin{minipage}{17cm} \begin{center} \caption{Three zones in the mass-semimajor axis diagram} \label{table1} \begin{tabular}{lccc} \hline Definition$^1$ & Mass range ($M_{\oplus}$) & Semimajor axis range (AU) & HP13$^2$ \\ \hline & & 0.01 $< r_p <$ 0.1 & Zone 1 \\ [-1ex] \raisebox{1.5ex}{Hot Jupiters} & \raisebox{1.5ex}{30 $< M_p<$ $10^4$} & 0.1 $< r_p <$ 0.5 & Zone 2 \\[1ex] \hline Exo-Jupiters & 30 $< M_p<$ $10^4$ & 0.5 $< r_p <$ 10 & Zone 3 \\[1ex] \hline Low-mass planets & 1 $< M_p<$ 30 & 0.01 $< r_p <$ 0.5 & Zone 5 \\ \hline \end{tabular} $^1$ the same definitions as HP14. $^2$ the definitions adopted in HP13. \end{center} \end{minipage} \end{table*} As shown below, we find that the total PFFs for all the three populations are correlated positively with metallicity. This arises from the nature of core accretion picture. The PFFs of the low-mass planets, which are formed as failed cores of gas giants and/or mini-gas giants in our model, correspond to those of the total at up to [Fe/H]$\simeq -1$ above which the population of the Jovian planets becomes non-negligible. Our results show that lower metallicity disks tend to create the hot Jupiters more easily than the exo-Jupiters, which originates from the combined effects of planet formation with planetary migration. We also demonstrate that the exo-Jupiters become dominant over the hot Jupiter population at [Fe/H]$\ga -0.7$. We finally examine $\braket{R_{rapid}}$ for the hot Jupiters as well as the low-mass planets, which essentially traces the difference in the efficiency of gas accretion between them, and find that the critical metallicity for gas giant formation is [Fe/H]$\simeq -1.2$. Our results therefore imply that the behavior of the PFFs for different planetary populations and the resultant characteristic metallicities may link deeply to important physical processes involved with planet formation. Thus, exoplanet observations around metal-poor stars may contain an invaluable potential to examine these processes. The plan of this paper is as follows. In Section \ref{model}, we briefly describe the semi-analytical model we have employed. In Section \ref{resu}, we present our results and derive the critical metallicity above which gas giant formation can take place. In Section \ref{disc}, we discuss potential issues that may arise when planet formation around metal-poor stars is considered. We also examine how valid our results are by comparing the exoplanet observations that are currently available. We finally present our conclusions in Section \ref{conc}. | \label{conc} We have quantitatively investigated various characteristic metallicities for planet formation that was motivated by the recent success of exoplanet observations. To achieve such a goal, we have adopted a formalism developed in a series of earlier papers (HP11, HP12, HP13, HP14). The main features of the model are planet traps at which rapid type I migration for planetary cores is halted. Three types of planet traps (dead zone, ice line, and heat transition) have been considered. For planetary growth, we have relied on the standard core accretion scenario, wherein the formation of planetary cores is sensitive to the dust density in disks or the metallicity ([Fe/H]). Coupling the scenario with the planet traps in viscously evolving disks with photoevaporation has enabled one to compute the evolution of planets in the mass-semimajor axis diagram (see Figure \ref{fig1}). We have utilized a set of theoretical evolutionary tracks of planets for deriving the planet formation frequency (PFF) as well as the statistically averaged orbital radius at which growing protoplanets undergo rapid gas accretion ($\braket{R_{rapid}}$, see Figure \ref{fig1}). Specification of $R_{rapid}$ is crucial in this study, because it allows one to estimate the critical metallicity for gas giant formation. This was achieved by dividing the mass-semimajor axis diagram into zones as well as counting the end points of tracks for each zone. Zoning the diagram is in fact inferred from the accumulation of observed exoplanets. We have considered three different planetary populations: hot and exo-Jupiters, and low mass planets (see Table \ref{table1}). We have obtained the PFFs for three types of planets as well as the total, as a function of metallicity (see Figure \ref{fig2}). We have shown that the total PFF is a steady increasing function of metallicity, which can be understood straightforwardly by the core accretion scenario. The PFFs of the low-mass planets follow those of the total until the population of the Jovian planets provide a significant contribution, which occurs at [Fe/H]$\ga -1$. We have also computed the PFFs for both types of the Jovian planets which show that the hot Jupiters can form at lower metallcities than the exo-Jupiters. Switching of the dominant population between these two types is a consequence of the intimate coupling of planet formation and migration, and takes place at [Fe/H]$\simeq -0.7$ that is referred to as the crossover metallicity in this paper. We have also estimated various characteristic metallicities for planet formation (see Figure \ref{fig2}, see also Table \ref{table5}). The minimum metallicity for low-mass planets is [Fe/H]$\simeq - 1.8$, although it probably provides only an upper limit (Section \ref{resu2}). We have quantified the critical metallicity for gas giant formation. This was derived from the behavior of $\braket{R_{rapid}}$ that essentially links to the different efficiency of gas accretion between the hot Jupiters and the low-mass planets. We have found that [Fe/H]$\simeq - 1.2$ is the critical metallicity for forming gas giants around metal-poor stars. This is a most important finding of this study. We have also pointed out that these values of metallicity depend on the processes of planet formation and migration. Our results therefore infer that the observations of exoplanets around metal-poor stars may be used as a probe for calibrating of these processes, and hence such observations are very important for examining the current understanding of planet formation in protoplanetary disks. We have discussed a number of potential issues that may affect our results (Section \ref{disc}). Specifically, we have examined the effects of metallicity on disk evolution as well as planet formation. The recent observations suggest that the reduction in metallicity shortens the disk lifetime significantly. It is obvious that the effect prevents planet formation. Nonetheless, we have neglected it, because more intensive observations are required to make a reliable modeling. Planet formation is also affected by lowering the metallicity. We have discussed the effects on gas accretion. It is important that the resultant opacity in planetary envelopes is unlikely to depend strongly on the metallicity of materials accreted by planetary cores. Thus, the setup adopted in this paper may be sufficient. We have also examined the non-linear effect on the relationship between the dust-to-gas ratio ($\eta_{dtg}$) and the metallicity. This was motivated by the recent observational progress on the relationship in the lower metallicity environment, wherein $\eta_{dtg}$ is very likely to decrease more rapidly than [Fe/H]. We have calibrated the effect, making use of one of the most recent results in which it is investigated how the relationship evolves with time. We have found that the corresponding metallicities that are derived from theoretical nonlinear $\eta_{dtg}$-[Fe/H] relation depend sensitively on the star formation timescale (see Table \ref{table5}). This is because the formation and evolution of stars play an important role in enriching the metallicity. Our results therefore may be useful for bridging the observations of exoplanets around metal-poor stars with the estimate of the star formation history through galaxy evolution. We have finally provided some implications for exoplanets around metal-poor stars that are currently observed so far. There is no example which violates our prediction at the moment. It is however obvious that more observational data are required to examine our results. In a subsequent paper, we will undertake a more comprehensive study in which the effect of stellar masses will be examined. Also, we will consider galaxy evolution simultaneously, which triggers the change of metallicity with time. Thus the study will allow a more complete discussion about when the first planets form in galaxies. | 14 | 4 | 1404.5462 |
1404 | 1404.0889_arXiv.txt | {The nature of the gamma-ray source \HESSJ\ that is located significantly off-set from the Galactic plane is not ascertained to date.} {Identifying the environment of an enigmatic object may help to constrain its nature.} {The path of the line of sight of \HESSJ\ through the Galaxy is compared to the characteristic length scales of stellar populations of different ages. Furthermore, for this object, the energy density in particles is contrasted to the magnetic field energy density and constraints on the distance based on equipartition between these two components are calculated.} {The line of sight of \HESSJ\ reaches a minimum distance to the Galactic center at around a galactocentric distance of 5.3~kpc at about 300~pc off the Galactic disc. This location coincides with the scale length and width of stars with an age of 1.2~Gyr which could in principle be an indication that \HESSJ\ is connected to a stellar population of similar age. For such a case the source appears to be strongly particle dominated. In a leptonic scenario, if a magnetic field in the source of 1~$\mu$G is assumed, equipartition between magnetic field and particles would be realized at a distance of $\gtrsim1$~Mpc. This could indicate an extragalactic origin of this object. However, an extragalactic origin is challenged by the extension of the source.} {The environment of \HESSJ\ still remains elusive. For the case where this source belongs to a new class of gamma-ray emitters, the distribution of related objects (if existing) may help to settle the respective environment and distance scale.} | Several unidentified very-high energy (VHE, E$>$~100~GeV) gamma-ray sources have been found by H.E.S.S. in a survey of the inner galaxy \citep{aharonian2008}. One particular source appears to be exceptional since it is the only unidentified sources that is located significantly off-set from the Galactic plane \citep[3.5$^{\circ},$][]{acero2011}. This VHE emitter is connected to a high energy (HE, 100~MeV~$<$~E~$<$~100~GeV) counterpart \citep[based on 24 month of \emph{Fermi}-Lat data,][]{nolan2012} and potentially also to a faint, diffuse X-ray counterpart \citep{acero2011}. The nature of the source has been disputed since its discovery. \citet{domainko2011a} concluded that the compactness of the source disfavors a supernova remnant (SNR) scenario. \citet{domainko2012} analyzed a larger HE data set of 34 month from the \emph{Fermi} satellite and found that the gamma-ray spectral energy distribution (SED) appears to be rather flat from the GeV to the TeV regime. In this paper it was further discussed that the measured gamma-ray SED, the compactness of the source and its off-set location from the Galactic plane challenge a pulsar wind nebula (PWN) scenario for HESS~J1507-622. \citet{vorster2013} fitted a PWN model to the multi-wavelength SED \citep[using the result of 24 month of Fermi exposure obtained by][]{nolan2012} and concluded in favor for a PWN scenario. \citet{acero2013} finally analyzed 45 month of Fermi data above 10 GeV and placed this object in their non-PWN sample. In this paper an alternative approach is adopted to explore the nature of HESS~J1507-622. Its exceptional position is used to investigate the properties of the stellar environment along the line of sight of the source. Similar approaches have been applied to constrain the origin of enigmatic objects in the past. Studies of the stellar ages and stellar environments have extensively been applied to investigate the nature of the progenitors of supernovae~Ia \citep[e.g.][]{maoz2011} and short gamma-ray bursts \citep[e.g.][]{berger2014}. Prospects for the origin of the VHE gamma-ray source HESS~J1747-248 have been presented based on its location in the vicinity of the Galactic globular cluster Terzan~5 \citep{abramowski2011,domainko2011b}. Finally, host galaxies of extragalactic gamma-ray emitters of BL~Lac-type have been studies in depth \citep[e.g.][]{cheung2003,shaw2013}. This paper is organized in the following way: In Sec.~\ref{sec:los} the Galactic stellar population along the line of sight of \HESSJ\ is explored. In Sec. \ref{sec:obj} other potential sources of VHE emission at Galactic off-plane locations and their relation to \HESSJ\ are discussed. In Sec. \ref{sec:equi} constraints on the distance to \HESSJ\ based on equipartition between the energy densities in particles and magnetic fields are evaluated. And in Sec. \ref{sec:ext} prospects for an extragalactic scenario for \HESSJ\ are explored. | In this paper the environment of the unidentified off-plane gamma-ray source \HESSJ\ is explored. Since the location on the sky of this object is unique with respect to the positions of other unidentified VHE gamma-ray sources, examining the environment may give additional insights in its nature. However, with the currently available informations the surroundings of \HESSJ\ could not be identified. For a Galactic origin of this source its location may indicate a parent stellar population as old as 1~Gyr. In this case the source appears to be rather strongly particle dominated. In principle, particle dominance seems to be possible for Galactic VHE gamma-ray emitters, with young PWNe also showing this feature. However, in a leptonic scenario, a case where energy in particles exceeds the energy in the magnetic field by a factor of 100, would still require a distance of about 40~kpc for this object (for $B = 1\, \mu$G). A situation where the energy density in particles roughly equals the energy density in the magnetic field for \HESSJ\ would place this object at an extragalactic distance ($\gtrsim 1$~Mpc). Such a scenario face the challenge to explain the connected rather large extension of the source. For the case where \HESSJ\ belongs to a new class of gamma-ray emitters, evaluation of the distribution of related objects (if existing) may further help to constrain the environment of HESS~J1507-622. | 14 | 4 | 1404.0889 |
1404 | 1404.2597_arXiv.txt | For three nebulae that have early-WN Wolf-Rayet exciting stars, NGC~6888, WR~8 and Abell~48, we have obtained {\em Herschel}-PACS line scans of the [N~{\sc iii}] 57 \micron\ and [O~{\sc iii}] 88 \micron\ lines, along with the 122 and 205 \micron\ lines of [N~{\sc ii}]. From the former two lines we have derived N$^{2+}$/O$^{2+}$ abundance ratios, equal to the overall N/O ratio under a wide range of nebular conditions. We find that all of the nebulae observed possess significant nitrogen enrichment, with derived N/O ratios greater than solar. The two nebulae with massive Wolf-Rayet exciting stars, NGC~6888 and WR~8 are found to have N/O ratios that are enhanced by factors of 7 - 10 relative to the solar N/O ratio, consistent with an origin as material ejected just before the onset of the Wolf-Rayet phase. The other nebula, Abell~48, has recently been reclassified as a member of the rare class of three planetary nebulae that have early-WN central stars and are not of Peimbert Type I. We derive a nebular N/O ratio for it that is a factor of 4 enhanced relative to solar and slightly above the range of N/O values that have been measured for the other three members of its [WN] planetary nebula class. | Core-collapse supernovae from massive stars are known to dominate the production of oxygen and heavier $\alpha$-particle elements in galaxies but massive stars can make an important contribution to the nitrogen enrichment of the ISM during the early evolution of galaxies \citep{2000ApJ...541..660H}. This can happen via the ejection of nitrogen-enriched material that has been heavily processed by the CNO-cycle during their Luminous Blue Variable (LBV) and ensuing WN Wolf-Rayet (WR) stages. Observational determinations of the quantities of nitrogen injected into the ISM by WN stars and/or their LBV precursors are limited in number. However, a subset of WR stars are surrounded by nebulae whose expansion ages, morphologies, and occasional abundance determinations (e.g. \citealt{1992AA...259..629E}; \citealt{2011MNRAS.418.2532S}), show them to consist of nitrogen-rich material that has been recently ejected by the star; these are termed `ejecta nebulae' (\citealt{1991IAUS..143..349C}; \citealt{2010MNRAS.409.1429S}). Amongst the small sample of known, or candidate, Wolf-Rayet ejecta nebulae, only a fraction have been probed spectroscopically and their abundances derived. Such efforts have been hampered by the high degree of extinction along their sight lines in the galactic plane. The usual suite of abundance determination methods (e.g. \citealt{1977RMxAA...2..181T}; \citealt{1994MNRAS.271..257K}; \citealt{2012MNRAS.422.3516W}) rely on complex empirical relationships to calibrate the densities, temperatures and ionization schemes used to derive reliable abundances. The main stumbling block for these schemes with respect to nebulae around hot, massive stars comes in the lack of optical transitions from some of the ionization states that are expected to dominate the ion populations. For example, nitrogen abundances in nebulae are commonly calculated using the [N~{\sc ii}] 6548/6584 \AA\ doublet, however N$^+$ is often not the dominant nitrogen ion, so ionization correction factors are employed to attempt to compensate. In addition heavy extinction by interstellar dust towards galactic plane WR stars typically means that the blue end of the optical spectrum is missing, and therefore abundance determinations cannot be easily made (e.g. \citealt{2011MNRAS.418.2532S}). At far-IR wavelengths the effect of dust extinction is essentially removed and the usually dominant ionization stages of oxygen and nitrogen (N$^{2+}$ and O$^{2+}$) have accessible fine structure lines whose low excitation energies render ionic abundances derived from them insensitive to the adopted nebular electron temperature. Using the PACS instrument \citep{2010A&A2...518L...2P} on the {\em Herschel Space Observatory} \citep{2010A&A...518L...1P}, we have obtained spectral data cubes of various fine structure lines in the PACS wavelength range. For each source the [N~{\sc iii}] and [O~{\sc iii}] lines at 57 and 88 \micron\ have been mapped, along with the [N~{\sc ii}] lines at 122 and 205 \micron, which we will employ to test assumptions about a) density and b) the ionization structure. Our {\em Herschel} program (\verb+OT2_dstock_3+) covered two WR ejecta nebulae (around WR~8 and WR~136, the latter's nebula better known as NGC 6888) along with the PN A66 48 (henceforth Abell~48). At the time of its PACS observations in 2012, Abell~48 was thought to have been generated by a massive WR star but two recent studies have shown it to be a classical PN, albeit one with a rare WN-type central star (\citealt{2013MNRAS.430.2302T2}; \citealt{2013arXiv1301.3994F}). | The degree of nitrogen enrichment in a selection of nebulae around WR stars has been measured using Herschel/PACS observations of their far-IR fine structure lines. Abundance studies are usually performed using optical spectra, which has the drawback of not including any lines of N$^{2+}$, which is often the dominant ionization stage for nitrogen. This effect is usually compensated for using ionization correction factor schemes to calculate the N$^{2+}$ abundance. The far-IR observations used in this paper include the 57 \micron\ line of N$^{2+}$, which should result in nitrogen abundances that are less susceptible to systematic errors. In addition, abundances obtained for N$^+$, N$^{2+}$ and O$^{2+}$ from their far-infrared lines have little or no sensitivity to the nebular electron temperature, due to their low excitation energies. The N/O ratios of 0.9 -- 1.3 found for the massive WR-star nebulae WR~8 and NGC 6888 are consistent with both nebulae representing material ejected during the pre-WR evolution of the stars. For NGC 6888, our measurements overlap those of previous authors who employed ionization correction factors to determine the N/O ratio from optical lines. Our observations confirm that the nebula around WR~8 has a significant component of ejected stellar material -- as predicted by the morphological categorization methods of \citet{1991IAUS..143..349C} which were employed by \citet{2010MNRAS.409.1429S} upon discovery of the nebulosity. The other object observed, Abell~48, is now known to be a rare type of planetary nebula with a WN4-type central star {and which are not of Peimbert Type I. Our far-infrared observations yield a nebular N/O ratio of 0.49, which is slightly greater than the ratios found for the two other Galactic members of the rare [WN] class of planetary nebulae. | 14 | 4 | 1404.2597 |
1404 | 1404.2845_arXiv.txt | With a clear circular aperture, the vortex coronagraph perfectly cancels an on-axis point source and offers a 0.9 or 1.75 \ld inner working angle for topological charge 2 or 4, respectively. Current and near-future large telescopes are on-axis, however, and the diffraction effects of the central obscuration, and the secondary supports are strong enough to prevent the detection of companions $10^{-3}$-$10^{-5}$ as bright as, or fainter than, their host star. \\ Recent advances show that a ring apodizer can restore the performance of this coronagraph by compensating for the diffraction effects of a circular central obscuration in a 1D modeling of the pupil. Our aim is to extend this work and design optimal apodizers for arbitrary apertures in 2D in order to tackle the diffraction effects of the spiders and other noncircular artefacts in the pupil. \\ We fold this analytical result into a numerical optimization scheme that yields hybrid coronagraph designs that combine the advantages of the vortex coronagraph (small in IWA) and of shaped pupils coronagraphs (robustness to central obscuration and pupil asymmetric structures). The transmission of the apodizer is maximized, while constraints are set on the extremum values of the electric field that is computed in chosen regions of the Lyot plane through closed form expressions derived for even topological charges. Optimal apodizers are computed for topological charges 2 and 4 vortex coronagraphs and for telescope apertures with 10-30\% central obscurations and 0\%, 0.5\%, and 1\% thick spiders. % \\ We put the results of our numerical optimizations in perspective with the analytical solutions and show that our apodizations converge to the ring apodizations. We then characterize the impacts of the obscuration ratio and the thickness of the spiders on the throughput and the IWA. For the apodized charge-2 vortex coronagraph the throughputs are slightly below those of the ring apodized vortex coronagraph, and the inner working angle is mostly unaffected by the apodization. The throughputs of the apodizers for the charge-4 vortex coronagraph are higher than those of the ring apodized vortex coronagraph. This effect increases with the obscuration ratio, though the inner working angle does, too, and it ranges between 2 and 3\ld. \\ The results presented in this paper show that high contrast at small inner working angles can be obtained with a vortex coronagraph for on-axis telescopes, in spite of the presence of a secondary mirror and its secondary support structures. | The spectral characterization of Earth-like planets around M, F, G, K stars at a few tens of parsecs from our Sun requires a $10^{-7}$ to $10^{-10}$ contrast at a few tens of milliarc-seconds (mas) from the host star in 20\% bandwidths. Self-luminous planets, which are only tens to hundred million years young, require a less demanding contrast to be imaged than older planets. Since the observation of the former must be preferably done in the infrared part of the spectrum, the chromatic scaling of the point-spread function (PSF) of the instrument partially compensates for this advantage, however. On-axis 30-40m extremely large telescopes equipped with next-generation coronagraphs may provide the contrast, the resolution, and the large number of photons that are mandatory for ground-based observations. Few coronagraphs, however, can efficiently cope with the diffraction effects of the central obscuration and the secondary supports. Adapting a coronagraph to an arbitrary aperture has been an intense research topic in the past few years. \cite{Soummer2009Arbitrary,Soummer2011} explain how the spheroidal prolate apodization of an apodized pupil Lyot coronagraph (APLC) can be adapted iteratively to a given aperture. \cite{Pueyo2013} study a similar problem, but explicitly constrains the contrast in chosen regions of the image plane, while in the previous case the high contrast was adjusted by varying the radius of the Lyot mask. Nonetheless, APLCs suffer from a rather large IWA. Shaped pupils, which were initially optimized for high-contrast imaging in one dimension \citep{Spergel2001,Vanderbei2003,Kasdin2007}, can be numerically optimized in two dimensions (2D) for any telescope aperture \citep{Carlotti2011, Vanderbei2012}. Their versatility, robustness, and achromaticity make them good candidates for compact coronagraphic instruments: unlike APLCs, shaped pupils do not rely on a Lyot mask or a Lyot stop to create a high contrast, although a field stop is probably mandatory, given the limited dynamic range of detectors. Like APLCs, 2D-shaped pupil coronagraph have relatively large IWA, usually 3-5 \ld for apertures with obscurations of 10-30\% and for a $10^{-7}-10^{-10}$ contrast. The smallest IWA are usually obtained at the expense of the size of the discovery space. All these coronagraphs require an extreme adaptive optics system to correct for the phase and the amplitude aberrations of the wavefront. This system can be composed of a single deformable mirror (DM), but corrections occur on only one side of the image plane \citep{Malbet1995}. As proposed in \cite{Pueyo2007} and demonstrated in \cite{Pueyo2009}, a system of two DMs in nonconjugate planes makes it possible to create symmetric dark holes in broadband. Such a system was recently test in JPL's high-contrast imaging testbed where it was used to obtain a 3$\times 10^{-10}$ in 10\% broadband \citep{Riggs2013}. As suggested by \cite{Kasdin2011}, it appears that the wavefront control system can be actively used to create high contrast with arbitrary apertures, thus relaxing the specifications of the coronagraph. \cite{Pueyo2013} show how to use two DMs to spatially redistribute the energy density in the pupil plane so as to artificially decrease the size of the spiders and, for segmented telescopes, the gaps between the segments. \cite{Carlotti2013SPIEc} detail methods to optimize stroke commands to be sent to a DM to create a $10^{-6}-10^{-7}$ contrast with a centrally obscured aperture. Pupil mapping is the core principle of the phase induced amplitude apodization (PIAA, \cite{Guyon2003}) technique. Combined with a complex amplitude focal plane mask (PIAACMC, \cite{Guyon2010}), it offers a very promising solution to the problem of small inner working angles as it results in much smaller IWA (down to 0.64\ld), while offering about 50\% throughput. The currently investigated manufacturing process of the focal plane mask involved in this instrumental concept remains challenging, however \citep{Newman2013}. With a clear circular aperture of diameter $D$, looking at a wavelength $\lambda$, the four-quadrant phase mask coronagraph (4QPM, \cite{Rouan2000}) and the vortex coronagraph (VC, \cite{Mawet2005}) perfectly cancel an on-axis, unresolved point source, and detect companions as close as 0.9-1.75 \ld (0.9 for the 4QPM and a vortex with a topological charge 2, and 1.75 for a VC with a topological charge 4). The 4QPM coronagraph is a second order coronagraph: its off-axis transmission goes as $\theta^2$, where $\theta$ is the angular distance to the star. This makes the 4QPM coronagraph quite sensitive to jitter and to the finite size of the star. Like the 4QPM coronagraph, a VC with a topological charge 2 is a second order coronagraph. A charge 4 VC is a fourth order coronagraph, however: its off-axis transmission goes as $\theta^4$ instead of $\theta^2$. It is thus much less sensitive to the finite stellar size and to low order aberrations, which would otherwise limit the performance of the VC as they do with the 4QPM. Another fourth order phase mask coronagraph is the eight-octant phase mask (8OPM, \cite{Murakami2008, Carlotti2009}), which is to the 4QPM, as the charge 4 VC is to the charge 2 VC. The 4QPM and the 8OPM attenuate off-axis sources along their phase edges, however, and this limits the extent of the discovery space space around the star, especially in the case of the 8OPM. Nonetheless, the performance of the 4QPM coronagraph and the VC is greatly reduced when the telescope is on-axis. For instance numerical simulations predict a $10^{-4}-10^{-5}$ contrast between 1 and 5 \ld from the star, for a VC used with a 14\% centrally obscured aperture such as one of the very large telescope (VLT) 8m-class unit telescopes (UT). On-sky results have been obtained with a VC installed on VLT/NACO \citep{Mawet2013VLT}. Recently the VC has also been installed at two other telescopes: the Subaru telescope, and the Large Binocular Telescope. A dual-stage coronagraph can be used to cancel the diffraction effects of a circular central obscuration with a 4QPM \citep{Galicher2011} or a VC \citep{Mawet2011}, but it can only partially attenuate those of the secondary supports (or any other artifacts in the pupil plane). It also requires twice as many components, making the alignment more difficult and increasing the size of the coronagraph.% It is possible to apodize the aperture to avoid the diffraction effects that prevent the 4QPM or the VC to create high-contrast at a small IWA with an on-axis telescope. As a matter of fact, a proof of concept for an apodized VC has already been successfully tested on the sky: a small, clear circular subaperture with a 1.5m diameter has been used at the Palomar telescope with a VC \citep{Serabyn2010Nat,Mawet2011APJL}. Unfortunately, this results in an effective resolution three times as small and a throughput eight times as small as what could have been obtained with the main telescope aperture. It was shown in \cite{Carlotti2013} that shaped pupils can be optimally designed for a given combination of an arbitrarily-shaped aperture and a phase mask. Examples of such designs were numerically optimized for one of the 8m unit telescopes of the VLT, and for a 4QPM coronagraph, creating a few $10^{-10}$ contrast at 1 \ld (41mas in the H-band) from an unresolved star with a system throughput of about 64\%. \cite{Mawet2013} shows that a ring-apodized vortex coronagraph (RAVC) can perfectly attenuate the on-axis light with a circular aperture with a circular central obscuration. Secondary supports are not taken into account, however. For a charge 2 VC this apodizer is composed of two rings: one is fully transmissive while the other is only partially transmissive. For a topological charge 4 vortex, a thin dark annulus separates the two previously described rings. The obscuration ratio of the aperture sets the radii of the rings and transmission of the outermost ring for which the throughput of the coronagraph is maximal. The Lyot stop is directly constrained by the optimal rings radii. The same property characterizes the apodized 4QPM: the throughput of the coronagraph depends on the choice of the Lyot stop, namely the ratio of its central obscuration. \begin{figure}[] \centering \includegraphics[width=0.9\textwidth]{NewLayout.pdf} \caption{Optical layout of an apodized vortex coronagraph. The apodizer, vortex phase mask, Lyot stop and camera are located in the successive pupil and image planes A, B, C, and D.} \label{NewLayout} \centering \end{figure} Fig. \ref{NewLayout} displays the optical layout of an apodized vortex coronagraph: an apodizer is located in a pupil plane A. In a subsequent image plane B, the Fourier transform of the electric field that goes through the apodizer is multiplied by the complex amplitude of the phase mask. In the reimaged pupil plane C, i.e., the Lyot plane, the Lyot stop blocks the diffracted on-axis light. Finally, the science camera could be located in a reimaged focal plane D. Shaped pupils can be numerically optimized for the VC as they have already been for the 4QPM coronagraph, but the complexity of the computation process is much higher than in the case of the 4QPM. This is due to the fact that the pupil-to-pupil transform described in Eq.11 of \cite{Carlotti2013} cannot be written as nested sums. It must be directly evaluated as a 2D sum instead of 2 nested 1D sums. As a consequence the memory requirements scale as the fourth power of the number of points chosen to discretize the pupil, while they only scale as the square for the case of the 4QPM. While this does not fundamentally preclude any computation, it makes the optimization of pupil apodizers much more demanding in terms of numerical resources, than their 4QPM counterparts \citep{Carlotti2013}. In this paper, we build upon and devise new methods to solve the limitations of the early papers \citep{Carlotti2013,Mawet2013} so as to design apodizers for 2D apertures and a VC. A new computer dedicated to solving large scale optimization problems has made possible the computation of apodizers for the VC, with two-fold symmetry masks computed over $512^{2}$ points in a few hours. This computer has a four-core 3.6 Ghz processor and 64 GB of RAM. AMPL, a mathematical programming language is used to transcribe the optimization problem in a language that can be understood by one of the available solvers. In addition to the LOQO solver, the CPLEX and Gurobi solvers have been used. LOQO does not currently use more than one core of a processor, contrary to CPLEX and Gurobi, which can both use multiple cores. It should be noted that AMPL itself does not support parallel computing either. To compute apodizers for the VC, we also had to modify the nature of the optimization problem. Indeed, there is a difference in the constraints set in the numerical optimization of apodizers for the VC and for the 4QPM coronagraph. Linear constraints were used for the 4QPM in \cite{Carlotti2013}. This was possible because, with an aperture with two axes of symmetry such as the VLT's, the 4QPM creates a purely real amplitude in the Lyot plane - and applying the constraints on the amplitude or the intensity does not make a difference. This is not the case with the VC: constraints must be set on the intensity of the electric field, which makes them quadratic. We present in this paper the properties of apodizers optimized for a charge 2 VC and charge 4 VC with a 32\ld outer working angle, and designed to attenuate the on-axis light that goes through the Lyot stop by a $10^{6}$ factor, which result in a $10^{-8}-10^{-10}$ contrast at 1-3\ld from the star depending on the topological charge and the telescope aperture. An exhaustive number of apertures have been considered, with 10-30\% central obscurations, and for each of them 0, 0.5 and 1\% thick spiders. We compare the apodizers computed for spider-free apertures to the ring-apodizers, and we study the impact that an increasing spider thickness has on the performance metrics of the coronagraph. Section \ref{Maths} details the mathematical formalism used to derive the closed form expressions of the pupil-to-pupil transforms used to compute the electric field in the Lyot plane. Section \ref{NOA} presents the optimization problem, and explains the methodology that is followed in the rest of the paper. Section \ref{Performance} details the throughput and the inner working angle of the numerical optimizations. For spiderless apertures it compares them with the results presented in \cite{Mawet2013}. It also addresses the limitations of broadband observations. Section \ref{Manufacturing} tackles the manufacturing aspects of this coronagraph. Section \ref{Conclusion} draws a conclusion to this paper. | This paper builds upon and devises new methods to solve the limitations of two early papers: \begin{itemize} \item \cite{Mawet2013} presented 1D ring apodizers analytically optimized to create high-contrast with a VC and a 1D circular, centrally obscured aperture, without spiders. \item \cite{Carlotti2013} presented 2D apodizers numerically optimized to create high-contrast with a 4QPM coronagraph and a 2D centrally obscured, arbitrarily shaped aperture, with spiders. \end{itemize} We have showed that apodizers can be numerically optimized in 2D to help restoring the high-contrast imaging capabilities of vortex coronagraphs when used with obscured apertures with arbitrary shapes and spiders. While the ring-apodizers have gray transmissions, these apodizers resemble the shaped pupils in that they have binary transmissions, and that they can be manufactured using the same processes. Closed form expressions for even topological charges have been derived and used to directly compute the electric field in the Lyot plane as a function of the electric field in the first pupil plane. These pupil-to-pupil transforms have the advantage of not explicitly sampling the intermediate image plane and the vortex phase mask located there. One of the constraints of using these transforms is that the angular extent of the mask is limited. Given the computer currently used, it is possible to numerically optimize apodizers that are discretized over several hundred points on each axis of the pupil plane. Because it is 2D, our formalism can be applied to the case of a segmented, noncircular aperture such as the pupil of one of the Keck telescopes. In practice the apodizer transmission is almost zero everywhere outside the inscribed circle defined by this noncircular aperture. Moreover, to maximize the transmission of the apodizer, the Lyot stop for which the apodizer is optimized must also be limited to that inscribed circle. This limitation most probably comes from the properties of the vortex mask, which is initially supposed to be used with a circular aperture. Apart from the apertures of the Keck telescopes, the GTC, or the JWST, only the apertures of the TMT and the E-ELT feature a noncircular outer edge, but their large number of segments make them almost circular, and this limitation does not affect them much. Hence, we have considered circular obscured apertures with spiders. Apodizers have been computed for five different central obscuration ratios: 10, 15, 20, 25, and 30\%. For each of these obscurations, we have considered three different spider thicknesses (0, 0.5 and 1\%). The spiders form an orthogonal pattern. Apodizers have been optimized for charge $l=2$ and charge $l=4$ vortex phase masks. We were able to compute apodizers for 64 \ld OWA masks, but we have chosen to set the OWA to 32\ld since the substantially shorter time taken by the optimizations, and the smaller required amount of RAM, make it possible to solve several optimization problems at the same time, and thus explore a large number of different cases. This was necessary to exhaustively characterize the performance of the coronagraph in terms of throughput, IWA, and contrast. In the optimization problems that we solve, the constraints are set on the intensity of the electric field computed using the pupil-to-pupil transform. We have chosen to set the attenuation of the on-axis light that goes through the Lyot stop to $10^{6}$. In practice this creates a $10^{-8}-10^{-10}$ contrast in the image plane depending on the transmission of the apodizer. The Lyot stops for which the coronagraphs have been designed have also been optimized, although their optimization has not been performed together with the optimization of the apodizers. Like all the apertures that we have considered, all Lyot stops are circular. In the case of the spider-free apertures, the results of the numerical optimizations are similar to the ring-apodizers computed using the closed form expressions derived in \cite{Mawet2013}. Both types of apodizers are characterized by multiple rings with different mean transmissions. A similar aspect was found in our masks: the radii of their rings are close, and so are their transmissions. For topological charges $l=2$, the throughputs are slightly smaller than those of the ring-apodized vortex coronagraphs. Like the charge $l=2$ vortex phase mask, the 4QPM is a $\theta^{2}$ coronagraph, and it is interesting to make an indicative comparison between the apodizer computed for the 4QPM in \cite{Carlotti2013} for the aperture of the VLT telescope. The throughput of this optimal apodized 4QPM is 65\%, while the throughput of the optimal solution for an AVC computed for the closest look alike aperture in the present paper (with a 15\% central obscuration, and 0.5\% thick spiders) is 46\%, which is substantially lower. This difference appears solely associated with the type of focal phase mask. For topological charges of $l=4$, the throughputs of the optimal solutions are close to or larger than those of the RAVC, especially for large central obscurations. For instance, for a 20\% obscured aperture, the throughput of the numerically optimized apodized $l=4$ VC is 42\%, while it is about 32\% with the RAVC. For a 30\% obscuration, these throughput becomes 30\% and 13\%, respectively. We explain this difference by (a) the finite OWA of our vortex masks, and (b) the nonzero on-axis intensity that remains in the Lyot plane. The influence on the performance of the coronagraph of these two degrees of freedom has not been characterized yet, and doing so will be one of our next objectives. Unlike the 1D apodizers showed in \cite{Mawet2013}, the 2D apodizers that we have presented take the aperture spiders into account. We chose to consider two nonzero thicknesses: 0.5 and 1\% of the diameter, the former being the thickness of the secondary supports of the 8m unit telescopes at the VLT. The throughput changes significantly with the spider thickness. While the throughputs associated with the 0.5\% thick spider apertures are - for both topological charges - about 3-10\% and 5-6\% smaller than those associated with spider-free apertures, the throughputs associated with the 1\% thick spider apertures are 9-33\% and 16-28\% smaller, respectively. In addition to the horizontal and vertical alignments that are required by apodized coronagraphs, taking the spiders into account requires a clocking alignment as well. The spiders for which the apodizer is designed can be oversized with respect to the aperture spiders to accommodate clocking errors. For small off-axis angles $\theta$, the transmission of off-axis sources follows a $\theta^{l}$ function, which confirms the fact that, like the VC, the AVC is an $l$-th order coronograph. The off-axis transmission of the AVC is not as monotonic as it is with the VC, however. The rate at which the transmission increases slows down, stalls or even decreases at around $\theta=1-1.2\ld$, and it only resumes its maximum value at around $\theta=1.5-2\ld$. The strength of this effect goes with the central obscuration. For $l=2$, this does not affect the IWA much: it remains close to 0.9\ld, except for the 1\% thick spiders for which the IWA becomes 1.1-1.5\ld. The same is not true for $l=4$. In this case the IWA of the AVC is larger than it is with the VC, and it is mostly affected by the obscuration ratio. It is close to 1.75\ld for a 10\% obscuration, and increases to 2.5\ld for a 20\% obscuration, and to 3.2\ld for a 30\% obscuration. It should be noted, however, that it is difficult to describe the resolution properties of the coronagraph by solely referring to the usual definition of the IWA, i.e., the distance at which 50\% of the light of the off-axis light is transmitted. In particular the angle associated with a 40\% transmission - about 1.4\ld - is very similar to that of the VC for obscuration values up to 20\%. The active compensation of aperture discontinuities (ACAD) presented in \cite{Pueyo2013} is a pupil mapping concept that uses two deformable mirrors to reduce the effective thickness of the spiders without loosing photons. ACAD could be used to implement the ring-apodizers presented in \cite{Mawet2013}. The apodizers presented in this paper are a compelling counterpart to ACAD, which could be affected by the malfunction of some of the DM actuators. In this view, they offer a more conservative solution at only a moderate cost in throughput. Because the spider thickness has an important influence on the throughput, apodizers designed for the VC could also take advantage of ACAD. Although shaped pupils are binary apodizers - which are inherently achromatic - these apodizers are designed for a fixed mask radius measured in units of \ld, and the fixed physical radius of the mask causes the PSF at different wavelengths to be attenuated in different ways. The chromatic effects may be small enough in some cases. For instance a 1.5$\times 10^{-8}$ maximum contrast is obtained in a 20\% bandwidth for an aperture with a 15\% central obscuration and 0.5\% spiders (resembling that of the VLT's UT). To make sure that lower contrasts are obtained in a large bandwidth, apodizers will have to be optimized for multiple mask sizes. | 14 | 4 | 1404.2845 |
1404 | 1404.0301_arXiv.txt | Luminosity functions have been determined for star cluster populations in 20 nearby (4--30 Mpc), star-forming galaxies based on ACS source lists generated by the Hubble Legacy Archive. These cluster catalogs provide one of the largest sets of uniform, automatically-generated cluster candidates available in the literature at present. Comparisons are made with other recently generated cluster catalogs demonstrating that the HLA-generated catalogs are of similar quality, but in general do not go as deep. A typical cluster luminosity function can be approximated by a power-law, $dN/dL \propto L^{\alpha}$, with an average value for $\alpha$ of $-2.37$ and RMS scatter = 0.18 when using the F814W (``$I$'')~band. A comparison of fitting results based on methods which use binned and unbinned data shows good agreement, although there may be a systematic tendency for the unbinned (maximum likelihood) method to give slightly more negative values of $\alpha$ for galaxies with steeper luminosity functions. We find that galaxies with high rates of star formation (or equivalently, with the brightest or largest numbers of clusters) have a slight tendency to have shallower values of $\alpha$. In particular, the Antennae galaxy (NGC~4038/39), a merging system with a relatively high star formation rate, has the second flattest luminosity function in the sample. A tentative correlation may also be present between Hubble Type and values of $\alpha$, in the sense that later type galaxies (i.e., Sd and Sm) appear to have flatter luminosity functions. Hence, while there do appear to be some weak correlations, the relative similarity in the values of $\alpha$ for a large number of star-forming galaxies suggests that, to first order, the LFs are fairly universal. We examine the bright end of the luminosity functions and find evidence for a downturn, although it only pertains to about 1\% of the clusters. Our uniform database results in a small scatter ($\approx$0.4 to 0.5~mag) in the correlation between the magnitude of the brightest cluster ($M_\mathrm{brightest}$) and log of the number of clusters brighter than $M_{I} = -9$ (log~N). We also examine the magnitude of the brightest cluster vs.\ log SFR for a sample including both dwarfs galaxies and ULIRGS. This shows that the correlation extends over roughly six orders of magnitudes but with scatter that is larger than for our spiral sample, probably because of the high levels of extinction in many of the LIRG galaxies. | Luminosity functions (LFs) provide a basic parameterization of the star cluster population in galaxies. While the cluster mass function is more fundamental, in many cases the multi-wavelength data necessary to age-date the cluster population, and hence determine the cluster masses, does not exist. In addition, the LF is directly observable and does not require the use of a stellar population model that is inherently uncertain. To the degree that the star formation history of different galaxies are similar, the luminosity function can serve as an approximate proxy for the mass function. Some recent questions being addressed using LFs include: 1)~how uniform are cluster luminosity functions and what properties do they correlate with (e.g., with star formation history?), 2)~what is the shape of the LF and is there evidence of a change of slope at either the faint or bright end, 3)~can the brightest cluster (hereafter $M_\mathrm{brightest}$) vs.\ log~N (number of clusters brighter than $M_{I} = -9$) relation be described as a single power law with a scatter which is only statistical in nature? Progress answering these questions is hampered by non-uniformity in both the available observational datasets and the criteria used to select clusters. In this paper we provide a large, uniform (Hubble observations using the Advanced Camera for Surveys [ACS]), and automatically-generated (Hubble Legacy Archive [HLA]) database to better address these and other related questions. The current paper is part of a larger project that aims to detect star clusters in several hundred galaxies using HST imaging. In this first paper, we outline the basic steps used in the determination of luminosity functions for 20 of the galaxies with the highest quality data. We pay particular attention to the selection of the clusters, making comparisons with other recently generated cluster catalogs in order to estimate the degree to which selection effects can impact the results. This paper is organized as follows. Section~2 describes the initial source lists created by the Hubble Legacy Archive. Section~3 describes some additional processing, and the method used to select the clusters. Section~4 presents the luminosity functions for the target galaxies, including coadditions of galaxies with similar properties (i.e., ``super galaxies''), and Section~5 discusses a variety of correlations and their implications. Finally, we summarize our main results in Section~6. The photometric catalogs used in this study are available at http://archive.stsci.edu/prepds/starclust-sfgal/. | Hubble observations using the ACS/WFC camera have been used to construct star cluster luminosity functions for 20 nearby, star-forming galaxies. Automatically generated source lists from the Hubble Legacy Archive (HLA) were employed for the project. These catalogs provide the largest set of uniform, automatically-generated cluster candidates we are aware of in the literature at present. The primary results are listed below. 1. Comparisons with other recently generated cluster catalogs (e.g., Bastian et~al.\ 2012; Chandar et~al.\ 2014) demonstrate that the HLA-generated catalogs are of similar quality, but in general do not go as deep as manually-generated catalogs. 2. A single power-law of the form $dN/dL \propto L^{\alpha}$ has been used to approximate the LF using three different fitting techniques: constant number and constant magnitude binning (e.g., see Maiz-Appellaniz \& Ubeda 2005 and Chandar et~al.\ 2010 for discussions), and a maximum likelihood method that does not require binning. The methods give comparable results, although there may be a tendency for the maximum likelihood method to give more negative values of $\alpha$ for the steeper LFs. 3. Using the mean from the two methods and the high S/N sample, the average value for $\alpha$ is $-2.37$, with a RMS scatter~= 0.18 when using the F814W (``$I$'') band. Our values of $\alpha$ are generally steeper than most past studies, with a difference of $\delta = 0.12 \pm 0.16$ when comparing galaxies one-to-one. 4. A weak correlation is found for galaxies with high values of the SFR (or equivalently galaxies with the brightest clusters or the largest number of clusters) to have shallower values of $\alpha$. The same trend is found for $\alpha$ from composite ``supergalaxies" with different SFRs, strengthening the case for the reality of this correlation. In addition, the Antennae galaxy (NGC~4038/39), a merging system with a relatively high star formation rate, has the second flattest luminosity function in the sample. 5. A weak correlation may be present between $\alpha$ and Hubble Type in the sense that later type galaxies (Sd--Sm) have lower values of $\alpha$. However, the cumulative distribution functions (CDFs) show mixed results, hence this result should be considered tentative. 6. While there appear to be some weak correlations, the relative similarity in the values of $\alpha$ for a large number of star-forming galaxies suggests that, to first order, the LFs are fairly universal. This is similar to results for mass functions (e.g., Whitmore et~al.\ 2010 and Fall and Chandar 2012---but see also Bastian et~al.\ 2012 and Chandar et~al.\ 2014). 7. An exercise using larger aperture photometry (radii~= 7~pixels) shows that the use of mean aperture corrections for small aperture photometry does not affect our results in a substantial way. 8. Based on both the LFs and the cumulative distribution function (CDFs) of composite ``super-galaxies,'' we find some evidence for a downturn at the bright end of the luminosity functions, although it only pertains to about 1\% of the clusters. 9. The $M_\mathrm{brightest}$ vs.\ log~N relation shows a small RMS scatter (0.4 to 0.5 mag). It appears that the reason that galaxies with more clusters have brighter clusters is primarily a statistical ``size-of-sample'' effect rather than being due to differences in the environments of starburst and quiescent galaxies. This is consistent with results found by Whitmore (2003) and Larsen (2002). The results for the $M_\mathrm{brightest}$ vs.\ log SFR relationship are similar, with even a smaller scatter ($\approx$ 0.4 mag). 10. The sample has been increased by including observations of both dwarf galaxies and LIRGS from studies by Bastian et~al.\ (2008) and Vavilkin (2010). This shows that the $M_\mathrm{brightest}$ vs.\ log SFR correlation extends over roughly six orders of magnitudes. However, higher levels of extinction appear to lead to larger scatter (0.9 magnitude) for the LIRG sample. The photometric catalogs used in this study are available at:\hfill\break http://archive.stsci.edu/prepds/starclust-sfgal/. | 14 | 4 | 1404.0301 |
1404 | 1404.5712_arXiv.txt | We propose the application of coronagraphic techniques to the spectroscopic direct detection of exoplanets via the Doppler shift of planetary molecular lines. Even for an unresolved close-in planetary system, we show that the combination of a visible nuller and an extreme adaptive optics system can reduce the photon noise of a main star and increase the total signal-to-noise ratio (S/N) of the molecular absorption of the exoplanetary atmosphere: it works as a spectroscopic coronagraph. Assuming a 30 m telescope, we demonstrate the benefit of these high-contrast instruments for nearby close-in planets that mimic 55 Cnc b ($0.6 \lambda/D$ of the angular separation in the K band). We find that the tip-tilt error is the most crucial factor; however, low-order speckles also contribute to the noise. Assuming relatively conservative estimates for future wavefront control techniques, the spectroscopic coronagraph can increase the contrast to $ \sim 50-130$ times and enable us to obtain $\sim 3-6 $ times larger S/N for warm Jupiters and Neptunes at 10 pc those without it. If the tip-tilt error can be reduced to $\lesssim 0.3$ mas (rms), it gains $\sim 10-30$ times larger S/N and enables us to detect warm super-Earths with an extremely large telescope. This paper demonstrates the concept of spectroscopic coronagraphy for future spectroscopic direct detection. Further studies of the selection of coronagraphs and tip-tilt sensors will extend the range of application of the spectroscopic direct detection beyond the photon collecting area limit. | To date, a small number of exoplanet atmospheres have been characterized via low-resolution spectroscopy from primary and secondary transits and direct imaging. Recently a novel technique to detect exoplanetary dayside atmosphere was successfully accomplished with high-dispersion spectroscopy \citep[][see also \cite{2010Natur.465.1049S} for transmission with a similar technique]{brogi,2012ApJ...753L..25R,2013A&A...554A..82D, 2013MNRAS.432.1980R,2013MNRAS.tmpL.152B,2014ApJ...783L..29L}. In this technique, high-dispersion ($R \sim 100,000$) spectra of the exoplanet + star are analyzed to detect the planet signature. Computing the cross-correlation function between the spectra and a template of molecular lines as a function of the Doppler shifts, allows separation of the planet signature from the stellar absorption lines and the telluric lines. Hence, it detects the change in the radial component of the planet's orbital motion, i.e., planetary radial velocity (PRV). The technique provides precious information on atmospheric compositions. Thus far, the 3-5 $\sigma$ detections of carbon monoxide and water of nearby hot Jupiters have been reported using this technique with CRIRES/VLT and NIRSPEC/Keck. \citet{2014A&A...561A.150D} investigated the cross-correlation signals for molecules not yet detected, methane, acetylene, and hydrogen cyanide. The application of this technique to reflected light was also proposed by \cite{2013MNRAS.436.1215M}, assuming extremely large telescopes (ELTs). Furthermore, such precise measurements of the PRV will also provide complementary physics, for instance, planetary rotation \citep{kawahara12}. The targets of the spectroscopic direct detection are currently limited to planets with low star-planet contrast, i.e., hot Jupiters with the equilibrium temperature $T_\mathrm{eff} \gtrsim 1000$ K. An open question is how to improve the signal-to-noise ratio (S/N) of the spectroscopic direct detection in order to apply this technique to other types of planets beyond hot Jupiters. To use larger telescopes is, of course, one of the solutions. ELTs can simply provide an S/N that is $\sim$ 3 times larger than that of current observations. Improvement in efficiency of high-dispersion instruments will also increase the S/N. Beyond the collecting power, if the photon noise from the host star can be reduced, the high-dispersion observations of the exoplanets will be of wider application. High-contrast instruments for direct imaging are designed exactly for the reduction of stellar flux. The aim of this paper is to consider the possibility of spectroscopic corongraphy, that is, an application of the high-contrast instruments to the spectroscopic direct detection technique. It is extremely difficult for the coronagraph to be capable of separating the star and the planet near 1 $\lambda/D$, corresponding to 0.1-0.2 AU at 10 pc for the ELTs. However, even if the coronagraph does not reduce the stellar halo at the planet location, but the full contrast difference even a slight reduction benefits this technique. In this paper, we show the visible nuller, as an example of coronagraphs, with the ELTs significantly reducing the relative noise of the planetary radial velocimetry of the dayside emission if the extreme adoptive optics (ExAO) works well. The paper is organized as follows. We first summarize the visible nuller and define the quantities that describe its benefit for this use in Section 2.1. We derive the analytical expressions of these quantities as a function of the finite effect of the stellar radius and the tip-tilt contamination in Sections 2.2-2.3. In Section 3, we perform numerical simulations assuming a 30 m telescope with a future ExAO system and consider the speckle noise. We discuss the feasibility of the spectroscopic coronagraph for nearby exoplanets. In Section 4, we also consider ways to further increase the S/N for future studies, as well as the limitations of our techniques. Finally we summarize our results in Section 5. | As described above, the suppression of the tip-tilt error and the improvement of the low-order wavefront sensing are crucial for our technique. Though further discussion of improvement of the ExAO is beyond the scope of this paper, we briefly mention several factors that we did not consider in our simulation. One of reasons why our ExAO simulation does not achieve $< 1$ mas of the tip-tilt error is the chromatic aberration -- the use of different bands for sensing (I band) and science (K band). The wavefront sensing with a band that is close to the science band will improve the low-order aberration. The tip-tilt sensors with science lights under development will improve the situation \citep[e.g.][]{2009ApJ...693...75G,2014arXiv1404.7201S}. They proved that the sensor can reduce the tip-tilt within $\sim 0.1 \lambda/D$ in the laboratory experiment and the theoretical limitation is $\sim 0.01 \lambda/D$ \citep{2009ApJ...693...75G}. For instance, the stellar light rejected by the Lyot stop for the wavefront sensing can be used for the wavefront sensing with the science band. In this paper, we have regarded the semimajor axis as the angular separation of the planets, i.e., we have assumed that the planet is located at the phase angle near $\beta \sim \pi/2$. The planets with less efficient redistribution of heat at this location have less emissivity than those at the far side of the star ($\beta \sim \pi$). This effect might reduce the benefit of the spectroscopic coronagraph. However, the PRV measurement for various phase angles is particularly important for the complementary applications of the PRV, such as the detection of the planetary spin or the zonal winds \citep[e.g.][]{kawahara12}. Though we have assumed the warm/hot planets close to a host star, the spectroscopic coronagraph is also applicable to the self-luminous planets. | 14 | 4 | 1404.5712 |
1404 | 1404.5706_arXiv.txt | We present improved constraints on an interacting vacuum model using \dw{updated} astronomical observations including the first data release from Planck. We consider a model with one dimensionless parameter, $\alpha$, describing the interaction between dark matter and vacuum energy (with fixed equation of state $w=-1$). The background dynamics correspond to a generalised Chaplygin gas cosmology, but the perturbations have a zero sound speed. The \dw{tension between the value of the Hubble constant, $H_0$, determined by Planck data plus WMAP polarisation (Planck+WP) and that determined by the Hubble Space Telescope (HST) can be alleviated by energy transfer from dark matter to vacuum ($\alpha>0$). A positive $\alpha$ increases the allowed values of $H_0$ due to parameter degeneracy within the model using only CMB data.} Combining with additional datasets of \dw{including} supernova type Ia (SN Ia) and baryon acoustic oscillation (BAO), we can significantly tighten the bounds on $\alpha$. Redshift-space distortions (RSD), which constrain the linear growth of structure, provide the tightest constraints on vacuum interaction when combined with Planck+WP, and prefer energy transfer from vacuum to dark matter ($\alpha<0$) which suppresses the growth of structure. Using the combined datasets of Planck+WP+Union2.1+BAO+RSD, we obtain the constraint on $\alpha$ to be $-0.083<\alpha<-0.006$ (95\% C.L.), allowing low $H_0$ consistent with the measurement from 6dF Galaxy survey. This interacting vacuum model can alleviate the tension between RSD and \dw{Planck+WP in the $\Lambda$CDM model for $\alpha<0$, or between HST measurements of $H_0$ and Planck+WP for $\alpha>0$, but not both at the same time.} | One of the biggest challenges in modern cosmology is to explain the apparent accelerated expansion of the Universe today \cite{Riess:1998May, Perlmuter:1999Dec}. A variety of possible explanations have been put forward \cite{Li:2011Mar, Yoo:2012Dec, Sami:2013Sep} including \tc{allowing for the existence of} dark energy in Einstein gravity \tc{and modification of general relativity}. Vacuum energy is possibly the simplest model of dark energy, without any new dynamical degrees of freedom and with a vacuum equation of state (EoS), $\check{P}=-\check{\rho}=-V$. In Einstein gravity, a covariantly conserved vacuum energy density, $\nabla_\mu V=0$, is equivalent to a cosmological constant, $\Lambda=8\pi G_N V$. This is the basis of the $\Lambda$CDM cosmology, which is a highly predictive model to explain the present acceleration of the Universe. However, the $\Lambda$CDM model suffers from fine tuning and coincidence problems. As a result, many researchers have considered dynamical models of dark energy with a non-vacuum equation of state, $P\neq -\rho$, leading to a time-dependent dark energy density, e.g., scalar field \tc{models, \eg, quintessence \cite{quintessence}, phantom \cite{phantom}, quintom \cite{quintom}, or dark fluids} \dw{\cite{Kamenshchik:2001Mar, Bento:2002Feb,Piattella:2009kt}}. These different theories can be probed by a range of observational datasets \cite{Weinberg:2012Jan}. In 2013 the Planck satellite provided a high-resolution measurement of \dw{anisotropies in the} \mv{cosmic microwave background} (CMB) \cite{Planck:2013Mar:map}. With the first release of Planck data, the cosmological \dw{analysis} from Planck collaboration showed that the standard spatially-flat $\Lambda$CDM model \dw{remains} an excellent fit to the \dw{CMB} data \cite{Planck:2013Mar:cos}. However, the results also pointed out some tension between Planck and other measurements of values of some cosmological parameters within the $\Lambda$CDM scenario \cite{Planck:2013Mar:cos}. Notably, the Planck collaboration presented a low value of the Hubble constant \footnote{\mvs{Besides the Planck data, there are also other observational estimations of the Hubble constant, which give a low value of $H_0$, see \eg, Ref.~\cite{Gott:2000Jun, Chen:2011May, Calabrese:2012May} using the median statistics method, Ref.~\cite{Beutler:2011Jun, Colless:2012Nov} from the 6dF Galaxy Survey, and Ref.~\cite{Busti:2014Feb, Verde:2014Mar} using Gaussian Processes by the measurements of $H(z)$.}}, $H_0=67.4\pm1.4$ km\,s$^{-1}$\,Mpc$^{-1}$ at 68\% C.L. from Planck data. When the sum of the masses of the active neutrinos is fixed to zero, the value of Hubble constant is changed slightly, giving $H_0=68.0\pm1.4$ km\,s$^{-1}$\,Mpc$^{-1}$. Both results from Planck data are \dw{in tension} with, for instance, direct measurements of $H_0$ by the Hubble Space Telescope (HST) observations of Cepheid variables, $H_0=73.8\pm2.4$ km\,s$^{-1}$\,Mpc$^{-1}$ \cite{Riess:2011Mar}. \dw{There is also some tension between the primary CMB anisotropies and measurements of the growth of structure, such as cluster number counts \cite{Ade:2013lmv}.} This tension between the $H_0$ value determined from Planck and direct measurements of the Hubble constant \mvs{by HST} could be due to an incomplete understanding of the astrophysical observations. The direct measurements of $H_0$ have been revisited through reanalysing Cepheid data to address possible inconsistencies \cite{Efstathiou:2013Nov}. On the other hand, the determination on $H_0$ from CMB data is based on the assumption of an underlying theoretical model, so it is worthwhile to study the predictions in extensions of $\Lambda$CDM model, for instance, the neutrino $\Lambda$CDM model \cite{Wyman:2013Jul, Hamann:2013Aug, Battye:2013Aug}, dynamical dark energy models \cite{Xia:2013Aug}, or coupled dark energy models \cite{Salvatelli:2013Apr, Xia:2013Nov, Costa:2013Nov}. A non-gravitational interaction between vacuum energy and matter provides an alternative framework in which to interpret the observational data. An interacting vacuum energy leads to a space- and time-dependent vacuum \cite{Wands:2012Mar, DeSantiago:2012Sep}, in which the gradient of the vacuum energy is given by a 4-vector, \begin{eqnarray} \nabla_{\mu}V=-Q_{\mu} \,. \end{eqnarray} The total energy-momentum must be conserved in a covariant theory, hence $Q_\mu$ describes the net energy-momentum transfer to the vacuum from other matter fields. \dw{Any} dark energy cosmology with exotic equation of state $P_X(\rho_X)$, can be decomposed \cite{Wands:2012Mar} into a cosmology with interacting vacuum energy density \begin{equation} \check\rho=-P_X \,, \end{equation} plus pressureless dark matter density \begin{equation} \rho_{\rm \tc{dm}}=\rho_X+P_X \,. \end{equation} In this paper we consider a cosmological model where the homogeneous background has the same behaviour as a generalised Chaplygin gas (GCG) \cite{Kamenshchik:2001Mar, Bento:2002Feb}. The GCG is parameterised by a single dimensionless parameter, $\alpha$, that in the interacting vacuum interpretation describes the energy transfer from matter to vacuum \cite{Bento:2004uh}. Thus we recover the $\Lambda$CDM model in the limit $\alpha\to0$. The original GCG model is severely constrained ($\alpha$ less than or of the order of $10^{-6}$) by large-scale structure formation since the barotropic dark fluid has a non-zero speed of sound for $\alpha\neq0$, which may lead to large oscillations, or instabilities, in the matter power spectrum \cite{Sandvik:2002Dec, Park:2009Oct}. Instead we will consider the interacting vacuum+matter model (a decomposed GCG model) where the energy-momentum transfer 4-vector is proportional to the matter 4-velocity. In this case there is no force on the dark matter particles in the dark matter rest frame and hence the dark matter follows geodesics. The sound speed of matter perturbations is zero and there are no oscillations in the matter power spectrum \cite{Wang:2013Jan, Borges:2013Sep}. We revisit the constraints on this decomposed GCG using the new CMB data, including the temperature anisotropies from Planck \cite{Planck:2013Mar:cos} and polarization anisotropies from WMAP9 \cite{WMAP9:2012}. Firstly we focus on investigating the consistency between the CMB data alone and HST constraints on $H_0$. Then we perform the constraints on the interacting vacuum model using CMB data combined with other data. We use the updated baryon acoustic oscillations (BAO) data from the 6dF Galaxy Survey \cite{Beutler:2011Jun}, Sloan Digital Sky Survey (SDSS) DR7 \cite{Padmanabhan:2012Feb}, Baryon Oscillation Spectroscopic Survey (BOSS) DR9 \cite{Anderson:2012Mar}, and WiggleZ Dark Energy Survey \cite{Blake:2011Aug}. \tc{We also use the measurements of redshift space distortions (RSD) \cite{Percival:2004Jun, Blake:2011Apr, Samushia:2011Feb, Reid:2012Mar, Beutler:2012Apr}, which provides information of the growth of structure.} This paper is organized as follows. In the next section, we review the interacting vacuum energy model and in particular the case of a decomposed GCG with geodesic flow. We examine the linear growth of structure and imprints on CMB power spectra in this model. In Section \ref{data}, we present the current observations and numerical analysis method. Then we show the results in Section \ref{results}. The conclusions and discussions are presented in Section \ref{summary}. | \label{summary} An interacting vacuum model provides an interesting alternative dark energy model in which to interpret the cosmological parameter constraints coming from the latest CMB data in combination with other data sets. Unlike other dark energy models such as non-vacuum fluid or scalar field \tc{models}, there are no additional degrees of freedom if the vacuum energy transfers energy-momentum to or from existing matter fields. In this paper we have considered \tc{a} particular example of an interacting vacuum cosmology, where the interaction is characterised by a single dimensionless parameter, $\alpha$, which reproduces the background dynamics of a GCG cosmology. However, we have considered a decomposed GCG model where the energy-momentum transfer, from dark matter to vacuum, is always proportional to the matter 4-velocity. As a result the dark matter particles follow geodesics \cite{Wands:2012Mar}, and in the limit of a vanishing interaction parameter, $\alpha\to0$, we recover the $\Lambda$CDM cosmology. We have used the latest observational data to test the model parameters, and in particular the interaction parameter, $\alpha$, against CMB data alone (WMAP9 or Planck+WP) and various combinations with other data, including the direct measurement of $H_0$ from HST, \mvs{the relatively low $H_0$ value measured from 6dF Galaxy Survey,} the Union2.1 supernova compilation, baryon acoustic oscillations and redshift-space distortions. In particular possible tension between Planck+WP constraints on $H_0$ and HST measurements is investigated in the interacting vacuum model. Using the WMAP9 alone, we obtain a value of Hubble constant, $H_0=72.1_{-6.2}^{+7.2}$ km\,s$^{-1}$\,Mpc$^{-1}$ (68\% C.L.), which is entirely consistent with the direct measurement of $H_0$ from HST. On the other hand, Planck+WP require $H_0= 67.0_{-5.5}^{+5.5}$ km\,s$^{-1}$\,Mpc$^{-1}$ (68\% C.L.). The low mean value from Planck+WP is discrepant with the HST measurement to $H_0$. However, there exists overlap between the marginalized distribution of $H_0$ from Planck+WP and the values of $H_0$ with $1\,\sigma$ errors from HST measurement. \mvs{Compared with another $H_0$ measurement from 6dF Galaxy Survey, it is found that the $H_0$ result from Planck+WP is in better agreement than that from WMAP9.} \tc{The constraint using CMB alone on the interacting vacuum model interaction parameter is too weak to be distinguished from the $\Lambda$CDM model.} Next, we combined CMB data with other data including the HST prior on $H_0$, \mvs{another low $H_0$ prior,} Union2.1 SN Ia, BAO or RSD. The combined data-sets can break degeneracies, yielding tighter constraints. The constraints on the interaction parameter from the combinations of WMAP9 and other data show that the interacting vacuum model is indistinguishable from the $\Lambda$CDM model within $1\,\sigma$ region. For the predictions of Hubble constant in the interacting vacuum model from different data, we find that the WMAP9 alone and WMAP9+HST favour high values of $H_0$, consistent with the HST prior. Using Planck+WP in combination with the HST prior on $H_0$ would favour a positive interaction, $\alpha>0$. However constraints on the Hubble constant in the interacting vacuum model using Planck+WP, \mvs{Planck+WP+lowH,} Planck+WP+Union2.1, Planck+WP+BAO and Planck+WP+RSD all yield low values for $H_0$, indicating a tension between Planck+WP and HST measurements of $H_0$. RSD are particularly sensitive to the interaction parameter and Planck+WP+RSD favour a negative interaction \tc{at more than 1.8 $\sigma$ level}. Finally, based on the above discussions about the consistency of Planck+WP and other data-sets, we use the combined data of Planck+WP+Union2.1+BAO+RSD to constrain the interacting vacuum model. A strong constraint on the interacting vacuum parameter is obtained, $\alpha= -0.043_{-0.020- 0.040}^{+0.019+0.037}$. We conclude that there is \tc{a hint} for a negative energy transfer $\alpha<0$ in the interacting vacuum model at 95\% confidence level. \tc{This model provides a possible solution to the problem of tension between the RSD and other measurements in the $\Lambda$CDM model. } It would be interesting to investigate further the Bayesian evidence for departures from $\Lambda$CDM using different criteria \cite{Liddle:2004nh} both in this particular decomposed GCG model and in more general interacting vacuum energy models. Negative $\alpha$ implies a slower growth rate for linear density perturbations and thus a lower value for $\sigma_8$. Thus one might also expect lower cluster number counts than predicted in $\Lambda$CDM \cite{Ade:2013lmv}. However halo collapse is a non-linear process and we have not yet studied non-linear collapse in this model. Our assumption that the energy-momentum transfer is proportional to the matter 4-velocity implies that the 4-velocity is proportional to the gradient of the vacuum energy, $u_\mu\propto \nabla_\mu V$, and thus irrotational. Recently Sawicki et al \cite{Sawicki:2013wja} have argued that non-linear collapse in unified dark matter models with irrotational flow will lead to the formation of central black holes rather than virtualised halos. \dw{Either the assumption of a irrotational flow must break down on some scale, or we would require only some fraction of the dark matter to interact with the vacuum energy in this way (and hence be irrotational). In this case the small value required for the interaction parameter $\alpha$ might represent the small fraction of dark matter which collapses into central (supermassive) black hole during halo collapse}. Investigation of this goes beyond the study of linear perturbation theory used in this paper and we leave this as an interesting open issue for future work. \dw{Note added: We have not included the latest BICEP2 results \cite{Ade:2014xna} which appeared while this paper was in preparation. These remarkable results show evidence for primordial gravitational waves at the time of CMB last scattering. If confirmed this implies there will be an additional contribution from gravitational waves to the CMB temperature power spectrum at low $\ell$ which appears to be in tension with the minimal $\Lambda$CDM model. It seems unlikely that an interacting vacuum model alone, whose main effect is to change the relation between CMB anisotropies and structure formation at late times, can resolve this apparent tension at low $\ell$. It will be interesting to study this in a broader class of models including interacting vacuum energy.} | 14 | 4 | 1404.5706 |
1404 | 1404.2310_arXiv.txt | We present a multiwavelength study of a sample of far-infrared (FIR) sources detected on the {\it Herschel} broad--band maps of the nearby galaxy M33. We perform source photometry on the FIR maps as well as mid-infrared (MIR), H$\alpha$, far-ultraviolet and integrated HI and CO line emission maps. By fitting MIR/FIR dust emission spectra, the source dust masses, temperatures and luminosities are inferred. The sources are classified based on their H$\alpha$ morphology (substructured versus not-substructured) and on whether they have a significant CO detection ($S/N>$3$\sigma$). We find that the sources have dust masses in the range 10$^2$-10$^4$~M$_\odot$ and that they present significant differences in their inferred dust/star formation/gas parameters depending on their H$\alpha$ morphology and CO detection classification. The results suggests differences in the evolutionary states or in the number of embedded HII regions between the subsamples. The source background--subtracted dust emission seems to be predominantly powered by local star formation, as indicated by a strong correlation between the dust luminosity and the dust-corrected H$\alpha$ luminosity and the fact that the extrapolated young stellar luminosity is high enough to account for the observed dust emission. Finally, we do not find a strong correlation between the dust-corrected H$\alpha$ luminosity and the dust mass of the sources, consistent with previous results on the breakdown of simple scaling relations at sub-kpc scales. However, the scatter in the relation is significantly reduced by correcting the H$\alpha$ luminosity for the age of the young stellar populations in the star--forming regions. | From the morphological point of view, the dust emission observed within nearby galaxies can be roughly described in terms of a clumpy and a smoother diffuse component. \let\thefootnote\relax\footnote{$\dagger$ The first two lead authors have been co-equal contributors to the majority of the work presented in this paper.} At least partially, the clumpiness of the dust emission morphology is determined by the gas mass distribution: the clumpy component can be associated with massive giant molecular clouds (GMCs), with sizes of the order of $\approx 10-100$\,pc, and the diffuse component with a more diffuse interstellar medium (ISM) gas, distributed on kpc scales. However, peaks of emission in the far-infrared (FIR) maps of galaxies can also be due to the presence of strong radiation sources heating the dust locally. In addition, for a given dust composition and size distribution, the diffuse dust emission spectrum will depend on the intensity and colour of the kpc scale radiation field produced by all the stellar populations in a galaxy. Therefore, the morphology of dust emission does not necessarily follow the ISM gas morphology. Understanding the intrinsic nature of the clumpy and diffuse components of dust emission is important since their spectral energy distributions carry information about both the ISM gas associated with them and the nature of the radiation sources powering them. Multiwavelength studies of dust emission in nearby galaxies using the {\it Herschel Space Observatory} have mainly relied on pixel-by-pixel analyses (e.g. Smith et al.\ 2010, Galametz et al.\ 2012, Mentuch-Cooper et al.\ 2012, Foyle et al.\ 2012, Bendo et al.\ 2012). This method consists of convolving all the maps considered in the analyses to the same resolution, corresponding to the resolution of the map characterized by the largest point spread function (PSF) beam, and then comparing the emission at each wavelength or the measured dust/stellar population parameters at each pixel position. This method is advantageous for its simplicity but it has the drawback of considering simultaneously both the clumpy and the diffuse components of the dust emission. By including both components, pixel-by-pixel analyses are not in the position of distinguishing their properties. A procedure to extract and measure the dust parameters of bright FIR compact sources within nearby galaxies has been introduced by Foyle et al. (2013, hereafter FN13) and applied to a set of multiwavelength data of the spiral galaxy M83. In order to perform the compact source photometry at the different wavelengths, FN13 used \textsc{getsources}, a multiwavelength source detection and photometry algorithm (Men'shchikov et al.\ 2012). This algorithm is designed to detect sources and extract the background--subtracted source photometry on {\it Herschel} maps in their original resolution, without degrading the maps. Thus, ideally, the highest resolution information is preserved. Furthermore, FN13 performed a two-component dust emission SED fitting to infer the dust parameters and measured star formation rates (SFR) from the dust--corrected H$\alpha$ source luminosity. This procedure provided insights on the nature of the bright FIR sources in M83 and their associated giant molecular associations (GMAs) and showed that the properties of the sources do not show radial variations, which is typically found in pixel-by-pixel studies that average over both clumpy and diffuse emission simultaneously (e.g. Foyle et al.\ 2012). In this paper we apply the same procedure developed by FN13 to a set of multiwavelength maps of the nearby galaxy M33. M33 is a flocculent spiral galaxy at a distance of only 0.859 Mpc (Barker \& Sarajedini 2008). Thus, it is an ideal target to study the characteristics of FIR compact sources on scales even smaller than those that can be observed in M83. The dust emission in M33 has already been the subject of several works (e.g. Tabatabaei et al. 2014, Kramer et al. 2013, Rela{\~n}o et al. 2013, Xilouris et al. 2012, Boquien et al. 2011, Braine et al. 2010, Verley et al. 2010, Kramer et al. 2010). In Rela{\~n}o et al. (2013; hereafter R13) they studied the dust properties of HII regions in M33 that they detected in H$\alpha$ emission. The sources were classified based on their H$\alpha$ morphology and, for each source, they measured the FIR colours and dust parameters. We take an alternative approach to R13, by detecting sources in the FIR emission of M33 instead of H$\alpha$. At first, it might seem that these two approaches might be comparable. However, although dust in and around HII regions can be seen as a bright MIR/FIR compact source, in principle clumpy dust emission can arise also from sources not clearly detected in H$\alpha$, either because the local star formation is not intense enough for H$\alpha$ emission to be detected or because H$\alpha$ is attenuated by dust. Furthermore, a single FIR source might be related to an entire ensemble of HII regions as well as single ones. In addition to the FIR emission, we also augment our data set with mid-infrared (MIR) and UV broad--band maps as well as H$\alpha$, HI 21cm and CO line emission maps. MIR data can be used together with the FIR measurements on the {\it Herschel} maps in order to obtain a complete MIR to FIR dust emission SED of the detected sources. Dust corrected H$\alpha$ and UV luminosities can be used to investigate star formation on different time scales, H$\alpha$ tracing more recent star formation ($10^7$ yr) than UV ($10^8$ yr). Finally, HI and CO gas maps can be used to elucidate the relation between the gas and the dust parameters. Specifically, in this work we address the following questions: \\ 1) What is the intrinsic nature of the bright FIR sources in M33? Are they associated with a single or with multiple HII regions? Are they mainly associated with the molecular gas detected in CO? \\ 2) How do the dust parameters vary depending on the radial distance, the H$\alpha$ morphology, the detection of molecular gas ? \\ 3) Is the source dust emission heated predominantly from local young stellar populations? Is there evidence of external heating? \\ 4) Assuming that the source dust mass traces the gas mass of the cloud associated with the cospatial HII regions, is there evidence for a scaling relation between dust mass and the recent star formation within the clouds? \\ The paper is structured as following. Section 2 presents the data set we used. In Section 3 we describe the source extraction technique and the photometry performed at all wavelengths. Section 4 describes the dust emission SED fitting technique applied to the MIR/FIR data. In Section 5 we describe the measurements of the star formation parameters. In Section 6 we explain the criteria adopted to select our best source sample and define subsamples of sources based on their H$\alpha$ morphology and the detection of CO emission. Section 7 presents the results and in Section 8 we discuss our findings. We conclude with a brief summary. | In this work we have presented a study of the dust, star formation and gas properties of a sample of FIR compact sources in M33. We performed the photometry of the sources both on the FIR maps from {\it Herschel} and on a set of multiwavelength data, including MIR, H$\alpha$, FUV, as well as integrated HI and CO gas line maps. We fit the dust emission SED in order to measure the dust mass, temperature and luminosity parameters and we estimated the dust corrected H$\alpha$ and FUV fluxes, by using the 24$\mu$m emission as a proxy for dust attenuation. We also used the dust-corrected FUV/H$\alpha$ ratio in order to estimate the age of the stellar populations associated with the FIR sources and we corrected the H$\alpha$ luminosity for age effects (assuming an instantaneous starburst). In order to differentiate between sources of intrinsically different types, we categorized the sources based on whether or not they demonstrated substructured in H$\alpha$ (SUB and NOSUB) and whether or not they demonstrated a significant ($>$3$\sigma$) CO detection within the source footprint (HighCO and LowCO). The main results of this work are the following:\\ (i) The sources have dust masses in the range $10^2$--$10^4M_\odot$, dust temperatures between 15-35K and dust luminosities of $10^{39} -10^{40}$ erg s$^{-1}$;\\ (ii) Compared to NOSUB sources, SUB sources are characterized by a lower PDR-to-total dust luminosity ratio and higher UV-to-H$\alpha$ luminosity ratio;\\ (iii) Compared with LowCO sources, HighCO sources are characterized by higher dust luminosities, higher dust corrected H$\alpha$ luminosities, lower UV-to-H$\alpha$ luminosity ratios and higher fractions of obscured H$\alpha$ luminosity;\\ (iv) We find that the source properties do not show strong trends with radial distance. However, the total dust luminosity and the cold dust temperature tend to decrease mildly with radius. Weaker trends are also shown by the dust corrected H$\alpha$ luminosity and by the fraction of absorbed H$\alpha$ luminosity. The HighCO sources in the inner regions are also embedded in an environment with a higher molecular gas fraction. \\ (v) The source dust luminosities and dust-corrected H$\alpha$ luminosities are well correlated. The bolometric young stellar population luminosity, extrapolated from the H$\alpha$ luminosity, assuming both a constant SFR or a single--age stellar population with ages of few times $10^6$\,yr, is well above the observed dust luminosity. Furthermore, the dust-to-H$\alpha$ luminosity present only a weak trend with radial distance. All these findings are consistent with dust being heated predominantly by local star formation; \\ (vi) We observe a dust mass -- dust temperature anticorrelation, which is at least partially due to the lower limit to the dust luminosity of the detectable sources;\\ (vii) We did not find a clear trend between the source dust masses and the local gas column density; \\ (viii) We did not find a good correlation between the dust--corrected H$\alpha$ luminosity and the dust mass of the sources. However, the scatter is substantially reduced by adopting the age--corrected H$\alpha$ luminosity. | 14 | 4 | 1404.2310 |
1404 | 1404.7190_arXiv.txt | A key test of the supernova triggering and injection hypothesis for the origin of the solar system's short-lived radioisotopes is to reproduce the inferred initial abundances of these isotopes. We present here the most detailed models to date of the shock wave triggering and injection process, where shock waves with varied properties strike fully three dimensional, rotating, dense cloud cores. The models are calculated with the FLASH adaptive mesh hydrodynamics code. Three different outcomes can result: triggered collapse leading to fragmentation into a multiple protostar system; triggered collapse leading to a single protostar embedded in a protostellar disk; or failure to undergo dynamic collapse. Shock wave material is injected into the collapsing clouds through Rayleigh-Taylor fingers, resulting in initially inhomogeneous distributions in the protostars and protostellar disks. Cloud rotation about an axis aligned with the shock propagation direction does not increase the injection efficiency appreciably, as the shock parameters were chosen to be optimal for injection even in the absence of rotation. For a shock wave from a core-collapse supernova, the dilution factors for supernova material are in the range of $\sim 10^{-4}$ to $\sim 3 \times 10^{-4}$, in agreement with recent laboratory estimates of the required amount of dilution for $^{60}$Fe and $^{26}$Al. We conclude that a type II supernova remains as a promising candidate for synthesizing the solar system's short-lived radioisotopes shortly before their injection into the presolar cloud core by the supernova's remnant shock wave. | Primitive meteorites offer a direct link between the production of heavy elements in stellar interiors and explosions and the incorporation of these elements into the pebbles and planetesimals that formed the planets of our solar system. Chondritic meteorites contain presolar grains, with exotic isotopic ratios indicative of their stellar origins, as well as cm-size refractory inclusions, thought to be the oldest surviving solids formed in the hottest regions of the solar nebula, based on their abundances of the decay products of short- and long-lived radioactive isotopes. An ongoing challenge is to use this rich meteoritical record to discern how the solar system came to be formed from the debris ejected by previous generations of wind-emitting and explosive stars (e.g., MacPherson \& Boss 2011). $^{60}$Fe requires nucleosynthesis in a high mass asymptotic giant branch (AGB) star or a type II supernova (SNe) for its production in significant quantities (e.g., Mishra \& Goswami 2014). The half-life of $^{60}$Fe has been redetermined to be $2.62 \pm 0.04$ Myr (Rugel et al. 2009). Evidence for the presence of live $^{60}$Fe during the formation of chondrites (e.g., Tachibana et al. 2006; Dauphas \& Chaussidon 2011) thus has been seen as the strongest argument in favor of the injection of $^{60}$Fe and other short-lived radioisotopes (SLRIs) into the presolar cloud (Boss 1995; Gritschneider et al. 2012) or the solar nebula (Ouellette et al. 2007, 2010) by a shock wave propagating from a massive star that synthesized the SLRIs. In support of the former (cloud) scenario, the W44 type II supernova remnant (SNR) is observed to be striking the W44 giant molecular cloud (GMC), within which are embedded molecular cloud cores that could be triggered into collapse by the W44 shock front (Sashida et al. 2013). However, cosmochemical support for either of these two scenarios has been in flux lately. Some laboratory work has lowered the inferred initial abundances of $^{60}$Fe (Moynier et al. 2011; Telus et al. 2012) to values that are more consistent with the galactic background abundance, rather than a nearby supernova or AGB star (Tang \& Dauphas 2012). This explanation might require the high levels of initial $^{26}$Al found in chondrites to be derived from a pre-SNe Wolf-Rayet (WR) star wind, which is expected to be rich in $^{26}$Al and poor in $^{60}$Fe (Tang \& Dauphas 2012). On the other hand, most recently Mishra \& Goswami (2014) used correlated initial $^{60}$Fe and $^{26}$Al abundances in chondrules from primitive chondrites to infer an initial $^{60}$Fe abundance for the solar nebula similar to that originally claimed (e.g., Tachibana et al. 2006). Hence the $^{60}$Fe evidence for a SNe or AGB origin seems to have now come full circle. Scenarios have also been advanced for accounting for the inferred levels of both $^{60}$Fe and $^{26}$Al through supernova injection into GMCs (Pan et al. 2012; Gounelle \& Meynet 2012; Vasileiadis et al. 2013), although abundance problems remain. The presence of live $^{26}$Al in refractory inclusions (e.g., calcium, aluminum-rich inclusions -- CAIs) was the original motivation for the SNe trigger hypothesis (Cameron \& Truran 1977). The fact that the FUN (fractionation unknown nuclear) refractory inclusions show no evidence for live $^{26}$Al, coupled with the significant $^{26}$Al depletions found in some CAIs and refractory grains, implies that these refractory objects may have formed prior to the injection, mixing, and transport of $^{26}$Al into the refractories-forming region of the solar nebula (Sahijpal \& Goswami 1998; Krot et al. 2012; Kita et al. 2013; Mishra \& Chaussidon 2014). The $^{26}$Al data alone, therefore, seems to require the late arrival of SLRIs derived from a SNe into the inner region of the solar nebula, as opposed to injection into a giant molecular cloud complex, followed by thorough mixing and SLRI homogenization prior to the collapse of the presolar cloud core. Detailed adaptive mesh refinement (AMR) hydrodynamical modeling has shown that SNe shock waves are preferred as a means for simultaneously achieving triggered collapse of the presolar cloud and injection of SLRIs carried by the shock wave (Boss \& Keiser 2013, hereafter BK13). Planetary nebula shock waves from AGB stars have thicknesses of $\sim 0.1 - 0.2$ pc (Jacoby et al. 2001; Pierce et al. 2004): BK13 found that such shocks were too thick to simultaneously trigger collapse and result in significant injection. WR star winds were found to be likely to shred cloud cores, rather than induce collapse (BK13). These studies also showed that injection into a {\it rotating} cloud can increase injection efficiencies by as much as a factor of 10. However, these models (BK13) were restricted to axisymmetry about the target cloud's rotation axis (i.e., two-dimensional -- 2D). Boss \& Keiser (2012, hereafter BK12) presented the first 3D AMR hydrodynamic calculations of the shock wave triggering and injection process, using the 3D Cartesian coordinate version of the FLASH2.5 AMR code. However, these 3D clouds were not assumed to be rotating. The pioneering calculations by Boss (1995) included rotating clouds, but the numerical code used contracting spherical coordinates and was not a fully AMR code. Here we extend the 3D AMR modeling effort to include rotating cloud cores, allowing protoplanetary disks to form along with the central protostellar objects. We wish to learn what effect these more realistic hydrodynamic models might have on SLRI injection efficiencies and hence on the SNe trigger and injection hypothesis. | These detailed 3D AMR hydrodynamics calculations have shown that SNe shock waves can trigger the collapse of rotating dense cloud cores, resulting in dynamic collapse leading to the formation of single, central protostars embedded in protostellar disks. Such systems are likely to evolve into solar-type protostars with protoplanetary disks similar to the solar nebula. Shock wave material carrying SLRIs produced by the SNe is injected into the collapsing regions through Rayleigh-Taylor fingers, leading to an initially inhomogeneous distribution, with SLRI abundances higher in the regions outside the densest regions of the protostellar disks, and lower abundances in the central protostar. This result is qualitatively consistent with the apparent need for late injection of SLRIs into the solar nebula (e.g., Sahijpal \& Goswami 1998; Krot et al. 2012; Kita et al. 2013; Mishra \& Chaussidon 2014). The estimated 3D model dilution factors for a SNR from a core-collapse SNe are in the range of $\sim 10^{-4}$ to $\sim 3 \times 10^{-4}$, in agreement with recent laboratory estimates, which require dilution factors in the range of $\sim 10^{-4}$ to $\sim 10^{-3}$, depending on the mass of the SNe. The significant anisotropy of isotopes observed in SNRs such as Cass A suggests that this level of agreement may be the best that can be expected, i.e., even this order of magnitude agreement should be considered a success. Our future 3D FLASH models will investigate the outcome of shock-cloud interactions where the target cloud's rotation axis is {\it perpendicular} to the direction of shock propagation, instead of aligned, as in the present set of models, to learn what effect such orientations might have on injection efficiencies. We also plan to include the loss of molecular line cooling once the clouds become optically thick in our future models, i.e., at densities above $\sim 10^{-13}$ g cm$^{-3}$, which will allow the collapsing regions to heat above 10 K and continue their collapse toward the formation of the first protostellar core, at $\rho_{max} \sim 10^{-10}$ g cm$^{-3}$ (e.g., Boss \& Yorke 1995). | 14 | 4 | 1404.7190 |
1404 | 1404.2898_arXiv.txt | Uranus has three known co-orbitals: 83982~Crantor~(2002~GO$_{9}$), 2010~EU$_{65}$ and 2011~QF$_{99}$. All of them were captured in their current resonant state relatively recently. Here, we perform a comparative analysis of the orbital evolution of these transient co-orbitals to understand better how they got captured in the first place and what makes them dynamically unstable. We also look for additional temporary Uranian co-orbital candidates among known objects. Our $N$-body simulations show that the long-term stability of 2011~QF$_{99}$ is controlled by Jupiter and Neptune; it briefly enters the 1:7 mean motion resonance with Jupiter and the 2:1 with Neptune before becoming a Trojan and prior to leaving its tadpole orbit. During these ephemeral two-body mean motion resonance episodes, apsidal corotation resonances are also observed. For known co-orbitals, Saturn is the current source of the main destabilizing force but this is not enough to eject a minor body from the 1:1 commensurability with Uranus. These objects must enter mean motion resonances with Jupiter and Neptune in order to be captured or become passing Centaurs. Asteroid 2010~EU$_{65}$, a probable visitor from the Oort cloud, may have been stable for several Myr due to its comparatively low eccentricity. Additionally, we propose 2002~VG$_{131}$ as the first transient quasi-satellite candidate of Uranus. Asteroid 1999~HD$_{12}$ may signal the edge of Uranus' co-orbital region. Transient Uranian co-orbitals are often submitted to complex multibody ephemeral mean motion resonances that trigger the switching between resonant co-orbital states, making them dynamically unstable. In addition, we show that the orbital properties and discovery circumstances of known objects can be used to outline a practical strategy by which additional Uranus' co-orbitals may be found. | Besides bound companions or natural satellites, planets may have unbound companions or co-orbitals, i.e. objects trapped in a 1:1 mean motion resonance with the planet. Co-orbital bodies are not only interesting curiosities found in the celestial mechanics studies, but also represent temporary reservoirs for certain objects as well as the key to understand the origin of retrograde outer satellites of the giant planets and the accretional processes in the early Solar system (see e.g. Namouni, Christou \& Murray 1999). These co-orbital bodies can be primordial, if they were captured in their present resonant state early in the history of the Solar system and have remained dynamically stable for billions of years, or transient, if they were captured relatively recently. \hfil\par Several thousand minor bodies are known to be currently trapped in the 1:1 mean motion resonance with Jupiter and most of them may have remained as such for Gyr (see e.g. Milani 1993; Jewitt, Trujillo \& Luu 2000; Morbidelli et al. 2005; Yoshida \& Nakamura 2005; Robutel \& Gabern 2006; Robutel \& Bodossian 2009; Grav et al. 2011; Nesvorn\'y, Vokrouhlick\'y \& Morbidelli 2013). Neptune also hosts a likely large population of co-orbitals both long-term stable (e.g. Kortenkamp, Malhotra \& Michtchenko 2004; Nesvorn\'y \& Vokrouhlick\'y 2009; Sheppard \& Trujillo 2006, 2010) and transient (e.g. de la Fuente Marcos \& de la Fuente Marcos 2012b,c). In sharp contrast, the number of asteroids currently engaged in co-orbital motion with Uranus appears to be rather small and its nature comparatively ephemeral. Uranus has Centaurs temporarily trapped in other mean motion resonances as well (Masaki \& Kinoshita 2003; Gallardo 2006, 2014). \hfil\par The theoretical possibility of finding primordial or transient Uranian co-orbitals, in particular Trojans, has been a subject of study for almost three decades. In general, numerical simulations predict that Uranus may have retained a certain amount of its primordial co-orbital minor planet population and also that short-term stable (for some Myr) co-orbitals may exist. Zhang \& Innanen (1988a,b) and Innanen \& Mikkola (1989) found that some tadpole orbits may survive for 10 Myr. Mikkola \& Innanen (1992) described tadpole orbits stable for at least 20 Myr and with libration amplitudes close to 100\degr; horseshoe orbiters were only stable for shorter periods of time ($<$10 Myr). Holman \& Wisdom (1993) found similar results. Gomes (1998) explained the observational absence of primordial Uranus Trojans as a side effect of planetary migration. Wiegert, Innanen \& Mikkola (2000) focused on quasi-satellites and found that some test orbits were stable for up to 1 Gyr but only at low inclinations ($<$2\degr) and with eccentricities in the range 0.1--0.15. Nesvorn\'y \& Dones (2002) concluded that any existing Uranus' primordial Trojan population should have now been depleted by a factor of 100. Gacka (2003) also found short-term stable tadpole orbits. In a very detailed study, Marzari, Tricarico \& Scholl (2003) identified a real absence of Trojan stable orbits at low libration amplitudes and also that, among the Jovian planets, Uranus has the lowest probability of hosting long-term stable Trojans. Horner \& Evans (2006) stated that Uranus appears not to be able to efficiently capture objects into the 1:1 commensurability today even for short periods of time. Lykawka \& Horner (2010) found that Uranus should have been able to capture and retain a significant population of Trojan objects from the primordial planetesimal disc by the end of planetary migration. These authors concluded that originally the orbits of these objects should have had a wide range of orbital eccentricities and inclinations. \hfil\par Predictions from numerical simulations appear to be generally consistent with the available observational evidence that transient Uranian co-orbitals do exist but primordial ones may not. So far, Uranus has only three known co-orbitals: 83982 Crantor (2002 GO$_{9}$) (Gallardo 2006; de la Fuente Marcos \& de la Fuente Marcos 2013b), 2010 EU$_{65}$ (de la Fuente Marcos \& de la Fuente Marcos 2013b) and 2011~QF$_{99}$ (Alexandersen et al. 2013a; Alexandersen et al. 2013b). Due to its present short data-arc (85 d), 2010 EU$_{65}$ is better described as a candidate. Asteroids Crantor and 2010 EU$_{65}$ follow horseshoe orbits in a frame of reference rotating with Uranus and 2011~QF$_{99}$ is an L$_4$ Trojan; the three of them are only short-term stable and, therefore, they must be captured objects. Most published studies focus on what makes a hypothetical primordial population of Uranian co-orbitals dynamically unstable, leaving the question of how the transient ones got captured unanswered. \hfil\par In absence of observational bias, the lack of a sizeable present-day population of minor bodies trapped in the 1:1 commensurability with Uranus is probably due to persistent perturbations by the other giant planets. Uranus' Trojans are affected by high-order resonances with Saturn (Gallardo 2006). In the case of current horseshoe librators, Saturn also appears to be the main source of the destabilizing force (de la Fuente Marcos \& de la Fuente Marcos 2013b). Dvorak, Bazs\'o \& Zhou (2010) studied the stability of hypothetical primordial Uranus' Trojans and concluded that the Trojan regions are mostly unstable. For these authors, the orbital inclination is the key parameter to characterize the stability of Uranus' Trojans; only the inclination intervals (0, 7)\degr, (9, 13)\degr, (31, 36)\degr and (38, 50)\degr appear to be stable (regions A, B, C and D, respectively, in Dvorak et al. 2010). The existence of these islands of stability enables the presence of Trojan companions to Uranus. Asteroid 2011~QF$_{99}$ appears to inhabit one of these stable areas in orbital parameter space as its current orbital inclination is nearly 11\degr but it is not a primordial Uranus' Trojan. \hfil\par Here, we revisit the subjects of capture and stability of current Uranian co-orbitals, providing an independent assessment of the 1:1 commensurability of the newly found Uranus' Trojan, 2011~QF$_{99}$, studying its future orbital evolution and looking into its dynamical past. Our numerical investigation is aimed at adding more pieces to the overall puzzle of the apparent scarcity of Uranian co-orbitals as we explore the role of multibody ephemeral mean motion resonances. On the other hand, the comparative study of both the dynamics of the few known co-orbitals and candidates, and their discovery circumstances, reveals important additional clues to solve this puzzle. This paper is organized as follows. In Section 2, we briefly discuss the numerical model used in our $N$-body simulations. The current status of 2011~QF$_{99}$ is reviewed in Section 3. The capture mechanism and stability of 2011~QF$_{99}$ are further studied in Section 4. We revisit the cases of Crantor and 2010 EU$_{65}$ in Section 5. Section 6 introduces a few new Uranus' co-orbital candidates. In Section 7, we discuss our results on the stability of current Uranian co-orbitals. We present a practical guide to discover additional objects in Section 8. Section 9 summarizes our conclusions. | In this paper, we have presented a detailed analysis of the orbital evolution and stability of present-day Uranus' co-orbitals, focusing on how they got captured in the first place and what makes them dynamically unstable. Our calculations show that these objects are submitted to multiple mean motion resonances and exhibit significant secular dynamics characterized by a complex structure that sometimes includes apsidal corotations. The dynamical behaviour analysed here is a typical example of highly nonlinear dynamics, resonances inside a resonance or even resonances inside a resonance inside a resonance. This is best studied using numerical simulations not analytical or semi-analytical work. Some of our results verify predictions made by Marzari et al. (2003) after studying the diffusion rate of Uranian Trojans. \hfil\par We confirm that 2011~QF$_{99}$ currently moves inside Uranus' co-orbital region on a tadpole orbit. The motion of this object is primarily driven by the influence of the Sun and Uranus, although both Jupiter and Neptune play a significant role in destabilizing its orbit. The resonant influence of Jupiter and Neptune was determinant in its capture as Uranus' co-orbital. The precession of the nodes of 2011~QF$_{99}$, which appears to be controlled by the combined action of Saturn and Jupiter, marks its evolution and short-term stability. A three-body mean motion resonance is responsible for both its injection into Uranus' co-orbital region and its ejection from that region. The object will remain as Uranus Trojan for (very likely) less than 1 Myr. Even if 2011~QF$_{99}$ is one of the most stable of the known bodies currently trapped in the 1:1 commensurability with Uranus, it is unlikely to be a primordial 1:1 librator. \hfil\par Our comparative study of currently known Uranus' co-orbitals and candidates shows that the candidate 2010~EU$_{65}$ is more stable than 2011~QF$_{99}$ because of its lower eccentricity (0.05 versus 0.18) even if 2010~EU$_{65}$ has higher orbital inclination (14\fdg8 versus 10\fdg80). On the other hand, a new candidate, 2002~VG$_{131}$, is found to exhibit dynamical behaviour very similar to the one discussed for 83982 Crantor (2002~GO$_{9}$) in de la Fuente Marcos \& de la Fuente Marcos (2013b) and here. This new candidate is the first identified quasi-satellite of Uranus; Crantor will also become a quasi-satellite in the near future. The presence of two objects characterized by similar dynamics and found by chance suggests that others, yet to be discovered, may share their properties. Asteroid 1999~HD$_{12}$ may signal the edge of Uranus' co-orbital region. In any case, all these objects have present-day dynamical ages much shorter than that of the Solar system; therefore, they are not members of a hypothetical population of primordial objects trapped in a 1:1 mean motion resonance with Uranus since the formation of the Solar system. They may be former primordial Neptune co-orbitals (Horner \& Lykawka 2010) though. \hfil\par Horner \& Evans (2006) argued that present-day Uranus cannot efficiently trap objects in the 1:1 commensurability even for short periods of time. However, the available evidence confirms that, contrary to this view and in spite of the destabilizing role of the other giant planets, Uranus still can actively capture temporary co-orbitals, even for millions of years. Regarding the issue of stability, both Crantor's and 2011~QF$_{99}$'s orbital inclinations are within one of the stability islands identified by Dvorak et al. (2010) for the case of Trojans. Both candidates 2002~VG$_{131}$ and 2010 EU$_{65}$ move outside the stability islands proposed in that study although they are not Trojans. The existence of 1999~HD$_{12}$ shows that not only inclination but also eccentricity play an important role in the long-term stability of Uranus' co-orbitals. A larger sample of Uranus' co-orbitals is necessary to understand better the complex subject of the stability of these objects although temporary Uranian co-orbitals are often submitted to complicated multibody ephemeral mean motion resonances that trigger the switching between the various resonant co-orbital states, making them dynamically unstable. \hfil\par Currently available evidence suggests that the small number of known transient Uranus' co-orbitals may have its origin in observational bias rather than in the strength of the gravitational perturbations by the other giant planets. Taking this into account, the number of yet undiscovered transient Uranian co-orbitals may likely be as high as that of the Neptunian ones. Our results can easily be applied to implement improved strategies for discovering additional Uranian co-orbitals. | 14 | 4 | 1404.2898 |
1404 | 1404.7159_arXiv.txt | We report interferometric imaging of \cii\ and \oh\ emission toward the center of the galaxy protocluster associated with the $z$=5.3 submillimeter galaxy (SMG) AzTEC-3, using the Atacama Large (sub)Millimeter Array (ALMA). We detect strong [C{\scriptsize II}], OH, and rest-frame 157.7\,$\mu$m continuum emission toward the SMG. The \cii\ emission is distributed over a scale of 3.9\,kpc, implying a dynamical mass of 9.7$\times$10$^{10}$\,\msol, and a star formation rate (SFR) surface density of $\Sigma_{\rm SFR}$=530\,\msol\,yr$^{-1}$\,kpc$^{-2}$. This suggests that AzTEC-3 forms stars at $\Sigma_{\rm SFR}$ approaching the Eddington limit for radiation pressure supported disks. We find that the OH emission is slightly blueshifted relative to the [C{\scriptsize II}] line, which may indicate a molecular outflow associated with the peak phase of the starburst. We also detect and dynamically resolve \cii\ emission over a scale of 7.5\,kpc toward a triplet of Lyman-break galaxies with moderate UV-based SFRs in the protocluster at $\sim$95\,kpc projected distance from the SMG. These galaxies are not detected in the continuum, suggesting far-infrared SFRs of $<$18--54\,\msol\,yr$^{-1}$, consistent with a UV-based estimate of 22\,\msol\,yr$^{-1}$. The spectral energy distribution of these galaxies is inconsistent with nearby spiral and starburst galaxies, but resembles those of dwarf galaxies. This is consistent with expectations for young starbursts without significant older stellar populations. This suggests that these galaxies are significantly metal-enriched, but not heavily dust-obscured, ``normal'' star-forming galaxies at $z$$>$5, showing that ALMA can detect the interstellar medium in ``typical'' galaxies in the very early universe. | The first massive galaxies in the universe are expected to rapidly grow in the most massive dark matter halos at early cosmic epochs (e.g., Efstathiou \& Rees \citeyear{er88}; Kauffmann et al.\ \citeyear{kau99}). Such high overdensities in the dark matter distribution are expected to be associated accordingly with overdensities of baryonic matter, and thus, protoclusters of galaxies (e.g., Springel et al.\ \citeyear{spr05}). The bulk of the stellar mass in the most massive galaxies in these halos likely grows in short, episodic bursts associated with major gas-rich mergers and/or peak phases of gas accretion from the intergalactic medium (e.g., Blain et al.\ \citeyear{bla04}). These starbursts, in turn, may significantly enrich the galaxy's environment with heavy elements through winds and outflows (e.g., McKee \& Ostriker \citeyear{mo77}; Sturm et al.\ \citeyear{stu11}; Spoon et al.\ \citeyear{spo13}). The identification of massive starburst galaxies at the highest redshifts may be the most promising way to find such exceptional cosmic environments. The most intense starbursts are commonly enshrouded by dust, rendering them difficult to identify at rest-frame UV/optical wavelengths (e.g., Smail et al.\ \citeyear{sma97}; Hughes et al.\ \citeyear{hug98}; Chapman et al.\ \citeyear{cha03}). The dust-absorbed stellar light is re-emitted at rest-frame far-infrared (FIR) wavelengths, making such galaxies bright in the observed-frame (sub-)millimeter at high redshift (so-called submillimeter galaxies, or SMGs; see review by Blain et al.\ \citeyear{bla02}). \begin{figure*} \epsscale{1.15} \plotone{f1} \vspace{-2mm} \caption{{\em HST}/ACS F814W ({\em left}) and ALMA 1.0\,mm continuum image (rest-frame 157.7\,$\mu$m; {\em right}) of the targeted region. Two pointings were observed to cover AzTEC-3 at $z$=5.3 and five candidate companion Lyman-break galaxies (positions are indicated by plus signs; LBG-1 contains three components). The 1.0\,mm continuum image was obtained by averaging the three [C{\scriptsize II}] line-free spectral windows (corrected for primary beam attenuation). The rms at the phase centers is $\sim$58\,$\mu$Jy\,beam$^{-1}$, and increases outwards due to the primary beam response. The synthesized beam size of 0.63\,$''$$\times$0.56\,$''$ is indicated in the bottom left corner of the {\em right} panel. \label{f1}} \end{figure*} We have recently identified AzTEC-3, a gas-rich SMG at $z$=5.3 (Riechers et al.\ \citeyear{rie10}, hereafter R10; Capak et al.\ \citeyear{cap11}, hereafter C11) in the AzTEC 1.1\,mm study of the Cosmic Evolution Survey (COSMOS) field (Scoville et al.\ \citeyear{sco07}; Scott et al.\ \citeyear{sco08}). AzTEC-3 has a relatively compact ($<$4\,kpc radius), highly excited molecular gas reservoir of 5.3$\times$10$^{10}$\,\msol\ (determined through the detection of three CO lines; R10), which gets converted into stars at a rate of $>$1000\,\msol\,yr$^{-1}$ (C11). Its current stellar mass is estimated to be $M_\star$=(1.0$\pm$0.2)$\times$10$^{10}$\,\msol\ (C11).\footnote{These estimates depend on the assumed stellar initial mass function, see, e.g., Dwek et al.\ (\citeyear{dwe11}).} The environment of AzTEC-3 represents one of the most compelling pieces of observational evidence for the hierarchical picture of massive galaxy evolution. The massive starburst galaxy is associated with a $>$11-fold overdense structure of ``normal'' star-forming galaxies at the same redshift\footnote{Based on photometric redshifts and several spectroscopic confirmations (C11).} that extends out to $>$13\,Mpc on the sky, with $>$10 galaxies within the central (co-moving) $\sim$2\,Mpc radius region (C11). The protocluster galaxies alone (including the SMG) place a lower limit of 4$\times$10$^{11}$\,\msol\ on the mass of dark and luminous matter associated with this region (C11). However, our current understanding of this exceptional cosmic environment is dominantly based on the rest-frame UV/optical properties of all galaxies except the SMG, and thus, may be incomplete due to lacking information on the gas and dust in their interstellar media (ISM). Here we report 158\,$\mu$m \cii, 163\,$\mu$m \oh, and rest-frame 157.7\,$\mu$m dust continuum imaging toward the center of the galaxy protocluster associated with the $z$=5.3 SMG AzTEC-3 with ALMA. The \cii\ line is the dominant cooling line of the cold\footnote{Cold here means $\ll$10$^4$\,K, i.e., in the regime where dust cooling through (far-)infrared emission is prevalent, and below the regime where cooling through hydrogen lines dominates.} ISM in star-forming galaxies (where it can carry up to 1\% of $L_{\rm FIR}$; e.g., Israel et al.\ \citeyear{isr96}), typically much brighter than CO lines, and traces regions of active star formation (photon-dominated regions, or PDRs) and the cold, neutral atomic medium (CNM; e.g., Stacey et al.\ \citeyear{sta91}). It thus is an ideal tracer for the distribution, dynamics, and enrichment of the ISM out to the most distant galaxies, but it was only detected in some of the most luminous quasars and starburst galaxies in the past (e.g., Maiolino et al.\ \citeyear{mai05}, \citeyear{mai09}; Walter et al.\ \citeyear{wal09}; Stacey et al.\ \citeyear{sta10}; Wagg et al.\ \citeyear{wag10}; Valtchanov et al.\ \citeyear{val11}; Riechers et al.\ \citeyear{rie13}; Wang et al.\ \citeyear{wan13}) -- i.e., systems that are much more extreme than typical protocluster galaxies. Previous searches for [C{\scriptsize II}] emission in typical and/or ultraviolet-luminous galaxies at $z$$>$5 have been unsuccessful (e.g., Walter et al.\ \citeyear{wal12}; Kanekar et al.\ \citeyear{kan13}; Ouchi et al.\ \citeyear{ouc13}; Gonzalez-Lopez et al.\ \citeyear{gl14}), and it is important to understand what role environment may play for the detectability of such objects. The far-infrared lines of the OH radical are important for the H$_2$O chemistry and cooling budget of star-forming regions, and they are critical tracers of molecular outflows (e.g., Sturm et al.\ \citeyear{stu11}; Gonzalez-Alfonso et al.\ \citeyear{ga12}), but OH was only detected in a single galaxy at cosmological distances to date (Riechers et al.\ \citeyear{rie13}). We use a concordance, flat $\Lambda$CDM cosmology throughout, with $H_0$=71\,\kms\,Mpc$^{-1}$, $\Omega_{\rm M}$=0.27, and $\Omega_{\Lambda}$=0.73 (Spergel \etal\ \citeyear{spe03}, \citeyear{spe07}). | We have detected [C{\scriptsize II}] emission toward the intensely star-forming SMG (AzTEC-3) and a triple Lyman-break galaxy system (LBG-1) associated with the $z$=5.3 AzTEC-3 protocluster environment (C11, R10). These member galaxies lie within a redshift range of d$z$$<$0.004, suggesting that the association of galaxies is not only close in the sky plane, but along the line of sight as well. We further detected \oh\ line and rest-frame 157.7\,$\mu$m continuum emission in the SMG AzTEC-3, and placed a stringent limit on its \pco\ luminosity. Our observations are consistent with a relatively compact ($\sim$2.5\,kpc diameter), highly-dispersed, warm, ``maximum starburst'' in its peak phase in the massive galaxy AzTEC-3, with possible evidence for outflowing gas from the star-forming regions, and/or tidal structure. There is no evidence for an AGN contribution to the excitation of the gas. Its overall properties are reminiscent of the most extremely active massive, dusty starburst galaxies found within the (general) SMG population (e.g., Riechers et al.\ \citeyear{rie13}). Our observations are also consistent with LBG-1 being a ``typical'', close to $L^\star_{\rm UV}$ galaxy following the star-forming ``main sequence'' at its cosmic epoch, with little evidence for old stellar populations or the presence of dust. LBG-1 is not detected in sensitive CO or far-infrared continuum observations, which is consistent with what is expected for a young starburst with perhaps sub-solar metallicity. LBG-1 shows a complex kinematic structure, perhaps representing a merger of three smaller galaxies. Using only a fraction of the full ALMA science array, we thus detect and spatially resolve the interstellar medium in both distant massive starbursts and ``typical'' $z$$>$5 star-forming galaxies at relative ease. We, however, do not detect two fainter candidate members of the protocluster, which suggests that they either are an order of magnitude fainter in [C{\scriptsize II}] emission than LBG-1, or that their systemic redshifts fall outside the range covered by our observations. The capabilities of ALMA in a more advanced stage of completion will be necessary to further address this issue. The detection of [C{\scriptsize II}] emission in LBG-1 is interesting for a number of reasons. Recent searches for [C{\scriptsize II}] emission in $z$$>$6.5 Lyman-$\alpha$ emitters (LAEs) and Lyman-$\alpha$ blobs (LABs) have been unsuccessful, even with ALMA (e.g., Walter et al.\ \citeyear{wal12}; Ouchi et al.\ \citeyear{ouc13}; Gonzalez-Lopez et al.\ \citeyear{gl14}). These systems have SFR$_{\rm UV}$ that are comparable to LBG-1, and even exceed it by a factor of a few in the most extreme cases, but they remain undetected in [C{\scriptsize II}] emission down to comparable, and sometimes deeper levels than required to detect LBG-1. The successful detection of LBG-1 may suggest that this is a selection effect. The difference in cosmic time between the redshift of LBG-1 and $z$=6.5 is only $\sim$250\,Myr. As such, it is not clear that the earlier epochs in which the LAEs and LABs were observed are the main deciding factor. We consider it more likely that the narrow-band Lyman-$\alpha$ selection technique that has led to the initial identification of the LAEs and LABs targeted in [C{\scriptsize II}] emission at $z$$>$6.5 selects against galaxies with sufficient metallicity, and thus carbon abundance, to produce enough [C{\scriptsize II}] line flux to be detectable. This is consistent with the detection of [C{\scriptsize II}] emission in other, albeit significantly more active and massive star-forming galaxy populations at comparable redshifts (e.g., Riechers et al.\ \citeyear{rie13}). Gonzalez-Lopez et al.\ (\citeyear{gl14}) have suggested that high-redshift galaxies with high UV continuum fluxes but low Lyman-$\alpha$ equivalent widths may be more likely to have sufficient metallicity to be detectable in the [C{\scriptsize II}] line. This is consistent with the [C{\scriptsize II}] detection of LBG-1, which has a comparatively low Lyman-$\alpha$ equivalent width (C11). In any case, our study shows that, even if the detection of dust in ``typical'' galaxies at very high redshift may require substantial integration times, their gas content appears to be detectable with ALMA in the [C{\scriptsize II}] line using only moderate amounts of observing time, with the possible exception of systems with the lowest metallicities (cf.\ Fisher et al.\ \citeyear{fis14}). It is also interesting to discuss the properties of LBG-1 in the context of the BR\,1202--0725 system at $z$=4.69. This system consists of two far-infrared-luminous (each $>$10$^{13}$\,\lsol ), massive galaxies, separated by 26\,kpc in projection, one of which is an optically-luminous broad absorption line quasar. Early ALMA observations have revealed two faint [C{\scriptsize II}]-emitting sources in close proximity to the quasar ($<$15\,kpc in projection), which appear to be associated with LAEs (components Ly$\alpha$-1 and Ly$\alpha$-2; e.g., Wagg et al.\ \citeyear{wag12}; Carilli et al.\ \citeyear{car13}). These LAEs, however, have very large Lyman-$\alpha$ equivalent widths due to Lyman-$\alpha$ lines with $>$1200\,\kms\ FWHM (e.g., Williams et al.\ \citeyear{wil14}). Given the strong tidal forces, and perhaps ongoing interaction between the two massive galaxies, the close proximity and characteristics of these LAEs thus have likely implications for the evolution (e.g., besides its strong radiation field, the quasar shows a possible outflow in the direction of one of the LAEs), and perhaps even the origin of these sources (e.g., it cannot be ruled out that they represent, or formed out of, tidal debris from the massive galaxies). As such, it is unclear to what degree the LAEs in this system can be considered ``typical'' galaxies. However, given the lack of detections of ``typical'' high-redshift galaxies in [C{\scriptsize II}] emission prior to our study, and since these LAEs are significantly less extreme than all other systems detected in [C{\scriptsize II}] at high redshift, it is instructive to compare the properties of LBG-1 to those of the LAEs in BR\,1202--0725 (we adopt their properties from the study of Carilli et al.\ \citeyear{car13} below). In contrast to LBG-1, the Ly$\alpha$-2 component in the BR\,1202--0725 system is detected in the far-infrared continuum, suggesting a FIR luminosity in excess of 10$^{12}$\,\lsol. Only part of the [C{\scriptsize II}] line in Ly$\alpha$-2 is detected at the edge of the bandpass, indicating a line FWHM of $>$338\,\kms. This suggests that the line is significantly broader than in LBG-1 (which has a total FWHM of 218$\pm$24\,\kms; Tab.~\ref{t1}). Ly$\alpha$-2 has a $L_{\rm CII}$/$L_{\rm FIR}$ ratio of $>$5$\times$10$^{-4}$. Assuming that at least half the [C{\scriptsize II}] line in Ly$\alpha$-2 is covered by the bandpass, this suggests an at least $\gtrsim$3--10$\times$ lower ratio than in LBG-1. These properties are consistent with Ly$\alpha$-2 being a luminous, dusty starburst system, perhaps not representative of $L^\star_{\rm UV}$ galaxies at $z$$\sim$4.7, but less extreme than other dusty starbursts at high redshift detected in [C{\scriptsize II}] previously. The Ly$\alpha$-1 component in the BR\,1202--0725 system is not detected in the far-infrared continuum, implying $L_{\rm CII}$/$L_{\rm FIR}$$>$5$\times$10$^{-4}$. This limit is by about an order of magnitude lower than that in LBG-1. It thus remains unclear how its $L_{\rm CII}$/$L_{\rm FIR}$ compares to normal, star-forming galaxies nearby. The [C{\scriptsize II}] line in Ly$\alpha$-1 has a FWHM of only 56$\pm$11\,\kms, corresponding to $\sim$4\% of the width of its Ly-$\alpha$ line (Williams et al.\ \citeyear{wil14}). This also corresponds to $\sim$60\% of the width of LBG-1a, i.e., the narrowest component of LBG-1. As discussed by Carilli et al.\ (\citeyear{car13}), it remains unclear if Ly$\alpha$-1 is a physically distinct system, or a local maximum in a tidal ``bridge'' connecting the massive, far-infrared-luminous galaxies. In any case, based on the existing constraints, the properties of Ly$\alpha$-1 and LBG-1 appear to be quite dissimilar as well, but more detailed ALMA data on the BR\,1202--0725 system will be required to further investigate possible similarities. It remains to be seen what role the environment plays in the evolution of LBG-1. To address this issue in more detail, a first step will be a complete study of the AzTEC-3 protocluster with ALMA (the current study only covered the center of the region) and similar environments to be discovered in the future. Equally importantly, sensitive studies of ``blank fields'' in the [C{\scriptsize II}] emission line will be necessary for an unbiased investigation of the [C{\scriptsize II}] luminosity function (an approximate, but independent measure of the atomic gas content of galaxies through cosmic times), and to properly constrain the ``hidden'', dust-obscured part of the star formation history of the universe through the detection of previously unknown faint, dusty star-forming galaxies. Such C$^+$ deep fields will be an important complement to similar studies in CO and continuum emission alone (studies of [C{\scriptsize II}] in continuum-preselected samples will only yield a biased view of this issue; e.g., Swinbank et al.\ \citeyear{swi12}). When ALMA is completed in the coming months, it will be an ideal tool for the most sensitive of these investigations. Given the relative strength of the [C{\scriptsize II}] line, CCAT will be able to detect [C{\scriptsize II}] emission over regions the size of the AzTEC-3 protocluster in a single shot using multi-object spectroscopy by the end of the decade. Ultimately, CCAT will also enable complementing, large-area C$^+$ blank field studies that may cover regions as large as the full COSMOS field to appreciable depth. | 14 | 4 | 1404.7159 |
1404 | 1404.3857_arXiv.txt | The most naive interpretation of the BICEP2 data is the chaotic inflation by an inflaton with a quadratic potential. When combined with supersymmetry, we argue that the inflaton plays the role of right-handed scalar neutrino based on rather general considerations. The framework suggests that the right-handed sneutrino tunneled from a false vacuum in a landscape to our vacuum with a small negative curvature and suppressed scalar perturbations at large scales. | 14 | 4 | 1404.3857 |
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1404 | 1404.4193_arXiv.txt | In this paper we propose a way to use optical polarisation observations to provide independent constraints and guide to the modelling of the spectral energy distribution (SED) of blazars, which is particularly useful when two-zone models are required to fit the observed SED. As an example, we apply the method to the 2008 multiwavelength campaign of PKS 2155-304, for which the required polarisation information was already available. We find this approach succesful in being able to simultaneously describe the SED and variability of the source, otherwise difficult to interpret. More generally, by using polarisation data to disentangle different active regions within the source, the method reveals otherwise unseen correlations in the multiwavelength behaviour which are key for the SED modelling. | Extragalactic jets are gigantic structures up to hundreds of kpc across, produced when highly collimated plasma is ejected at relativistic speeds from the nucleus of active galaxies (AGN).The AGN system has a strongly non-isotropic radiative output, with a system of relativistic jets emanating at opposite diections from the central engine which produces a collimated emission pattern in the flow direction. When the observer's line-of-sight happens to be aligned with the outflow direction, the object is called a blazar~\citep{urr95}. The radiation Doppler boost resulting from this chance alignment renders blazars the most extreme of all AGN and the dominant extragalactic source class in the sky above 100 GeV~\citep{hin09}. Modelling of the broadband spectral energy distribution (SED) is a well established technique to study the physics of blazars~\citep{ghi98, tav98}. The general double-hump structure of the SED of blazars is well explained as synchrotron and inverse-Compton radiation from a highly energetic population of electrons. Evidence from multiwavelength (MWL) observations, from radio to $\gamma$-rays, shows that the AGN emission is variable at all frequencies, and contemporaneous measurements indicate the SED is remarkably correlated~\citep{fos98}. Although one-zone models~\citep{mar92, sik94, blo96} have been very successful in describing the SED of blazars, recent MWL observations, with better temporal resolution and more complete spectral coverage, have revealed the necessity of adopting multi-zone models at least in some cases~\citep{ale12, abr12}. Given the degeneracy and large number of parameters present in these inhomogeneous SED models, some independent insight into the properties of different particle populations that are simultaneously contributing to the observed emission would be decisive to better motivate and provide additonal constraints to models. The polarised emission from blazars was discovered early on in the observations of these objects, as the signature of synchrotron radiation from a non-thermal distribution of relativistic particles~\citep{ang80}. Since then it has been an important technique to study the physics of blazar jets, allowing to probe the state of the magnetic field and particle populations at the emission sites as well as aspects of the source structure~\citep{bri86, jon88, lyu05}. Recently, a number of campaings have detected episodes of large and smooth rotation of the polarisation angle of blazars far in excess of 180 degrees, not compatible with turbulent or random behaviour~\citep{dar09, mar13}. These have been interpreted as the signature of a ubiquitous, large-scale magnetic field component, with specific geometry, responsible for the flow collimation and acceleration~\citep{mar08, abd10}. In radio, milli-arcsecond resolution polarisation interferometry allows for a mapping of the magnetic field state along the jet and the possibility to physically locate the active emission regions~\citep{dar09, agu11}. In this paper we present an original approach to the modelling of blazar SEDs which uses information provided by optical polarimetric observations to put additional constraints and guide the model fits with independently-motivated physical inputs. The optical polarimetric analysis at the basis of the technique~\citep{bar10} (henceforth BA10) allows to identify the single component which contributes the most to the source activity in optical polarisation, separating it from the rest of the ``quiescent jet.'' This is equivalent to deciding if an one- or two-zone model must be adopted to explain the polarisation behaviour in the optical band. In addition, the polarisation analysis provides a description of the characteristics of the ``active'' and ``quiescent'' components, such as their individual contributions to the total flux, which is in turn used to provide further constraints to the multi-zone SED model. The term {\it ``polarimetric tomography''} stresses that such use of the data has the capacity to disentangle some of the source's internal structure, even when it is impossible to resolve individual zones via direct imaging. In this paper we are concerned with a description of the technique and its potential, as presented in Section 2. A case study is shown in Section 3, where we apply the method to the modelling of the quiescent-state SED of PKS 2155-304. There we present an alternative, self-consistent two-zone solution to the SED, motivated by a previously undetected correlation in the dataset revealed by this approach. \section[]{POLARIMETRIC TOMOGRAPHY} Even if the inner jets of blazars cannot be resolved in optical waveband, polarisation observations are an avenue to probe their internal structure. Turbulence is long believed to dominate the plasma flow at small scales~\citep{moo82}. Plasma turbulence reflects in the state of the magnetic field, resulting in a tangled structure which reduces the mean source polarisation to a few percent and imprints randomness to the source behaviour, except when some mechanism is at play that (if only temporarily) imparts order to the field, either locally (e.g., by shock compression;~\cite{lai80, hug89}) or globally (e.g., a toroidal or helical B-field configuration;~\cite{nak01, lov02}). Moreover, when internal shocks, for example, enhance the emissivity of a portion of the jet, the polarisation of this active zone can dominate that of the entire source, adding coherence to it. Since the polarisation is usually quite high in the active sites, such zones can dominate the source emission as seen in polarised light even when the photometric output of the region is far less than that from the rest of the ``quiescent'' jet. When this is the case, we are in a situation where the polarisation has the potential to probe and disentangle the emission of an otherwise invisible, but very active sub-structure of the jet -- hence the term {\it ``tomography.''} When applied in itself, the polarisation analysis allows to draw a simple, two-zone model of the state of the source in optical. By analysing the variability of the Stokes parameters of the source, one can evaluate if it is best described by the evolution of a single, dominant component, or if the superposed contribution of multiple varying polarised regions needs to be considered to explain the temporal behaviour of the data~\citep{hag08}. If the temporal changes of the Stokes Q and U parameters is dominated by the evolution of a single polarised region, then its polarisation quantities (polarisation degree and angle) can be derived (see Section 3.1 of BA10). Once this is established, one can use equations 1-2 in BA10 to model the total observed polarisation from the source as the result of the action of this changing component, superposed on the less active, but still polarised remainder of the jet. The jet structure and behaviour in optical is now interpreted as the combined emission of two components whose properties and temporal evolution are constrained by the polarisation data. The real potential of the analysis is nevertheless unveiled in a MWL context, as it introduces new and independetly motivated information with which to construct a model for the SED. Since one can expect the variable polarised region to likely be active at higher frequencies, characterising it at low energies can be key to understanding the SED behaviour. As will be shown next, with this technique we can follow independently the SED of the alleged active zone, identifying what is its individual contribution to the multiband source behaviour, thus better constraining an otherwise degenerate two-zone SED model. \begin{figure} \vspace*{-2.6truecm} \includegraphics[width=0.55\textwidth]{lc.ps} \vspace*{-2.8 truecm} \caption{Black triangles show the {\it RXTE} (2-10 keV) lightcurve for PKS 2155-304 in 2008. Red squares represent the optical flux (in $\nu F_\nu$) behaviour of the variable component as derived by BA10. Note the correlation between the source's total X-ray flux and the variability of the active optical component. The optical flux for the variable component is from a reanalysis of the data presented in BA10, following the same procedures presented in that paper but with improved numerical accuracy to the analysis. The blue open circles show the total optical flux light curve (multiplied by a factor 0.1 to fit the image scale) that does not show the same clear correlation with the X-ray data. Error bars represent the 1-sigma confidence intervals.} \label{lc} \end{figure} | In this paper we have presented a new approach to the modelling of blazar SEDs which uses an analysis of the optical polarisation state of the source to provide additional, independent observational constraints to the SED parameters. In particular, the polarisation information can be used to motivate the necessity of a multi-zone model of the SED, being also able to derive some of the fundamental properties of the two components, such as their relative flux and polarisation. Such information is then used to parameterise the inhomogeneous SED model, better constraining it. The technique was illustrated by applying it to data from a campaign on PKS 2155-304, for which the complex variability behaviour and the lack of physical constraints for a two-zone model rendered it difficult explaining the SED. Based on the parameters derived from the polarisation analysis we were able to derive a two-component model for the source which described its behaviour and temporal correlations in good detail, and a simple physical analysis of the results provides a self-consistent picture of the source. The fact that the polarisation analysis can disentangle the behaviour of a sub-component of the jet whose flux might only be a small fraction of the total emission is the key strength of the technique. In the particular case presented here, the optical counterpart to the X-ray variability, previously interpreted as uncorrelated, was revealed to come from such a zone responsible for not more than 10\% of the total optical output. This suggests that such kind of analysis might bear relevance to understanding MWL correlations and orphan flares in blazars. Of particular relevance to the general understanding of a blazar SED is the fact that our result suggests that during states of lower activity, a two-component model seems to give a better description of the emission. It is still to be verified what the application of the technique could say about high-states, for which the strong MWL correlations hint toward the correlated signature of a single-zone. This question should be answered once we extend the analysis to a larger number of campaigns. | 14 | 4 | 1404.4193 |
1404 | 1404.6828_arXiv.txt | We present a maximum-likelihood weak lensing analysis of the mass distribution in optically selected spectroscopic Galaxy Groups (G$^3$Cv5) in the Galaxy And Mass Assembly (GAMA) survey, using background Sloan Digital Sky Survey (SDSS) photometric galaxies. The scaling of halo mass, $M_h$, with various group observables is investigated. Our main results are: 1) the measured relations of halo mass with group luminosity, virial volume and central galaxy stellar mass, $M_\star$, agree very well with predictions from mock group catalogues constructed from a GALFORM semi-analytical galaxy formation model implemented in the Millennium $\Lambda$CDM N-body simulation; 2) the measured relations of halo mass with velocity dispersion and projected half-abundance radius show weak tension with mock predictions, hinting at problems in the mock galaxy dynamics and their small scale distribution; 3) the median $M_h|M_\star$ measured from weak lensing depends more sensitively on the lognormal dispersion in $M_\star$ at fixed $M_h$ than it does on the median $M_\star|M_h$. Our measurements suggest an intrinsic dispersion of $\sigma_{\log(M_\star)}\sim 0.15$; 4) Comparing our mass estimates with those in the catalogue, we find that the G$^3$Cv5 mass can give biased results when used to select subsets of the group sample. Of the various new halo mass estimators that we calibrate using our weak lensing measurements, group luminosity is the best single-proxy estimator of group mass. | Even though the nature of dark matter will ultimately be determined by observations of its particle properties, its gravitational effect has so far been the cleanest way to map its distribution in the universe. Weak gravitational lensing is one of the main techniques for mapping dark matter on large and intermediate scales~\citep[e.g.][]{Bartelmann01}. As its name suggests, weak lensing is the production of weak distortions (shear) in the shapes of background, or source, galaxies by foreground masses. Usually one has no prior knowledge of the intrinsic shape of a source galaxy, resulting in uncertainties much larger than the gravitational shear signal, so the extraction of shape distortions has to be done in a statistical way, for example by measuring the shear-shear correlation function on large scales~\citep[e.g.,][]{CFHTCosmicShear}, or by stacking a large number of source galaxies around many lenses on smaller scales. Early applications of stacked lensing to low mass groups have been carried out by \citet{Hoekstra01} and \citet{Parker05} who measured the average mass-to-light ratio of groups in the Canadian Network for Observational Cosmology Field Galaxy Redshift Survey (CNOC2). Stacked lensing measurements have also been made using galaxies and groups in many current large surveys, including the SDSS~\citep{Mandelbaum06b,Mandelbaum06a,Johnston07,Sheldon09}, CFHT Lensing Survey~\citep{CFHTVelander,CFHTHudson}, COSMOS~\citep{COSMOS12} and Deep Lens Survey~\citep{DLS}. These studies estimate the average density profile of the dark matter haloes of the lenses, and derive scaling relations between halo mass and other observational properties. Even though stacked lensing analyses can give a non-parametric estimate of the matter density profile around lenses with similar properties, the interpretation of the stacked signal can be difficult. This is because the stacked profile is an average over all the contributing haloes of unknown mass distribution, and this average typically has a complicated weighting determined by the error of each shape measurement, the number of pairs within each radial bin, and the redshifts of lenses and sources. To account somewhat for these averaging effects, one usually parametrizes the distribution of halo masses and the clustering of haloes using the framework of halo occupation distribution (HOD) models \citep[e.g.][]{HODrev,Mandelbaum05a,COSMOS12}, and fits for the HOD parameters given the stacked profiles.% In this work we carry out a weak lensing analysis of galaxy groups from the Galaxy And Mass Assembly~\citep[GAMA, ][]{GAMA} survey. GAMA is an ongoing spectroscopic survey of moderate sky coverage. % As large scale surveys go, it has deep spectroscopy as well as uniform, yet high, completeness ($>98$\%) down to $r_{\rm AB}=19.8$. This makes possible the construction of a large and accurate galaxy group catalogue~\citep[G$^3$Cv5,][]{G3C}, able to reach lower halo masses than other existing catalogues of the local universe. In addition, the survey region of GAMA was selected to overlap several companion surveys at different wavelengths, ranging from radio to x-ray. These complementary data provide a detailed picture of the properties of GAMA galaxies. The variation of galaxy properties with environment, defined by the mass distribution probed by weak lensing, can be investigated using gravitational shear measurements of background galaxies taken from the photometric SDSS data in the same region. Fortunately, the redshift distribution of GAMA groups peaks at $z\sim 0.2$, where the lensing efficiency of the SDSS galaxy sample also peaks. These lens and source samples are described in more detail in Section~\ref{sec_data}. Since our default lens sample is subject to a survey flux limit and a group multiplicity selection, most of the measured mass-observable relations in this work are subject to some selection effects and should not be taken as general relations for a volume-limited sample. In order to draw some general conclusions on galaxy formation, however, we only compare our measurements with mock galaxy catalogues that incorporate the same selection function. These mock catalogues are also described in Section~\ref{sec_data}. As the galaxy number density of our source sample ($\sim 1~\mathrm{arcmin}^{-2}$) is much lower than some dedicated lensing surveys (e.g., $\sim 20~\mathrm{arcmin}^{-2}$ in CFHTLS and $\sim 70~\mathrm{arcmin}^{-2}$ in COSMOS), and because the lens sample is restricted by the small GAMA sky coverage ($\sim 150 \mathrm{deg}^2$ in this work) compared with SDSS for instance, we do not have any obvious advantage in signal-to-noise over existing measurements. Hence efficient utilization of the lensing signal is crucial to our analysis. To this end, we go beyond the popular stacked analyses, and perform a maximum-likelihood analysis on the shapes of individual background galaxies, broadly following the method in \cite{Hudson98} \citep[see also][]{Schneider97, Hoekstra03, Hoekstra04}. The key difference between our approach and stacked lensing is that we fit the shapes of each source galaxy explicitly, while stacked lensing only estimates or fits the average tangential shear for sub-samples of sources binned in radius, and around lenses binned according to mass proxies. Our method requires no binning in the source sample, and can be applied with or without binning in the lens sample. Not binning the data avoids information losses, leading to good measurements with our small sample. Another advantage of our method is that it is free from the averaging ambiguity associated with stacking, since the mass of each lens is explicitly modelled. With this method, the large number of available observational properties associated with GAMA groups can now all be linked with the underlying halo masses, to provide valuable constraints on galaxy formation models. We will also show that our maximum-likelihood weak lensing method is an ideal tool for model selection, to pick up the tightest mass-observable relation observationally. We describe our method in Section~\ref{sec_method}, and its practical application in Section~\ref{sec_app}. As a first application of our maximum-likelihood weak lensing (MLWL) method, we extract the scaling relations of halo mass to various group observables, including velocity dispersion, luminosity, radius, virial volume and stellar mass of the group's central galaxy. With MLWL we give both non-parametric measurements of these relations by binning only the lens sample according to observable, and parametric fits by modelling the mass-observable relation as a power-law with no binning at all. The G$^3$Cv5 comes with estimated halo masses calibrated using mock catalogues. These mass estimates are also examined with MLWL, to see if they differ from our measurements. Starting from MLWL we also construct several new mass estimators, which we compare with predictions from a semi-analytical galaxy formation model and previous measurements. These results are described and discussed in Sections~\ref{sec_result} and \ref{sec_estimators}, with all the fits summarized in Table~\ref{table_par}. Weak lensing measurements can be compared with predictions from galaxy formation models to gain insight into the various physical processes in the model. In this comparison, it is crucial that one properly accounts for the observational selection effects. \citet{Hilbert10} first compared the weak lensing measured mass-richness relation with the prediction from semi-analytic galaxy formation models. They construct mock clusters by picking cluster haloes from simulation snapshots, and applying observational selection functions to the member galaxies of the mock clusters. In this work, we improve the treatment of selection effects in two aspects. First, a light-cone galaxy catalogue~\citep{Merson13} is constructed from a semi-analytic galaxy formation model, to account fully for the selection function of the galaxy survey. Second, identical group finding algorithms~\citep{G3C} are applied to both the real and mock galaxy catalogues, to account fully for the selection effect introduced by group finding. We also have compared many more mass-observable relations. All the relations in Table~\ref{table_par} are subject to sample selection, and we only compare them with mock catalogues constructed with the same selection function as the real data. The only exception is in the comparison of our stellar mass-halo mass relation with those from other works, where we make an additional measurement for a volume-limited central galaxy sample. To summarize the structure of the paper, we describe our lens and source samples in Section~\ref{sec_data} along with the mock catalogues to which we compare our measurements; the general MLWL method is described in Section~\ref{sec_method}, with its application to our samples described in Section~\ref{sec_app}; the results are presented and discussed in Sections~\ref{sec_result} and \ref{sec_estimators}; finally, we conclude in Section~\ref{sec_conclusion}. The units throughout this paper, wherever not explicitly specified, are ${\rm km\,s}^{-1}$ for velocity, $h^{-1}\rm{Mpc}$ for length, $\msunh$ for halo mass, $\msunhh$ for galaxy stellar mass, and $\lsunhh$ for luminosity, where $H_0=100h$~km s$^{-1}$ Mpc$^{-1}$. The $\log()$ function throughout is the common (base 10) logarithm, while the natural logarithm is $\ln()$. Unless explicitly stated, the lens sample covers groups with three or more members. The relevant cosmological parameters, which only appear in the distance calculations of our measurements, are $\Omega_M=0.3$ and $\Omega_\Lambda=0.7$. \footnote{The mock catalogues with which we compare are constructed from the $\Lambda$CDM Millennium simulation which has a different cosmology ($\Omega_M=0.25$, $\Omega_\Lambda=0.75$). However, our lensing measurements are very insensitive to cosmology. Switching to Millennium/WMAP9/Planck cosmologies only introduces a $\sim 1$ percent difference into the fitted parameters.} % | We have carried out a maximum-likelihood weak lensing analysis on a set of SDSS source galaxies located in the GAMA survey regions, in order to derive halo masses for the GAMA galaxy groups. The group mass distribution is modelled with an NFW profile, with a mass-concentration relation fixed by previous simulation results. This enables us to predict the gravitational shear produced by each halo with a single parameter, namely halo mass. Comparing the predicted shear with the observed shapes of background galaxies allows us to fit the halo mass of our foreground lenses. By splitting the G$^3$Cv5 group sample according to various observed properties, we have explored the scaling relations between halo mass and these observables. With power-law parametrization of these relations, global fits over the entire sample are also performed. The resulting likelihood ratios quantify the intrinsic tightness of each mass-observable relation. All the fitted results are summarized in Table~\ref{table_par}. The dominant systematic uncertainty in our measured mass-observable relations comes from the assumed halo mass dispersion around the median, modelled as a lognormal distribution in mass. We emphasize that the majority of our measurements are based on the multiplicity-limited G$^3$Cv5 group sample, and are subject to the group selection function described by $V_N\leq V_N^{\rm lim}(z)$. The only exception is the measured halo mass-stellar mass relation where a volume-limited stellar mass sample is specially constructed. Proper comparison of our results with theory or other measurements have to take the selection effect into account. To help interpret our results and to compare with theoretical predictions we have constructed mock catalogues based on the application of the GALFORM semianalytic model of galaxy formation \citep{Bower06} to halo merger trees in the $\Lambda$CDM Millennium N-body simulation \cite{Millennium}. The mock catalogues are generated using the selection function of the real GAMA survey. For the first time, identifical group finding algorithms and selection functions have been applied to both observational data and lightcone galaxy mocks to enable side-by-side comparisons between lensing measurements and a semi-analytic model. Overall there is very good agreement between our measured mass-observable relations and those predicted by the galaxy formation model. In particular, we find that: \begin{itemize} \item The halo mass scales roughly in proportion to group luminosity, multiplicity volume and central galaxy stellar mass in the multiplicity limited G$^3$Cv5 sample. These relations are in excellent agreement with predictions from the mocks. \item For given stellar mass of the central galaxy, the halo mass strongly depends on the number of galaxies in the group. To compare our measurement with existing HOD models, we have constructed a volume limited central galaxy catalogue, and measured the stellar mass-halo mass relation free from selection effects. We find the measurement of the $M_h(M_\star)$ relation provides a very powerful constraint on the HOD scatter of the $M_\star(M_h)$ relations. A dispersion $\sigma_{\log(M_\star)}=0.2$, or $0.15$ after subtracting the stellar mass measurement noise, is able to yield a good agreement between our measurement and all the HOD predictions that we considered. \item The measured $M_h(\sigma_v)$ relation shows a slightly different slope from that in the mocks, which could originate from the velocity bias of galaxies with respect to dark matter. The measured $M_h(R_{50})$ relation is also in slight tension with those in the mock catalogues at small $R_{50}$. Such a small scale discrepancy is also obvious in the $L_{\rm grp}(R_{50})$ scaling of groups. It can be partly explained by the limited spatial resolution of the Millennium simulation, and may also reflect the treatment of orphan galaxies in the model. \item The G$^3$Cv5 mass estimators are biased when used for stacking. Luminosity mass has a small but constant bias, while dynamical mass can have a large and mass-dependent bias. A globally calibrated mass-to-light relation can serve as a very good mass estimator for groups, and is the tightest halo mass to single observable relation in our sample. The estimation can be slightly improved when combined with $V_N$. The mass estimates from dynamical measurements can be much improved when combining $\sigma_v$ with $V_N$ instead of $R_{50}$, or when combined with group luminosity and redshift. \item The dominant source of systematic uncertainty in our mass estimators comes from the assumed dispersion in halo mass about the median value, modelled with a lognormal distribution in mass. For a mass dispersion of $0.5-0.7$ dex, the resulting overestimation in median lens mass is typically $0.2-0.3$ dex. This is slightly counteracted by smaller underestimations caused by uncertainties in the redshifts of background photometric galaxies and the positions of gravitational centres of foreground lenses. Selection cuts in the data do not cause significant biases in the results. The systematic uncertainties considered here change the slopes of the mass-observable relations by only $0.01$, but do have a greater impact on the significance of the results, reducing $TS$ for the fits by a factor of $2-5$. \end{itemize} In this work we have taken a galaxy-by-galaxy maximum-likelihood approach to extract the lensing signal of galaxy groups. Compared with stacked weak lensing, our approach makes much more efficient use of the information contained in individual galaxy shapes. In addition, our utilization of the information carried by individual lenses is also more efficient, since our fitting can be done free from binning. In contrast, stacked weak lensing usually measures a weighted average density profile of the underlying, to be modelled, matter distribution. This involves averaging over the distribution of halo masses and redshift. A direct fitting without knowing the underlying sample distribution and the stacking weights leaves the result difficult to interpret, or gives biased results if bravely interpreted as the average mass of the sample. A further complication in stacked lensing comes from the redshift evolution of halo profiles. Haloes evolve with redshift, as do the definitions of the halo mass and edge, so the same halo mass does not correspond to the same profile in either physical or comoving coordinates. It is not clear what is the best coordinate system for stacking. In contrast, our likelihood fitting deals with each halo separately, and can properly incorporate any distribution and evolution in halo density profiles. We note that stacked lensing could complement MLWL by providing a non-parametric measurement of the average density profile. In this work we only do stacked weak lensing for visualization of the measured and fitted profiles. We plan to explore the mass-concentration relation and the halo mass function probed by GAMA in subsequent papers. This methodology would also be well suited for higher redshift, using the combination of the VIPERS survey \citep{VIPERS}, which has 100,000 spectroscopic galaxies with $0.5<z<1.2$, and the CFHTLens source catalogue, which has a median redshift $\sim0.75$ and a source density of $17~\rm{arcmin}^{-2}$. The KiDS survey \citep{KIDS} has just come to its first data release of $50$ square degree data overlapping with GAMA. Adopting the KiDS shear catalogue, we expect to have more than a factor of 3 improvement in signal to noise ratio. | 14 | 4 | 1404.6828 |
1404 | 1404.1914_arXiv.txt | High-scale supersymmetry (SUSY) with a split spectrum has become increasingly interesting given the current experimental results. A SUSY scale above the weak scale could be naturally associated with a heavy unstable gravitino, whose decays populate the dark matter (DM) particles. In the mini-split scenario with gravitino at about the PeV scale and the lightest TeV scale neutralino being (a component of) DM, the requirement that the DM relic abundance resulting from gravitino decays does not overclose the Universe and satisfies the indirect detection constraints demand the reheating temperature to be below $10^9 - 10^{10}$ GeV. On the other hand, the BICEP2 result prefers a heavy inflaton with mass at around $10^{13}$ GeV and a reheating temperature at or above $10^9$ GeV with some general assumptions. The mild tension could be alleviated if SUSY scale is even higher with the gravitino mass above the PeV scale. Intriguingly, in no-scale supergravity, gravitinos could be very heavy at about $10^{13}$ GeV, the inflaton mass scale, while gauginos could still be light at the TeV scale. | \label{sec:intro} Supersymmetry (SUSY) has long been a favorite theoretical framework of physics beyond the Standard Model (SM). However, given the current null results of all SUSY searches, if SUSY is realized in Nature, it is unclear at what scale it will manifest itself. At the moment, theoretical studies of SUSY fall into two broad catalogues: one direction is to still focus on weak-scale natural SUSY and design non-trivial structures of flavor and Higgs sectors to evade the direct search constraints and explain the observed Higgs mass. The other direction is take seriously high-scale fine-tuned SUSY, in particular, split SUSY, with scalars heavier than gauginos. The virtues of this approach include simplicity, automatic amelioration of SUSY flavor and CP problems, preservation of gauge coupling unification and the lightest neutralino being a dark matter (DM) candidate. The idea of split SUSY, in particular, mini-split with scalars one-loop factor heavier than gauginos, was actually predicted a while ago by the simplest version of anomaly mediation~\cite{Giudice:1998xp, Randall:1998uk} (and later by a wide variety of moduli mediation scenarios~\cite{Choi:2005ge,Choi:2005uz,Conlon:2006us,Conlon:2006wz,Acharya:2007rc,Acharya:2008zi}). Since 2003, split SUSY has started to be taken as a viable possibility despite the presence of a fine-tuned EWSB and gained more attention recently given the increasing tension between data and naturalness~\cite{Wells:2003tf, ArkaniHamed:2004fb,ArkaniHamed:2004yi,Giudice:2004tc,Acharya:2007rc,Acharya:2008zi,Hall:2011jd,Ibe:2011aa,Arvanitaki:2012ps,ArkaniHamed:2012gw,Hall:2012zp, Hall:2013eko, Altmannshofer:2013lfa, Baumgart:2014jya, Dhuria:2012bc}. In split SUSY, the high SUSY breaking scale could naturally lead to a heavy unstable gravitino. In the mini-split scenario based on anomaly mediation, there is a loop factor separating the gravitino and gaugino mass scales with gravitino at about ($10^2 - 10^3$) TeV and gaugino at the TeV scale. In this scenario, the neutralino DM particles produced by late-time gravitino decays could not annihilate efficiently and thus inherit the number density of the gravitinos which adds to its thermal number density. During the reheating era, the thermal scattering of the SM superpartners contributes (at least part of) the gravitino primordial relic abundance, which is approximately proportional to the reheating temperature $T_R$. Consequently the requirement that the neutralino DM does not overclose the Universe sets an interesting upper bound on $T_R$ as a function of DM mass. This upper bound could be tightened if wino is (a component of) DM. Indirect detection looking for excesses in the photon continuum spectrum or a monochromatic photon line sets a strong bound on allowed wino DM relic abundance for the whole mass range assuming NFW or Einasto DM profiles~\cite{Cohen:2013ama, Fan:2013faa}. The bound could be relaxed if the Milky Way DM distribution near the galactic center deviates considerably from the standard DM-only $N$-body simulation predications. However, the bound does not necessarily disappear entirely. For example, even if the Milky Way DM profile has a significant core with a radius of 1 kpc, light non-thermal wino with mass below 400 GeV as a single-component DM is excluded~\cite{Fan:2013faa}. We will present the derivation of the upper bound on $T_R$ from the constraints of the relic abundance of neutralino DM, in particular, wino DM in Sec.~\ref{sec:relic} and Sec.~\ref{sec:indirect}. On the other hand, the discovery of $B$-mode by the BICEP2 collaboration gives us some clues of the inflation scale~\cite{Ade:2014xna}. The observation could be fit by a lensed $\Lambda$CDM plus tensor model with a tensor-to-scalar ratio $r = 0.2 ^{+0.07}_{-0.05}$. Such a large $r$ prefers large field inflation with a heavy inflaton and very likely a high reheating temperature. We will present estimates of inflaton mass scale and reheating temperature in Sec.~\ref{sec:bicep}. We find that in the mini-split scenario based on anomaly mediation, $T_R$ is bounded to be at or below $10^9 - 10^{10}$ GeV while the BICEP2 data prefers $T_R$ to be around or above $10^9$ GeV. The BICEP2 result has some tension with the mini-split scenario with a heavy gravitino. In other words, the BICEP2 result favors a splitting between gravitinos and gauginos larger than the loop factor predicted by anomaly mediation. Intriguingly, if SUSY breaking is tied up with gravity, e.g., through the Scherk-Schwarz mechanism, gravitinos could be as heavy as $10^{13}$ GeV, which is the same mass scale of the inflaton inferred from the BICEP2 result while gauginos could still be light at the TeV scale. The implications for SUSY scales will be discussed in Sec.~\ref{sec:implications}. See Refs.~\cite{Harigaya:2014qza, Pallis:2014dma, Harigaya:2014pqa, Ibanez:2014zsa, Craig:2014rta, Ellis:2014rxa, Lyth:2014yya, Hamaguchi:2014mza, Hall:2014vga} for some other recent discussions of implications of the BICEP2 result for SUSY. We conclude in Sec.~\ref{sec:con} and present a discussion of gravitinos from inflaton decays in the appendix. | \label{sec:con} In this paper, we study the implication of DM indirect detection and BICEP2 in the split SUSY scenario with a heavy unstable gravitino. In the mini-split spectrum with scalars/gravitinos only one-loop factor above the TeV-scale gauginos, the reheating temperature has to be low to avoid overproduction of DM particles from gravitino decays. In particular, we demonstrate that indirect detection requires the reheating temperature to be below about $10^9$ GeV if the wino is (a component of) DM. On the other hand, the large tensor-to-scalar ratio observed by BICEP2 favors large-field-inflation with a reheating temperature around or above $10^9$ GeV. Given this mild tension and the phenomenological upper bound on the gravitino mass derived by requiring the gauginos to be at the TeV scale, it is tempting to think more seriously of the (highly) split SUSY scenario in which inflaton/gravitino are at around $10^{13}$ TeV and gauginos are still at the TeV scale with lightest neutralino being (part of) DM.\footnote{Axion could be the dominant DM component.} Indeed this picture has recently been discussed in the framework of Intermediate Scale SUSY~\cite{Hall:2014vga}. In general, given the BICEP2 result, it is very interesting to use the scale of inflation to probe the full range of split SUSY scenarios through observables such as equilateral non-gaussianity~\cite{Craig:2014rta}. It will also be of interest to study the implications of the BICEP2 result for baryogenesis. For example, thermal leptogenesis works for a reheating temperature above $2\times 10^9$ GeV~\cite{Giudice:2003jh}, which fits well with the BICEP2 result. | 14 | 4 | 1404.1914 |
1404 | 1404.6533_arXiv.txt | The hypothesis of a universal initial mass function (IMF) -- motivated by observations in nearby stellar systems -- has been recently challenged by the discovery of a systematic variation of the IMF with the central velocity dispersion, $\sigma$, of early-type galaxies (ETGs), towards an excess of low-mass stars in high-$\sigma$ galaxies. This trend has been derived so far from integrated spectra, and remains unexplained at present. To test whether such trend depends on the {\sl local} properties within a galaxy, we have obtained new, extremely deep, spectroscopic data, for three nearby ETGs, two galaxies with high $\sigma$ ($\sim 300$~$\rm km \, s^{-1}$), and one lower mass system, with $\sigma \sim 100 \, \rm km \, s^{-1}$. From the analysis of IMF-sensitive spectral features, we find that the IMF depends significantly on galactocentric distance in the massive ETGs, with the enhanced fraction of low-mass stars f mostly confined to their central regions. In contrast, the low-$\sigma$ galaxy does not show any significant radial gradient in the IMF, well described by a shallower distribution, relative to the innermost regions of massive galaxies, at all radii. Such a result indicates that the IMF should be regarded as a local (rather than global) property, and suggests a significant difference between the formation process of the core and the outer regions of massive ETGs. | The stellar Initial Mass Function (IMF) characterises the distribution of stellar masses at birth in star forming regions. The IMF is therefore a crucial ingredient of galaxy formation and evolution. It sets the mass-scale of galaxies, determining their (stellar) mass-to-light ratio, and drives stellar feedback as well as chemical enrichment into the ISM. While resolved stellar population studies support the idea of an invariant IMF in environments with quite different local properties such as metallicity or density \citep{kroupa,bastian,kroupa13}; recent studies of early-type galaxies (ETGs), based on both dynamics \citep[][]{cappellari,thomas11,wegner12,dutton13,tortora13} and stellar populations \citep[][]{saglia,cenarro,vandokkum,spiniello12,ferreras,labarbera} have found that the IMF varies with galaxy mass. { The same result has also been obtained by a combination of gravitational lensing and dynamical studies \citep[][but see \citealt{smith13}]{treu,auger}.} In particular, dynamical studies have found a significant increase of the stellar mass-to-light ratio, with respect to that expected for a ``standard'', Milky-Way-like IMF, towards high-mass systems. The analysis of gravity-sensitive features in the integrated spectra of ETGs has revealed that this trend in the ``normalization'' of the IMF is driven by an increase of the fraction of dwarf-to-giant stars, i.e. a change towards steeper IMF slopes with higher velocity dispersion \citep[][hereafter LB13]{cenarro,jesus,cappellari,ferreras,labarbera}. { Although some discrepancies can be found between dynamical and stellar population studies, the agreement is remarkable, considering the fundamental differences of both approaches \citep{smith}.} One should notice that the results from stellar population studies are derived from integrated spectra, therefore correspond mostly to the bright central regions of ETGs. Therefore, the question of whether radial variations {\sl within} a galaxy occur, follows naturally. Are these variations in the IMF driven by a large-scale (e.g. galaxy mass) or a local property (e.g. local velocity dispersion) ? Despite the importance of this question to constrain the overall picture of galaxy formation and evolution, no reliable spatially-resolved measurement of the IMF has been performed so far. Only a few early attempts tried to investigate this issue. \citet{carter} found strong radial gradients of Na and TiO spectral features in ETGs, interpreting it as the contribution from metal-rich populations of dwarf stars, concentrated towards the centres of the most massive galaxies. This interpretation was dismissed by \citet{cohen,hardy88} and \citet{delisle92}, who suggested instead metallicity alone as the driver of these radial trends. Due to the lack of accurate stellar population models and high-quality data at the time, these pioneering attempts remained inconclusive. Over twenty years later, in the present work, we show that after considerable improvement in the state-of-the-art stellar population synthesis models, analysis tools, observational facilities, and instrumentation, we are now able to address the issue of a radial variation of the IMF in unresolved stellar populations. Targeting a set of optical and Near-Infrared (NIR) gravity-sensitive spectral features in two high-$\sigma$ ($\rm \sim 300 \, km \, s^{-1}$) and one low$-\sigma$ ($\rm \sim 100 \, km \, s^{-1}$) ETGs, we find that variations in the IMF of these systems should be regarded as a local property. The outline of the paper is the following. In Section~2, we describe the sample of ETGs and data reduction. Section 3 presents the stellar population analysis. Section~4 shows the main results of the present work, i.e. the IMF trend as a function of galactocentric distance in ETGs. In Section~5, we present results from a number of tests performed to assess the robustness of our results. In Section~6 we discuss several effects that might mimic an IMF gradient, showing that none of them can account for all the available data. { Our results are discussed in Section~7, and conclusions are given in Section~8. Further material is presented in Appendix~B, to address possible technical issues of the stellar population analysis.} | We have analysed the spectra of two nearby ETGs: a massive galaxy, NGC~4552, and a low-mass counterpart, NGC~4387. Results for an additional high-mass galaxy, NGC\,5557 (with lower quality data), are also discussed. Comparing observed line-strengths to predictions of state-of-art stellar population models, we have found that: \begin{enumerate} \item Massive galaxies show a steep radial variation of the IMF slope, with an enhanced fraction of low-mass stars in the centre and a standard Kroupa-like distribution at the effective radius (Fig.~\ref{img:gamma}). \item The IMF gradient of the low-mass galaxy is rather flat, mildly steeper than that for a Kroupa-like IMF throughout (Fig.~\ref{img:gamma}). \item Our result naturally explains the IMF-slope vs central velocity dispersion relation of ETGs, as a luminosity-weighted average of the underlying IMF radial gradient, \end{enumerate} We therefore suggest that the IMF of nearby ETGs should be regarded as a ``local'' property, with an excess of low-mass stars being produced by processes driving the formation of their cores -- during the early phases of star formation. Although simple, phenomenological models provide explanations to this scenario \citep{Hopkins:13,weidner:13}, detailed ab initio numerical simulations are required to understand this fundamental link between the growth of structures and the ``baryon'' physics of galaxy formation. \vspace{0.2in} \small{ \footnotesize{\textit{{Acknowledgements}}} { We would like to thank the anonymous referee, for the many helpful comments, that helped us to significantly improve this manuscript.} We would like to thank the GTC astronomers Antonio Cabrera, David Garc\' ia and Antonio Garc\'ia for their work during the observations. This work has benefited from interesting discussions with C. Weidner and M. Beasley. IMN would like to specially thank Luis Peralta de \mbox{Arriba} for his comments during this work. This work has been supported by the Programa Nacional de Astronom\'ia y Astrof\'isica of the former Spanish Ministry of Science and Innovation under grant AYA2010-21322-C03-02. {Based on observations made with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof\'\i sica de Canarias, in the island of La Palma.}} | 14 | 4 | 1404.6533 |
1404 | 1404.0535_arXiv.txt | We discuss cosmological models for an eternal universe. Physical observables show no singularity from the infinite past to the infinite future. While the universe is evolving, there is no beginning and no end - the universe exists forever. The early state of inflation is described in two different, but equivalent pictures. In the freeze frame the universe emerges from an almost static state with flat geometry. After entropy production it shrinks and ``thaws'' slowly from a ``freeze state'' with extremely low temperature. The field transformation to the second ``big bang picture'' (Einstein frame) is singular. This ``field singularity'' is responsible for an apparent singularity of the big bang. Furthermore, we argue that past-incomplete geodesics do not necessarily indicate a singularity or beginning of the universe. Proper time ceases to be a useful concept for physical time if particles become massless. We propose to define physical time by counting the number of zeros of a component of the wave function. This counting is independent of the choice of coordinates and frames, and applies to massive and massless particles alike. | \label{Introduction} Can the universe exist forever, without beginning and end? Since the failure of steady state cosmologies and the general acceptance of the big bang it is widely believed that the universe must have had some type of ``beginning''. The Friedmann-Lema\^{i}tre cosmological solution becomes singular as the big bang is approached. It can therefore not be extended to an infinite past. Assuming the strong energy condition Penrose and Hawking have shown the presence of a past singularity or geodesic incompleteness for rather arbitrary cosmological solutions \cite{Pen,Haw}. With the advent of inflation the strong energy condition has been abandoned. Still, with the rather mild assumption that the universe is expanding in the average (more precisely, that the average Hubble parameter is positive) it has been established that geodesics cannot be complete towards the past \cite{BGV,AV}. From this observation the conclusion was drawn that the universe becomes singular in the finite past, or at least cosmology becomes incomplete, necessitating a ``beginning''. For a a wide class of inflationary models or alternative ``pre big bang models'' an extension to the infinite past seems unfeasible. Recently, simple models have been proposed \cite{CWUE,CWSF} for which no past singularity occurs. These cosmologies can be extended to the infinite past. In terms of only a few parameters these models can describe all present observations, including inflation, an end of inflation, radiation - and matter-domination and the present transition to a new dark energy dominated period. They are thus fully consistent and constitute counter examples to the view that the universe must have had a beginning. The evolution of the universe is typically very slow in these models - the characteristic time scale is never much shorter than the present inverse Hubble parameter $\sim 10^{10}$yr. The geometry approaches flat space in the infinite past. All geometrical invariants built from the curvature tensor and its covariant derivatives, contracted with the inverse metric, vanish for the infinite past, $t\to-\infty$. In this ``freeze picture'' it seems rather obvious that no singularity is encountered, with a cosmological solution extending to the infinite past. Nevertheless, the same models can be mapped by a conformal transformation (Weyl scaling) to an equivalent ``big bang picture''. In this Einstein frame the primordial cosmology is of a standard inflationary type. Field relativity \cite{CWUE,CWQ1} states that the two pictures are fully equivalent. The absence or presence of physical singularities should be the same in both pictures. The big bang picture has a geometry with geodesics that become incomplete in the past. If the presence of incomplete geodesics would really indicate a physical singularity it would be hard to understand how the freeze picture could be free of singularities. In this note we address the connections between incomplete geodesics, curvature singularities, and the possible existence of physical singularities in the light of transformations between different frames. This will shed new light on the role of ``singularity theorems''. The discussion will lead to four central findings: \begin{itemize} \item [(i)] Field transformations, as the conformal transformation between different frames, can be singular. A detected singularity in some frame may therefore arise from a singularity in the field transformation, while in some other frame everything is regular. Such ``field singularities'' do not reflect a physical singularity, in analogy to ``coordinate singularities'' arising from the choice of a particular coordinate system. (They are singularities in ``field-coordinates''.) The absence of physical singularities is guaranteed if one frame exists where all relevant physical observables are found to be regular. \item [(ii)] Cosmological solutions can have attractor properties. As a consequence, after an evolution over a certain time interval only a restricted range of field values and their derivatives will be found at some given time $t_0$. Inversely, if one tries to extrapolate backwards, with ``initial conditions'' at $t_0$ outside this allowed range, one typically encounters a singularity. Even for a regular universe the most general solutions with arbitrary ``initial conditions'' at $t_0$ will not remain regular towards the infinite past. In this case the presence of singular solutions neighboring a regular solution should not be misinterpreted as a sign that a ``beginning'' of the universe is needed. For example, an attractive regular isotropic solution may be surrounded by anisotropic solutions that become singular in the past. \item [(iii)] Physical time must not only be coordinate independent but also frame independent. Frame independent quantities are dimensionless, as proper time multiplied by the particle mass, evaluated on the trajectory of a massive particle. Proper time by itself is changed by field transformations. Even dimensionless proper time is no longer a useful physical clock if the ratio momentum/mass diverges. In this case a particle behaves like a photon. A reasonable coordinate and frame independent physical time may be defined by counting the number of oscillations of a wave function. \item [(iv)] The presence of timelike geodesics that are incomplete towards the past does not necessarily indicate a singularity or incompleteness of cosmology. Particles behave as massive particles only for a finite ratio momentum/mass, and only in this case proper time is a useful measure of time. For finite momentum/mass in the infinite past the allowed velocities $u(t_0)$ at some finite time point $t_0$ are restricted. Past-incomplete geodesics can be precisely those with $u(t_0)$ outside the allowed range. In this case particles behave like photons in the infinite past and proper time ceases to be a useful measure of physical time. \end{itemize} We start by specifying our criteria for an eternal cosmology that is free of singularities from the infinite past, $t\to-\infty$, to the infinite future, $t\to\infty$: (i) The cosmological solution should be regular for all $t$. (ii) For a suitable definition of physical time the time-distance to the infinite past and infinite future should both be infinite. (iii) For massive particles and in suitable units the proper time elapsed from some given time $t_0$ to the infinite future should be infinite. (iv) Also the proper time from the infinite past to $t_0$ should be infinite if momentum/mass remains finite. (v) Furthermore, we require that no trajectory of a massive or massless particle encounters a singularity in the whole range between the infinite past and future. A few comments on these criteria are in order: For momentum/mass $\to\infty$ particles behave as photons and proper time becomes unsuitable. The condition for the use of proper time for measurements of physical time may be weakened by requiring only finite momentum and a finite suitable time averaged ratio momentum/mass, such that particles do not behave as photons for most of their history. Obviously, the ``eternity'' of the universe has to be defined in a coordinate-independent concept as proper time or ``oscillation time''. We can always choose a time coordinate $t$ that covers an infinite range from $-\infty$ to $+\infty$, even for a cosmology with a physical singularity. Our general strategy is rather simple. For a given model we first consider the freeze frame where it is rather easy to get convinced that observables remain regular from the infinite past to the infinite future. The singular map to the Einstein frame is then used to understand the singularities of the big bang as an inappropriate choice of time or geometry. These singularities appear to be field singularities, while physical observables remain regular. We demonstrate our points with two specific models of gravity coupled to a scalar field. This field is responsible for both inflation and late dark energy. A crossover between two fixed points is responsible for the transition from the inflationary primordial cosmology to ``late cosmology''. In sect. \ref{Crossover model with flat space in the infinite past} we present our first model which admits asymptotic solutions where the infinite past corresponds to Minkowski space with constant scale factor. For $t\to-\infty$ the Hubble parameter vanishes $\sim(-t)^{-3}$ while particle masses go to zero with a different inverse power of $-t$. The geometry is obviously regular and geodesically complete. In sect. \ref{Focus property of primordial cosmology} we show that this family of asymptotic solutions is an attractor for increasing time, to which neighboring isotropic and homogeneous cosmologies converge. As a consequence, the general solution with arbitrary integration constants fixed at some finite $t_0$ cannot be continued to the infinite past - this is only possible for the family of attractor solutions. In sect. \ref{Physical time} we address possible definitions of physical time in this cosmology. We find that proper time evaluated on the trajectories of massive particles is not suitable for this purpose. All masses vanish in the infinite past such that particles with nonzero momentum behave as photons. We propose to use instead the counting of the oscillations of the wave function which works both for massive and massless particles. For this coordinate- and frame-invariant ``physical time'' both the infinite past and future are at infinite distance. The model is mapped to the Einstein frame in sect. \ref{Singularities in the Einstein frame}, where our solutions describe power-law inflation. The conformal transformation of the metric becomes singular in the infinite past, which is the root of the apparent singularities in the big bang picture. While particle trajectories are mapped to particle trajectories, this does not hold for geodesics. Also proper time is not invariant under a change of frame, while the counting of oscillations remains the same in all frames. For ``oscillation time'' the geometric singularity remains in the infinite past. In turn, this geometric singularity is due to a particular choice of metric, while for a different choice the geometry remains regular. In sect. \ref{Crossover model for de Sitter inflation} we turn to our second model which describes de Sitter inflation in the Einstein frame. In the freeze frame the scale factor vanishes faster than a power and slower than an exponential, with vanishing curvature invariants in the infinite past. For this model singularities in the curvature invariants are absent in both frames, despite the singularity of the conformal transformation. We discuss in detail the interpretation of geodesic incompleteness of de Sitter space. It is linked to the property that particles with finite momentum become photon-like in the infinite past, such that proper time is no longer suitable for a definition of physical time. We demonstrate in sect. \ref{Eternal Universe and inflation} that the class of crossover models to which our two models belong are viable candidates for an inflationary epoch of the universe. For this purpose we discuss a whole family of models that interpolate between the two models of sects. \ref{Crossover model with flat space in the infinite past} and \ref{Crossover model for de Sitter inflation}. They lead to realistic scenarios for inflation, typically with large tensor fluctuations. Our models are therefore not only rather simple examples for an eternal universe. They can also be taken as realistic candidates for the description of our observed world. Our conclusions are presented in sect. \ref{Conclusions}. | \label{Conclusions} In this note we have put the emphasis on ``past eternity''. ``Future eternity'' for $t\to+\infty$ is rather generic for many cosmologies, including the Friedman universe. For our models \eqref{1a}, \eqref{2a} the universe produces entropy after the end of inflation \cite{CWCI,HMSS}. The subsequent radiation- and matter-dominated periods correspond to the approach to a fixed point for $\chi\to\infty$ for which scale symmetry becomes an exact symmetry which is spontaneously broken \cite{CWQ2,CWVG}. For $\chi^2\gg m^2$ we assume that the masses of all particles except for neutrinos scale $\sim \chi$ (perhaps with different coefficients as for $\chi^2\ll m^2$), and dimensionless gauge and Yukawa couplings are close to their constant fixed point values. Bounds on the time variation of fundamental constants are therefore obeyed. During radiation- and matter-domination the universe shrinks in the freeze picture, with slowly increasing temperature and particle masses \cite{CWUE,CWSF}. The scaling solution predicts a small fraction of early dark energy \cite{CWQ2,CWA,DLW,SDW,CWE,DR}, $\Omega_e=n/\alpha^2$, with $n=4(3)$ for radiation (matter) domination. We may assume that for the present epoch the neutrino masses increase faster than $\sim \chi$ (in the freeze frame), due to a crossover in a sector of heavy singlets \cite{CWVG}. Neutrinos becoming non-relativistic trigger a recent transition to a dark energy dominated epoch, with present dark energy related to the average neutrino mass \cite{GNQ1,GNQ2}. The models are compatible with all present cosmological observations \cite{CWSF,CWUE}. A measurement of primordial tensor fluctuations \cite{BICEP} will restrict the allowed ranges of $\tilde \alpha$ and $\alpha$. In conclusion, we have presented consistent cosmological models for which solutions of field equations can describe an eternal universe, in contrast to the opinion based on earlier ``no-go theorems''. This does not imply that the history of the universe must have followed these solutions since the infinite past. Since the solutions are stable attractors, many other possibilities for a primordial universe can approach such attractors as time increases. Information on the primordial state is then largely lost - predictions for observations will be the same as for a primordial state following the ``eternal attractor solution'' since the infinite past. One could imagine a chaotic inflation \cite{Lin,SW} primordial state, governed by quantum fluctuations in flat space. Once a region is homogeneous enough such that the homogeneous field equations become valid, it will subsequently follow the inflation history according to the eternal attractor solution. Our approach allows for a differentiated view of several basic cosmological concepts. No big bang singularity is needed. The big bang picture in the Einstein frame provides for a very useful description of observations, but may be inappropriate for a good picture of the regular structure of the eternal universe. Gravity needs not to become strong in the ``beginning'' of the universe. The concept of the quantum effective action assumes a quantum field theory for gravity. Nevertheless, for our solutions gravity remains always a weak interaction. The concepts of time and geometry are ambiguous. This extends beyond the issue of general coordinate transformations. Field transformations leave observables invariant, but can map very different geometries into each other. Apparent singularities in a given frame may be ``field singularities'' associated to a particular choice of fields, while physical observables remain regular. \bigskip\noindent {\bf Acknowledgment.} The author would like to thank P.~Steinhardt for stimulating discussions that motivated this work, and A.~Linde and A.~Vilenkin for useful comments. \vspace{2.0cm}\noindent | 14 | 4 | 1404.0535 |
1404 | 1404.5917_arXiv.txt | {We present a three-loop model of neutrino mass whose most-general Lagrangian possesses a softly-broken accidental $Z_2$ symmetry. In the limit that a single parameter vanishes, $\lambda\rightarrow0$, the $Z_2$ symmetry becomes exact and the model contains a stable dark-matter candidate. However, even for finite $\lambda\ll1$, long-lived dark matter is possible, giving a unified solution to the neutrino mass and dark matter problems that does not invoke a new symmetry. Taken purely as a neutrino mass model, the new physics can be at the TeV scale. When dark matter is incorporated, however, only a singlet scalar can remain this light, though the dark matter can be tested in direct-detection experiments.} | } The observation of neutrino oscillations in solar, atmospheric and reactor experiments confirms that neutrinos are massive and that the Standard Model (SM) is incomplete. Another strong motivation for beyond-SM physics comes from astrophysical observations, which motivate a new gravitating particle species referred to as dark matter (DM). It is sensible to ask if these two problems could have a common solution. Models with radiative neutrino mass~\cite{Zee:1980ai} offer a promising direction for a unified solution to these problems (for a discussion of radiative models see e.g.~\cite{Angel:2012ug}). If the coupling to DM is related to the source of lepton number symmetry breaking, DM can propagate inside the loop diagram that generates neutrino mass, killing the proverbial two birds with one stone. An early proposal along these lines was put forward by Krauss, Nasri and Trodden (KNT)~\cite{Krauss:2002px} (for analysis see Refs.~\cite{Baltz:2002we,Cheung:2004xm,Ahriche:2013zwa,Ahriche:2014cda}). In this paper we investigate a three-loop model of neutrino mass that is related to the KNT model. The model differs in its field content but employs a three-loop diagram with the same topology. The use of distinct beyond-SM multiplets produces some key differences. Recall that the KNT model utilizes a discrete ($Z_2$) symmetry, which serves two purposes: It precludes tree-level neutrino mass, which would otherwise dominate the loop mass, and it gives a stable particle that is taken as the DM. Consequently, the KNT model gives a unified solution to the neutrino mass and DM problems. Different from the KNT model, the present model does not require a new symmetry to preclude tree-level neutrino mass, despite sharing the same loop-topology. It is therefore a viable model of radiative neutrino mass independent of any DM considerations. Interestingly, the most-general Lagrangian for the model possesses a softly-broken accidental $Z_2$ symmetry. In the limit where a single parameter vanishes, $% \lambda\rightarrow0$, this symmetry becomes exact and the model contains a stable DM candidate. As a result, the DM width goes like $\Gamma_{DM}\propto \lambda^2$ for nonzero $\lambda$, and one can always make this sufficiently small to obtain long-lived DM, or simply take $\lambda\rightarrow0$ for absolutely stable DM. Thus, DM is possible with or without the $Z_2$ symmetry. This gives a unified solution to the DM and neutrino mass problems that does not require a new symmetry. Importantly, the limit $\lambda\rightarrow0$ does not affect the predictions for neutrino mass. The $Z_2$ symmetry is essentially the same one found in the KNT model (and the related triplet model~\cite{Ahriche:2014cda}), though in those cases the most-general Lagrangian contains multiple symmetry breaking terms, including ones that give tree-level neutrino mass. We shall see that the phenomenology of the model depends on the region of parameter space considered. Taken purely as a model of neutrino mass, the new physics can be at the TeV scale and may be probed in collider experiments. When DM is incorporated one requires $M_{DM}\sim10$~TeV, putting some of the new multiplets beyond the reach of colliders. None the less, a singly-charged scalar that appears in the model can remain at the TeV scale, with or without the inclusion of DM. Even when DM is included, prospects for testing the model in direct-detection experiments are good. We note that one-loop models of neutrino mass that admit DM candidates but do not require a symmetry to exclude tree-level masses exist \cite% {Law:2013saa}, with one model further studied in Ref.~\cite{Brdar:2013iea}. Other works studying connections between neutrino mass and DM include Refs.~% \cite% {Ma:2006km,Kajiyama:2013zla,Kanemura:2011mw,Ho:2013hia,MarchRussell:2009aq}. For a review see \cite{BMV}. The layout of this paper is as follows. In Section~\ref{sec:model5} we describe the basic details of the model. Neutrino masses are calculated in Section~\ref{sec:nuetrino_mass5} and important flavor-changing constraints are discussed in Section~\ref{sec:constraints5}. We consider DM in Section~% \ref{sec:dark_matter5}, discussing the issue of longevity and the relic abundance. Our main numerical results and discussion are given in Section~% \ref{sec:results} and we comment on collider phenomenology in Section~\ref% {sec:collider}. We briefly describe interesting generalizations of our model in Section~\ref{sec:generalize_KNT}, and conclude in Section~\ref{sec:conc5}. | } We presented a three-loop model of neutrino mass whose most-general Lagrangian contains a softly-broken accidental $Z_{2}$ symmetry. In the limit that a single parameter vanishes, $\lambda \rightarrow 0$, the $Z_{2}$ symmetry becomes exact and the model contains a stable DM candidate. Even for nonzero $\lambda \ll 1$, however, the model can give a long-lived DM candidate. The model is related to the KNT model and its triplet variant, with the $Z_{2}$ symmetry being equivalent to the symmetry imposed in those models. In the present case, though, the symmetry is not needed to preclude tree-level neutrino mass, giving a viable model of neutrino mass irrespective of DM considerations. For sufficiently small $\lambda $, the model gives a unified solution to the DM and neutrino mass problems, with the novel feature of not requiring that a symmetry be imposed. We showed that neutrino mass can be generated and that important flavor-changing constraints can be satisfied. Taken purely as a neutrino mass model, the new physics can be $\mathcal{O}(\mathrm{TeV})$, allowing the model to be explored at colliders. However, when DM is included the quintuplet fields must be heavy, with $M_{F}\sim 10$~TeV, so that only the singlet scalar $S$ can be within reach of colliders. None the less, the DM can be tested in future direct-detection experiments. We also noted interesting generalizations of this model in which DM stability results from an exact accidental symmetry, the simplest of which uses septuplet $SU(2)$ fields instead of quintuplets. | 14 | 4 | 1404.5917 |
1404 | 1404.2476_arXiv.txt | We present updated chemical evolution models of two dwarf spheroidal galaxies (Sculptor and Carina) and the first detailed chemical evolution models of two ultra-faint dwarfs (Hercules and Bo\"otes I). Our results suggest that the dwarf spheroidals evolve with a low efficiency of star formation, confirming previous results, and the ultra-faint dwarfs with an even lower one. Under these assumptions, we can reproduce the stellar metallicity distribution function, the $[\alpha/Fe]$ vs. $[Fe/H]$ abundance patterns and the total stellar and gas masses observed at the present time in these objects. In particular, for the ultra-faint dwarfs we assume a strong initial burst of star formation, with the mass of the system being already in place at early times. On the other hand, for the classical dwarf spheroidals the agreement with the data is found by assuming the star formation histories suggested by the Color-Magnitude diagrams and a longer time-scale of formation via gas infall. We find that all these galaxies should experience galactic winds, starting in all cases before $1$ Gyr from the beginning of their evolution. From comparison with Galaxy data, we conclude that it is unlikely that the ultra-faint dwarfs have been the building blocks of the whole Galactic halo, although more data are necessary before drawing firm conclusions. | Orbiting around the Milky Way, there is a large number of satellite galaxies, most of which have so low average surface brightnesses and small effective radii that their detection was very difficult in the past: from 1937 up to 1994, only nine of them were discovered and that number remained unchanged until 2005. They are the so-called \textit{classical dwarf spheroidal galaxies} (dSphs), which are among the least luminous and most dark matter (DM) dominated galaxies which are observed today in the Universe. Dwarf spheroidal galaxies are classified as early-type since they are observed to possess very low gas mass at the present time and their stars are very iron-poor when compared to the Sun (see \citealt{tolstoy2009} and \citealt{koch2009} for an exhaustive review). \par Color-magnitude diagram (CMD) fitting analysis revealed star formation rate (SFR) in dSphs to have been either continuous for a long time or occurring in bursts. All dSph galaxies host an underlying very old stellar population with age $\ga10$ Gyr (e.g. \citealt{grebel1997}), and some of them are dominated by an intermediate-age stellar population with age in the range $4-8$ Gyr \citep{dall'ora2003}. Very few dSphs have been observed to host younger stars, which populate the so-called ``blue plume'' in the CMD, sign of a relatively recent star formation activity, which occurred up to $\sim2-3$ Gyr ago \citep{monelli2003}. \par All such features led cosmologists to hypothesize dSphs to be the evolved small progenitor systems which merged in the past to form the actual large structures in the Universe as the stellar halo of the Milky Way, in the framework of the $\Lambda$CDM standard cosmological model \citep{helmi1999,bullock2001,harding2001,bullock2005}. However, successive deeper investigations revealed them not to possess all the right properties to be the aforementioned hypothetical survived progenitors of the Galactic halo (see \citealt{helmi2006} and \citealt{catelan2009} and references therein). \par The Sloan Digital Sky Survey (SDSS) allowed in the past few years (from 2005 up to the present time) to discover a large number of new dwarf galaxies orbiting around the Milky Way with physical properties very similar to dSph galaxies but average surface brightnesses and effective radii even much smaller (see, e.g., \citealt{belokurov2007,belokurov2010}): for such reasons, they have been named as \textit{ultra-faint dwarf spheroidal galaxies} (UfDs). That is a mere naming convention, without any real physical motivation, since UfDs extend to fainter magnitudes and lower masses the same observed physical properties of dSphs. In fact UfD galaxies do not contain any gas at the present time and their stars are on average very iron-poor, with age $\ga10-12$ Gyr \citep{okamoto2012,brown2013}. So UfDs do not show any recent star formation activity. Such stellar systems soon aroused great interest in the scientific community, either for their extreme observed characteristics, or because such characteristics might shed light on the conditions of the Universe in the first billion years of its evolution (see \citealt{belokurov2013} for a detailed discussion). The UfD environment constitutes the best candidate for verifying whether a first population of very massive and extremely metal-poor stars (the so-called Population III) might have existed or not. Such stars, at their death, should have enriched the interstellar medium (ISM) with some metals and therefore they might have left a chemical signature in the stars which were born immediately after, as some of the UfD stars (\citealt{ferrara2012}). As \citet{salvadori2012} had envisaged, this hypothesis might be supported by the observation of carbon-enhanced metal-poor (CEMP) stars in some UfD galaxies \citep{norris2010a,gilmore2013}, which might be directly linked to the CEMP-Damped Ly-$\alpha$ systems observed in the spectra of quasars at high redshift \citep{cooke2011a,cooke2011b}. In this scenario, the latter might be the high-redshift unevolved counterparts of some of the UfD galaxies. % \par Aim of this work is to study how dSph and UfD galaxies have evolved, by reconstructing - going back in time - the chemical enrichment history of their ISM, starting from the chemical abundances derived today in the atmospheres of their stars. We will adopt a detailed chemical evolution model which is able to follow the evolution of several chemical species (H, He, C, N, O, $\alpha$-elements, Fe-peak elements, s- and r- process elements). This model is based on that presented by \citet{lanfranchi2004} and then used also in the works of \citet{lanfranchi2006a}, \citet{lanfranchi2006b}, \citet{lanfranchi2007}, \citet{lanfranchi2008}, \citet{cescutti2008}, and \citet{lanfranchi2010}. \par \citet{lanfranchi2004} modeled the chemical evolution of six dSphs of the Local Group including Sextans, Sculptor, Sagittarius, Draco, Ursa Minor and Carina. Their main conclusions were that dSphs suffered from very low star formation efficiency, which caused the iron pollution from Type Ia SNe to become important when the $[Fe/H]$ of galaxy ISM was still very low. In this manner, and by assuming also intense galactic winds, they were able to explain the observed decrease in the trends of $[\alpha/Fe]$ vs. $[Fe/H]$. Galactic winds prevent the galaxy to form stars soon after the onset of the outflow and this leads the stellar metallicity distribution function (MDF) in dSphs to be peaked towards low $[Fe/H]$ abundances, almost $1.5$ dex below the one of Milky Way disc in the solar neighborhood, in agreement with observations. \par As interesting papers appeared recently, \citet{romano2013} modeled the chemical evolution of Sculptor by means of a new approach in a full cosmological framework, whereas \citet{koch2012,koch2013} present a first chemical evolution model of the Hercules UfD, based on the same numerical code we use in this work. \par Here we focus on the chemical evolution of Sculptor and Carina, for which newer data are available, but especially we model the evolution of UfDs: Hercules and Bo\"otes I. In Section \ref{section2} we describe the adopted chemical evolution model. In Section \ref{section3} the data sample is presented and in Section \ref{section4} the results are shown. Finally, in Section \ref{section5} some conclusions are drawn. | \label{section5} \begin{figure} \includegraphics[width=9cm]{MDFBootesI.eps} \caption{ In this Figure, we show the comparison between the observed stellar MDF of the Bo\"otes I UfD (data from \citealt{lai2011}) and the predictions of our models with $\omega=10$ (normal wind) and $M_{inf}=2.5\cdot10^{7}\;M_{\odot}$. Again, as in the case of the Hercules UfD, the dataset is built up on a sample of only $41$ stars, highly concentrated in a very tight $[Fe/H]$ range. We are not able to reproduce the height of the observed-MDF peak. The model which best reproduces the $[Fe/H]_{peak}$ abundance of the observed MDF turns out to have $\nu=0.01\;Gyr^{-1}$ and $\omega=10$. } \label{mdfbootesi} \end{figure} \subsubsection{Summary on dSph chemical evolution} In this paper, we have assumed that dSph galaxies form by accretion of an \textsl{infall mass} of $M_{inf}=1.0\cdot10^{8}\;M_{\odot}$ with primordial chemical composition. The infall rate obeys to a decaying exponential law with an \textsl{infall time- scale} $\tau_{inf}=0.5$ Gyr. The mass content and the core radius of the DM halo have been taken from the observations. In particular, here we modeled Sculptor and Carina and our results can be summarized as follows. \begin{enumerate} \item Only by assuming low star formation efficiencies ($\nu=0.05-0.5\;Gyr^{-1}$) relative to the Milky Way ($\nu\sim1\;Gyr^{-1}$ in the solar vicinity, \citealt{chiappini1997}), we have been able to explain the decline in the $[\alpha/Fe]$ abundance ratios observed at very low $[Fe/H]$. In fact, the lower the $\nu$ parameter, the lower is the amount of iron produced by Type II SNe; this causes the $[Fe/H]$ of the ISM, at which Type Ia SNe become predominant in the iron pollution, to be lower. This precisely determines the decrease in the $[\alpha/Fe]$ at very low $[Fe/H]$. This is due to the fact that most of $\alpha$-elements originates in Type II SNe whereas most of Fe originates in Type Ia SNe exploding on a large range of times (time-delay model). \item Low star formation efficiencies increase the star formation time-scales, giving rise to stellar MDFs peaked towards very low $[Fe/H]$, in very good agreement with the observations indicating that dSphs are very metal-poor stellar systems. \item Galactic winds - driven by SN explosions - play a relevant role in the dSph chemical evolution. We adopted for dSphs a \textsl{normal} wind, i.e. a wind with an efficiency equal for all the chemical elements. The net effect of the galactic wind is to diminish further the SFR and cause the $[\alpha/Fe]$ to follow a steeper decline as $[Fe/H]$ increases. Thanks to the strong outflow rates, our models predict very low final total gas masses, according to observations. \item Only by adopting star formation episodes occurring far beyond the reionization epoch, our models were able to build up final total stellar masses of the same order of magnitude as the observed ones ($M_{star,obs}\sim10^{6}\;M_{\odot}$), and they could also reproduce the other observed features of dSph galaxies. Our assumptions were based on the results of the CMD-fitting analysis, which have been able, in the past few years, to derive the SFH of many dwarf galaxies of the Local Group. \item We adopted the \citet{salpeter1955} IMF for all the models. In a recent paper, \citet{mcwilliam2013} suggested that to explain the abundance data in Sagittarius an IMF with a lower fraction of massive stars than a Salpeter-like IMF should be preferred. However, by testing an IMF with a steeper slope in the massive star range, we found a neglibible difference in our results. \item Our best models are in good agreement with the previous works \citep{lanfranchi2004,lanfranchi2006b} and confirm their goodness. Our best model for Sculptor requires $\nu=0.05\;Gyr^{-1}$ and $\omega=10$, whereas our best model for Carina requires $\nu=0.2\;Gyr^{-1}$ and $\omega=10$. \end{enumerate} \subsubsection{Summary on UfD chemical evolution} We modeled Hercules and Bo\"otes I, by adopting the same numerical code of dSphs but with different characteristic input parameters. In what follows, we summarize the main features of our UfD chemical evolution models: \begin{enumerate} \item Since UfDs are known today to be the faintest and most DM dominated galaxies, we adopted \textsl{infall masses} $M_{inf}=(1.0-5.0)\cdot10^{7}\;M_{\odot}$, which are lower than the ones assumed for dSphs and supported by observations. Such initial reservoir of gas, with primordial chemical composition, was accreted in the galaxy DM halo on a very short typical time-scale ($\tau_{inf}=0.005$ Gyr). \item Our best model for Hercules requires $\nu=0.003\;Gyr^{-1}$, $\omega=10$, $M_{inf}=1.0\cdot10^{7}\;M_{\odot}$ and $\tau_{inf}=0.005$ Gyr, whereas our best model for Bo\"otes I requires $\nu=0.01\;Gyr^{-1}$, $\omega=10$, $M_{inf}=2.5\cdot10^{7}\;M_{\odot}$ and $\tau_{inf}=0.005$ Gyr. \item The $[\alpha/Fe]$ abundance ratios are observed to steeply decrease at very low $[Fe/H]$. This is clearly a signature of very low star formation efficiencies ($\nu=0.001-0.01\;Gyr^{-1}$), even lower than for the dSph ones ($\nu\approx0.05-0.5\;Gyr^{-1}$). In fact, Type Ia SNe start to dominate in the iron pollution of the ISM when the $[Fe/H]$ of the ISM is still very low. This result is in agreement with the previous studies of UfD galaxies, such as \citet{salvadori2009} \item The very low adopted star formation efficiencies cause the stellar MDFs to be peaked at very low $[Fe/H]$, in very good agreement with observations. \item From the CMD-fitting analysis, as well as from the study of the pulsation and metallicity properties of their variable stars, UfDs host very old stellar populations, with ages $>10-12$ Gyr. So, we assumed them to have undergone star formation only in the first gigayears of their chemical evolution history. This fact, coupled with the very low star formation efficiencies, causes the building up of very low final total stellar masses $M_{\star,fin}\sim10^{4}-10^{5}\;M_{\odot}$, which are much lower than the observed dSph ones, and in agreement with observational values. \item The actual total gas masses in UfDs are negligible or even undetected. This is a clear evidence of intense galactic winds, which are efficient in the gas removal from the galaxy potential well and started very soon in the galaxy evolution. We tested models with \textsl{normal wind}, $\alpha$-enhanced \textsl{differential wind}, and iron-enhanced \textsl{differential wind}. All such models agree in predicting negligible final total gas masses but each of them has a different effect in the $[\alpha/Fe]$ vs. $[Fe/H]$ diagram. \item Both \textsl{normal} and $\alpha$-enhanced galactic winds predict a trend of the $[\alpha/Fe]$ vs. $[Fe/H]$ diagram which well agrees with observations. On the other hand, an iron-enhanced \textsl{differential wind} predicts the $[\alpha/Fe]$ to increase as $[Fe/H]$ grows once the galactic wind has started, at variance with observations. We suggest the galactic wind to be normal with an efficiency $\omega=10$, which is the same value adopted in this work for reproducing the main properties of dSph galaxies. \item Our chemical evolution models have been able to reproduce, at the same time and reasonably well, all the observed features of the two UfD galaxies studied, such as the abundance ratio patterns of the $\alpha$-elements, the stellar MDF, and the total stellar and gas masses at the present time. From the main characteristics of our chemical evolution models and from the observed trend of the UfD chemical abundances, we suggest that the hypothesis that UfDs would have been the survived ``building blocks'' of the Milky Way halo is unlikely, since the two seem to have undergone very different galactic chemical enrichment histories. In particular, the Galactic halo abundance pattern suggests more vigorous star formation and galactic wind, together with a longer time-scale of gas accretion (see \citealt{brusadin2013}). However, more data on UfDs are necessary before drawing firm conclusions. \end{enumerate} | 14 | 4 | 1404.2476 |
1404 | 1404.6313_arXiv.txt | Supernovae of type IIP are marked by the long plateau seen in their optical light curves. The plateau is believed to be the result of a recombination wave that propagates through the outflowing massive hydrogen envelope. Here, we analytically investigate the transition from a fully ionized envelope to a partially recombined one and its effects on the SN light curve. The motivation is to establish the underlying processes which dominate the evolution at late times when recombination takes place in the envelope, yet early enough so that $^{56}$Ni decay is a negligible source of energy. We assume a simple, yet adequate, hydrodynamic profile of the envelope and study the mechanisms which dominate the energy emission and the observed temperature. We consider the diffusion of photons through the envelope while analyzing the ionization fraction and the coupling between radiation and gas. We find that once recombination starts, the observed temperature decreases slowly in time. However, in a typical red supergiant (RSG) explosion, the recombination wave does not affect the bolometric luminosity immediately. Only at later times, the cooling wave may reach layers that are deep enough to affect the luminosity. We find that the plateau is not a generic result of a recombination process in expanding gas. Instead it depends on the density profile of the parts of the envelope which undergo recombination. Our results are useful to investigate the light curves of RSG explosions. We show the resulting light curves of two examples of RSG explosions according to our model and discuss their compatibility with observations. In addition, we improve the analytical relations between the plateau luminosity and plateau duration to the properties of the pre-explosion progenitor \cite[]{arnett80,popov93}. | Type IIP supernova (SN) is the most common supernova type \citep{Li11}. It is marked by H lines in its spectra and by a long, $\approx$100 days optical plateau that starts between a few days to a few weeks after the explosion. The progenitors of type IIp SNe are red supergiants (RSGs), which exhibit an extended H envelope \cite[]{smartt04,van_dyk03,maund09}. The initial temperature of the envelope as it starts to expand, after the shock crossing, is high ($> 10^5$ K), but it drops with time due to adiabatic loses. The observed temperature drops rapidly until it reaches the H recombination temperature, $\approx$7000 K, where it remains rather constant during the entire plateau phase. For that reason it is believed that recombination is the source of the long lasting optical plateau. The initial conditions for the beginning of the recombination phase are set by the radiation dominated shock that crosses the envelope and explodes the star. The shock accelerates in the decreasing density gradient near the edge of the stellar envelope and determines the velocity and internal energy profile of the envelope. Once the shock reaches to a point where the distance to the edge of the star is comparable to the shock's width, it ``breaks out''. This is the first electro-magnetic signal of a SN explosion \cite[]{colgate74,folk78,klein_chevalier78,imshennik_etal81}. The envelope continues to accelerate while photons continuously diffuse out through it \cite[]{matzner&mckee}. The acceleration ends before a considerable expansion takes place and at the end of this phase there is a hot, ionized, radiation dominated envelope in a homologous expansion. The internal regions are dense with large optical depth and they lose energy adiabatically. The external regions have a lower optical depth and photons can diffuse through them over a dynamical time. The expansion reduces the envelope optical depth, enabling photons to diffuse from deeper regions in the envelope. At breakout, the temperature of the external regions from where radiation can diffuse to the observer is $\sim 30$ eV \cite[]{ns10}. It drops over a week or two until it reaches the recombination temperature. Until that time the entire envelope is ionized and its opacity is Thomson opacity. Once recombination starts in the outer layers it leads to a sharp drop in the opacity of these layers. The fast escape of radiation via the low opacity recombined regions causes a fast drop in the temperature also in the ionized regions which lies just behind the recombined layer. This cooling leads to farther recombination which in turn leads to drop in the opacity and so on. The resulting picture is a recombination wave, followed by cooling, which propagates inward (in Lagrangian sense) through the envelope. The propagation of this wave depends on the velocity and on the internal energy profiles of the envelope and obtaining an analytic understanding of this process is the goal of this paper. In this work we derive an analytical model to study the effect of recombination on SNe light curves. We examine the problem of a homologous expanding envelope which cools adiabatically, together with energy transport by diffusion of photons. We assume that $^{56}$Ni radioactive decay is a negligible source of energy. This condition holds for a typical explosion of an RSG, in which the radioactive decay luminosity is low compared to the release of the thermal energy deposited by the shock (see discussion in appendix \ref{app:Ni}). In addition, we neglect the effect of radioactive decay on the opacity, due to non-thermal photoionization. Our model is based on recent work by~\citet[]{ns10} (NS10 hereafter) where early light curves, before recombination has a significant role, were derived. As a result, we can draw the evolution of the light curves from the initial pulse (shock breakout) up to the time when most of the envelope is recombined. We find that it is essential to take into account the coupling between matter and radiation since in the recombined gas the opacity can vary by orders of magnitude while the temperature changes only by a factor of two. For that reason it is essential to find the exact temperature in this layer and thus the opacity drop. Here, the radiation-gas coupling plays the main role since a drop in the temperature reduces the coupling (along with the opacity), while in order for the temperature to drop a minimal coupling is required. This feedback of the coupling on the temperature is what sets the exact temperature and opacity drop in the recombined layer. By solving self consistently for the radiation-gas coupling and the opacity drop, within the expanding gas velocity and internal energy profiles, we find a solution for the propagation of the recombination wave and for the resulting observed radiation. The propagation of a recombination wave in SNe envelope was studied analytically in previous works \citep{grassberg71,grass_nad76,popov93,rabinak11}. However, these works used more limited assumptions compared to our model, such as full coupling between gas and radiation. In addition, some of these models were derived for physical conditions which are not applicable for SNe envelope, such as homogeneous envelope \cite[]{popov93}. A comparison to these previous works is discussed in section \ref{sec:comparison}. We also compare qualitatively between our results and the results from recent numerical works, such as \cite{utrobin07,woosley&kasen09} and \cite{bersten11}, which examined the light curves of type IIPs and discussed in detail the properties of the recombination wave in the envelope. The paper is organized as follows. In section \ref{sec:shells} we introduce the hydrodynamical profile of the envelope we use in our model. In section \ref{sec:NS} we discuss the evolution at early stages, up to the onset of recombination, according to NS10. Then, in section \ref{sec:Receffect} we describe how recombination, through the decrease in the ionization fraction, affects the diffusion of energy and production of new photons in the envelope. In section \ref{sec:LC} we introduce the solution to these equations and calculate the luminosity and the observed temperature for a given hydrodynamical profile of the envelope. We treat separately two different cases. The first is the realistic case where the ionization fraction is parametrized as a continuous function of the temperature (\S\ref{sec:mrec}). The second is the academic, yet enlightening, case where opacity is parametrized by a step function of the temperature (appendix \ref{app:const}). In section \ref{sec:application} we apply the results of \S\ref{sec:mrec} and appendix \ref{app:const} to an analytic description of a typical RSG expanding envelope. In addition, we apply the model to profiles given numerically from a simulation of RSG explosion and derive the corresponding light curves semi-analytically. In section \ref{sec:comparison} we compare results from previous analytical and numerical works to our results. Finally in \ref{sec:summary} we summarize our findings. | \label{sec:summary} We study analytically the effect of recombination on the evolution of SNe light curves. The process of recombination reduces the number of free electrons, reducing both the opacity and the radiation-gas coupling (via the ability of the gas to absorb and emit photons). The balance between the two, opacity and coupling, is what determines the radiation temperature and ionization level in the recombined gas. Once recombination starts a wave of recombination, which is followed by cooling, starts to propagate inward through the envelope. We develop a model which describes the properties of the relevant shells of the envelope- the shells which dominates the bolometric luminosity and the observed temperature. The concept of the model is to consider three characteristic shells which dominate the light curves: (1) The luminosity shell, which is the source of the observed luminosity. This shell determines the radiative flux through all the shells external to it. (2) The color shell which is the outermost shell in which photons can be thermalized over the diffusion time. This shell dictates the color of the observed temperature. (3) The recombination shell which is the shell where recombination takes place. It is the outermost shell which is fully ionized on its inner boundary and it is highly recombined on its outer boundary. We proved that this shell coincides with the color shell once recombination starts and at late times it also coincides with the luminosity shell. The main advantage of our model over previous analytical studies of the process is that it takes into account the coupling between the radiation and the gas, which is found to be crucial in finding the ionization level at the point where the observed temperature is determined. It can, therefore, provide a reliable estimate of the evolution of the observed temperature and of the bolometric luminosity. Our model provides new insight into the recombination process and to the relations between the observables and the progenitor and explosion properties. We find that when recombination starts it first affects only the temperature, which becomes almost constant with time. The bolometric luminosity, at first, continues to drop very slowly without being affected by recombination. Only later the recombination wave reaches the luminosity shell. The temperature from that point evolves even more slowly, while the bolometric luminosity stops dropping or even rises slowly. The effect of this transition is rather mild in the optical but it should cause significant flattening of the UV light. Whether the recombination wave reaches the luminosity shell before the end of the plateau depends on the progenitor properties (e.g., it is more likely to take place in less extended progenitors). We farther find that the radiation-gas coupling limit the drop of the ionization fraction in the recombination shell to 0.01-0.1. This in turn is the origin of the very slow drop in the observed temperature, which is $T_{\rec}=6,500-7,000$ K when recombination starts and $5,000-6,000$ K when the plateau ends. Another interesting result of our analysis is that the observed plateau is not a generic property of the propagation of a recombination wave in expanding ionized gas. The generic property is the much slower evolution of the observed temperature once recombination starts (due to the strong feedback of the temperature drop on the coupling). This fixes the observed temperature around the $R$ and $I$ bands. However, the slow evolution of the bolometric luminosity is a result of the typical hydrodynamical structure of exploding stellar envelopes. Different structures can result in a much faster decay or rise of the bolometric luminosity. Slightly different stellar structures is probably the main source of the various behaviors seen in type IIp SNe. The derivation of a fully analytical solution requires the following approximations- (1) power-law profile for the density and adiabatic cooling at late times; (2) neglecting the density dependence in the ionization fraction; (3) power-law relation between the ionization fraction and the temperature; (4) neglecting radioactive energy from $^{56}$Ni; (5) assuming free-free as the most efficient process for photon production. However, the basic ideas of our model- (1) separation of the envelope into successive shells; (2) finding the recombination shell by the properties of its boundaries, can be used for more general assumptions than (1)-(6) above, as is described in appendix \ref{App_num}. The simple equations introduced in \eqref{eq:num_equations} can be extended even further by changing the function $\eta$ such that it includes bound-free process or by adding energy from radioactive decay. Hence, our model serve as a simple tool to examine the effect of some basic mechanisms on the evolution of SNe light curves. | 14 | 4 | 1404.6313 |
1404 | 1404.1019_arXiv.txt | The ionosphere is the part of the atmosphere that contains ionized gases. The primary process is photoionization of thermospheric gases by the Sun's extreme ultraviolet radiation, and X-rays. Both of these radiations are $\sim 100$ times stronger at solar maximum than at solar minimum. Secondary processes include ionization by photoelectrons and scattered or reemitted radiation. The ionosphere, at all latitudes, has a tendency to separate in different regions, despite the fact that different processes dominate in different latitudinal domains. The regions: D, E, and F with two layers F$_{1}$ and F$_{2}$ are distinct only in the daytime ionosphere at mid-latitudes. The different regions are generally characterized by density maximum at a certain altitude and density decreases with altitudes on both sides of the maximum. The lowest region of the ionosphere the D-region, $50 \leq h \leq 90$ km, is formed primarily by the action of solar Lyman-alpha radiation (121.6 nm) on nitric oxide. At night, the ionospheric plasma densities decreases most rapidly at the lowest altitudes and at 90 km altitude it decreases from $10^{11}$ to $10^{8}$ m$^{-3}$ (Schunk and Nagy, 2000). Very Low Frequency (VLF, 3 - 30 kHz), and Low Frequency (LF, 30 - 300 kHz) radio signals propagate inside the waveguide formed by the lower ionosphere and the Earth's surface (Wait and Spies,1964; Mitra, 1974). A range of dynamic phenomena occurs in D-region, and some of them are: \emph{diurnal effect (day/night), a seasonal effect (summer/winter), correlation with solar activity (sunspot level and solar flares), effects of lightning induced electron precipitation and red sprites}. All these phenomena are followed by changes in electron density of lower ionosphere, which affects the subionospheric VLF/LF propagation as an anomaly in amplitude and/or phase. During solar flare X-ray irradiances rapidly increase and X-rays with wavelengths below 1 nm are able to penetrate to the D-region, causing ionization of the neutral constituents, predominantly nitrogen and oxygen (Mitra, 1974). | The purpose of this work was to examine perturbations of amplitude and phase on VLF/LF radio signals propagating over great circle path with distances smaller than 1000 km, so called short path. The receiver at Belgrade station continuously monitor the amplitude and phase of coherent and subionospherically propagating radio signals operated in Sicily, NSC at 45.90, kHz and in Isola di Tavolara ICV at 20.27 kHz, with great circle distances of 953 km and 976 km, respectively. Geographically and in according to conductivity properties these two short paths are vary similar to each other. The main difference is in the transmitter frequency, and for that reason was done detailed study around 200 events of SID and their influence to amplitude and phase on ICV/20.27 kHz and NSC/45.90 kHz signals (see Fig.4). Measured data were obtained during period of six years covering minimum and maximum of solar activity. The first our result is that the amplitude of ICV/20.37 kHz signal is more sensitive then phase on the disturbances caused by X-ray solar flare. In all events increasing X-ray irradiance induced increase of amplitude and phase on signal. It was shown that difference between perturbed and normal amplitude changed from $\Delta A$ = 1dB up to $\Delta A$ = 10 dB. It is presented on Figure 4a, showing monotonous increase of $\Delta A$ with logarithm of the max. solar X-ray irradiance ($\Delta A$ is nearly proportional to the logarithm of $I_{x}$). Analyzing propagation characteristics of NSC/45.90 kHz signal and perturbed amplitude and phase caused by solar X-ray flare we are able to make following conclusions. Perturbations of phase on NSC/45.90 kHz signal are very remarkable. Minor solar flare, as B8.8 class, induced increase of phase, $\Delta \Phi$ $\sim$ $30^{0}$. Shape of perturbed phase is very similar to time variation of X-ray irradiance. During occurrence of solar flares, classified as minor and small flare up to C3 class, amplitude on signal NSC/45.90 kHz does not have significant perturbations. Solar flare in range from C3 to M3 classes induced increase of amplitude on signal. Moderate solar flares classified larger then M3 class induced oscillation of amplitude around base level before beginning of flare (Figure 5b). The stability and reproducibility of the received amplitude and phase on NSC/45.90 kHz signal were found in many examined events recorded during six years period. This is illustrated on Fig 5a and 5b. This reproducibility gives the possibility that only in looking measured data we are able to define class of solar X-ray flare which induced that perturbation. As the presence of electrons in the ionospheric D-region strongly affects the VLF/LF radio wave propagation we present a method for determination of the electron density. Using measured $\Delta A$ and $\Delta \Phi$ as very important quantities and LWPC program we calculated electron density in the D-region. Also it is possible to calculate electron density profile as a function of time, to follow increase during time interval of peak irradiance, and to study decrease of electron density during recovery period. It can be noticed that the time distribution of the electron density follows the time variation pattern of the registered solar flux on GOES-15 satellite. In the case we analyzed, the electron concentration (at reference height) has values within the order of magnitude $10^{8}$ - $10^{9}$ m$^{-3}$ during this flare (see Tab.2). Finally, we can see (Fig.7) that the considered solar flare, as expected, causes larger increases in electron concentration at higher altitudes. | 14 | 4 | 1404.1019 |
|
1404 | 1404.2936_arXiv.txt | { We report the results of a statistical analysis performed with the four foreground-cleaned Planck maps by means of a suitably defined {\it local-variance} estimator. Our analysis shows a clear dipolar structure in Planck's {\it variance map} pointing in the direction $(l,b) \,\simeq\, (220^{\circ},-32^{\circ})$, thus consistent with the North-South asymmetry phenomenon. Surprisingly, and contrary to previous findings, removing the CMB quadrupole and octopole makes the asymmetry stronger. Our results show a maximal statistical significance, of $98.1\%$ CL, in the scales ranging from $\ell=4$ to $\ell=500$. Additionally, through exhaustive analyses of the four foreground-cleaned and individual frequency Planck maps, we find unlikely that residual foregrounds could be causing this dipole variance asymmetry. Moreover, we find that the dipole gets lower amplitudes for larger masks, evidencing that most of the contribution to the variance dipole comes from a region near the galactic plane. Finally, our results are robust against different foreground cleaning procedures, different Planck masks, pixelization parameters, and the addition of inhomogeneous real noise.} \begin{document} | \label{introduction} The temperature fluctuations of the Cosmic Microwave Background radiation (CMB), recently released by the {\em Planck collaboration}~\cite{PLA-I}, confirmed with outstanding precision the concordance cosmological model, $\Lambda$CDM~\cite{PLA-XV,PLA-XVI,WMAP9}. Such exquisite set of cosmological information allows us to test two fundamental properties of the universe expected after the standard inflationary phase~\cite{Bartolo04,Komatsu1,Bassett2006,Linde2008}, namely that the CMB field is, at large-angles, nearly Gaussian and statistically isotropic (see, e.g.,~\cite{Abramo10,PLA-XXIII} and refs. therein). Previous studies using WMAP data indicate significant departure from either gaussianity or statistical isotropy at the largest angular scales -- an unexpected result in the $\Lambda$CDM model~\cite{Abramo06,Abramo09,Aghanim:2013suk,Pereira09,Bernui06,Bernui07,Bernui2008b,Bernui2009a,Bielewicz04,Copi04a,Copi04b, Copi06,Copi07,Copi10,Copi13a,Copi13b,Cruz05, Eriksen04,Eriksen07,Gordon,Gruppuso10,Gruppuso11,Mandolesi, Hansen04a,Hansen04b,Huterer,Jaffe,Kahniashvili,Koivisto,Land05,Land07,OCTZ,TOCH,Paci,Rath,% Samal08,Samal09,Vielva04,Vielva06,Vielva07,Urban,Zhao,% Fabre,Hansen12,Kashino,Rath13,Rassat14}, though possibly disputable \cite{WMAP7}. These phenomena, also called {\it anomalies}, have been now confirmed with similar high confidence levels, $\sim 3 \sigma$, by the {\em Planck collaboration} with CMB foreground-cleaned maps~\cite{PLA-XXIII}. On the other side, only small magnitude Gaussian deviations from primordial origin have been detected in Planck data~\cite{PLA-XXII,PLA-XXIV}. However, there are more potential sources of non-Gaussianity (NG) in the CMB data than just primordial NG~\cite{Komatsu2,PNG-Liguori,Chen-2010,WMAP-7yr-Jarosik,% Su-Yadav,Komatsu03}. These include galactic foregrounds remnants and secondary anisotropies coming from processes after the last scattering surface~\cite{WMAP-7yr-Gold,PLA-XXIV,Munshi,Aghanim,Novaes12,% Chiang03,Naselsky,Delabrouille08,Novaes,Saha,Pietrobon09,Pietrobon10a,% Pietrobon10b,Pratten,Smith,Vielva09,Zhao12}. In particular, Gaussian analyses for large angular scales are delicate because galactic foregrounds contaminations are not completely understood and, as a consequence, galactic cut-sky masks are still necessary in CMB data analyses~\cite{PLA-XXIV}. Monteser\'{\i}n et al. (2008)~\cite{Monteserin08} reported an anomalously low variance distribution in WMAP3 maps at $98.7\%$~CL. Cruz et al. (2011)\cite{Cruz11} confirmed this result in WMAP5 and WMAP7 data, also pointing that some regions near the galactic plane present an anomalously high variance ($95.6\%$ CL) in the south ecliptic hemisphere. Their analyses, using various galactic cut-sky masks, suggest that foreground residuals could explain the results, besides a possible connection with the CMB quadrupole-octopole alignment was investigated. Gruppuso et al. (2013) \cite{Gruppuso13}, using a different estimator, also found a low variance at large scales in WMAP9 data, basically in agreement with~\cite{Monteserin08,Cruz11}. More recently, the {\em Planck collaboration}~\cite{PLA-XXIII} and Akrami et al. (2014)~\cite{Akrami} studied the local variance in hemispheres and disks finding again an anomalous high variance in the south ecliptic hemisphere. In recent works~\cite{BR09,BR10,BR12} one of us have proposed two large-angle NG estimators based on skewness and kurtosis momenta performed on spherical caps on the CMB sphere. We found that this directional mapping approach is suitable when a cut-sky mask has to be used because it minimizes the effect of incomplete data in the CMB sky. These indicators provide a directional map of local NG due to its possible non-uniform distribution in the CMB maps, also giving information about the angular scale dependence of such contributions. Results obtained in previous analyses~\cite{BR09,BR10} using WMAP maps suggest that the NG captured there is not of primordial origin, although it might have a primordial component. The aim of the present work is to conduct an analysis of the local variance in Planck foreground-cleaned maps, using a prescription similar to that of Refs.~\cite{BR09,BR10,BR12}. For this we implement a simple estimator of statistical variance, applying it to patches of the CMB sky. The information from all the patches is then used to produce an associated {\em Variance}-map, or simply $V\!-$map, which contains the signatures of the analysed CMB map. Our analyses investigate the possibility that foreground remnants in the galactic region could be the source of departures from Gaussianity and statistical isotropy, by considering several cut-sky Planck masks and three frequency band Planck maps, in addition to the four foreground-cleaned maps. To calculate the confidence level of our results we shall compare properties of these $V\!-$maps from Planck data with $V\!-$maps from simulated Monte Carlo (MC) CMB maps. These maps are obtained as Gaussian and statistically isotropic realisations from a seed angular power spectrum corresponding to the $\Lambda$CDM concordance model. Accordingly, the masking procedure applied to Planck CMB data is also applied to the MC maps. In section~\ref{pla-maps} we briefly review the main features of the four foreground-cleaned {\em Planck} maps and the masks to be used in the analyses. In section~\ref{method} we describe our variance estimator and explain the methodology to study the statistical Gaussian and isotropy attributes of Planck maps. The procedure delineated in this section will be used, in section~\ref{results}, to investigate directional large-angle deviations from the standard statistical scenario of the Planck data as compared with simulated maps. Our analysis includes realistic features of the Planck data, like their inhomogeneous noise maps and galactic cut-sky masks. Finally, in section~\ref{conclusion}, we summarize our main results, present our conclusions and final remarks. | \label{conclusion} The Gaussian and statistically isotropic scenario, on which the $\Lambda$CDM concordance model is based, can be rigorously tested with precise CMB data from the four foreground-cleaned Planck maps. Although questions regarding the statistical homogeneity of the universe's large-scale structure wait for future large and deep surveys~\cite{JPAS}, other stimulating questions can be addressed with the highly precise CMB data from the Planck satellite. Using a directional variance estimator, based on the {\em variance} statistical momentum, we performed a statistical analyses of the four foreground-cleaned Planck maps in several angular-scales intervals. In all the intervals investigated our results reveal a net dipolar distribution. In particular, in the angular scales $\ell \in[4,40]$ and $\ell \in[41,500]$ the significance is moderate, $\sim 2 \sigma$. Moreover, for the multipoles range $\ell \in[4,500]$, the result is highly significant $\sim 2.4 \sigma$ (see Table~\ref{table3}), with the variance dipole pointing in the direction $(l, b) \,\simeq\, (220^{\circ},-32^{\circ})$, close to the direction of the NS-asymmetry phenomenon. Additionally, we found that the Planck's variance dipole magnitude gets lower values for larger sky-cut masks, independent of the map analysed. This fact is coherent with the result that the variance dipole direction, for all the angular-scale intervals analysed, points relatively near the galactic plane (see Table~\ref{table3}): in such a case, larger masks (i.e., lower $f_{\mbox{\footnotesize sky}}$) cut-off larger regions near this plane where most of the power is located. Moreover, we found that foreground residuals are absent in our analyses because, considering the same mask, all the foreground-cleaned maps have essentially the same variance dipole value (with a slight dispersion of $\pm 3\%$, see Fig.~\ref{fig3}). On the one other hand, this variance dipole stands robust in magnitude and direction against frequency dependence, in the 70, 100, and 143 GHz maps, disfavouring the foreground residuals cause, in agreement with~\cite{PLA-XXIII}. Furthermore, an important part of the analyses of the foreground-cleaned Planck maps that validate our results was the robustness tests, where such examinations considered realistic features of the data like the inhomogeneous noise maps and galactic cut-sky masks (information released by the {\em Planck collaboration}~\footnote{Based on observations obtained with Planck (http://www.esa.int/Planck), an ESA science mission with instruments and contributions directly funded by ESA Member States, NASA, and Canada.}). The inhomogeneous noise comes out as a result of the non-uniform way the CMB sky is measured by the Planck probe. In fact, the regions near the ecliptic poles were observed by the probe many more times than others. The pixel's inhomogeneous noise data were released together with the foreground-cleaned Planck maps and are crucial to assert its influence in the hemispherical asymmetry found in the $V^{\mbox{\footnotesize\sc pla}}\!-$maps. In fact, although this noise has small magnitude, i.e. $|T| \lesssim 18 \, \mu$K at 1$\sigma$ level, the inhomogeneous noise has to be included in the analyses in order to quantify its impact in the results, and most importantly, to test the robustness of our outcomes. Our results show (see Table~\ref{table2}) that including pixel's inhomogeneous noise in the data analyses does not modifies appreciably our confidence level's calculation listed below. For instance, for the {\sc smica+valmask} map, with and without noise, we obtain: $v_1^{\text smica+noise} / v_1^{\text smica} = 0.985$. Summarizing, we conclude that our directional variance estimator shows a clear dipolar structure in the four foreground-cleaned and the individual frequency Planck maps, results that appear robust against the component separation algorithms, various Planck masks, map's pixelization parameters, and the addition of inhomogeneous pixel's noise. The magnitude of this dipole is highly significant, $\sim 2.4 \sigma$, in the angular scale interval $\ell \in[4,500]$, attaining less significant values in the scales $\ell \in[4,40]$ and $\ell \in[41,500]$ (Table~\ref{table3}). We also discover that this significance is not so high in the range $\ell \in[2,500]$ just because the $C_2$ and $C_3$ values in Planck CMB maps are manifestly lower than the corresponding values in the MC maps we use for analyses, which are based on $\Lambda$CDM spectrum. As a matter of fact, if we increase these multipoles values in Planck maps to be equal to those in MC data, we found that the statistical significance in this interval increases from 82.8\% to 98.3\%, i.e., $ 2.4 \sigma$. \vspace{4mm} | 14 | 4 | 1404.2936 |
1404 | 1404.2107_arXiv.txt | { Clusters of polycyclic aromatic hydrocarbons (PAHs) have been proposed as candidates for evaporating very small grains, which are thought to be precursors of free-flying PAHs. Evaporation rates have been calculated so far only for species containing up to a few 100-C atoms, whereas interstellar PAH clusters could contain up to $\sim1000$ C atoms.} { We present a method that generalises the calculation of the statistical evaporation rate of large PAH clusters and provides rates for species containing up to $\sim1000$ C-atoms.} { The evaporation of non-rotating neutral homo-molecular PAH clusters containing up to 12 molecules from a family of highly symmetric compact PAHs is studied. Statistical calculations were performed and completed with molecular dynamics simulations at high internal energies to provide absolute values for the evaporation rate and distributions of kinetic energy released. The calculations used explicit atom-atom Lennard-Jones potentials in the rigid molecule approximation. A new method is proposed to take both inter- and intra-molecular vibrations into account.} {Without any parameter adjustment, the calculated evaporation rates agree well with available experimental data. We find that the non-rotation assumption has a limited impact on the evaporation rates. The photostability of PAH clusters increases dramatically with the size of molecules in the clusters, and to a lesser extent with the number of molecules in the clusters. For values of the UV radiation field that are typical of the regions where evaporating very small grains are observed, the smallest clusters in this study ($\sim 50$ C-atoms) are found to be quickly photo-evaporated, whereas the largest clusters ($\sim 1000$ C-atoms) are photostable. } {Our results support the idea that large PAH clusters are good candidates for evaporating very small grains.} | \label{sec:introduction} Astronomical observations have revealed a set of emission bands in the mid-infrared range, the so-called infrared aromatic bands (AIBs), the most intense falling at 3.3, 6.2, 7.7, 8.6, 11.3, and 12.7 $\mu$m. Following the studies of \citet{leger_identification_1984} and \citet{allamandola_polycyclic_1985}, this emission is generally attributed to polycyclic aromatic hydrocarbons (PAHs), and this proposal has motivated numerous studies on PAHs \citep[see][for a recent compilation of works on this topic]{joblin_pahs_2011}. \citet{rapacioli_spectroscopy_2005} have analysed the spectral variations of the AIBs in photodissociation regions (PDRs) and suggest that free PAHs are produced by evaporation of very small grains (VSGs) containing at least ${\sim400}$ carbon atoms. They propose that VSGs are made of PAH clusters that evaporate under UV irradiation. \citep {pilleri_evaporating_2012} confirm this mechanism over a wide range of physical conditions and propose to call these species evaporating very small grains (eVSG). PAH clusters are also considered as key species in flames and circumstellar shells, where they could be involved in the transition from molecular growth to nucleation of soot particles \citep{frenklach_reaction_2002, cherchneff_formation_2011}. The dimerisation of pyrene (\ch{16}{10}) and sometimes of other PAHs has been invoked in numerous studies \citep[][and references therein]{schuetz_nucleation_2002} as a critical step in soot formation models. However, the experimental results of \citet{sabbah_exploring_2010} contradict this proposal unless larger species than pyrene are involved. The size distribution of PAH clusters in natural environments, such as flames, PDRs, or circumstellar shells, results from the balance between nucleation and evaporation processes. To our knowledge there is only one experimental study of the evaporation properties of large PAH clusters by \citet{schmidt_coronene_2006}, while several theoretical studies address the questions of their structure and stability \citep{rapacioli_stacked_2005,herdman_intermolecular_2008}. In addition, \citet{rapacioli_formation_2006} initiated a theoretical investigation on the formation and photo-evaporation in PDRs of neutral clusters containing up to $\sim 300$ C-atoms. They show that in regions where eVSGs are observed, these clusters are photo-evaporated much faster than they can be reformed by collisions. However, this study was based on coronene (\ch{24}{12}), whereas we have recently shown that PAHs smaller than $\sim50-70$ carbon atoms are strongly photo-dissociated, and therefore larger PAHs have to be considered \citep{montillaud_evolution_2013}. In this study, we aim at providing absolute evaporation rates for neutral PAH clusters of large molecules. These rates are calculated as a function of the total excess energy in the clusters, defined as the sum of inter- and intra-molecular potential energy and of kinetic energy. To sample the parameter space of PAH cluster size, we focussed on three highly symmetric and compact species, namely coronene \ch{24}{12}, circumcoronene \ch{54}{18}, and circumcircumcoronene \ch{96}{24}, forming clusters containing up to 12 molecules. For the sake of simplicity, we limit the study to non-rotating clusters. We show in Sect.~\ref{sec:PSTinput} and Appendix~\ref{anx:sensitivity} that this assumption has no strong impact on the applicability of our results in the astrophysical context. The calculations of absolute evaporation rates by \citet{rapacioli_formation_2006} were based on the statistico-dynamical method \citep{weerasinghe_absolute_1993, calvo_statistical_2003}. It consists in combining the assets of (i) the phase space theory (PST), which provides accurate relative data over broad energy ranges and (ii) molecular dynamics (MD) simulations to get absolute data, but only for a limited range at high energies. When applied to the evaporation of large molecular clusters, the need for long MD trajectories usually makes it necessary to simplify the simulations by assuming that molecules are rigid. This approximation raises difficulties for taking both the intra- and inter-molecular vibrations into account when combining PST and MD results. We propose here a simple method for circumventing this difficulty while relaxing the rigid molecule approximation to some extent. To assess the reliability of this method and of obtained molecular data, we compare our results on coronene clusters with the experimental data by \citet{schmidt_coronene_2006}. The paper is structured as follows. The methods used to compute the structures, energetic properties, and evaporation rates of PAH clusters are presented in the next section. Further details on the methods can be found in the appendix. In Sect.~\ref{sec:result_disc}, we report our absolute evaporation rates and compare them with the available experimental results. The first astrophysical consequences of our new molecular data are discussed in Sect.~\ref {sec:appli_astro}. A summing-up of this work with perspectives on possible extensions of our method, the remaining open questions, and astrophysical modelling concludes the paper. Readers mostly interested in using the molecular data and in their astrophysical consequences may skip the following section dedicated to methods. | \label{sec:conclusion} We have computed the absolute evaporation rates of non-rotating neutral PAH clusters of astrophysical interest, made of 2 to 12 molecules of coronene \ch{24}{12}, circumcoronene \ch{54}{18}, or circumcircumcoronene \ch{96}{24}. We thereby provided essential data for testing the relevance of PAH clusters as models for the so-called eVSGs whose sizes span the range between $\sim 100$ to $\sim 1000$ C-atoms \citep{rapacioli_spectroscopy_2005, pilleri_evaporating_2012}. We performed the calculations using the statistico-dynamical approach proposed by \citet{weerasinghe_absolute_1993}, and further analysed and developed by \citet{calvo_statistical_2003}. We proposed an extension of the method that enables taking the distribution of the excess energy into account amongst all the inter- and intra-molecular modes in a microcanonical framework, despite the use of the rigid molecule approximation. A successful comparison with the experimental results of \citet{schmidt_coronene_2006} on coronene clusters, without any fitting parameter, gives us confidence in the method. The evaporation rates exhibit very regular trends that we found to be related to the structural similarities between the studied species. When considering clusters of molecules with different geometries, as well as heteroclusters, one should expect deviations from these trends that could be interesting to consider for studying natural mixtures, such as in astrophysical environments or in flames. The absolute values of the evaporation rates decrease strongly with the number of molecules in the cluster, and even more with the size of molecules, indicating that clusters of large PAHs are more likely to survive in PDRs. These results also indicate that large PAHs could play a significant role in the nucleation process of soot particles. We evaluated the impact of most approximations that have been made, on our results. The sensitivity of evaporation rates to the accuracy of the geometric and the long-range interaction parameters used in PST should be considered of second order compared to the sensitivity to other approximations made in the calculations. Rather small errors result from the use of our rates to PAH clusters with rotational temperatures up to a few hundred K. For higher temperatures, the initial angular momentum of parent clusters should be considered, and a more accurate evaluation of the geometric and long-range interaction parameters could then be necessary \citep {calvo_statistical_2004}. The anharmonicity of intramolecular vibrations was estimated to play a minor role thanks to the dispersion of energy among numerous intra-molecular modes. On the contrary, the anharmonicity of intermolecular modes is crucial for reproducing the variations in the evaporation rates with excess energy revealed by molecular dynamics. Only the anharmonicity resulting from the coupling between inter- and intra-molecular modes cannot be modelled with our method. A comparative study with full-atom methods could help quantify the effects of this coupling on the statistical and dynamical properties of molecular cluster evaporation. We used our molecular data to study the evolution of PAH clusters in conditions typical of PDRs. We showed that the whole range of photostability properties, from very easily photo-evaporated to extremely photostable, is covered when considering clusters made of PAHs with sizes in the expected range for astrophysical PAHs. Our results therefore reinforce the idea that PAH clusters are good candidates for eVSGs, if the size of individual units is large enough ($\gtrsim 50$ C-atoms). This work provides most of the elements needed to investigate the survival of neutral PAH clusters in the interstellar medium. Nevertheless, numerous studies are needed to have a complete set of data that would enable modelling realistic interstellar PAH clusters, including the effects of the charge state, the blending of molecules, and the rotation of the clusters. Apart from the molecular data, valuable progress in our understanding of the nature of eVSGs now relies on a closer comparison of the results of modelling and astronomical observables. \begin{acknowledgement} The authors gratefully acknowledge A. Simon, who kindly provided the results of DFT calculations presented in this work, and thank F. Spiegelman, M. Rapacioli, and P. Parneix for stimulating discussions and helpful comments. \ J. Montillaud acknowledges the support of the French Agence Nationale de la Recherche (ANR), under grant GASPARIM "Gas-phase PAH research for the interstellar medium", ANR-2010-BLANC-0501. \end{acknowledgement} | 14 | 4 | 1404.2107 |
1404 | 1404.2277_arXiv.txt | \noindent Recent null results from LHC8 SUSY searches along with the discovery of a SM-like Higgs boson with mass $m_h\simeq 125.5$ GeV indicates sparticle masses in the TeV range, causing tension with conventional measures of electroweak fine-tuning. We propose a simple {\it Fine-tuning Rule} which should be followed under any credible evaluation of fine-tuning. We believe that overestimates of electroweak fine-tuning by conventional measures all arise from violations of this rule. We show that to gain accord with the Fine-tuning Rule, then both Higgs mass and the traditional $\Delta_{BG}$ fine-tuning measures reduce to the model-independent electroweak fine-tuning measure $\Delta_{EW}$. This occurs by combining dependent contributions to $m_Z$ or $m_h$ into independent units. Then, using $\Delta_{EW}$, we evaluate EW fine-tuning for a variety of SUSY models including mSUGRA, NUHM1, NUHM2, mGMSB, mAMSB, hyper-charged AMSB and nine cases of mixed moduli-anomaly (mirage) mediated SUSY breaking models (MMAMSB) whilst respecting LHC Higgs mass and $B$-decay constraints (we do not impose LHC8 sparticle mass constraints due to the possibility of compressed spectra within many of these models). We find mSUGRA, mGMSB, mAMSB and MMAMSB models all to be highly fine-tuned. The NUHM1 model is moderately fine-tuned while NUHM2 which allows for radiatively-driven naturalness (RNS) allows for fine-tuning at a meager 10\% level in the case where $m(higgsinos)\sim 100-200$ GeV and the TeV-scale top squarks are well-mixed. Models with RNS may or may not be detect at LHC14. A $\sqrt{s}\sim 500$ GeV $e^+e^-$ collider will be required to make a definitive search for the requisite light higgsinos. \vspace*{0.8cm} | It has long been claimed that electroweak naturalness requires that the superpartners of the SM fields exist with masses of order the weak scale\cite{eenz,bg,kane,ac1,dg,ccn,ellis2,king,casas,fp,Nomura:2005qg,ross,derm_kim,shafi,perel,antusch,hardy,sug19,Fichet:2012sn,Younkin:2012ui,Kowalska:2013ica,han,Dudas:2013pja,Arvanitaki:2013yja,Fan:2014txa,Gherghetta:2014xea,Kowalska:2014hza,feng,ltr,rns,comp,deg,Martin:2013aha,Fowlie:2014xha,azar_xt} $m(sparticles)\sim m_{weak}\sim m_Z$. Already at LEP2, the lack of signal for chargino pairs called into question whether there might exist a ``Little Hierarchy Problem''\cite{barbstrum} characterized by $m(sparticle)\gg m_Z$. This viewpoint has seemingly been strengthened by \bi \item the lack of any signal for sparticles at LHC8\cite{atlas_susy,cms_susy} which requires $m_{\tg}\agt 1.8$ TeV for models with $m_{\tq}\sim m_{\tg}$ and $m_{\tg}\agt 1.3$ TeV for models with $m_{\tq}\gg m_{\tg}$ and \item the rather large value of $m_h\simeq 125.5$ GeV\cite{atlas_h,cms_h} which requires multi-TeV top squarks with small mixing or TeV-scale top squarks with large mixing\cite{mhiggs,hpr,h125,arbey}. \ei If indeed weak scale SUSY is highly fine-tuned in the electroweak sector, then likely SUSY is not as we know it since the twin requirements of parsimony and naturalness cannot be met simultaneously\cite{craig}. Abandoning parsimony is not a step lightly taken since the further one strays from known physics the more likely one is to be wrong. But before jumping to such strong conclusions-- which may well guide support for and construction of future HEP experimental facilities-- it is worthwhile to scrutinize the available measures of electroweak fine-tuning (EWFT) in SUSY models. Indeed, in a recent paper we have claimed that {\it conventional measures tend to overestimate EWFT in supersymmetric models}, often by several orders of magnitude\cite{comp}. In order to ascertain when a claim of fine-tuning is legitimate, we propose a simple {\bf Fine-tuning Rule} which may act as a guide: \begin{quotation} {\it When evaluating fine-tuning, it is not permissible to claim fine-tuning of {\bf dependent} quantities one against another.} \end{quotation} We believe the over-estimates of EWFT by conventional measures referred to above all come from violations of this rule. To be explicit, most theories contain several, perhaps many, parameters. Some of these may be set equal to measured values, while others may be undetermined or at least constrained, but may vary over a wide range of values. The parameters are frequently introduced to parametrize our ignorance of more fundamental physics, and their variation allows one to encompass a wide range of possibilities. We can think of each parameter as a dial, capable of being adjusted to specific, or alternatively a wide range of values. If some contribution to a measured quantity ({\it e.g.} $m_h^2$ or $m_Z^2$ in this paper) in a theory blows up, and we have an adjustable parameter which may be dialed independently to compensate, then we may legitimately evaluate fine-tuning: is a huge, unnatural cancellation required? Alternatively, if as a consequence of one contribution blowing up, a related dial/parameter is driven to large, opposite-sign compensating values, then any claimed fine-tuning would violate our rule (the quantities would be {\it dependent}) and some regrouping of terms into independent quantities should be found. We will meet some clarifying examples in the subsequent sections of this paper. \subsection{Simple electroweak fine-tuning} In most supersymmetric models based on high scale input parameters-- {\it i.e.} SUSY models with soft term boundary conditions imposed at a scale $\Lambda\gg m_{weak}$ where $\Lambda$ may range as high as $m_{GUT}\simeq 2\times 10^{16}$ GeV or even the reduced Planck mass $M_P\simeq 2\times 10^{18}$ GeV-- the soft SUSY breaking terms are input at the scale $\Lambda$ and then evolved to the electroweak scale $m_{weak}$ via renormalization group (RG) running.\footnote{Here we differentiate the superpotential Higgs/higgsino mass term $\mu$ from the soft breaking terms, as do most model builders, and we return to the SUSY $\mu$ problem later.} At the weak scale, the scalar potential is minimized and checked to ensure that EW symmetry is properly broken. The value of $\mu$ is then fixed in terms of the weak scale soft SUSY breaking terms $m_{H_u}^2$ and $m_{H_d}^2$ by requiring that the measured value of $m_Z\simeq 91.2$ GeV is obtained: \be \frac{m_Z^2}{2}=\frac{m_{H_d}^2 + \Sigma_d^d - (m_{H_u}^2+\Sigma_u^u)\tan^2\beta}{\tan^2\beta -1} -\mu^2 \simeq -m_{H_u}^2-\Sigma_u^u-\mu^2 \label{eq:mZs} \ee where $\Sigma_u^u$ and $\Sigma_d^d$ are radiative corrections that arise from the derivatives of $\Delta V$ evaluated at the minimum. The radiative corrections $\Sigma_u^u$ and $\Sigma_d^d$ include contributions from various particles and sparticles with sizeable Yukawa and/or gauge couplings to the Higgs sector. Expressions for the $\Sigma_u^u$ and $\Sigma_d^d$ are given in the Appendix of Ref.~\cite{rns}. Already at this point: if $-m_{H_u}^2 (weak)$ in the right-hand-side of Eq. \ref{eq:mZs} is large positive ($\gg m_Z^2$), then the value of $\mu$ must be fine-tuned by hand to ensure the measured value of $m_Z^2$ is obtained. Since most researchers these days run automated computer codes\cite{codes} to calculate the weak scale spectrum of SUSY and Higgs particles, this represents a {\it hidden} fine-tuning that ought to be accounted for. Alternatively, if soft SUSY breaking terms {\it and} $\mu$ are input parameters, then much higher values of $m_Z\gg 91.2$ GeV are expected from scans over SUSY model parameter space. For example, in Fig. \ref{fig:mz} we plot the value of $m_Z$ which is generated from a scan over pMSSM parameter space\cite{pmssm}\footnote{The pMSSM, or phenomenological MSSM, is the MSSM defined with weak scale input parameters where all CP violating and flavor violating soft terms have been set to zero. Also, usually first/second generation soft terms are set equal to each other to avoid flavor-violations.}. The 20 dimensional pMSSM parameter space then includes \bea M_1,\ M_2,\ M_3,\\ m_{Q_1},\ m_{U_1},\ m_{D_1},\ m_{L_1},\ m_{E_1},\\ m_{Q_3},\ m_{U_3},\ m_{D_3},\ m_{L_3},\ m_{E_3},\\ A_t,\ A_b,\ A_{\tau},\\ m_{H_u}^2,\ m_{H_d}^2,\ \mu,\ B. \eea The usual strategy is to use the EW minimization conditions\cite{wss} to trade the bilinear parameter $B$ for the ratio of Higgs vevs $\tan\beta \equiv v_u/v_d$ and to exchange $m_{H_u}^2$ and $m_{H_d}^2$ for $m_Z^2$ and $m_A^2$\cite{wss}. This procedure reduces the number of free parameters to 19 (since $m_Z$ is fixed) but hides the fine-tuning embedded in Eq. \ref{eq:mZs} since now $m_{H_u}^2$ is an output. Here we will avoid the $m_Z^2$ constraint and scan over the 20 dimensional pMSSM space for the range of scalar and gaugino mass soft terms from $0-10$ TeV, $-10\ {\rm TeV}< A_i<10$ TeV, $\mu :0-3$ TeV and $\tan\beta :3-60$, while requiring the lightest neutralino $\tz_1$ as lightest SUSY particle (LSP) and $m_{\tw_1}>103.5$ GeV (in accord with LEP2 constraints).\footnote{This limit diminishes to $\sim 91.9$ GeV in the case of a wino-like WIMP.} Our results are shown in Fig. \ref{fig:mz}. Here, we see that the most probable value of $m_Z$ is $\sim 2.5$ TeV with a large spread to both higher and lower values. It is highly unlikely to generate the measured value $m_Z=91.2$ GeV: this is the essence of the Little Hierarchy problem. \begin{figure}[tbp] \includegraphics[height=0.4\textheight]{mz} \caption{Plot of value of $m_Z$ generated from a scan over pMSSM model parameter space while {\it not} implementing the $m_Z^2$ constraint. \label{fig:mz}} \end{figure} Alternatively, the fact that $m_Z=91.2$ GeV along with $m_h\simeq 125.5$ GeV tells us from Eq. \ref{eq:mZs} that to naturally generate the measured value of $m_Z$ (and $M_W$) and $m_h$, then \bi \item $|\mu|\sim m_Z\sim 100-200$ GeV \item $m_{H_u}^2$ should be driven to small negative values such that $-m_{H_u}^2\sim 100-200$ GeV at the weak scale and \item that the radiative corrections are not too large: $\Sigma_u^u\alt 100-200$ GeV \ei The first two of these conditions are shown in Fig. \ref{fig:Qrun} as soft term and $\mu$ RG running versus $Q$ for a radiatively-driven natural SUSY benchmark point from Ref. \cite{ilcbm8} where $\mu =110$ GeV and $\Delta_{EW}=16$. \begin{figure}[tbp] \includegraphics[height=0.4\textheight]{Qrun} \caption{Renormalization group evolution of $sign (m_{H_u}^2) \sqrt{|m_{H_u}^2|}$, $\sqrt{m_{H_d}^2}$ and $\mu$ versus energy scale $Q$ for the RNS benchmark point from Ref. \cite{ilcbm8}. The value $m_A=1$ TeV $\simeq m_{H_d}(weak)$ and $\mu (weak) =110$ GeV. \label{fig:Qrun}} \end{figure} Formally, these conditions arise from requiring the {\it electroweak fine-tuning measure} $\Delta_{EW}$ be not too large, where \be \Delta_{EW} \equiv max_i \left|C_i\right|/(m_Z^2/2)\;, \ee may be constructed, with $C_{H_d}=m_{H_d}^2/(\tan^2\beta -1)$, $C_{H_u}=-m_{H_u}^2\tan^2\beta /(\tan^2\beta -1)$ and $C_\mu =-\mu^2$. Also, $C_{\Sigma_u^u(k)} =-\Sigma_u^u(k)\tan^2\beta /(\tan^2\beta -1)$ and $C_{\Sigma_d^d(k)}=\Sigma_d^d(k)/(\tan^2\beta -1)$, where $k$ labels the various loop contributions included in Eq. \ref{eq:mZs}. The largest of the radiative corrections comes from the top squark sector $\Sigma_u^u(\tst_{1,2})$. These radiative corrections can be minimized for large stop mixing from a large trilinear $A_t$ parameter, which also raises up the value of $m_h$ to the 125 GeV regime for top squark masses in the 1-4 TeV range\cite{ltr}. An advantage of $\Delta_{EW}$ is that it is model-independent in the sense that any model which yields the same weak scale mass spectrum will generate the same value of $\Delta_{EW}$. \subsection{Fine-tuning of the Higgs mass} \subsubsection{SM case:} An alternative measure of EWFT is to require that the (regularized) divergent radiative corrections $\delta m_h^2$ to the squared Higgs mass $m_h^2$ be not too large: say $\delta m_h^2\alt m_h^2$. In the SM we have \be m_{H_{SM}}^2 = 2\mu^2 +\delta m_{H_{SM}}^2 \label{eq:mHSM} \ee where the tree-level squared mass $2\mu^2$ and the quadratically divergent radiative corrections \be \delta m_{H_{SM}}^2\simeq \frac{3}{4\pi^2}\left(-\lambda_t^2+\frac{g^2}{4}+\frac{g^2}{8\cos^2\theta_W}+\lambda\right)\Lambda^2 \ee are {\it independent} (here, $\lambda_t$ is the SM top Yukawa coupling, $g$ is the $SU(2)_L$ gauge coupling, $\lambda$ is the SM Higgs quartic coupling and $\Lambda$ is the effective theory energy cutoff scale). Thus, by the EWFT Rule, this is a legitimate fine-tuning evaluation. For large $\Lambda$, the large radiative corrections must be balanced by a fine-tuning of $2\mu^2$ such that $m_{H_{SM}}^2$ maintains its physical value. Alternatively, to maintain naturalness, then $\delta m_{H_{SM}}^2\sim m_{H_{SM}}^2$ which requires $\Lambda\alt 1$ TeV, {\it i.e.} the SM is only valid below about the $\Lambda\sim 1$ TeV scale. \subsubsection{MSSM case:} In the MSSM, it is found that \be m_h^2\simeq \mu^2 + m_{H_u}^2+\delta m_{H_u}^2 \ee where now $\mu^2$ is the {\it supersymmetric} Higgs/higgsino bilinear term which gives mass to both SM particles (the gauge and Higgs bosons) and the SUSY partner higgsinos. In addition, $m_{H_u}^2$ is the soft SUSY breaking (SSB) up-Higgs mass term. If we assume the MSSM is valid up to the GUT scale, then the value of $\delta m_{H_u}^2$ can be found by integrating the renormalization group equation (RGE)\cite{bbo}: \be \frac{dm_{H_u}^2}{dt}=\frac{1}{8\pi^2}\left(-\frac{3}{5}g_1^2M_1^2-3g_2^2M_2^2+\frac{3}{10}g_1^2 S+3f_t^2 X_t\right) \label{eq:mHu} \ee where $t=\ln (Q^2/Q_0^2)$, $S=m_{H_u}^2-m_{H_d}^2+Tr\left[{\bf m}_Q^2-{\bf m}_L^2-2{\bf m}_U^2+{\bf m}_D^2+{\bf m}_E^2\right]$ and where $X_t=m_{Q_3}^2+m_{U_3}^2+m_{H_u}^2+A_t^2$. By neglecting gauge terms and $S$ ($S=0$ in models with scalar soft term universality but can be large in models with non-universality), and also neglecting the $m_{H_u}^2$ contribution to $X_t$ and the fact that $f_t$ and the soft terms evolve under $Q^2$ variation, then this expression may be readily integrated from $m_{SUSY}$ to the cutoff $\Lambda$ to obtain \be \delta m_{H_u}^2 \sim -\frac{3f_t^2}{8\pi^2}(m_{Q_3}^2+m_{U_3}^2+A_t^2)\ln\left(\Lambda^2/m_{SUSY}^2 \right) . \label{eq:DBoE} \ee Here, $\Lambda$ may be taken as high as $m_{GUT}\simeq 2\times 10^{16}$ GeV or even the reduced Planck mass $m_P\simeq 2.4\times 10^{18}$ GeV. Also, we take $m_{SUSY}^2 \simeq m_{\tst_1}m_{\tst_2}$. By requiring\cite{kn,papucci,brust,Evans:2013jna} $\Delta_{HS}\sim \delta m_{H_u}^2/(m_h^2/2)\alt 10$ one then expects $m_{\tst_{1,2},\tb_1}\alt 600$ GeV. Using the $\Delta_{HS}$ measure along with $m_h\simeq 125$ GeV then one finds some popular SUSY models to be electroweak fine-tuned to 0.1\%\cite{comp}. Two pitfalls occur within this approach, which are {\it different} from the case of the SM. \bi \item The first is that $m_{H_u}^2(\Lambda )$ and $\delta m_{H_u}^2$ are {\it not} independent: the value of $m_{H_u}^2$ feeds directly into evaluation of $\delta m_{H_u}^2$ via the $X_t$ term. It also feeds indirectly into $\delta m_{H_u}^2$ by contributing to the evolution of the $m_{Q_3}^2$ and $m_{U_3}^2$ terms. In fact, the larger the value of $m_{H_u}^2(\Lambda )$, then the larger is the cancelling correction $\delta m_{H_u}^2$. Thus, this fine-tuning measure fails under the Fine-tuning Rule. \item The second is that whereas $SU(2)_L\times U(1)_Y$ gauge symmetry can be broken at tree level in the SM, in the SUGRA case where SUSY is broken in a hidden sector via the superHiggs mechanism then $m_{H_u}^2\sim m_{3/2}^2>0$ and EW symmetry is not even broken until one includes radiative corrections. For SUSY models valid up to some high scale $\Lambda\gg m_{weak}$, EW symmetry is broken radiatively by $m_{H_u}^2$ being driven to large negative values by the large top quark Yukawa coupling\cite{rewsb}. \ei By combining dependent terms, then we have a regrouping\cite{ltr,rns} \be m_h^2|_{phys}=\mu^2+\left(m_{H_u}^2(\Lambda )+\delta m_{H_u}^2 \right) \label{eq:mh} \ee where now $\mu^2$ and $\left(m_{H_u}^2(\Lambda )+\delta m_{H_u}^2 \right)$ are each independent so each should be comparable to $m_h^2$ in order to avoid fine-tuning. It is often claimed that under such a regrouping, then the SM Higgs mass would also not be fine-tuned. But here we see that in the MSSM case-- since the $m_{H_u}^2$ and $\delta m_{H_u}^2$ terms are dependent-- the situation is different from the SM and one must lump dependent terms together. The regrouping in Eq. \ref{eq:mh} of contributions to $m_h^2$ into independent terms leads back to the $\Delta_{EW}$ measure. \subsection{$\Delta_{BG}$ and model-dependence} The more traditional measure $\Delta_{BG}$ was proposed by Ellis {\it et al.}\cite{eenz} and later investigated more thoroughly by Barbieri and Giudice\cite{bg}. The starting point is to express $m_Z^2$ in terms of weak scale SUSY parameters as in Eq. \ref{eq:mZs}: \be m_Z^2 \simeq -2m_{H_u}^2-2\mu^2 \label{eq:mZsapprox} \ee where the partial equality obtains for moderate-to-large $\tan\beta$ values and where we assume for now the radiative corrections are small. An advantage of $\Delta_{BG}$ over the previous large-log measure is that it maintains the correlation between $m_{H_u}^2(\Lambda )$ and $\delta m_{H_u}^2$ by replacing $m_{H_u}^2 (m_{weak})= \left( m_{H_u}^2(\Lambda )+\delta m_{H_u}^2\right)$ by its expression in terms of high scale parameters. To evaluate $\Delta_{BG}$, one needs to know the explicit dependence of $m_{H_u}^2$ and $\mu^2$ on the fundamental parameters. Semi-analytic solutions to the one-loop renormalization group equations for $m_{H_u}^2$ and $\mu^2$ can be found for instance in Ref's \cite{munoz}. For the case of $\tan\beta =10$, then\cite{abe,martin,feng} \bea m_Z^2& \simeq & -2.18\mu^2 + 3.84 M_3^2+0.32M_3M_2+0.047 M_1M_3-0.42 M_2^2 \nonumber \\ & & +0.011 M_2M_1-0.012M_1^2-0.65 M_3A_t-0.15 M_2A_t\nonumber \\ & &-0.025M_1 A_t+0.22A_t^2+0.004 M_3A_b\nonumber \\ & &-1.27 m_{H_u}^2 -0.053 m_{H_d}^2\nonumber \\ & &+0.73 m_{Q_3}^2+0.57 m_{U_3}^2+0.049 m_{D_3}^2-0.052 m_{L_3}^2+0.053 m_{E_3}^2\nonumber \\ & &+0.051 m_{Q_2}^2-0.11 m_{U_2}^2+0.051 m_{D_2}^2-0.052 m_{L_2}^2+0.053 m_{E_2}^2\nonumber \\ & &+0.051 m_{Q_1}^2-0.11 m_{U_1}^2+0.051 m_{D_1}^2-0.052 m_{L_1}^2+0.053 m_{E_1}^2 , \label{eq:mZsparam} \eea where all terms on the right-hand-side are understood to be $GUT$ scale parameters. Then, the proposal is that the variation in $m_Z^2$ with respect to parameter variation be small: \be \Delta_{BG}\equiv max_i\left[ c_i\right]\ \ {\rm where}\ \ c_i=\left|\frac{\partial\ln m_Z^2}{\partial\ln a_i}\right| =\left|\frac{a_i}{m_Z^2}\frac{\partial m_Z^2}{\partial a_i}\right| \label{eq:DBG} \ee where the $a_i$ constitute the fundamental parameters of the model. Thus, $\Delta_{BG}$ measures the fractional change in $m_Z^2$ due to fractional variation in high scale parameters $a_i$. The $c_i$ are known as {\it sensitivity coefficients}\cite{feng}. The requirement of low $\Delta_{BG}$ is then equivalent to the requirement of no large cancellations on the right-hand-side of Eq. \ref{eq:mZsparam} since (for linear terms) the logarithmic derivative just picks off coefficients of the relevant parameter. For instance, $c_{m_{Q_3}^2}=0.73\cdot (m_{Q_3}^2/m_Z^2)$. If one allows $m_{Q_3}\sim 3$ TeV (in accord with requirements from the measured value of $m_h$) then one obtains $c_{m_{Q_3}^2}\sim 800$ and so $\Delta_{BG}\ge 800$. In this case, SUSY would be electroweak fine-tuned to about 0.1\%. If instead one sets $m_{Q_3}=m_{U_3}=m_{H_u}\equiv m_0$ as in models with scalar mass universality, then the various scalar mass contributions to $m_Z^2$ largely cancel and $c_{m_0^2}\sim -0.017 m_0^2/m_Z^2$: the contribution to $\Delta_{BG}$ from scalars drops by a factor $\sim 50$. The above argument illustrates the extreme model-dependence of $\Delta_{BG}$ for multi-parameter SUSY models. The value of $\Delta_{BG}$ can change radically from theory to theory even if those theories generate exactly the same weak scale sparticle mass spectrum. The model dependence of $\Delta_{BG}$ arises due to a violation of the Fine-tuning Rule: one must combine dependent terms into independent quantities before evaluating EW fine-tuning. \subsection{When is $\Delta_{BG}$ a reliable measure of naturalness?} In Ref. \cite{comp}, it was argued that in an ultimate theory (UTH), where all soft parameters are correlated, then $\Delta_{BG}$ should be a reliable measure of naturalness. In fact, most supersymmetric theories with SUSY breaking generated in a hidden sector fulfill this requirement. For instance, in supergravity theories with hidden sector SUSY breaking via the superHiggs mechanism, then all soft breaking parameters are expected to be some multiple of the gravitino mass $m_{3/2}$. (For example, in string theory with dilaton-dominated SUSY breaking\cite{kl,Brignole:1993dj}, then we expect $m_0^2=m_{3/2}^2$ with $m_{1/2}=-A_0=\sqrt{3}m_{3/2}$). For any fully specified hidden sector, we expect each SSB term to be some multiple of $m_{3/2}$: {\it e.g.} \bea m_{H_u}^2&=&a_{H_u}\cdot m_{3/2}^2,\label{eq:1} \\ m_{Q_3}^2&=&a_{Q_3}\cdot m_{3/2}^2,\\ A_t&=&a_{A_t}\cdot m_{3/2},\\ M_i&=&a_i\cdot m_{3/2},\\ & & \cdots \label{eq:5} . \eea Here, the coefficients $a_i$ {\it parametrize our ignorance} of the exact model for SUSY breaking. By using several adjustable parameters, we cast a wide net which encompasses a large range of hidden sector SUSY breaking possibilities. But this doesn't mean that each SSB parameter is expected to be independent of the others. It just means we do not know how SUSY breaking occurs, and how the soft terms are correlated: it is important not to confuse parameters which ought to be related to one another in any sensible theory of SUSY breaking with independently adjustable soft SUSY breaking terms. Now, plugging the soft terms \ref{eq:1}-\ref{eq:5} into Eq. \ref{eq:mZsparam}, one arrives at the expression \be m_Z^2=-2.18\mu^2 +a\cdot m_{3/2}^2 . \ee The value of $a$ is just some number which is the sum of all the coefficients of the terms $\propto m_{3/2}^2$. For now, we assume $\mu$ is independent of $m_{3/2}$ as will be discussed shortly. In this case, we can compute the sensitivity coefficients:\footnote{In mAMSB, the soft terms are also written as multiples of $m_{3/2}$ or $m_{3/2}^2$. In mGMSB, the soft terms are written as multiples of messenger scale $\Lambda_m$. The argument proceeds in an identical fashion in these cases.} \bea c_{m_{3/2}^2} &=& |a\cdot (m_{3/2}^2/m_Z^2)|\ \ {\rm and}\label{eq:A} \\ c_{\mu^2} &=& |-2.18 (\mu^2/m_Z^2 )|.\label{eq:B} \eea For $\Delta_{BG}$ to be $\sim 1-10$ (natural SUSY with low fine-tuning), then Eq. \ref{eq:B} implies \bi \item $\mu^2 \sim m_Z^2$ \ei and also Eq. \ref{eq:A} implies \bi \item $a\cdot m_{3/2}^2\sim m_Z^2$. \ei The first of these conditions implies light higgsinos with mass $\sim 100-200$ GeV, the closer to $m_Z$ the better. The second condition can be satisfied if $m_{3/2}\sim m_Z$\cite{bg} (which now seems highly unlikely due to a lack of LHC8 SUSY signal\footnote{For instance, in simple SUGRA models, then the scalar masses $m_0=m_{3/2}$. Since LHC requires rather high $m_0$, then we would also expect rather large $m_{3/2}$.} and the rather large value of $m_h$) {\it or} if $a$ is quite small: in this latter case, the SUSY soft terms conspire such that there are large cancellations amongst the various coefficients of $m_{3/2}^2$ in Eq. \ref{eq:mZsparam}: this is what is called radiatively-driven natural SUSY\cite{ltr,rns} since in this case a large high scale value of $m_{H_u}^2$ can be driven radiatively to small values $\sim -m_Z^2$ at the weak scale. Furthermore, we can equate the value of $m_Z^2$ in terms of weak scale parameters with the value of $m_Z^2$ in terms of GUT scale parameters: \be m_Z^2\simeq -2\mu^2(weak)-2m_{H_u}^2(weak) \simeq -2.18\mu^2(GUT)+a\cdot m_{3/2}^2 . \ee Since $\mu$ hardly evolves under RG running (the factor 2.18 is nearly 2), then we have the BG condition for low fine-tuning as \be -m_{H_u}^2(weak) \sim a\cdot m_{3/2}^2\sim m_Z^2 , \ee {\it i.e.} that the value of $m_{H_u}^2$ must be driven to {\it small} negative values $\sim - m_Z^2$ at the weak scale. These are exactly the conditions required by the model-independent EWFT measure $\Delta_{EW}$: {\it i.e.} we have \be \lim_{n_{SSB}\to 1} \Delta_{BG}\to \Delta_{EW} \ee where $n_{SSB}$ is the number of {\it independent} soft SUSY breaking terms. Of course, this approach also reconciles the Higgs mass fine-tuning measure (with appropriately regrouped independent terms) with the $\Delta_{BG}$ measure (when applied to models with a single independent soft breaking term such as $m_{3/2}$). \subsection{The $\mu$ parameter and some solutions to the $\mu$ problem} One of the central problems of supersymmetric theories concerns the origin of the superpotential $\mu$ term: $W\ni \mu H_u H_d$. Since this term is supersymmetric (does not arise from SUSY breaking) its value might be expected to be $\mu\sim M_P$. However, phenomenology dictates instead that $\mu\sim m_{weak}$. A variety of solutions to the SUSY $\mu$ problem arise in the literature. Here we comment briefly on three of them. \subsubsection{NMSSM} In the Next-to-Minimal Supersymmetric Standard Model (NMSSM)\cite{nmssm}, one assumes some symmetry forbids the usual $\mu$ term, but then a visible sector gauge singlet superfield $S$ is added with superpotential \be W\ni \lambda_S SH_uH_d . \ee The scalar component of $S$ develops a vev $\langle S\rangle\sim m_{3/2}$ which generates a $\mu$ term: $\mu =\lambda_S \langle S\rangle\sim m_{3/2}$. In addition to the $\mu$ term, one obtains new physical Higgs particles along with a singlino. An additional contribution to the Higgs mass is also generated which some authors find appealing. A drawback to this scenario is that introduction of true gauge singlets may lead back to destabilizing the gauge hierarchy via tadpole diagrams\cite{ell,bp}. This destabilization can be avoided by introducing $S$ as a composite object\cite{rr} although this leads to possibly recondite models and a movement away from parsimony. \subsubsection{Giudice-Masiero} In the Giudice-Masiero (GM) mechanism\cite{GM}, it is assumed that the usual $\mu$ term is forbidden by some symmetry which is applicable to the visible sector but which is not respected by hidden sector fields. In such a case, then there may exist a (non-renormalizable) coupling of Higgs doublets to the hidden sector such as \be K\ni \lambda h_m H_u H_d /M_P \ee where $h_m$ is a hidden sector field. When $h_m$ develops a SUSY breaking vev $\langle F_h\rangle\sim m_s^2$ where $m_s$ is the hidden sector mass scale (with $m_{3/2}\sim m_s^2/M_P$), then a $\mu$ term is generated with \be \mu\sim\lambda \langle F_h\rangle/M_P\sim \lambda m_{3/2} . \ee Thus, in the GM solution, we expect $\mu\sim m_{3/2}$. If we expect $m_{3/2}\gg 1$ TeV scale due to lack of LHC signal, then we would arrive at high EW fine-tuning unless $\lambda$ was tiny.\footnote{ In a recent paper\cite{Leggett:2014mza}, the authors argue that no-scale SUSY models contain only one free parameter $m_{3/2}$, and where $\mu\sim m_{3/2}$ is generated via GM mechanism so that $m_Z^2=a\cdot m_{3/2}^2$ where $a$ is some constant. In such a case, it is a tautology that $\Delta_{BG}=c_{m_{3/2}}=|\partial\ln m_Z^2/\partial\ln m_{3/2}^2 |=1$ and there is no fine-tuning. However, in this case the authors do not produce an explicit hidden sector-visible sector coupling which produces exactly the right $\mu$ value which is required to generate $m_Z=91.2$ GeV. In the absence of an explicit hidden sector model, then one must regard instead $\mu$ as a free parameter which parametrizes our ignorance of the hidden sector, so that there are actually two free parameters with $m_Z^2\sim -2.18 \mu^2 +a\cdot m_{3/2}^2$. Then as usual large $\mu$ will require high fine-tuning. } \subsubsection{Kim-Nilles} The Kim-Nilles (KN) mechanism\cite{KN} arises as a byproduct of the PQ solution to the strong CP problem and is the supersymmetric extension of the DFSZ axion model\cite{dfsz}. In KN, the $H_u$ and $H_d$ superfields carry PQ charges $Q_u$ and $Q_d$ so the usual $\mu$ term is forbidden by PQ symmetry. An additional visible sector field $P$ carrying PQ charge $-(Q_u+Q_d)/2$ is then required so that the superpotential term \be W_{DFSZ}\ni \lambda P^2 H_u H_d/M_P \ee is present. The PQ symmetry is broken, for instance, by a superpotential\cite{chun_dfsz} \be W_{PQ}\ni \lambda_S S\left( PQ-f_a^2 \right) \ee (the PQ charge of $Q$ and $S$ is $-Q_P$ and 0 respectively) which leads to $\langle P\rangle\sim \langle Q\rangle\sim f_a$. The axion-axino-saxion fields are combinations of the $P$ and $Q$ fields. A $\mu$ term is then generated with \be \mu\sim \lambda f_a^2/M_P . \ee Originally, Kim-Nilles had sought to identify the PQ scale $f_a$ with the hidden sector SUSY breaking scale $m$. However, now we see that in fact the developing Little Hierarchy $\mu\ll m_{3/2}$ is nothing more than a reflection of an apparent mis-match between the PQ breaking scale and hidden sector SUSY breaking scale $f_a\ll m_s$. Guided by electroweak naturalness, we expect $\mu\sim 100-200$ GeV so that with $\lambda\sim 1$, then we expect \be f_a\sim 10^{10}\ {\rm GeV} . \ee In this case, since the axion mass $m_a\sim 6.2\ \mu {\rm eV}\left( \frac{10^{12}\ {\rm GeV}}{f_a}\right)$ then {\it the Higgs mass tells us where to look for the axion}: $m_a\sim 620\mu{\rm eV}$ with DFSZ couplings. Furthermore, in such a scenario then one expects dark matter to consist of a DFSZ axion along with a higgsino-like WIMP: {\it i.e. two} dark matter particles\cite{dfsz1}. | In this paper, we have re-examined electroweak fine-tuning in light of recent LHC results on the Higgs discovery with $m_h\simeq 125.5$ GeV and the lack of any sort of signal for sparticles. This situation has lead to various claims that the MSSM is no longer viable, or at least highly fine-tuned in the EW sector. Alternatively, it has been claimed that conventional measures, applied conventionally, overestimate EWFT. To clarify the situation, we have proposed a Rule of Fine-tuning: When evaluating fine-tuning, it is not permissible to claim fine-tuning of {\it dependent} quantities one against another. In the case of Higgs mass fine-tuning, we find that the measure $\Delta_{HS}$ violates this rule by measuring non-independent terms which can lead to large cancellations. Then, Higgs mass fine-tuning can grossly overestimate-- often by orders of magnitude-- the electroweak fine-tuning. By appropriately combining dependent terms, then $\Delta_{HS}$ reduces to the model independent $\Delta_{EW}$ measure: the offending large logs are still present, but can now cancel against other non-independent terms. We have also examined the traditional measure $\Delta_{BG}$. In this case, the measure appears at first sight to be highly model-dependent. The model-dependence is traced to the fact that most users regard the multiple parameters of most popular SUSY models as {\it independent} when in fact their independence is only an artifact of trying to construct a model which encompasses a wide range of hidden sector SUSY breaking possibilities. If instead one relates the various soft parameters-- such as multiples of $m_{3/2}$ as expected in supergravity models with SUSY broken via the superHiggs mechanism-- then it is shown that $\Delta_{BG}$ also reduces to the model-independent electroweak measure $\Delta_{EW}$. For low $\Delta_{EW}$, then it is required that 1. $\mu\sim 100-300$ GeV, 2. $m_{H_u}^2$ is radiatively driven to small negative values $\sim m_Z$ and 3. the top-squarks are in the few TeV range with large mixing. The large mixing reduces top-squark radiative contributions to $\Delta_{EW}$ while lifting $m_h$ into the 125 GeV range. We also evaluated $\Delta_{EW}$ values from a scan over parameters of 15 models: mSUGRA, NUHM1, NUHM2, mGMSB, mAMSB, HCAMSB and nine cases of mixed moduli-anomaly (mirage) mediated SUSY breaking. Our overall results are summarized in Fig. \ref{fig:histo} where we show the range of $\Delta_{EW}$ generated on the $y$-axis versus models on the $x$-axis. Only one model-- NUHM2-- reaches to the rather low $\Delta_{EW}\sim 10$ values, indicating just 10\% EWFT. This can be so because the freedom in the soft Higgs sector allows arbitrarily low values of $\mu$ (subjectto LEP2 constraints) to be generated while at the same time driving $m_{H_u}^2$ to just small negative values, while also accommodating TeV-scale top squarks with large mixing. For the remaining models, their inherent constraints make satisfying these conditions with $m_h\sim 125$ GeV very difficult unless they are highly fine-tuned. The best of the remainder models include $NUHM1$ which allows for min $\Delta_{EW}$ as low as 30. Thus, $\Delta_{EW}$ does indeed put SUSY models under seige. Luckily, at least NUHM2 and its generalizations survive, and even thrive. In the case of the surviving NUHM2 spectra (those with $\Delta_{EW}\alt 30$), a discovery at LHC14 might take place provided $m_{\tg}\alt 2$ TeV\cite{lhc}: this reach covers about half of parameter space\cite{rns}. The definitive search for SUSY would have to take place at a linear $e^+e^-$ collider where $\sqrt{s}$ could extend beyond $2m(higgsino)$-- in this case $\sqrt{s}\sim 500-600$ GeV is required for a thorough search.\footnote{The proposed TLEP $e^+e^-$ collider with projected maximal $\sqrt{s}\sim 350$ GeV may not have sufficient energy to thoroughly explore natural SUSY\cite{tlep}.} Such a machine would either discover SUSY or rule out SUSY naturalness\cite{snowmass2}. We may also expect an ultimate discovery of a Higgsino-like WIMP and a DFSZ-type axion, since models such as SUSY DFSZ solve the strong CP fine-tuning problem and the $\mu$ problem while at the same time allowing naturally for a Little Hierarchy of $f_a\ll m_s$, where $m_s\sim 10^{11}$ GeV represents the mass scale usually associated with hidden sector SUSY breaking. That hierarchy is then reflected by the hierarchy $\mu\ll m_{3/2}$ which seems to be what naturalness combined with LHC data is telling us. \begin{figure}[tbp] \includegraphics[height=0.3\textheight]{histogram_b} \caption{Histogram of range of $\Delta_{EW}$ values generated for each SUSY model considered in the text. We would consider $\Delta_{EW}\alt 30$-- the lower the better-- as acceptable values for EW fine-tuning. This region is located below the dashed red line. \label{fig:histo}} \end{figure} We end by confessing that the general features of some of our viewpoints have been articulated previously by Giudice\cite{gian}: \begin{quotation} ``It may well be that, in some cases, Eq. \ref{eq:DBG} overestimates the amount of tuning. Indeed, Eq. \ref{eq:DBG} measures the sensitivity of the prediction of $m_Z$ as we vary parameters in ``theory space''. However, we have no idea how this ``theory space'' looks like, and the procedure of independently varying all parameters may be too simple-minded.'' \end{quotation} Amen! | 14 | 4 | 1404.2277 |
1404 | 1404.2870_arXiv.txt | {In 2010 a sub-stellar companion to the solar analog pre-main sequence star PZ Tel and member of the about 12 Myr old $\beta$~Pic moving group was found by high-contrast direct imaging independently by two teams.} {In order to determine the basic parameters of this companion more precisely and independent of evolutionary models, hence age independent, we obtained follow-up spectroscopic observations of primary and companion.} {We use the Spectrograph for INtegral Field Observations in the Near Infrared (SINFONI) at the Very Large Telescope Unit 4/YEPUN of ESO's Paranal Observatory in H+K band and process the data using the spectral deconvolution technique. The resulting spectrum of the companion is then compared to a grid of {\sc Drift-Phoenix} synthetic model spectra, a combination of a general-purpose model atmosphere code with a non-equilibrium, stationary cloud and dust model, using a $\chi^2$ minimization analysis.} {We find a best fitting spectral type of G6.5 for PZ Tel A. The extracted spectrum of the sub-stellar companion, at a spatial position compatible with earlier orbit estimates, yields a temperature T$_{\rm eff}$=\,2500\,$^{+138}_{-115}$\,K, a visual extinction $A_{V}$=\,0.53\,$^{+0.84}_{-0.53}$\,mag, a surface gravity of $\log{g}$=\,3.50$^{+0.51}_{-0.30}$\,dex, and a metallicity at the edge of the grid of [M/H]=\,0.30$_{-0.30}$\,dex.} {We derive a luminosity of $\log(L_{bol}/L_{\odot})$=\,-2.66$^{+0.06}_{-0.08}$, a radius of R=\,2.42$^{+0.28}_{-0.34}$\,R$_{\mathrm{Jup}}$ and a mass of M=\,7.5$^{+16.9}_{-4.3}$\,M$_{\mathrm{Jup}}$ for the PZ Tel companion, being consistent with most earlier estimates using photometry alone. Combining our results with evolutionary models, we find a best fitting mass of about 21 Jupiter masses at an age corresponding to the recently determined lithium depletion age of 7$^{+4}_{-2}$ Myr. Hence, the PZ Tel companion is most likely a wide brown dwarf companion in the 12$^{+8}_{-4}$ Myr old $\beta$~Pic moving group.} | In 2010 two groups performing high-contrast direct imaging surveys around young nearby stars \citep{2010A&A...523L...1M,2010ApJ...720L..82B} independently reported the discovery of a sub-stellar companion around the young solar analog pre-main-sequence star \object{PZ Tel} (HD 174429, HIP 92680), a likely member of the 12$^{+8}_{-4}$ Myr old $\beta$~Pic moving group \citep{2001ApJ...562L..87Z,2006A&A...460..695T} having a spectral type of G5 -- K8 \citep{1936pmsz.book.....S,2010A&A...520A..15M} at an age of 12.8\,$\pm$\,2.2 Myr \citep{2011MNRAS.410..190T}. While not detectable in 2003 because of its proximity to the host star \citep{2005ApJ...625.1004M}, the sub-stellar companion was first observed on its orbit in 2007 at a projected separation of 0.255 arcsec (13 au at 51.5\,$\pm$\,2.6 pc \citep{2007A&A...474..653V}), identified by \citet{2010A&A...523L...1M} in archival data of \citet{2010A&A...509A..52C} after detection at 0.337 arcsec in 2009 by \citet{2010A&A...523L...1M}. \citet{2008ApJ...681.1484R} detected excess emission in the spectral energy distribution of PZ Tel at 70 $\mu$m with MIPS/Spitzer, indicating the star is surrounded by a low-mass, cold ($\sim$41\,K) debris disk. On the basis of further astrometric data \citet{2012MNRAS.424.1714M} could show that the preliminary determined orbital parameters of the PZ Tel companion are compatible with this disk being circumbinary (around both components), but not with being circumstellar, and that a semimajor axis of the nearly edge-on orbit not exceeding 25 au is likely. \begin{table*} \caption{VLT/SINFONI observation log} \label{table:1} \centering \begin{tabular}{llccccccccc} \hline\hline Object & JD - 2450000 & Date of & DIT & NDIT & Number & Airmass & DIMM$^a$ & $\tau_{0}^b$ \\ & $[\mathrm{days}]$ & observation & [s] & & of images & & Seeing & [ms] \\ \hline PZ Tel & 5795.62984 & 22 Aug 2011 & 5 & 9 & 16 & 1.17 & \ \, 1.35 & 1.2 \\ \object{HIP 94378} & 5795.65222 & 22 Aug 2011 & 2 & 5 & 1 & 1.11 & $\sim$1.49 & 1.1 \\ \hline \end{tabular} \begin{flushleft} \textbf{Remarks}: All observations were done in H+K band and 0.025 mas/spaxel scale (FoV: 0.8 arcsec x 0.8 arcsec). (a) Differential image motion monitor (DIMM) Seeing average of all images (b) coherence time of atmospheric fluctuations. \end{flushleft} \end{table*} \begin{figure*} \centering \resizebox{0.8\textwidth}{!}{\includegraphics{PSFRemoval.eps}} \caption{Averaged data cubes obtained of the PZ Tel companion in H-band (\textit{upper row}) and K-band (\textit{lower row}) at position angle -30$^\circ$. \textit{From left to right in each row}: Cube after data reduction, eastern part of cube after 2 dimensional polynomial fit of the primary PSF and removal of the primary halo, cube after subtration of the radial symmetric part of the primary PSF, cube after subtration of the radial symmetric part of the primary PSF and additional spectral deconvolution. For clarity flux is inverted in the latter 3 images of each row. See text for details.} \label{FigPSFRemoval} \end{figure*} Both \citet{2010ApJ...720L..82B} using NICI at Gemini-South and \citet{2010A&A...523L...1M} using NACO at ESO VLT concluded from photometric data in their discovery papers that the imaged object is likely a brown dwarf companion to the $\beta$~Pic moving group member PZ Tel. \citet{2010ApJ...720L..82B} find best fitting parameters of 2702\,$\pm$\,84 K and log g of 4.20\,$\pm$\,0.11 dex, hence 36\,$\pm$\,6 M$_{\mathrm{Jup}}$, while \citet{2010A&A...523L...1M} find 2500--2700 K, hence 28$^{+12}_{-4}$ M$_{\mathrm{Jup}}$, both using evolutionary models \citep{2000ApJ...542..464C}. \citet{NeuhSchmidt2012} noted that given this lower mass limit, the PZ Tel companion could even be a planetary mass object, considering the planet definition by \citet{2011A&A...532A..79S}. Recently, \citet{2012MNRAS.420.3587J} derived an age of the system of 24\,$\pm$\,3 Myr, based on evolutionary models and chromospheric activity of the primary, contrasting with their own age determination of 7$^{+4}_{-2}$ Myr obtained from lithium depletion. This higher age estimate yields a higher effective temperature 2987\,$\pm$\,100 K, surface gravity ($\log{g}$) 4.78\,$\pm$\,0.10 dex and mass 62\,$\pm$\,9 M$_{\mathrm{Jup}}$. They moreover determined the metallicity [Fe/H] of the system to be 0.05\,$\pm$\,0.20 dex. In order to determine the basic parameters of the PZ Tel companion more precisely and independent of evolutionary models we obtained follow-up spectroscopy. Here we present our results from these observations, targeted to identify the nature of the sub-stellar companion. | Using the photometry of PZ Tel A from the Two Micron All Sky Survey (2MASS) catalog \citep{2003tmc..book.....C,2006AJ....131.1163S} of $K$\,=\,6.366\,$\pm$\,0.024\,mag we can estimate all further parameters of the sub-stellar companion using all results from the spectroscopic analysis described in the previous section. As no absolute photometric calibration is possible with the spectroscopic standard, we preliminary estimate the parameters of the PZ Tel companion assuming negligible photometric variability of both sources, most likely not correct according to variability indications presented in the previous sections. We derive a luminosity of $\log(L_{bol}/L_{\odot})$=\,-2.66$^{+0.06}_{-0.08}$ for the PZ Tel companion from the extinction corrected apparent brightness Ks$_{0}$= 11.86$^{+0.07}_{-0.10}$\,mag \cite[from the 2MASS brightness, the magnitude difference (Table~\ref{table:2}), $A_{V}$=\,0.53\,$^{+0.84}_{-0.53}$\,mag and extinction law by][]{1985ApJ...288..618R} using a bolometric correction of B.C.$_{K}$\,=\,3.1\,$\pm$\,0.1\,mag from \citet[][for spectral type M6--L0]{2004AJ....127.3516G} at a distance of 51.49$^{+2.74}_{-2.47}$\,pc \citep{2007A&A...474..653V}. From the luminosity and temperature T$_{\rm eff}$=\,2500\,$^{+138}_{-115}$\,K, we calculate the radius to be R=\,0.25$^{+0.03}_{-0.04}$\,R$_{\odot}$ or 2.42$^{+0.28}_{-0.34}$\,R$_{\mathrm{Jup}}$. From radius and surface gravity $\log{g}$=\,3.50$^{+0.51}_{-0.30}$\,dex, we find a mass of the PZ Tel companion of M=\,0.0071$^{+0.0161}_{-0.0041}$\,M$_{\odot}$ or 7.5$^{+16.9}_{-4.3}$\,M$_{\mathrm{Jup}}$. For the bolometric correction we used the spectral type corresponding to the temperature range found here. Using the H$_2$O index defined in \citet{2007ApJ...657..511A} we find a possible spectral range of L1.5 -- L4 for the sub-stellar companion, using the modified version in \citet{2014A&A...562A.127B} we find a possible spectral range of M7 -- L9, roughly consistent with our findings of M6 -- L0. \citet{2014A&A...562A.127B} modified the index to avoid noisy regions, definitely necessary in the present case, as the blue part of the H-band has the lowest signal to noise. Our derived surface gravity uncertainties are about equal to the values of 0.5 dex, as computed by \citet{2014A&A...562A.127B} for similar objects. The derived values, diagramed in Figs.~\ref{FigContourExtinction}--\ref{FigContourMetallicity}, agree within 1 $\sigma$ with the extinction $A_{V}$ and metallicity [M/H] for PZ Tel A by \citet{2011MNRAS.411..435B} and \citet{2012MNRAS.420.3587J}, respectively as well as with the temperature by \citet{2010A&A...523L...1M}. Temperature and surface gravity deviate in regard to literature estimates by 1.2 \& 1.3 $\sigma$ \citep{2010ApJ...720L..82B} and 2.9 \& 2.5 $\sigma$ \citep{2012MNRAS.420.3587J}, respectively. Finally our mass result deviates by 1.2 $\sigma$ \cite[28$^{+12}_{-4}$\,M$_{\mathrm{Jup}}$,][]{2010A&A...523L...1M}, by 1.6 $\sigma$ \cite[36\,$\pm$\,6\,M$_{\mathrm{Jup}}$,][]{2010ApJ...720L..82B} and by 3.2 $\sigma$ \cite[62\,$\pm$\,9\,M$_{\mathrm{Jup}}$,][]{2012MNRAS.420.3587J}. Although our mass estimate is independent of evolutionary models, we can use them as comparison to put our results into context and to check which age is indicated by the models for our spectroscopic results. According to \citet{2000ApJ...542..464C} DUSTY models best fits are achieved between 5 -- 10 Myr isochrones, fitting our spectral results for temperature, surface gravity and luminosity within 1 $\sigma$ errors. This age range is consistent with the age of the $\beta$~Pic moving group (12$^{+8}_{-4}$ Myr), deviant from the age determined by \citet{2012MNRAS.420.3587J} (24\,$\pm$\,3 Myr), while very well consistent with the lithium depletion age of PZ Tel A of 7$^{+4}_{-2}$ Myr by the same authors. Very recently \citet{2014MNRAS.438L..11B} combined data of eight low-mass candidates with literature data of $\beta$~Pic moving group members and find a lithium depletion age of 21\,$\pm$\,4 Myr, being also inconsistent with the age found here. Finally we arrive at a possible mass range of 3.2 -- 24.4 M$_{\mathrm{Jup}}$. According to these estimates the PZ Tel companion is most likely a brown dwarf of about 21 Jupiter masses, as the evolutionary models reject a $\log{g}$\,=\,3.5\,dex to be only valid for objects younger than 1 Myr and predict a surface gravity $\log{g}$\,$\sim$\,3.95\,dex for the given lithium depletion age range, being within the 1 $\sigma$ uncertainty of our results. However, spectra at improved observing conditions and with longer spectral range, especially including alkali metal lines for a more precise surface gravity determination should be able to narrow down the parameters of the PZ Tel companion in the future. Fortunately such spectra are increasingly easy to acquire because of the strong orbital separation increase, probably persistent for the upcoming years to decades \citep{2012MNRAS.424.1714M}. | 14 | 4 | 1404.2870 |
1404 | 1404.3271_arXiv.txt | { Hot exozodiacal dust is thought to be responsible for excess near-infrared (NIR) emission emanating from the innermost parts of some debris disks. The origin of this dust, however, is still a matter of debate. } { We test whether hot exozodiacal dust can be supplied from an exterior parent belt by Poynting--Robertson \mbox{(P--R)} drag, paying special attention to the pile-up of dust that occurs due to the interplay of \mbox{P--R} drag and dust sublimation. Specifically, we investigate whether pile-ups still occur when collisions are taken into account, and if they can explain the observed NIR excess. } { We compute the steady-state distribution of dust in the inner disk by solving the continuity equation. First, we derive an analytical solution under a number of simplifying assumptions. Second, we develop a numerical debris disk model that for the first time treats the complex interaction of collisions, \mbox{P--R} drag, and sublimation in a self-consistent way. From the resulting dust distributions we generate thermal emission spectra and compare these to observed excess NIR fluxes. } { We confirm that P--R drag always supplies a small amount of dust to the sublimation zone, but find that a fully consistent treatment yields a maximum amount of dust that is about 7 times lower than that given by analytical estimates. The NIR excess due this material is much smaller ($\lesssim$10$^{-3}$ for \mbox{A-type} stars with parent belts at $\gtrsim$1~AU) than the values derived from interferometric observations ($\sim$10$^{-2}$). Pile-up of dust still occurs when collisions are considered, but its effect on the NIR flux is insignificant. Finally, the cross-section in the innermost regions is clearly dominated by barely bound grains. } {} | Circumstellar dust in debris disks reveals the location and dynamical state of larger bodies, and hence sheds light on the architecture of planetary systems in the aftermath of planet formation (see \citealt{2008ARA&A..46..339W} for a review). The dust can be studied by observing its infrared and (sub-)millimeter emission, as well as the stellar radiation it scatters, and is usually found at large distances from the star \citep[tens of AUs,][]{2009ApJS..181..197C}. Recently, interferometric observations have found excess near-infrared (NIR) emission emanating from the innermost parts of several debris disks, which has been interpreted as thermal emission from hot ($>$1000~K) dust \citep[see Tbl.~\ref{tbl:obs} for an overview]{2001ApJ...559.1147C,2006A&A...452..237A, 2008A&A...487.1041A,2009ApJ...704..150A,2007A&A...475..243D,2009ApJ...691.1896A,2011A&A...534A...5D,2012A&A...546L...9D}. This material is known as hot exozodiacal dust. Its origin, and hence what it can tell us about planet formation, is still unclear. In this work, we investigate one possible scenario to explain hot exozodiacal dust. \begin{table*}[!t] \centering \caption{NIR interferometric detections of hot exozodiacal dust, together with associated outer debris belt locations} \label{tbl:obs} \begin{tabular}{cc|cr@{ $\pm$ }lccc|ccc} \hline Object & Sp. type & Band & \multicolumn{2}{c}{Excess} & FOV\tablefootmark{a} & Instrument & Refs. & Outer belt distance\tablefootmark{b} & Refs. \\ & & & \multicolumn{2}{c}{[\%]} & [AU] & & & [AU] & \\ \hline Vega & A0V & $H$ & 1.23 & 0.53 & 6 & IOTA/IONIC & D11 & 10--14, 80 & D00, S13 \\ Vega & A0V & $K$ & 1.26 & 0.27 & 3 & CHARA/FLUOR & A06, A13 & 10--14, 80 & D00, S13 \\ Vega & A0V & $K$ & \multicolumn{2}{c}{$5^{+1}_{-2}\;\;$} & 4 & PTI & C01 & 10--14, 80 & D00, S13 \\ $\upzeta$~Aql & A0V & $K$ & 1.69 & 0.27 & 10 & CHARA/FLUOR & A08, A13 & no detectable outer belt & A08, P09 \\ $\upbeta$~Leo & A3V & $K$ & 0.94 & 0.26 & 4 & CHARA/FLUOR & Ak09, A13 & 19 & C06 \\ $\uplambda$~Gem & A3V & $K$ & 0.74 & 0.17 & 12 & CHARA/FLUOR & A13 & no detectable outer belt & M09, G13 \\ Fomalhaut & A4V & $K$ & 0.88 & 0.12 & 6 & VLTI/VINCI & Ab09 & 2, 8--11, 133 & K05, L13, S13 \\ $\upbeta$~Pic\tablefootmark{c} & A6V & $H$ & 1.37 & 0.16 & 4 & VLTI/PIONIER & D12 & 10--40\tablefootmark{d} & L94, P97 \\ $\upbeta$~Pic\tablefootmark{c} & A6V & $K$ & 0.76 & 0.49 & 1.3 & VLTI/VINCI & D04, D12 & 10--40\tablefootmark{d} & L94, P97 \\ $\upalpha$~Aql & A7V & $K$ & 3.07 & 0.24 & 2 & CHARA/FLUOR & A13 & no detectable outer belt & A13 \\ $\upalpha$~Cep & A7IV & $K$ & 0.87 & 0.18 & 6 & CHARA/FLUOR & A13 & no detectable outer belt & C05 \\ $\upeta$~Lep\tablefootmark{e} & F1V & $K$ & 0.89 & 0.21 & 6 & CHARA/FLUOR & A13 & 1--16, 18 & L09, E13 \\ 110~Her\tablefootmark{e} & F6V & $K$ & 0.94 & 0.25 & 8 & CHARA/FLUOR & A13 & 70--500 & M13 \\ 10~Tau\tablefootmark{e} & F9V & $K$ & 1.21 & 0.11 & 6 & CHARA/FLUOR & A13 & $>$5.8 & T08 \\ $\upxi$~Boo\tablefootmark{e} & G8V & $K$ & 0.74 & 0.20 & 3 & CHARA/FLUOR & A13 & no detectable outer belt & A13 \\ $\uptau$~Cet & G8V & $K$ & 0.98 & 0.18 & 1.5 & CHARA/FLUOR & D07, A13 & 10--55 & G04 \\ $\upkappa$~CrB\tablefootmark{e} & K1IV & $K$ & 1.18 & 0.20 & 12 & CHARA/FLUOR & A13 & 20, 41 & B13 \\ \hline \end{tabular} \tablefoot{ \\ \tablefoottext{a}FOV denotes the approximate linear field-of-view radius at half maximum. \\ \tablefoottext{b}For the outer belt distance ($r\sub{0}$ in our models) we list literature estimates of the radial distance to (the inner edge of) ``cold'' and ``warm'' outer belts, derived from SED fitting and/or resolved imaging. \\ \tablefoottext{c}The NIR excess of $\upbeta$~Pic contains a significant contribution from stellar light scattered by the outer belt \citep{2012A&A...546L...9D}. \\ \tablefoottext{d}The debris disk around $\upbeta$~Pic is seen edge-on, making it hard to determine the parent belt location. The values given mark the radial range in which the particle density is derived to decrease. \\ \tablefoottext{e}For $\upeta$~Lep, 110~Her, 10~Tau, $\upxi$~Boo, and $\upkappa$~CrB, the possibility that the observed NIR excess is due to a low-mass companion within the field-of-view cannot be excluded \citep{2013A&A...555A.104A}. } \tablebib{ (A06)~\citet{2006A&A...452..237A}; (A08)~\citet{2008A&A...487.1041A}; (Ab09)~\citet{2009ApJ...704..150A}; (Ak09)~\citet{2009ApJ...691.1896A}; (A13)~\citet{2013A&A...555A.104A}; (B13)~\citet{2013MNRAS.431.3025B}; (C01)~\citet{2001ApJ...559.1147C}; (C05)~\citet{2005ApJ...634.1372C}; (C06)~\citet{2006ApJS..166..351C}; (D00)~\citet{2000MNRAS.314..702D}; (D04)~\citet{2004A&A...426..601D}; (D07)~\citet{2007A&A...475..243D}; (D11)~\citet{2011A&A...534A...5D}; (D12)~\citet{2012A&A...546L...9D}; (E13)~\citet{2013A&A...555A..11E}; (G04)~\citet{2004MNRAS.351L..54G}; (G13)~\citet{2013ApJ...768...25G}; (K05)~\citet{2005Natur.435.1067K}; (L94)~\citet{1994Natur.369..628L}; (L09)~\citet{2009ApJ...705...89L}; (L13)~\citet{2013A&A...555A.146L}; (M09)~\citet{2009ApJ...699.1067M}; (M13)~\citet{2013A&A...557A..58M}; (P97)~\citet{1997A&A...327.1123P}; (P09)~\citet{2009ApJ...698.1068P}; (S13)~\citet{2013ApJ...763..118S}; (T08)~\citet{2008ApJ...674.1086T}. } \end{table*} Dust grains in debris disks have relatively short lifetimes, due to their destruction by collisions and removal by radiation forces. The detection of these grains around mature stars therefore implies the existence of a mechanism that continuously replenishes them. Cold dust populations at large distances from the star can be maintained by a collisional cascade grinding down much larger bodies that act as a reservoir of mass \citep{1993prpl.conf.1253B}. Closer to the star, however, the pace at which material is processed by collisions is much higher, and hence the lifetime of a debris belt in collisional equilibrium is much shorter there \citep{2003ApJ...598..626D,2007ApJ...658..569W}. For this reason, hot exozodiacal dust cannot be explained by in-situ planetesimal belts \citep{2007ApJ...658..569W,2013A&A...555A.146L},\footnote{ \citet{2013MNRAS.433.2334K} find that ``warm'' exozodiacal dust around solar-type stars can be explained by in-situ planetesimal belts. This type of exozodiacal dust is detected at mid-infrared wavelengths and has a typical temperature of a few hundred K, placing it around 1~AU from the star.} and a different mechanism is needed to replenish it, and/or the lifetime of the dust needs to be extended by some process. Many of the systems that exhibit NIR excess also feature a debris belt at a large distance from the star (see Tbl.~\ref{tbl:obs}). Inward transport of material from an outer belt may therefore be a natural explanation for the existence of hot exozodiacal dust. A possible transportation mechanism is Poynting--Robertson (\mbox{P--R}) drag \citep[see, e.g.,][]{1979Icar...40....1B}. Because \mbox{P--R} drag acts on a timescale that is much longer than that of collisions, it is sometimes disfavored as possible mechanism for maintaining exozodiacal dust \citep[e.g.,][]{2006A&A...452..237A}. However, as long as there are no mechanisms that prevent inward migration, a small amount of dust is always transported to the innermost part of the disk \citep{2005A&A...433.1007W}, where it produces a NIR signal. Morphological models of exozodiacal dust disks, constrained by the NIR observations, indicate that the hot dust is concentrated in a sharply peaked ring, whose inner boundary is determined by dust sublimation \citep{2011A&A...534A...5D,2013ApJ...763..119M,2013A&A...555A.146L}. The process of dust sublimation may therefore play an important role in shaping exozodiacal clouds. \citet{2009Icar..201..395K} find that the interplay between \mbox{P--R} drag and dust sublimation can lead to a local enhancement of dust in the sublimation zone, leading to radial distributions of dust reminiscent of those found by the morphological models. However, they only investigate this pile-up effect for drag-dominated systems, in which collisions are unimportant, and it is unclear what happens to the phenomenon if collisions are taken into account. In this work, we examine whether it is possible to maintain a pile-up of dust in the sublimation zone of a collisionally active debris disk, and whether such a pile-up could explain the exozodiacal NIR emission observed very close to some stars. To do this, we compute the steady-state distribution of dust in the inner parts of debris disks, under the influence of collisions, \mbox{P--R} drag, and sublimation, by solving the continuity equation. First, we find an analytical solution, using a number of simplifying assumptions (Sect.~\ref{s:analytic}). Subsequently, we solve the continuity equation numerically using a debris disk model that for the first time treats the complex interaction of collisions, \mbox{P--R} drag, and sublimation in a self-consistent way (Sect.~\ref{s:numeric}). From the obtained steady-state dust distributions, we compute emission spectra to compare with observational data (Sect.~\ref{s:seds}). We discuss our findings in Sect.~\ref{s:discussion}, and give conclusions in Sect.~\ref{s:conclusions}. Details of the numerical techniques employed by the debris disk model are given in Appendix~\ref{s:app_num}, model verification tests are described in Appendix~\ref{s:app_verif}, and the post-processing of model output into useful physical quantities in described in Appendix~\ref{s:app_postproc}. | \label{s:conclusions} In this work, we investigated hot dust in the inner regions of debris disks, whose presence is suggested by interferometrically resolved excess NIR emission observed in some debris disk systems (Tbl.~\ref{tbl:obs}). We tested whether the hot dust can be supplied by \mbox{P--R} drag from a distant parent belt, and whether the pile-up of dust in the sublimation zone still occurs if collisions are considered. Our main conclusions are as follows: \begin{enumerate} \item As predicted by \cite{2005A&A...433.1007W}, \mbox{P--R} drag always brings a small amount of dust from an outer debris belt into the sublimation zone. The maximum geometrical optical depth that can be reached in the innermost parts of the disk depends on the mass of the central star and distance to the parent belt (Fig.~\ref{fig:max_tau}). When the production of dust is treated self-consistently, this maximum is found to be a factor of about 7 lower than the analytical estimate (Fig.~\ref{fig:num_tau}). This is because small dust particles, which are dragged inwards efficiently by radiation forces, are also put on highly eccentric orbits by those radiation forces, and therefore suffer more collisional destruction. \item Dust that reaches the sublimation zone produces some NIR emission, but this excess flux is insufficient to explain the interferometric observation. While the observed excess ratios are of the order of $\sim$10$^{-2}$, the maximum flux ratio due to material supplied by \mbox{P--R} drag is $\lesssim$10$^{-3}$ for \mbox{A-type} stars with parent belts at $\gtrsim$1~AU (Fig.~\ref{fig:flux_ratio}). \item The pile-up of dust due to the interplay of \mbox{P--R} drag and sublimation still occurs when collisions are considered (Fig.~\ref{fig:num_tau}), as long as the parent belt from which the dust originates is distant enough to allow for sufficient circularization of the orbits, and the central star is luminous enough to blow small dust grains out of the system. Collisions do not interfere with the pile-up process, since in the inner disk, the collisional timescale is longer than the \mbox{P--R} drag timescale for the barely bound grains that are the most important for the pile-up. The fractional luminosity provided by dust in the pile-up is relatively small, so the pile-up does not influence the disk SED significantly (Fig.~\ref{fig:seds}). \item In the inner parts of dense debris disks, the cross section is clearly dominated by barely bound ($\beta \approx 0.5$) grains, and the size distribution features a prominent wave pattern, related to the discontinuity in the size distribution at the blowout size (Fig.~\ref{fig:size_prtail}). In the pile-up, there is an enhancement of particles with $0.5 \lesssim \beta < 1$ (Fig.~\ref{fig:size_pileup}). These particles are still bound, because of their almost circular orbits at the start of substantial sublimation. \end{enumerate} | 14 | 4 | 1404.3271 |
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