subfolder
stringclasses 367
values | filename
stringlengths 13
25
| abstract
stringlengths 1
39.9k
| introduction
stringlengths 0
316k
| conclusions
stringlengths 0
229k
| year
int64 0
99
| month
int64 1
12
| arxiv_id
stringlengths 8
25
|
|---|---|---|---|---|---|---|---|
1609 | 1609.04832_arXiv.txt | We use the {\it Wide-field Infrared Survey Explorer} ({\it WISE}) and the Sloan Digital Sky Survey (SDSS) to confirm a connection between dust-obscured active galactic nuclei (AGNs) and galaxy merging. Using a new, volume-limited ($z\leq0.08$) catalog of visually-selected major mergers and galaxy-galaxy interactions from the SDSS, with stellar masses above $2\times10 ^ {10} ~ {\rm M}_{\odot}$, we find that major mergers (interactions) are 5--17 (3--5) times more likely to have red $[3.4]-[4.6]$ colors associated with dust-obscured or `dusty' AGNs, compared to non-merging galaxies with similar masses. Using published fiber spectral diagnostics, we map the $[3.4]-[4.6]$ versus $[4.6]-[12]$ colors of different emission-line galaxies and find one-quarter of Seyferts have colors indicative of a dusty AGN. We find that AGNs are five times more likely to be obscured when hosted by a merging galaxy, half of AGNs hosted by a merger are dusty, and we find no enhanced frequency of optical AGNs in merging over non-merging galaxies. We conclude that undetected AGNs missed at shorter wavelengths are at the heart of the ongoing AGN-merger connection debate. The vast majority of mergers hosting dusty AGNs are star-forming and located at the centers of ${\rm M}_{\rm halo}<10 ^ {13} ~ {\rm M}_{\odot}$ groups. Assuming plausibly short duration dusty-AGN phases, we speculate that a large fraction of gas-rich mergers experience a brief obscured AGN phase, in agreement with the strong connection between central star formation and black hole growth seen in merger simulations. | \label{sec:intro} % A connection between major galaxy mergers and active galactic nuclei (AGNs) remains a debate in galaxy evolution research. In simulations, major encounters between similar mass (typically $\leq$4:1 mass ratio), gas-rich galaxies are predicted to drive gas to the centers of interacting and merging systems triggering new star formation (SF) and fueling an AGN \citep{Volonteri+03,Hopkins+08, DiMatteo+05,Springel+05, DeBuhr+11}. Many observational studies support the correlation between AGNs and merging systems \citep{Karouzos+10, Treister+12, Cotini+13, Ellison+13b, Nazaryan+14, Satyapal+14, Rosario+15}. However, other researchers, particularly those working at shorter wavelengths, do not find such a connection \citep{Cisternas+11, Kocevski+12, Fan+14, Scott+14, Villforth+14}. One possible reason for this debate is dust obscuration caused by SF in the center of some merging systems \citep{Goulding+09}, indicating that longer wavelengths, such as the infrared, may be able to provide a better understanding of the AGN-merger connection. In this study, we perform a simple test of whether or not highly disturbed galaxies and major pairs with indicators of tidal activity have an excess obscured-AGN frequency. In the larger context of galaxy evolution, there are many compelling reasons to expect a connection between major gas-rich mergers and supermassive black hole (SMBH) growth. The hierarchical assembly of massive structures is a key feature of $\Lambda$CDM cosmology \citep{White+78}. The growth of large-scale structures is predicted to drive galaxy mergers \citep{Kauffmann+93, Baugh+96, Cole+00}, which in turn have long been tied to the formation of galactic bulges and spheroidal galaxies \citep{Lake+86, Shier+98, Rothberg+06}. The masses of galaxy spheroids are strongly correlated with the masses of their SMBHs \citep{Magorrian+98}. Moreover, massive, bulge-dominated galaxies are predominantly passive and old \citep{Kauffmann+03}, requiring one or more processes to shut down star production and maintain SF quenching. An oft-cited theoretical quenching process is AGN feedback \citep{Schawinski+07, DiMatteo+08, Kaviraj+11}, which is the release of energy from black hole accretion, either through gas outflows \citep{Granato+14}, often associated with gas-rich mergers \citep{DiMatteo+05, Springel+05, Hopkins+06}, or heating of the interstellar medium \citep{Hopkins+10a}. Such feedback is especially important if gas-rich mergers trigger new strong SF activity as simulations predict \citep{Kauffmann+00, DiMatteo+05, Springel+05, Hopkins+08, Cox+08}. All of the above has been neatly folded into the modern merger hypothesis and nicely summarized by \citet{Hopkins+08}. Briefly, \citet{Hopkins+08} produced the following gas-rich major-merger model, in which quasar activity from z = 0 -- 6 was accurately reproduced through the merger process. First, two equal stellar mass, gas-rich galaxies pass one another, causing morphological disturbances, such as tidal tails, and causing a small rise in SF ({\it interacting} phase). As the galaxies are gravitationally pulled back into one another, the gravitational torques cause gas inflows into the nucleus, triggering both SF and black hole growth \citep{Barnes+91,Mihos+96}, with the rates of both limited by the amount of gas in the merger ({\it ongoing merger} phase, \citealt{Kennicutt+98}). As the gas supply is used by SF and black hole accretion in this coalescence, it will shroud the center of the merger with large obscuring columns of dust. When the gas supply is terminated $10^7 - 10^8$ years later \citep{Hopkins+08}, the system will enter a brief unobscured quasar phase \citep{Storchi-Bergmann+01, Schawinski+09}, lasting 10 - 100 Myr \citep{Martinez-Sansigre+09}. This will be followed by a halt in the black hole accretion, leaving behind a decaying galaxy. Over time, the merger remnant will evolve into a spheroid or, if the gas content in the surrounding halo is still high enough for SF, a spheroidal disk \citep{Barnes+02, Springel-Hernquist+05, Hopkins+09}. The connection to AGN activity predicted by simulations is supported by many studies that find high incidences of tidal features associated with AGNs \citep{Treister+12, Cotini+13, Ellison+13b, Satyapal+14, Rosario+15}, including \citet{Karouzos+10}, who found that nearly 30\% of active galaxies showed signs of an interaction or merger in the optical and infrared. \citet{Nazaryan+14} performed an optical study of 180 Markarian galaxy pairs and found that ongoing mergers are 7 times more likely to contain an AGN than interacting pairs. In addition, AGN activity increased with decreasing pair separation. \citet{Treister+12} found that the AGN-merger connection has a luminosity dependence, such that mergers overall made up only 10\% of their AGN sample, but increased to $\sim$ 70 - 80\% for the most luminous AGNs ($L_{\rm bol} > 46$ erg/s). \citet{Satyapal+14} used a Wide-Field Survey Explorer ({\it WISE}) color-color cut to find that 9\% of post-mergers and 1\% of close projected pairs at redshift z $<$ 0.2 are obscured AGNs. Their control population in the same redshift range was found to be only 0.5\% obscured AGNs, suggesting that optically obscured AGNs are more prevalent in merging systems. This connection is further supported by the work of \citet{Kocevski+15}, who used X-ray spectral analysis to select Compton-thick AGNs with z $<$ 1.5 and found that obscured AGNs are three times more likely to display merger or interaction signatures compared to unobscured AGNs. In this work, we aim to replicate the \citet{Satyapal+14} study to lend support to the dusty AGN-merger connection, as well as add valuable information about the properties of dusty AGN-mergers. While simulations and many observational studies find a link between merging systems and AGNs, the topic is still a debate. Many studies, especially those in the X-ray regime, do not find a correlation between mergers and AGN activity \citep{Cisternas+11, Kocevski+12, Bohm+13, Fan+14, Scott+14, Villforth+14}. \citet{Villforth+14} studied the morphologies of 60 X-ray AGNs at 0.5 $<$ z $<$ 0.8 and found that, compared to a simulated control, AGN host galaxies showed no increase in asymmetries or disturbances. Their sample showed a maximum of 6\% of AGNs were related to a major merger. In stark contrast to the simulation-predicted AGN-merger connection, \citet{Scott+14} used optical data to analyze the Seyfert fraction as a function of pair separation in an interacting sample. They found a decrease in Seyferts as pair separation dropped, indicating a drop in AGN activity as interactions begin to merge. The majority of connection-lacking studies in the X-ray and optical regimes all suffer from one important implication of the simulation: they can miss AGNs due to dust obscuration caused by SF in the nucleus. The relationship between SF and interacting systems is a well-documented phenomenon \citep{Kennicutt+87, Barton+00, Lambas+03, Alonso+04, Ellison+08, Ellison+11}. The tidal forces in the interaction funnel cold gas to the center of the merging system, which collapses into stellar nurseries. SF has been found to increase with decreasing pair separations in interacting pairs with $d_{\rm sep}\leq150$\,kpc \citep{Patton+13}. Dust is produced in stellar nurseries and distributed through the interstellar medium via two mechanisms: AGB stars and supernovae \citep{Clemens+13}. As these methods would imply, the SF rate in galaxies correlates to cold dust mass; the more SF, the more dust in the galaxy. A large portion of a galaxy's bolometric luminosity can be absorbed by this dust and re-emitted in the infrared \citep{Kennicutt+98, Treister+10}. The addition of dust from SF in a merging system can make AGNs hard to detect. As the simulations predict \citep{Springel+05, Hopkins+06, Hopkins+08, DeBuhr+11}, SF occurring in the center of a merging galaxy may also produce large obscuring columns, which limit the detection of the AGN. Because of this obscuration, shorter wavelength regimes can be ineffective at isolating obscured AGNs \citep{Treister+10, Goulding+11}, which would be the AGN type most likely to occur in the major merger model \citep{Hopkins+08}. Optical spectroscopic surveys can miss as much as half of the AGN population due to obscuration, particularly that caused by dust from SF \citep{Goulding+09}. Below 10 keV, the X-ray regime can also be affected by dust obscuration \citep{Treister+10, Kocevski+15}. \citet{Koss+10} use the {\it SWIFT} BAT AGN survey (hard X-rays; 14--195 keV) and do find an AGN-merger connection, verifying that soft X-rays might not be adequate for obscured AGN selection in mergers. The likelihood of dust obscuration from increased SF in merging and interacting systems leads to the use of the infrared wavelength regime to isolate AGNs, as countless other studies have done \citep{Stern+05, Goulding+09, Jarrett+11, Stern+12, Assef+13, Yan+13}. While the infrared regime has drawbacks of its own (see \S \ref{sec:55discussion_IRlimitations}), it will allow us to isolate a subpopulation of {\it dusty} AGNs \citep{Cardamone+08}. Following work by \citet{Satyapal+14}, we search for obscured AGNs in a complete sample of visually selected major mergers and interactions from the SDSS, using near- and mid-infrared data from {\it WISE} \citep{Wright+10}. {\it WISE} provides all-sky coverage at wavelengths between 3 and 22 microns with sensitivities better than IRAS and DIRBE, making it the best database to look for obscured AGNs in SDSS galaxies. Using the infrared in this study allows us to quantify the incidence of {\it dusty} AGNs in merging and interacting systems. Using a sample of interacting pairs and ongoing mergers visually selected from a large parent catalog of $\sim$ 65,000 Sloan Digital Sky Survey (SDSS) galaxies, combined with mid-infrared colors from the {\it WISE} All-Sky survey, we isolate a population of dusty AGNs and compare their relative frequency to that of a control sample. We find strong evidence in support of the AGN-merger connection. We also analyze the properties of the infrared-selected AGNs to identify any unique trends. In addition, we discuss the AGN-merger connection for both optical and infrared selection to emphasize the dusty AGN-merger connection. In \S \ref{sec:2sample}, we describe our sample of merging and interacting galaxies. In \S \ref{sec:3WISEanalysis}, we show our analysis and highlight the results of different {\it WISE} color-color methods to select AGNs. We give a summary of {\it WISE} AGN properties for our interacting and merging sample in \S \ref{sec:4nature}. We provide an overall summary of our results and how they compare to literature in \S \ref{sec:5discussion} and \S \ref{sec:6summary}. Throughout this paper, we assume a $\Lambda$CDM cosmological model with ${\Omega}_{m}$ = 0.3, ${\Omega}_{\Lambda}$ = 0.7, and a Hubble constant of $H_{0} = 70$\,km ${\mathrm{s}^{-1}}\mathrm{Mpc^{-1}}$. | % We perform a simple test of whether or not highly disturbed galaxies and major pairs with indicators of tidal activity have an excess obscured-AGN frequency. The results presented in \S \ref{sec:3WISEanalysis} and \S \ref{sec:4nature} raise several interesting questions about the merger process and the AGN-merger connection. We find that merging (interacting) galaxies are 5 -- 17 (2.6 -- 4.9) times more likely to host a dusty {\it WISE} AGN than a non-merging, non-interacting galaxy. These results are similar for the four {\it WISE}-based dusty AGN criteria that we explore. This finding demonstrates a link between dusty AGNs and galaxy merging, in agreement with a similar study done by \citet{Satyapal+14}, who found that post-mergers are 10 -- 20 times more likely to host a dusty AGN than non-merging galaxies. \citet{Satyapal+14} studied close projected pairs and post-mergers with $z\leq 0.2$, using a different definition of {\it WISE} AGNs (see \S \ref{sec:31WISEcolors}). In general, a {\it dusty} AGN-merger connection is consistent with theoretical predictions of a link between gas-rich major mergers, AGNs and central SF as outlined in the Introduction. A dusty AGN-merger connection has been inferred in the literature \citep[e.g.,][]{Hopkins+10b} owing to the strong connection between ULIRGs and galaxy merging first noted by \citet{Sanders+88a}. This connection is observationally supported by the work of \citet{Kocevski+15}, who found that obscured AGNs are three times more likely to display merger or interaction signatures over unobscured AGNs. This scenario naturally explains the studies that found no AGN-merger link \citep{Cisternas+11, Scott+14, Villforth+14}, as these were at wavelengths incompatible with severe dust attenuation \citep{Alexander+01,Brandt+05, Kartaltepe+10, Treister+10}. Our results suggests that many AGNs in merging galaxies may be missed due to nuclear obscuration, in agreement with merger simulations that include the impact of dust obscuration \citep{Snyder+13} and IR observations \citep{Goulding+09, Goulding+10, Treister+10, Satyapal+14}. In this section, we discuss the frequency of nuclear obscuration in merging galaxies hosting an AGN, the incidences of different AGNs to be hosted by a merger or interaction, the likely physical reasons for why many AGNs are {\it not} hosted by merging/interacting galaxies, and the role that SF plays in the dusty AGN-merger connection. We also address the various limitations of infrared color selection of AGNs. \subsection{How Common is Obscured AGN Activity in Mergers?} Studies done in the optical and X-ray may miss important AGN activity due to dust attenuation in the galaxy \citep{Papovich+04, Goulding+09, Goulding+10}. As predicted in major merger simulations \citep{Barnes+91,Mihos+96} and demonstrated observationally \citep{Haan+09}, the gravitational torques in a merging pair cause gas in the pair to lose angular momentum and fall to the nucleus of the system, fueling new SF and AGN activity. The lack of a merger-AGN connection in optical and X-ray studies begs the question: how likely is the AGN to be obscured in a merging or interacting galaxy? To answer this, we compute an obscured AGN fraction: \begin{equation} f_{\rm obscured} = \frac{N({\rm {\it WISE}\,\, AGN})}{N({\rm all\,\, AGN})} , \end{equation} \noindent where the numerator is the number of {\it WISE} AGNs in a given population and the denominator is the sum of {\it WISE} AGNs plus non-{\it WISE}, emission-line Seyfert galaxies. We also calculate the obscured AGN fraction based on the Extended {\it WISE} AGN population. We present these fractions in Table~\ref{Obscuration_fraction_table} for merging, interacting, and possibly interacting galaxies, as well as the control sample described in \S \ref{sec:31WISEcolors}. We find that an AGN in an ongoing merger is 2 -- 6 times more likely to be obscured than an AGN of a non-merging and non-interacting host galaxy. Galaxies that are clearly interacting are nearly as likely as mergers to host a dusty AGN, while the likelihood drops for possibly interacting galaxies that may be simply chance projections of normal galaxies. When considering our less conservative Extended {\it WISE} definition of dusty AGNs, the high obscured AGN fraction remains for merging and interacting subsets compared to the control sample, but is not as large as for {\it WISE} AGNs. We emphasize that $f_{\rm obscured}$ is an estimate based solely on {\it WISE} and SDSS identifications of AGNs, which does not include other detections using shorter and longer wavelengths. Yet, this simple analysis shows that a large fraction (here $f_{\rm obscured} \sim 50\%$) of AGNs in mergers and interactions are dusty or at least partially obscured. This value is consistent with work done by \citet{Treister+10}. Coupled with the fact that merging and interacting galaxies are significantly more likely to host a dusty AGN, our results suggests that the major merging process typically produces AGNs accompanied by substantial amounts of dust. This is consistent with the idea that these mergers trigger fresh centrally-concentrated SF that supplies the dust that obscures the AGN in optical and X-ray surveys. We expand on the SF connection in \S~\ref{sec:54discussion_sf}. \begin{table} \caption{The fraction of AGNs that are obscured ("obscuration fraction") for the following populations given in Column (1): merging galaxies, interacting pairs, possibly interacting pairs, and non-merging, non-interacting control galaxies. Column (2): obscured AGN percentages for combining the Seyfert population and {\it WISE} AGN population using the criteria defined by J11. Column (3): obscured AGN percentages for combining the Seyfert population and Extended {\it WISE} AGN population using the criteria defined in \S \ref{sec:312extendedWISEAGN}.} \label{Obscuration_fraction_table} \begin{tabular}{ccc} \hline Type & {\it WISE} AGN & Ext. {\it WISE} AGN\\ (1) & (2) & (3)\\ \hline \hline mergers & $46_{-25}^{+26}$\% & $58_{-26}^{+23}$\%\\ int. pair & $37_{-18}^{+22}$\% & $75_{-18}^{+12}$\%\\ poss. int. pair & $23_{-10}^{+14}$\% & $55_{-12}^{+12}$\%\\ control & $9.9_{-1.3}^{+1.4}$\% & $29.6_{-2.0}^{+2.0}$\%\\ \hline \end{tabular} \end{table} \subsection{Which AGNs are Hosted by Mergers or Interactions?} We find a connection between merging/interacting galaxies and dusty AGNs, which implies that galaxy merging produces such AGNs. Yet, not all AGNs are dusty and not all AGNs are associated with galaxy mergers and interactions, which suggests that other physical processes besides galaxy merging can produce AGNs. For example, \citet{Scott+14} studied the incidence of BPT-selected AGN in merging galaxies and found no clear connection. Here, we combine IR ({\it WISE} and Extended {\it WISE}) and optical (emission-line Seyfert) AGNs to find the fraction of different AGN subpopulations that are hosted by a merger or interaction. In Table~\ref{AGN_Fractions_table}, we tabulate the separate host merger and host interaction fractions for {\it WISE} AGNs, Extended {\it WISE} AGNs, emission-line Seyferts (including {\it WISE} AGNs), and combinations of each, which we compare to the fractions among non-AGN galaxies. In all cases, the fraction of AGNs that are hosted by a merging or interacting galaxy is quite small ($<10\%$). Yet, we find that the dusty AGNs are the most likely to be involved with galaxy merging; e.g., {\it WISE} AGNs are 4 -- 16 (2 -- 5) times more likely to be hosted by a merger (interaction) than non-AGN galaxies. We find a similar likelihood for Extended {\it WISE} AGNs. In contrast, the percentage of mergers and interactions found in the Seyfert population is similar to that found in the non-AGN population. Thus, while many AGNs must be triggered by non-merging processes, dusty AGNs are much more likely to be associated with merging activity than non-dusty AGNs, which are just as likely to be hosted by normal galaxies as by merging/interacting systems. \begin{table*} \caption{Fraction of merging and interacting systems for the following AGN populations given in Column (1): {\it WISE} AGN as defined by J11, the Extended {\it WISE} AGN cut discussed in \S \ref{sec:31WISEcolors}, emission-lineSeyfert galaxies, the {\it WISE} AGN population combined with Seyfert galaxies, the Extended {\it WISE} AGN population combined with Seyfert galaxies, and all non-AGN systems. Column (2): the number (N) of galaxy systems contained in that population. Columns (3) and (4): the percentage of an AGN population that consists of merging galaxies or interacting pairs, respectively.} \label{AGN_Fractions_table} \begin{tabular}{cccc} \hline Population & N & Merging Galaxies & Interacting Pairs\\ (1) & (2) & (3) & (4)\\ \hline \hline {\it WISE} AGN & 210 & $2.38_{-1.36}^{+3.07}$\% & $8.10_{-2.98}^{+4.48}$\%\\ Extended {\it WISE} AGN & 673 & $1.04_{-0.54}^{+1.09}$\% & $8.02_{-1.82}^{+2.30}$\%\\ Seyfert & 1909 & $0.37_{-0.19}^{+0.38}$\% & $2.83_{-0.66}^{+0.84}$\%\\ {\it WISE} AGN \& Seyfert & 1973 & $0.56_{-0.25}^{+0.44}$\% & $3.19_{-0.69}^{+0.87}$\%\\ Ext. {\it WISE} AGN \& Seyfert & 2171 & $0.55_{-0.31}^{+0.41}$\% & $4.05_{-0.75}^{+0.92}$\%\\ non-AGNs & 41670 & $0.28_{-0.04}^{+0.06}$\% & $2.35_{-0.14}^{+0.15}$\%\\ \hline \end{tabular} \end{table*} Owing to the strong association between dusty AGNs and merging, we visually reinspected the images of 188 {\it WISE} AGNs with normal (non-merging and non-interacting) classifications and find that 15 $\pm$ 6\% of this population are visually disturbed or show signs of recent or ongoing merger or interaction (major or minor) activity; examples shown in Figure~\ref{control_WAGN_images}. Most of these galaxies appear to be ongoing minor interactions (nyu27822, nyu592000, nyu636555) or later-stage post-merger remnant ellipticals with dust lanes (nyu818795 and nyu8110), which may be the result of minor merging \citep{Kauffmann+03, Kaviraj+09, Martini+13}. The fact that a closer inspection of {\it WISE} AGNs reveals additional examples with signs of recent tidal activity indicates that the association between dusty AGNs and merging is stronger than our results indicate, and that minor interactions may also trigger dusty AGNs. \begin{figure} \center{\includegraphics[scale=0.34, angle=0]{Fig17_control_WISE_AGN_SDSSimages.png}} \caption{Examples of Misclassified Control Galaxies in the {\it WISE} AGN Population (described in \S \ref{sec:31WISEcolors}). All images are $50 \times 50$ kpc cutouts of $gri$-combined color images, centered on the {\it WISE} AGN, downloaded from the SDSS Image List Tool. The top six galaxies all show clear signs of merger or interaction activity, including double nuclei and tidal features. The bottom three galaxies are all candidates for a minor merger (nyu636555) or the post-merger phase. The galaxy identification numbers for the galaxies are provided (from the DR4 NYU-VAGC; \citealt{Blanton+05}).} \label{control_WAGN_images} \end{figure} In addition to visually inspecting those control galaxies classified as dusty AGNs, we also visually inspect the subset of 1711 control Seyfert galaxies that are not classified as {\it WISE} AGNs, and are presumably unobscured. We find that 1.2 -- 2.5 \% of these galaxies show signs of recent or ongoing minor mergers or interactions. While this result further supports the AGN-merger connection, it also illustrates a deeper connection between major mergers and {\it dusty} AGNs, as demonstrated throughout this work. This discovery also supports the hypothesis that merging (major or minor) is not the cause of the majority of AGNs. We note that deeper data could reveal a larger selection of merging or interacting galaxies in our control sample, whose signatures of interaction are too faint to detect in SDSS DR4 \citep{Bessiere+12}. \begin{figure} \center{\includegraphics[scale=0.275, angle=0]{Fig18_control_Unobs_Seyfert_SDSSimages.png}} \caption{Examples of Misclassified Control Galaxies in the unobscured Seyfert AGN Population. All images are $50 \times 50$ kpc cutouts of $gri$-combined color images, centered on the unobscured AGN, downloaded from the SDSS Image List Tool. All galaxies show signs of an ongoing minor merger or interaction. The galaxy identification numbers for the galaxies are provided (from the DR4 NYU-VAGC; \citealt{Blanton+05}).} \label{control_unobsSey_images} \end{figure} \subsection{Why Do Most Mergers Lack an AGN?} While we find a clear dusty AGN-merger connection, we also find that only 5 -- 15 \% of merging galaxies are classified as optical Seyferts or {\it WISE} AGNs. Here, we explore several reasons for why the majority of ongoing mergers lack an AGN. First, our AGN selection criteria are based solely on optical emission-lines and near-IR {\it WISE} colors, thus, we may be missing some mergers that host AGNs that are detected only at other wavelengths. While studies comparing AGN detection at different wavelengths find some fraction of previously unidentified sources in one passband compared to another, they find substantial overlap when comparing identifications in the optical and X-ray \citep[e.g.,][]{Grupe+99,Anderson+03}, the X-ray and radio \citep[e.g.,][]{Brinkmann+00}, and the optical and radio \citep[e.g.,][]{Ivezic+02}. By using {\it WISE} we are accounting for dust obscuration which is the strongest cause of missed AGNs in optical surveys \citep{Goulding+09}, although \citet{Snyder+13} demonstrated that significant dust can even obscure near-IR detections of very luminous AGNs during merging coalescence. Given these findings, we do not expect the frequency of mergers hosting AGNs to be significantly higher than what we find, but we note that a thorough accounting of merger-driven AGNs over a wide range of wavelengths is needed to constrain this definitively. Second, not all major galaxy-galaxy interactions are predicted to produce an AGN. The simulations that predict AGNs in mergers \citep{Volonteri+03, DiMatteo+05, Springel+05, Hopkins+08, DeBuhr+11} require the presence of gas, which can be funneled into the nucleus of the system by gravitational torques \citep{Barnes+91,Mihos+96}. If the merger is dry (little to no gas), it is reasonable to assume that a dusty AGN will not occur, which is consistent with our finding that statistically zero {\it WISE} AGNs are hosted by passive mergers/interactions (\S~\ref{sec:43starformation}). Even if gas is present, simulations \citep{Cox+08,Johansson+09} and observations \citep{Haines+15} have found that not all gas-rich mergers make a nuclear starburst (and presumably a dusty AGN). \citet{Cox+08} showed that an excess amount of gas can decrease the starburst efficiency in a merger. If the starburst efficiency is decreased, and AGNs and SF are thought to be intimately connected \citep{Hickox+14}, it may be possible that too much gas can also decrease AGN efficiency. \citet{Johansson+09} demonstrated that the nuclear black hole accretion rate decreases with increasing merger progenitor mass ratio; i.e., 1:1 mergers will produce stronger AGNs than 4:1 mergers. It is impossible to discern progenitor mass ratios for visually identified `train wreck' mergers. Additionally, the orbital geometry can have a large effect on gas dynamics in a merger, with coplanar mergers having the highest gas inflow to the nucleus \citep{Mihos+96}. In short, only {\it idealized} major encounters (finely-tuned gas fraction, mass ratio, and orbital configuration of the merger progenitors) produce the brief starbursts and dusty AGNs seen in simulations of the modern merger hypothesis such as presented in Fig. 1 of \citet{Hopkins+08}. To give a quantitative constraint on the number of mergers we would expect to fit this perfect scenario, we look to our sample of 307 interacting pairs. Using $urz$ star-forming colors as an indicator of gas content and mass ratios less than two (described in \S \ref{sec:21SDSSsample}), we find that 11 -- 19\% of interacting pairs fit the idealized case and should, in theory, produce an obscured AGN. This number is higher than our {\it WISE} AGN merger sample would suggest. Yet another probable reason why the majority of mergers lack AGNs is differences in the merger observability timescales and AGN lifetimes. For example, depending on progenitor mass ratio and gas fractions, the strong asymmetric features typically used to identify major mergers at or near the time of coalescence (i.e., our ongoing merger definition; see \S \ref{sec:21SDSSsample}) have timescales that range from $\sim$0.2--0.5\,Gyr \citep{Lotz+10a,Lotz+10b}. In comparison, AGN phase lifetime estimates range from 0.01--1\,Gyr \citep{Martini+01,Marconi+04} to as little as a repeating $\sim 10^5$\,years `AGN flicker' \citep{Schawinski+15}. Given these ranges of timescales it is, therefore, possible that all/most major gas-rich mergers do produce AGNs if the AGN phase is typically on order 10 times shorter than the merger observability time. But, owing to our lack of knowledge about progenitor mass ratios, gas content and orbits in our sample of visually identified mergers, it is impossible to test this. \subsection{The Role of Star Formation in the Dusty AGN-Merger Connection} \label{sec:54discussion_sf} % We find that a high majority (72 -- 97\%) of merging/interacting galaxies hosting a {\it WISE} AGN have $urz$ star-forming colors. This indicates a link between merging, SF, and the triggering of an obscured AGN. This is consistent with the major merger simulations by \citet{Hopkins+08} and others \citep{Barnes+91, Mihos+96}, which predict that the gas brought into the nucleus by gravitational torques in a gas-rich merger should simultaneously fuel the production of new stars and accrete onto the black hole. A natural consequence of the new SF would be centrally-concentrated dust obscuration, the amount of which depends on the rate of SF \citep{Goulding+12}. A sufficient amount of dust obscuration will produce an infrared (IR) AGN. Assuming that SF plays a critical role in obscuring AGNs hosted by merging/interacting galaxies, we test whether the incidence of dusty AGNs is higher among star-forming mergers and interactions. We find no increase in the incidence of WISE AGNs in mergers over the control sample (5 -- 18 times). However, we find that the vast majority of {\it WISE} AGNs are found in star-forming systems for both merging or interacting galaxies and the control sample, confirming that star formation in the host galaxy is intimately linked to infrared AGNs, as other studies have found \citep[e.g.,][]{Hickox+09, Snyder+13}. Additionally, we repeat all of the K-S tests described in \S \ref{sec:4nature} to test for the unique nature of $urz$-selected star-forming mergers and interactions that host dusty AGNs. Specifically, for each property we compare the {\it WISE} (Extended {\it WISE}) subset distribution against that of the Region C control sample distribution using only star-forming merging/interacting galaxies. We find no statistical differences for any of the properties explored except for a $\sim$3-sigma difference between the Extended {\it WISE} and Region C star-forming systems in terms of pair separation, compared to the 2-sigma result discussed in \S \ref{sec:pairsep}. As such, it appears that star-forming merging or interacting galaxies that host dusty AGNs are not different from others that lack a dusty AGN. This lack of difference could support the idea that all star-forming merging and interacting galaxies have a dusty AGN phase. \subsection{The Limitations of Infrared Color Analysis for Isolating Merging AGNs} \label{sec:55discussion_IRlimitations} % There are many AGN selection techniques across the wavelength spectrum. While optical and ultraviolet can select unobscured AGNs, they will often miss obscured sources \citep{Alexander+01}. The X-ray wavelengths are commonly regarded as the most complete AGN selection method available, but X-ray surveys can miss obscured AGNs \citep{Alexander+01,Brandt+05, Kartaltepe+10, Treister+10}. In our search for obscured AGNs, we choose to use an infrared color selection, as many other studies have done \citep{Jarrett+11, Stern+12, Assef+13, Yan+13, Satyapal+14}. While the main advantage of the infrared is sensitivity to obscured AGNs \citep{Cardamone+08}, it does have limitations. One downside is the possible contamination of the mid-infrared bands from SF in the host galaxy \citep{DelMoro+16, Lange+16}. Cold dust emission from SF tends to dominate the far-IR, peaking in the 100 - 160 ${\mu}$m range, but the mid-IR bands can also be affected. Another possible source of error that arises out of mid-IR AGN selection is incompleteness of low-luminosity AGNs. The mid-IR color selection techniques tend to preferentially select the brightest AGNs \citep{Cardamone+08}, and miss a significant number of low-luminosity sources. Using other selection methods could find this missing population of low-luminosity AGNs in our sample, thus strengthening our AGN-merger connection. However, the true effect of this bias cannot be accurately determined. \citet{Treister+12} found that major mergers are tied only to the most luminous AGNs, thus we should expect this bias not from the data but from the merger process. While we select use of the infrared to account for dust obscuration, \citet{Snyder+13} demonstrated that significant dust can even obscure near-IR detections of very luminous AGNs during merging coalescence. All of these limitations suggest that our merger-AGN rate is a lower limit, and would benefit from the addition of X-ray and radio data for a full picture of the AGN-merger connection. Throughout this paper, we assume that {\it WISE} color AGN selection should select obscured AGNs. From the major merger model, which predicts high amounts of SF and therefore dust, we also assume that the dust from SF acts as the obscuring material in these special systems. We note that the AGN Unification Model \citep{Urry+95} describes AGN obscuration as a result of the viewing angle; the torus around an AGN can obscure the AGN itself. This would imply that obscured AGNs selected in this sample are not different from other AGNs due to merging, but rather to viewing angle. However, recent work by \citet{Kocevski+15} shows that the viewing angle of an AGN cannot be the only property differentiating populations of AGNs, but cites a recent merger event as a plausible source of differing AGN populations. % We combine data from {\it WISE} and the SDSS to explore the relationship between dust-obscured AGNs and galaxy mergers within the context of the current major merger model \citep{Volonteri+03, DiMatteo+05, Springel+05, Hopkins+08, DeBuhr+11}. We present a new, volume-limited ($z\leq 0.08$) catalog of visually-selected major mergers and galaxy-galaxy interactions from the SDSS, with stellar masses ${\rm M}_{\rm star} > 2 \times 10 ^ {10} ~ {\rm M}_{\odot}$. We use SDSS fiber spectroscopy diagnostics from the MPA-JHU emission-line analysis \citep{Kauffmann+03, Brinchmann+04} to map the locations of over 40,000 normal galaxies with different emission types from \citet{McIntosh+14} in the $[3.4]-[4.6]$ versus $[4.6]-[12]$ color-color plane. We test multiple dusty AGN selection methods and find that one-quarter of Seyferts have redder $[3.4]-[4.6]$ colors than $\sim99\%$ of non-Seyferts. We use this empirical criterion to define an `Extended' {\it WISE} AGN selection of dusty AGNs. We perform a simple test of whether or not highly disturbed galaxies and major pairs with indicators of tidal activity have an excess obscured-AGN frequency. We use the normal galaxies as a control sample against which we quantify the amount of dusty AGN activity in mergers and interactions. We confirm a dusty AGN-merger connection, consistent with the major merger model by \citet{Hopkins+08} and others \citep{Volonteri+03, DiMatteo+05, Springel+05, DeBuhr+11, Snyder+13}, and observationally supported by \citet{Satyapal+14}, in which gravitational torques drive gas inflows to the center of the merging system, feeding the AGN. Our key results are summarized as follows: (i) We find an excess of obscured AGN activity in merging galaxies when compared to a control sample with the same redshift and stellar mass constraints, indicating that merging (interacting) systems are 5 -- 17 (3 -- 5) times more likely to host an obscured AGN compared with non-merging, non-interacting galaxies, in agreement with \citet{Satyapal+14}. (ii) We find that mergers hosting a dusty AGN favor smaller pair separations and smaller dark matter halo masses than other mergers and interactions. We find that most dusty AGN mergers are located at the centers of ${\rm M}_{\rm halo} < 10 ^ {13} ~ {\rm M}_{\odot}$ groups; this relationship also supports the \citet{Hopkins+08} major merger picture, in which mergers favor halos at the small group scale. (iii) We find that the vast majority of mergers hosting dusty AGNs have star-forming SDSS $urz$ colors. This connection is also consistent with major merger models which predict heightened SF at the time of the merger (and the concomitant AGN). (iv) We find that AGNs also classified as ongoing mergers are five times more likely to be obscured than AGNs in non-merging, non-interacting galaxies. Half of all AGNs hosted by a merger are dusty, suggesting that shorter wavelengths are inadequate in selecting AGNs in merging systems. (v) We find no enhanced frequency of optical BPT-selected AGNs in merging over non-merging galaxies at this redshift, indicating that the missed detection of dusty AGNs at optical and shorter wavelengths is likely the reason for the ongoing AGN-merger connection debate. From this study, we find strong evidence in favor of the major merger model, in which gas-rich mergers produce central bursts of SF and fuel AGNs. The SF produces dust, which obscures the AGN and reradiates in the thermal infrared. Because of this obscuration, surveys at shorter wavelengths may see not only an incomplete picture of the merger-AGN connection, but are also biased against measuring the true merger, SF, and AGN rates. | 16 | 9 | 1609.04832 |
1609 | 1609.01626_arXiv.txt | Chlorine abundances are reported in 15 evolved giants and one M dwarf in the solar neighborhood. The Cl abundance was measured using the vibration-rotation 1-0 P8 line of H$^{35}$Cl at 3.69851 $\mu$m. The high resolution L-band spectra were observed using the Phoenix infrared spectrometer on the Kitt Peak Mayall 4m telescope. The average [$^{35}$Cl/Fe] abundance in stars with --0.72$<$[Fe/H]$<$0.20 is [$^{35}$Cl/Fe]=(--0.10$\pm$0.15) dex. The mean difference between the [$^{35}$Cl/Fe] ratios measured in our stars and chemical evolution model values is (0.16$\pm$0.15) dex. The [$^{35}$Cl/Ca] ratio has an offset of $\sim$0.35 dex above model predictions suggesting chemical evolution models are under producing Cl at the high metallicity range. Abundances of C, N, O, Si, and Ca were also measured in our spectral region and are consistent with F and G dwarfs. The Cl versus O abundances from our sample match Cl abundances measured in planetary nebula and \ion{H}{2} regions. In one star where both H$^{35}$Cl and H$^{37}$Cl could be measured, a $^{35}$Cl/$^{37}$Cl isotope ratio of 2.2$\pm$0.4 was found, consistent with values found in the Galactic ISM and predicted chemical evolution models. | A full knowledge of stellar abundance patterns in a variety of stellar sources is useful to understand the production of each element and the chemical enrichment history of stellar populations. Galactic chemical evolution models rely on theoretical yields which are tested through observations of stellar abundances. Multiple elements have been well studied in galactic evolution, particularly the alpha elements and iron peak elements in Galactic populations. Some odd atomic number light elements are difficult to measure due to their low abundances and spectral features that lie outside optical wavelengths. Thus the light, odd elemental abundance patterns are poorly constrained \citep{nomoto2}. This work focuses on chlorine, an odd Z element with two stable isotopes, $^{35}$Cl and $^{37}$Cl. Both chlorine isotopes are formed during hydrostatic and explosive oxygen burning phases \citep{woosley}, although the explosive oxygen burning phase during supernova produces a higher yield than hydrostatic burning \citep{woosley}. A model for a 25 M$_{\odot}$ supernova explosion shows the $^{35}$Cl abundance generated from hydrostatic burning is 4.82 x 10$^{-4}$ M$_{\odot}$ while explosive oxygen burning generates an abundance of 7 x 10$^{-4}$ M$_{\odot}$ \citep{woosley}. $^{35}$Cl is thought to be primarily produced when $^{34}$S captures a proton. The other isotope, $^{37}$Cl is thought to be primarily produced from radioactive decay of $^{37}$Ar, and can be created during neon burning \citep{woosley}. Models of chlorine production in both core collapse supernova (CCSNe) \citep{woosley, kobayashi6, nomoto, kobayashi11} and Type Ia supernova \citep{travaglio} show chlorine yields vary as a function of mass and metallicity of the progenitor star. These yields have led Galactic enrichment models to predict constant [Cl/Fe]\footnote{[A/B] $\equiv$ log(N$_{A}$/N$_{B}$)$_{star}$ - log(N$_{A}$/N$_{B}$)$_{\odot}$ } ratios over a range of metallicities \citep{kobayashi11}. Measurement of the chlorine abundances in stellar atmospheres is extremely difficult and little empirical data are available to compare with Cl evolution models. The solar Cl abundance in particular highlights the difficulties in Cl abundance measurements; no chlorine abundance measurement is possible from the quiet photosphere. An early attempt using near infrared measurements of weak atomic Cl lines provided inconclusive abundance measurements and gave an upper limit on the chlorine abundance\footnote{A(X)=12+log(X/H)}, A(Cl) $\leq$ 5.5 \citep{lambert}. Chlorine can also be measured in molecular form. Hydrogen chloride (HCl) molecular vibrational-rotational lines are found in the L-band spectrum of stars. However, the low dissociation potential of HCl limits the molecule to lower temperature stellar atmospheres. HCl features in the spectral range 3.633 $\mu$m and 4.166 $\mu$m have been measured in solar sunspot umbrae spectra and resulted in a solar Cl abundance of 5.5$\pm$0.3 \citep{hall}. Chlorine features at x-ray wavelengths can also be present during solar flares; an abundance of A(Cl)=5.75$\pm$0.26 has been measured using the \ion{Cl}{14} line in solar flare spectra \citep{sylwester}. Due to the difficulties in measuring the Cl abundance in stellar atmospheres, \citet{asplund} suggested that a Cl abundance of A(Cl)=5.32$\pm0.07$ derived from nearby \ion{H}{2} regions from \citet{garcia} may be a suitable proxy for the solar abundance. Finally, the the meteoric value for Cl of 5.25$\pm$0.06 \citep{lodders} may also be a proxy for the Cl abundance in the Sun. While no direct chlorine measurements have been reported in the photospheres of stars, forbidden Cl lines, such as features at $\sim$5500$\AA$ in the optical regime, provide chlorine measurements in planetary nebulae and \ion{H}{2} regions. More recent Cl abundance measurements \citep{esteban} in \ion{H}{2} regions were derived by measuring multiple ions of Cl without using ion correction factors. These improved measurements have lowered the Cl abundance measured in nearby \ion{H}{2} regions and allowed the measurement of the Galactic radial Cl abundance gradient. The radial slope finds a Cl abundance at the solar galactocentric radius of A(Cl)=5.05 \citep{esteban}. Both \ion{H}{2} and planetary nebulae surveys have shown that the gradients of Cl and O with galactocentric distance are nearly identical, \citep{esteban} for \ion{H}{2} observations and \citep{henry} for PN observations, implying Cl and O production are highly correlated. Other planetary nebula studies used Cl as a proxy for the iron abundance, consistent with current models of Cl production \citep{delgado}. Millimeter and submillimeter HCl emission features have been measured in the interstellar medium and provide tests of the $^{35}$Cl/$^{37}$Cl ratio in both Galactic and extragalactic sources. The solar system $^{35}$Cl/$^{37}$Cl ratio of 3.13 was found from meteoric Cl isotope abundances \citep{lodders}. Measurements of proto-planetary cores have found a $^{35}$Cl/$^{37}$Cl ratio of 3.2 $\pm$0.1 \citep{kama} matching solar values. A survey of 27 star forming regions, molecular clouds, and the circumstellar envelops of evolved stars, observed with the Caltech Submillimeter Observatory, found $^{35}$Cl/$^{37} $Cl ratios that varied between 1 and 5 (uncertainties ranged from 0.3 to 1.0) with the majority of sources having a ratio between 1.1 and 2.5 \citep{peng}. Chlorine has also been detected in extragalactic sources; recently, H$_{2}$Cl$^{+}$ has been detected in a lensed blazar with a measured $^{35}$Cl/$^{37}$Cl ratio of 3.1$^{0.3}_{0.2}$ at a redshift of 0.89 \citep{muller}. We report here our Cl abundances measured in stars using HCl molecular lines at infrared wavelengths. Previous infrared spectroscopic studies found HCl molecular lines in the 4 $\mu$m wavelength regime in the atmospheres of cool AGB stars \citep{lebzelter}. This paper describes the observations, source selection, and data reduction in section \ref{sec::reduction}. Section \ref{sec::abund} describes how the line-list was constructed, the spectral synthesis implementation, and the uncertainties in our abundance measurements. Section \ref{sec::discussion} discusses the atmospheric parameters necessary for HCl to form in a solar atmosphere, the Cl isotopic abundance, and comparisons to theoretical Cl enrichment models. | We used L-band infrared spectroscopy to measure the abundance of chlorine in stars with effective temperatures below 3900 K, with the exception of the metal-rich HD 138481 which has a temperature of 3970 K. Theoretical log gf values were used and compared to astrophysical log gf values derived from fitting synthetic spectra to Arcturus, a quiet-sun photosphere spectrum, and a solar sunspot umbrae spectrum. Of the sample, 16 stars showed measurable Cl features in their spectra. The main results from the abundance analysis are summarized below. \begin{enumerate} \item{Our sample consisted of M and K giants and dwarfs. The H$^{35}$Cl molecular feature is detected in 15 giants and one M-dwarf, all with effective temperatures below 3900 K except for HD 138481 which has a temperature of 3970 K. The masses of the evolved stars are determined from stellar evolution models and are found to be between 1 and 3 M$_{\odot}$ } \item{Chlorine and oxygen abundances in stars are consistent with measurements made in planetary nebulae \citep{henry, delgado} and \ion{H}{2} regions \citep{esteban}.} \item{A $^{35}$Cl/$^{37}$Cl isotope ratio of 2.2$\pm$0.4 is found in RZ Ari. This result is consistent with measurements in the interstellar medium \citep{peng} and is near the solar value of 3.13 \citep{lodders}. It is also comparable to predicted isotope ratios of $\sim$ 1.8-1.9 from supernova yields \citep{kobayashi11}} \item{Abundance measurements are determined for C, N, O, Si, and Ca are consistent with similar abundances in warmer stars in our sample ($\sim$ 4300 K). The abundances from our L-band spectra also matched abundances determined previously for these stars from the literature. Our abundances also matched F and G dwarfs in the solar neighborhood \citep{reddy}. } \item{[$^{35}$Cl/Fe] measurements are consistent with the slope of Galactic chemical evolution models from \citet{kobayashi11} but show on average a higher [$^{35}$Cl/Fe] abundances than predicted by 0.16 dex. This offset is also seen in [$^{35}$Cl/Ca] and [$^{35}$Cl/Si] where chlorine is offset by $\sim$0.35 dex compared to chemical evolution models \citep{nomoto2}. An additional processes producing chlorine may be necessary to explain the overabundance of Cl compared to predictions. The $\nu$ process may affect Cl production \citep{kobayashi15} and should be considered. } \item{Chlorine abundances in two Ba-rich stars are similar to the chlorine abundance in other, non s-process rich stars in the sample. The similarity of these chlorine abundances suggests that additional A($^{35}$Cl) is not produced through the s-process} \end{enumerate} | 16 | 9 | 1609.01626 |
1609 | 1609.04145_arXiv.txt | A new frontier in the search for dark matter (DM) is based on the idea of detecting the decoherence caused by DM scattering against a mesoscopic superposition of normal matter. Such superpositions are uniquely sensitive to very small momentum transfers from new particles and forces, especially DM with a mass below 100 MeV. Here we investigate what sorts of dark sectors are inaccessible with existing methods but would induce noticeable decoherence in the next generation of matter interferometers. We show that very soft, but medium range (0.1 nm - 1 $\mu$m) elastic interactions between nuclei and DM are particularly suitable. We construct toy models for such interactions, discuss existing constraints, and delineate the expected sensitivity of forthcoming experiments. The first hints of DM in these devices would appear as small variations in the anomalous decoherence rate with a period of one sidereal day. This is a generic signature of interstellar sources of decoherence, clearly distinguishing it from terrestrial backgrounds. The OTIMA experiment under development in Vienna will begin to probe Earth-thermalizing DM once sidereal variations in the background decoherence rate are pushed below one part in a hundred for superposed 5-nm gold nanoparticles. The proposals by Bateman \emph{et al.}\ and Geraci \emph{et al.}\ could be similarly sensitive, although they would require at least a month of data taking. DM that is absorbed or elastically reflected by the Earth, and so avoids a greenhouse density enhancement, would not be detectable by those three experiments. On the other hand, the aggressive proposals of the MAQRO collaboration and Pino \emph{et al.}\ would immediately open up many orders of magnitude in DM mass, interaction range, and coupling strength, regardless of how DM behaves in bulk matter. | \label{sec:introduction} One of the basic challenges facing fundamental physics in the 21$^{\rm st}$ century is finding ways to learn more about the nature of the dark matter (DM) that makes up some 80\% of the matter in the Universe. If it is a particle, then we would like to know whether it is a boson or a fermion, to measure its mass, and to understand what interactions, other than gravity, it has with itself as well as with the particles we are made of. Even if we restrict ourselves to the case of fermionic DM, in which case galactic phase-space considerations generally require masses greater than $\mathcal{O}(100)$ eV, the allowed mass range is still very large. Given our deep ignorance about the basic properties of DM, it is important to devise experiments to cover as much of the parameter space as possible. The most developed programs looking for DM above the keV mass range are: direct detection experiments; indirect detection observations; and direct production at colliders. Direct detection experiments look for anomalous energy deposition at the keV range from collisions with dark matter with a mass greater than a GeV and weak (and now sub-weak) cross sections \cite{supercdmscollaboration2016new,pandax-iicollaboration2016dark,angloher2016results,luxcollaboration2017results}. These experiments are insensitive for masses below a GeV because the kinetic energy of such particles in the halo is below a keV and they do not impart enough energy to be detected. Recently, promising new ideas for experiments targeting lighter DM in the keV--GeV mass range have emerged~\cite{Essig:2011nj,graham2012semiconductor,essig2013dark,lee2015modulation, hochberg2016detecting, hochberg2016superconducting, hochberg2016directional} and the first limits were announced in Ref.~\cite{Essig:2012yx}; these exploit the increased energy transfer if electrons, rather than heavier nucleons, are struck. Alongside the lower mass, the cross sections targeted by these experiments are generally considerably higher than weak scale (1--1000 pb). Detection through indirect observations searches for the annihilation or decay of dark matter into stable forms of matter, such as photons, protons, electrons and their antiparticles~\cite{essig2013dark,essig2013constraining}. These processes must be sufficiently frequent and energetic to be distinguished from background, which becomes more challenging below a DM mass of a GeV. The most notable hints in this area arise in searches for anomalous x-ray lines in the keV range~\cite{essig2013constraining}. Finally, searches for the production of DM at colliders looking for excess events with large missing energy are sensitive to DM with a large mass range that is only limited by the available center-of-mass energy. These searches are generally limited to production cross sections somewhat larger than weak scale. These different approaches to learning more about the nature of DM are of course overlapping and act to inform and complement each other. A particularly challenging task is to detect DM with a mass in the MeV range and below, especially through interactions with the nucleus. The available kinetic energy of such particles in the halo is below an electron-volt and there are currently no proposals utilizing conventional means that can search for collisions involving such low energy depositions. Recently, a novel approach based on detecting the decohering effects due to DM interactions with matter was suggested by Riedel in Ref.~\cite{Riedel:2012ur}. While the proposal delineated the achievable sensitivity in cross section, it remained unclear what type of interactions can actually give rise to such a signal. In this paper we close this gap and show that it is interactions mediated by new long range forces between matter and DM that can be effectively searched for with this technique. The key insight underlying our work is this: \textsl{the big advantage decoherence has over other techniques is in detecting collisional processes with a cross section that is dominated by extremely low momentum transfers}. This compliments a recent derivation of a standard quantum limit for diffusion, showing that a given test mass is strictly more sensitive to small momentum transfers when placed in an extended spatial superposition than in any localized (even zero-temperature) state \cite{Riedel:2015xx}. It is important to recognize that the answer to the question ``What is the nature of DM?", may not be unique. DM, just like us, may be composed of several different stable relics interacting through a variety of forces. Laboratory experiments looking for DM are generally sensitive even to cosmological relics that only form a subcomponent of DM. Astrophysical constraints on the interactions of the dominant component of DM, which may be inapplicable to a subcomponent, should therefore not limit our vision for what is possible to look for in laboratory experiments. We close this introduction with two comments. First, it should be duly noted that the signals we discuss in this paper are extremely weak and will require great control over the experimental apparatus. It will likely take quite a few more years before the experiments reach the required sensitivity. Decoherence is ubiquitous and may arise from a variety of other mundane sources. Once a signal is seen it would be necessary to run several crosschecks (discussed later) before rejecting alternative explanations and confidently attributing the signal to DM. Second, the interactions between matter and DM that we consider in this paper, while physically consistent, are not motivated by any deep principle or any other consideration. This may seem unappealing to some. Despite these two cautionary remarks, we believe that experiments utilizing large quantum superpositions represent a promising new frontier to look for new physics and new fundamental interactions. The purpose of this paper is to expose the type of new physics such experiments can probe and to serve as a proof of principle that such interactions are physically consistent. Sec.~\ref{sec:interactions} begins with the key aspects of decoherence of quantum superpositions and discusses the concrete DM scenarios on which they have the largest advantage. Sec.~\ref{sec:experiment} reviews the relevant experimental considerations, including the most promising interferometric devices, the properties of and constraints on the DM scenario, the decoherence process itself, and methods for isolating signal from background. Sec.~\ref{sec:results} presents the results, summarized in Figs.~\ref{fig:sensitivity-mdm-big} and~\ref{fig:sensitivity-mdm-many}, and Sec.~\ref{sec:discussion} concludes with brief discussion. | \label{sec:discussion} Future interferometers can maximize their sensitivity by increasing the mass, spatial extent, and exposure time of the superpositions produced. Sensitivity increases quadratically with mass (in the coherence scattering regime), quadratically with spatial extent $\DeltaX$ (until this is larger than typical momentum transfer), and linearly with exposure time $T$. In particular, the Wan \emph{et al.}\ proposal is hampered mostly by its unusually short exposure time, and modestly more aggressive parameters (an increase in radius by $\sim\!20\%$, or a tripling of exposure time) would make it sensitive to unexcluded DM with $\mDM \approx 1\keV$. (This threshold behavior is related to the saturation of the cross section during the breakdown of the Born approximation, as discussed in Appendix~\ref{sec:born}.) The fast data-gathering rate of the OTIMA interferometer means its sensitivity is limited by the sidereal decoherence background from conventional sources in the laboratory, the magnitude of which is currently unknown and assumed here to be $\etairr \approx 10^{-3}$. Better understanding of this background would be very valuable, and the DM reach of OTIMA would increase linearly with its suppression. In contrast, the proposals by Pino \emph{et al.}\ and the MAQRO collaboration are limited by the amount of data that can be collected in a reasonable time (taken here to be one month), and so are not particularly sensitive to this assumption. The proposals by Bateman \emph{et al.}\ and Geraci \emph{et al.}\ are intermediate between these cases. Let us briefly point out two other possibilities, albeit with little \emph{a priori} motivation, that would produce an enhanced DM signal. First, relatively strong matter-DM interactions might lead to DM clumping in the Solar System \cite{damour1999new,peter2008particle,adler2009flyby}, although this is not thoroughly understood and gravitational three-body interactions are not effective \cite{edsjo2010comments}. Direct constraints on the DM mass density in the vicinity of the Earth are weak, being compatible with an increase of $10^5$ above the interstellar average if distributed smoothly through the Solar System \cite{iorio2006solar, khriplovich2007density, frere2008bound, pitjev2013constraints} and $10^{13}$ if concentrated within the orbit of the Moon \cite{adler2008placing}. Second, depending on the exact shape and size of the superposed target, resonance scattering -- which occurs outside the region of validity for the Born approximation and would be especially important for $\mDM \gtrsim 10\MeV$ -- could greatly enhance the scattering cross section. Resonant behavior is illustrated in Ref~\cite{bateman2015existence} for a related low-mass DM search proposal using matter interferometers.\footnote{Note that the DM candidate considered in Ref.~\cite{bateman2015existence} appears to violate constraints on the annihilation rate arising from power injection into the cosmic microwave background because thermal DM with this little mass can reionize hydrogen by annihilation during matter-radiation equality \cite{Lin:2011gj,madhavacheril2014current}. We thank Gordan Krnjaic for bringing this to our attention.} To conclude: the impressive metrological power of matter interferometers complements their exciting but speculative role testing the foundations of quantum mechanics \cite{Nimmrichter:2011x2,Arndt:2014xx,Kaltenbaek:2015x2,pino2016quantum,romero-isart2016coherent}. Even in the absence of dark matter, they put model-independent limits on anomalous sources of weak diffusion, especially from any interstellar sources shielded by the Earth. | 16 | 9 | 1609.04145 |
1609 | 1609.01283_arXiv.txt | We present \emph{Hubble Space Telescope} imaging confirming the optical disappearance of the failed supernova (SN) candidate identified by \citet{Gerke15}. This $\sim$$25~M_{\odot}$ red supergiant experienced a weak $\sim$$10^{6}~L_{\odot}$ optical outburst in 2009 and is now at least 5 magnitudes fainter than the progenitor in the optical. The mid-IR flux has slowly decreased to the lowest levels since the first measurements in 2004. There is faint (2000-$3000~L_{\odot}$) near-IR emission likely associated with the source. We find the late-time evolution of the source to be inconsistent with obscuration from an ejected, dusty shell. Models of the spectral energy distribution indicate that the remaining bolometric luminosity is $>$6 times fainter than that of the progenitor and is decreasing as $\sim$$t^{-4/3}$. We conclude that the transient is unlikely to be a SN impostor or stellar merger. The event is consistent with the ejection of the envelope of a red supergiant in a failed SN and the late-time emission could be powered by fallback accretion on to a newly-formed black hole. Future IR and X-ray observations are needed to confirm this interpretation of the fate for the star. \\ \\ | Supernova (SN) surveys for the deaths of massive stars search for a sudden brightening of a source. However, it is expected that some fraction of massive stars experience a failed SN, forming a black hole without a luminous SN. While this idea is most widely accepted for very high mass stars at lower metallicity \citep{Heger03}, evidence has recently emerged suggesting that failed SN may also occur in red supergiants (RSGs) with solar metallicity. First, there is the lack of higher-mass SN progenitors, which suggests that higher mass stars may end their lives as failed SNe \citep{Kochanek08}. \citet{Smartt09b} and \cite{Smartt15} more clearly demonstrated that the known progenitors of Type IIP SNe have an upper mass limit of $\lesssim18~M_{\odot}$ --- well below the expected mass range for RSG at death. Although there are alternative hypotheses for the missing SN progenitors, such as post-RSG evolution occuring at lower masses \citep[e.g.,][]{Smith11b,Groh13} or enhanced dust formation prior to core collapse \citep[e.g.,][]{Walmswell12,Beasor16}, the dearth of higher-mass SN progenitors is supported by analyses of stellar populations near SN remnants \citep{Jennings14} and the absence of any Type IIP SNe with the nucleosynthetic signatures of higher-mass ($>20~M_{\odot}$) progenitors \citep{Jerkstrand14}. Interestingly, the mass range for failed SNe suggested by the missing progenitors corresponds to stars with progenitor structures that make them more difficult to explode \citep{OConnor11,Ugliano12,Pejcha15,Ertl16,Sukhbold16}. Second, having a significant fraction of core-collapses resulting in failed SNe naturally explains the compact remnant mass function \citep{Kochanek14b,Kochanek15}. When black holes are formed by ``fall back" onto the proto-neutron star during successful SNe, the mass distributions of black holes and neutron stars are continuous because there is no natural mass scale for the amount of fall back \citep{Zhang08,Fryer12}. Such continous distributions are inconsistent with observations showing a significant gap between neutron star and black hole masses \citep{Ozel12,Kreidberg12}. If the core collapse fails to explode a RSG, the resulting black hole mass is the mass of the progenitor's helium core \citep{Lovegrove13}, naturally producing the observed gap between neutron star and black hole mass distributions and the observed black hole masses. Third, there is evidence that the massive star formation rate may exceed the SN rate (\citealp{Horiuchi11}, but see \citealp{Botticella12} and \citealp{Xiao15}). Finally, the recent detection of gravity waves from a pair of merging black holes with masses of $36^{+5}_{-4}~M_{\odot}$ and $29^{+4}_{-4}~M_{\odot}$ \citep{Abbott16a} likely requires the existence of failed SNe \citep{Abbott16b,Belczynski16,Woosley16}. These lines of evidence for the existence of failed supernovae, while indirect, motivate the direct search for failed SNe. The formation of a black hole has never been observed and little is known about the range of possible observational signatures. Some stars likely collapse to form black holes without significant transients \citep{Woosley12}. However, a failed SN in a RSG likely leads to a visible transient. \citet{Nadezhin80} suggested, and \citet{Lovegrove13} confirmed with hydrodynamic simulations, that the nearly instantaneous loss of gravitational mass through neutrino emission when a core collapses will lead to a hydrodynamic shock capable of unbinding the loosely bound hydrogen envelope of a RSG. The resulting optical signature is a shock breakout with $L\sim10^{7}~L_{\odot}$ that lasts for 3-10 days \citep{Piro13} followed by a cool ($\sim3000$ K), $\sim$1 year-long, $\sim$$10^{6}~L_{\odot}$ transient powered by the recombination of the unbound envelope \citep{Lovegrove13}. Once sufficiently cool, the slowly expanding ejecta is an ideal environment for dust formation, but this would only occur after the transient has already begun to fade \citep{Kochanek14c}. Regardless of the nature of any intervening transient the end result is the disappearance of the progenitor. \citet{Kochanek08} proposed a novel survey to monitor the evolved stars in nearby galaxies to search for failed SNe as disappearing stars. \citet{Gerke15} presented the results of the first four years of such a survey undertaken with the Large Binocular Telescope (LBT) and found one good failed SN candidate. This source, in NGC 6946 at RA 20:35:27.56 and Dec +60:08:08.29, which we will hereafter refer to as N6946-BH1, experienced an outburst in 2009 March, first brightening to $\gtrsim$$10^{6}~L_{\odot}$ but then fading to $\sim$$10^{5}~L_{\odot}$ \emph{below} its pre-outburst luminosity. \citet{Gerke15} found that a coincident source experienced a similar, but slower outburst in the mid-IR. \citet{Gerke15} also identified the progenitor in earlier archival \emph{Hubble Space Telescope} (\emph{HST}) images with $23.09\pm0.01$ in $F606W$ and $20.77\pm0.01$ in $F814W$. \citet{Reynolds15} performed a similar search for failed SNe using archival \emph{HST} data and also identified a candidate. A new kind of search is vulnerable to new kinds of false positives. The initial candidate selection was based on a decline in multiple optical bands, but a surviving star could be hidden by dust. There are several classes of sources known to have transient, heavily-obscured phases. Some variable stars, such as R Cor Bor stars, may become optically faint for hundreds of days due to dust forming in their atmospheres \citep{Okeefe39}. Stellar mergers can cause the envelope of the primary star to be ejected at low velocities --- ideal conditions for dust formation --- and result in a merger remnant that is luminous in the IR but optically obscured \citep{Crause03,Pejcha16,Pejcha16b}. Luminous blue variables may experience eruptive mass loss that obscures a surviving star following a weak transient --- a SN ``impostor" --- as $\eta$ Carinae did in the mid-1800s \citep[e.g.,][]{Humphreys94,Smith11}. There are also SN ``impostors" that arise from self-obscured super-AGB stars --- SN 2008S-like transients --- that quickly become re-enshrouded in dust \citep{Prieto08,Kochanek11b,Thompson09}, though some SN ``impostors," from both super-AGB stars and more massive stars, may be lower-luminosity SNe \citep[see][]{Adams15,Adams16}. Thus, multi-wavelength follow-up is needed to vet failed SN candidates and determine whether the star survived. In this work we present follow-up observations and analysis of N6946-BH1. New \emph{HST} imaging confirms that the identified progenitor has disappeared in the optical but a fainter, coincident source is detected in the near-IR (see Fig. \ref{fig:imaging}). We present the data in \S\ref{sec:data} and describe our spectral energy distribution (SED) modeling in \S\ref{sec:models}. In \S\ref{sec:results} we present detailed analysis of the progenitor, the outburst, and the post-outburst observational constraints. While we find the failed SN interpretation for this event to be the most compelling, we consider alternative explanations in \S\ref{sec:alternatives} before closing with our summary and conclusions in \S\ref{sec:summary}. Following \citet{Gerke15}, we adopt a distance of 5.96 Mpc to NGC 6946 \citep{Karachentsev00} and a Galactic foreground extinction of $E$($B$--$V)=0.303$ based on the \citet{Schlafly11} recalibration of \citet{Schlegel98}. In this paper, all magnitudes are in the Vega system. | 16 | 9 | 1609.01283 |
|
1609 | 1609.06376_arXiv.txt | KIC~3230227 is a short period ($P\approx 7.0$ days) eclipsing binary with a very eccentric orbit ($e=0.6$). From combined analysis of radial velocities and {\it Kepler} light curves, this system is found to be composed of two A-type stars, with masses of $M_1=1.84\pm 0.18M_{\odot}$, $M_2=1.73\pm 0.17M_{\odot}$ and radii of $R_1=2.01\pm 0.09R_{\odot}$, $R_2=1.68\pm 0.08 R_{\odot}$ for the primary and secondary, respectively. In addition to an eclipse, the binary light curve shows a brightening and dimming near periastron, making this a somewhat rare eclipsing heartbeat star system. After removing the binary light curve model, more than ten pulsational frequencies are present in the Fourier spectrum of the residuals, and most of them are integer multiples of the orbital frequency. These pulsations are tidally driven, and both the amplitudes and phases are in agreement with predictions from linear tidal theory for $l=2, m=-2$ prograde modes. | % Heartbeat stars (HBs), named after the resemblance between their light curves and an electrocardiogram, are binary or multiple systems with very eccentric orbits. The HBs that have been studied in detail include a late B-type star (Maceroni et al.\ 2009), A or F-type stars (Handler et al.\ 2002; Welsh et al.\ 2011; Hambleton et al.\ 2013, 2016; Smullen \& Kobulnicky 2015), and red giant stars (Beck et al.\ 2014; Gaulme et al.\ 2013, 2014). Recently, Shporer et al.\ (2016) presented spectroscopic orbits for 19 single-lined HBs. The {\it Kepler} eclipsing binary catalog (Kirk et al.\ 2016) contains over 150 of these stars with the flag `HB'. The distribution of eccentricity ($e$) and orbital period ($P$) for {\it Kepler} eclipsing binaries (EBs) and the 19 HBs is shown by Shporer et al.\ (2016), who note that the HBs occupy the upper envelope of the $(P,e)$ diagram. The distributions of orbital period and $T_{\rm eff}$ of over 150 HBs in {\it Kepler} EB catalog are shown in Figure 1. The effective temperatures are taken from Armstrong et al.\ (2014). The majority of HBs seem to have orbital period shorter than $30$ days. Their range of effective temperatures ($\sim 5000-7500$ K) suggests that most of them are of spectral type earlier than G (mostly G, F, and A). KIC~3230227 (HD181850, BD+38 3544; $K_p=9.002$, $\alpha_{2000}$=$19$:$20$:$27.0253$, $\delta_{2000}$=$+38$:$23$:$59.459$) is an eclipsing binary, first included in the {\it Kepler} EB catalog by Slawson et al.\ (2011) and Prsa et al.\ (2011). The original catalog listed the time of eclipse minimum and orbital period as $T_0=54958.702188$ (BJD-2,400,000) and $P=14.094216$ days, respectively. Later, the period was found to be half of the original value ($P=7.0471062$ days). Uytterhoeven et al.\ (2011) analyzed the {\it Kepler} light curves of $\sim 750$ A- and F-type stars. Among them, KIC~3230227 was classified as an eclipsing binary with $\gamma$ Doradus pulsations. Thompson et al.\ (2012) studied light curves of 17 heartbeat stars, including KIC~3230227. Thanks to the special light curves of HBs, they derived orbital parameters including the orbital inclination ($i$), eccentricity ($e$), and argument of periastron ($\omega_p$). Armstrong et al.\ (2014) derived the effective temperatures of $9341\pm 350$K and $7484\pm 606$K for the primary and secondary, respectively, by fitting the SED (Spectral Energy Distribution) to the observed magnitudes. Niemczura et al.\ (2015) made a detailed analysis of their high resolution spectra of KIC~3230227. Atmospheric parameters were inferred from Na D, H Balmer, and metal lines. They found $T_{\rm eff}=8150\pm 220$K (from the Na D lines and SED), $T_{\rm eff}=8200\pm 100$K (from Balmer and metal lines), $\log g=3.9\pm 0.1$ and $v \sin i=50\pm 4$ km s$^{-1}$. They also obtained abundances for many individual elements (C, N, O, Ne, Na, Mg, etc), as listed in their Table 4. Most of these abundances are close to solar values (Asplund et al.\ 2009; Lodders et al.\ 2009). We summarize the aforementioned results in Table 1. | The unprecedented light curves from the {\it Kepler} satellite offer us opportunities to study the effect of tides on stellar oscillations. Heartbeat stars in eclipsing systems are among the best laboratories since the model independent fundamental stellar parameters such as mass and radius can be determined. We presented a study of KIC~3230227, which consists of two A-type stars in an eccentric orbit with a period of 7 days. The observed pulsations, mostly orbital harmonics, can be explained by the tidally induced $l=2, m=-2$ prograde modes. This is supported by a comparison of their observed and modeled phases and amplitudes. The fundamental parameters of KIC~3230227 are determined only to $10\%$ in mass and $5\%$ in radius. Further analysis could take advantage of the high resolving power spectra and more phase coverage in the RV curve. This is already underway \footnote{While our paper was under review, we learned about the preliminary work by Lampens et al.\ presented as a poster at the KASC8/TASC1 meeting. The orbital parameters derived from their high resolving-power spectra agree with our result. They found that this binary is actually a triple system, and the estimated flux contribution of the third star at $5300$\ \AA \ is about $4\%$. Our light curve solution may change slightly with the inclusion of a small third light, but it will not change our conclusions about the pulsational properties. However, the third star could have a great influence on the evolution history of orbital parameters (eccentricity, spin-oribit alignment, and rotation rate) for this system.} (K. Hambleton, private communication). Once more accurate parameters are determined, asteroseismic modeling of these tidal oscillations can be performed, as was done in Burkart et al.\ (2012). To solidify the result of this work, mode identification techniques can be applied to the line profiles variations as well as to the time series of multi-color photometry. It is also worthwhile studying the Fourier spectrum more closely, identifying individual modes, and analyzing the non-linear mode couplings. Another weakness of this work is that we are unable to tell which star is pulsating or if both stars are pulsating. A study of pulsations during eclipse may help to clarify this issue (B{\'{\i}}r{\'o} \& Nuspl 2011). | 16 | 9 | 1609.06376 |
1609 | 1609.06695_arXiv.txt | The Z Cam-type dwarf nova AT Cnc displays a classical nova (CN) shell, demonstrating that mass transfer in cataclysmic binaries decreases substantially after a CN eruption. The hibernation scenario of cataclysmic binaries predicts such a decrease, on a timescale of a few centuries. In order to measure the time since AT Cnc's last CN eruption, we have measured the radial velocities of a hundred clumps in its ejecta with SITELLE, CFHT's recently commissioned imaging Fourier transform spectrometer. These range from -455 to +490 km/s. Coupled with the known distance to AT Cnc of 460 pc (Shara 2012), the size of AT Cnc's shell, and a simple model of nova ejecta deceleration, we determine that the last CN eruption of this system occurred $330_{-90}^{+135}$ years ago. This is the most rapid transition from a high mass transfer rate, novalike variable to a low mass transfer rate, dwarf nova yet measured, and in accord with the hibernation scenario of cataclysmic binaries. We conclude by noting the similarity in deduced outburst date (within a century of 1686 CE) of AT Cnc with a ``guest star" reported in the constellation Cancer by Korean observers in 1645 CE. | Dwarf novae (DN) and classical novae (CN) are all close binary stars, wherein a white dwarf (WD) accretes hydrogen-rich matter from its red dwarf (RD), Roche lobe-filling companion, or from the wind of a nearby giant. In DN, a thermal instability episodically dumps much of the accretion disk onto the WD \citep{1974PASJ...26..429O}. The liberation of gravitational potential energy then brightens these systems by up to 100-fold as DN eruptions occur, typically every few weeks or months. This accretion process in DN must inevitably build an electron degenerate, hydrogen-rich envelope on the white dwarf \citep[]{1986ApJ...311..163S}. Theory and detailed simulations predict that once the accreted mass reaches of the order of 10$^{-5}$ M$_\odot$, a thermonuclear runaway (TNR) will occur in the degenerate layer of accreted hydrogen \citep{1972ApJ...176..169S, 1978A&A....62..339P}. The TNR causes the rapid rise to $\sim 10^5$ L$_\odot$ or more, and the high-speed ejection of the accreted envelope in a classical nova explosion. The longterm evolution of cataclysmic binaries (CB) is driven by the mass accretion rate between nova eruptions. If that rate decreases by one or more orders of magnitude in the centuries following a CN eruption, as predicted by the hibernation scenario of cataclysmic binaries \citep{1986ApJ...311..163S,1986ApJ...311..172P,1987Ap&SS.131..419K}, then the predicted relative numbers of long and short period CB, the relative numbers of DN and novalike binaries, and the lifetimes of CBs all change dramatically. Population synthesis codes that model CB and their effects on the chemical evolution of galaxies \citep{2003A&A...405...23M,2016MNRAS.458.2916C} can only provide realistic predictions if accurate mass transfer rate histories are an inherent part of those codes. The accretion rates onto the WDs in DN are typically 10-100 times smaller than those observed in the WD-RD, mass-transferring binaries known as novalike variables. \citet{2009AJ....138.1846C} demonstrated that almost all pre- and post-nova binaries, observed in the century before or after eruption, are high mass-transfer rate novalike variables. Thus the discovery of a CN shell, almost one degree in diameter, surrounding the prototypical dwarf nova Z Cam \citep[]{2007Natur.446..159S} was unexpected, and has important implications for our understanding of the longterm evolution of CBs. The derived shell mass of Z Cam matches that of classical novae, and is inconsistent with the mass expected from a dwarf nova wind or a planetary nebula. The Z Cam shell observationally linked, for the first time, a prototypical DN with an ancient CN eruption and the CN process. This was the first-ever confirmation of a key prediction of CB TNR theory: the accreting white dwarfs in DN must eventually erupt as CN. It also demonstrated that, 1300-2100 years after its CN eruption \citep{2012ApJ...756..107S}, Z Cam's central binary is {\it not} a novalike variable. Instead, it exhibits DN eruptions, indicative of a lower mass-transfer rate than is seen in old novae up to one century after eruption. The hibernation scenario of CBs predicts that the transition from high to low mass transfer state in old novae is just the WD cooling time after a CN eruption - a few centuries. A nova that erupted more recently than Z Cam is required to more stringently test the predicted transition timescale. Thus motivated, we have been searching for other CN shells surrounding DN. One of our targets was the Z Cam-like DN AT Cancri. Short and long-term variability in the spectrum of AT Cnc has been well documented by \citet{1999PASJ...51..115N} and references therein, who detected a clear radial velocity variation with a period of 0.2011d, a semi-amplitude of 80 km$^{-1}$ and a systemic velocity of 11 km$^{-1}$. Superhumps were detected by \citet{2004A&A...419.1035K}, who suggested that AT Cnc has a large mass ratio, and may host a magnetic white dwarf. Optical [NII] narrowband imaging of AT Cnc \citep[]{2012ApJ...758..121S} revealed highly fragmented rings, about 3 arcmin in diameter, surrounding the star. The spectrum of one of the brightest blobs in the ejecta is dominated by lines of [NII], [OII] and [OIII]; oxygen and nitrogen are the products of a nova TNR. The geometry of the rings suggests that we are looking at an hourglass-shaped ejection reminiscent of that of other old novae such as HR Del \citep{2003MNRAS.344.1219H}. We present in this paper a kinematical analysis of a hundred emission-line blobs around AT Cnc, based on a hyperspectral datacube obtained with the Canada-France-Hawaii Telescope's newly commissioned imaging Fourier Transform Spectrometer (iFTS), SITELLE. We briefly describe SITELLE in section 2, and the observations of AT Cnc and their reductions in section 3. The results are presented, and the time since the last CN eruption of AT Cnc is deduced, in section 4. We summarize our results in section 5. The spectrum of AT Cnc, and a discussion of its possible association with the Korean "guest star" of 1645 CE are discussed in appendices. | We have measured the radial velocities of 100 blobs in the ejecta of the old nova (and currently dwarf nova) AT Cnc. The fastest moving blobs have velocities of 475 km/s. Combined with the observed angular size of the ejecta, and the distance to AT Cnc, we have determined that the CN which generated the ejecta occurred $330_{-90}^{+135}$ years ago. It is the best-determined transition time, to date, for an old nova to become a dwarf nova. It is also consistent with the cooling time of a WD after a CN eruption, and the timescale predicted by the hibernation scenario of CB for mass transfer to decline substantially are a CN eruption. The deduced date of AT Cnc's nova eruption (within a century of 1686 CE) is remarkably close in time and location to a ``guest star" reported by Korean observers in Cancer in 1645 CE. | 16 | 9 | 1609.06695 |
1609 | 1609.00716.txt | This is all Guys. In these lectures we have started from the shortcomings of Big Bang Cosmology that motivated inflation. We have seen how a period of accelerated expansion fixes all these problems. With simple estimates that are helpful to develop intuition, we have seen how inflation produces a quasi scale-invariant, quasi-Gaussian, stochastic but classical, spectrum of density perturbations, and how some qualitative predictions of inflation have been confirmed in the data. We have also seen that it would be great to have something more to look for. For this reason, we have introduced the Effective Field Theory of Inflation, which shows that Inflation is essentially a theory of a Goldstone boson. We have seen that there are new spectacular signatures in inflation: the non-Gaussianity of the density perturbation. They contain a huge amount of information, and they represent the interactions, and therefore the non-trivial dynamics, of the inflationary Lagrangian. Inflationary physics is very ample, and there are many aspects that we could not touch. For example we did not discuss how some inflationary models are embedded in string theory, or, in any detail, that beautiful phase called eternal inflation, according to which quantum effects change the asymptotic of the space-time, arise. In any event, for all what concerns the phenomenology of Inflation and its connection to the data, you should be good to go. Thank you very much for your attention and your interactions. Teaching here has been a wonderful experience for me, and it has been a pleasure to have you around and discuss with you. I hope you'll find these lectures useful for your future research in Physics and Cosmology. It is a great moment for our field. My best wishes. | 16 | 9 | 1609.00716 |
||
1609 | 1609.05375_arXiv.txt | We analyze the relationships between atomic, neutral hydrogen (\ion{H}{1}) and star formation (SF) in the 12 low-mass SHIELD galaxies. We compare high spectral ($\sim$0.82\,\kms\,ch$^{-1}$) and spatial resolution (physical resolutions of 170\,pc\,--\,700\,pc) \ion{H}{1} imaging from the VLA with \halpha\ and far-ultraviolet imaging. We quantify the degree of co-spatiality between star forming regions and regions of high \ion{H}{1} column densities. We calculate the global star formation efficiencies (SFE, $\Sigma_{\rm SFR}$\,/\,$\Sigma_{\rm \HI}$), and examine the relationships among the SFE and \ion{H}{1} mass, \ion{H}{1} column density, and star formation rate (SFR). The systems are consuming their cold neutral gas on timescales of order a few Gyr. While we derive an index for the Kennicutt-Schmidt relation of $N$\,$\approx$\,0.68$\pm$0.04 for the SHIELD sample as a whole, the values of $N$ vary considerably from system to system. By supplementing SHIELD results with those from other surveys, we find that HI mass and UV-based SFR are strongly correlated over five orders of magnitude. Identification of patterns within the SHIELD sample allows us to bin the galaxies into three general categories: 1) mainly co-spatial \ion{H}{1} and SF regions, found in systems with highest peak \ion{H}{1} column densities and highest total \ion{H}{1} masses; 2) moderately correlated \ion{H}{1} and SF regions, found in systems with moderate \ion{H}{1} column densities; and 3) obvious offsets between \ion{H}{1} and SF peaks, found in systems with the lowest total \ion{H}{1} masses. SF in these galaxies is dominated by stochasticity and random fluctuations in their ISM. | \label{S1} \subsection{Stars and Gas in Galaxies} \label{S1.1} The conversion of gas into stars is one of the most fundamental processes in astronomy. Yet, despite decades of effort, a simple prescription of star formation (SF) that successfully describes all observations of galaxies across a range of halo masses has remained elusive. In broad terms, more massive star-forming galaxies will have larger gas reservoirs (both atomic and molecular) and higher global star formation rates (SFR) than less massive systems \citep[see, e.g., ][]{kennicutt1998a}. However, the gas mass fractions in star forming galaxies tend to increase with decreasing mass \citep[e.g.,][]{fishertully1975}. Empirical correlations between gas properties and various tracers of instantaneous (using H$\alpha$ emission, with a characteristic timescale of $\lsim$ 10 Myr) or ongoing (using FUV emission, with a characteristic timescale of $\lsim$ 100 Myr) SF have been numerous in the literature. The most common parameterization relates a SFR surface density to a gas surface density: \begin{equation} \Sigma_{\rm SFR} \propto (\Sigma_{\rm gas})^{N} \end{equation} \noindent with the SFR surface density ($\Sigma_{\rm SFR}$) in units of \msun\,yr$^{-1}$\,kpc$^{-2}$, the gas surface density ($\Sigma_{\rm gas}$) in units of \msun\,pc$^{-2}$, and $N$ being a positive number. \citet{schmidt1959} found that $N \approx 2$, and similar indices have been derived numerous times over the last half-century (see Elmegreen 2011\nocite{elmegreen2011} for a recent review). For example, \citet{kennicutt1998b} found $N =$ 1.4\,$\pm$\,0.15 for 61 large spiral galaxies when relating the \halpha-based SFR to the total gas surface density (via both \ion{H}{1} and CO observations, where the CO is used as a tracer for molecular gas). In a study of this relation on sub-kpc scales, \citet{bigiel2008} found that the relationship between the total gas surface density and the SFR surface density varied dramatically among and within individual spiral galaxies, and that most of the sample showed little or no correlation between $\Sigma_{\rm \HI}$ and $\Sigma_{\rm SFR}$. In an associated paper, \citet{leroy2008} found a molecular Schmidt power-law slope of $N = 1.0 \pm 0.2$ in 18 nearby spiral galaxies; similarly, \citet{momose2013} found $N =$ 1.3 - 1.8 for 10 nearby spiral galaxies. In a subsequent study, \citet{bigiel2010} find no clear evidence for SF thresholds and emphasize that it may not be realistic to expect them. Molecular gas in low mass galaxies remains largely undetectable via traditional CO tracers, thus studying the relationship between atomic gas and SF is especially important in these metal-poor low-mass systems \citep[e.g., ][]{bolatto2013}. In fact, very few detections of CO gas exist at metallicities less than $\sim$10\% Z$_{\odot}$, even in systems that are actively forming stars (see, e.g., {Taylor \etal\ 1998}\nocite{taylor1998}, {Schruba \etal\ 2012}\nocite{schruba2012}, {Warren \etal\ 2015}\nocite{warren2015}). For low mass galaxies, this implies that studying the relationship between $\Sigma_{\rm SFR}$ and $\Sigma_{\rm gas}$ as a function of galaxy mass is necessarily constrained to only the atomic gas component. It is thus interesting to note that a correlation between $\Sigma_{\rm \HI}$ and $\Sigma_{\rm SFR}$ appears to hold in some galaxies and not in others. For example, \citet{bigiel2008} find that $\Sigma_{\rm \HI}$ and $\Sigma_{\rm SFR}$ are not related in individual spiral disks. This can be compared to the results in \citet{skillman1987}, which show that 10$^{21}$ cm$^{-2}$ (corresponding to 7.9 \msun\ pc$^{-2}$ or 10.6 \msun\ pc$^{-2}$ when accounting for helium) represents a requisite threshold \ion{H}{1} surface density for massive SF. Similarly, \citet{wyder2009} examined 19 low surface-brightness galaxies and found an apparent threshold in the \ion{H}{1} gas surface density in the range 3 $-$ 10 \msun\ pc$^{-2}$ below which very little SF (traced by \halpha) is observed. Extending to even lower masses, \citet{roychowdhury2009} and \citet{roychowdhury2011} find that all \ion{H}{1} gas in their galaxies with $\Sigma_{\rm \HI}$ $\gtrsim$ 10 \msun\ pc$^{-2}$ ($\approx$ 1.2$\times$10$^{21}$ cm$^{-2}$) have associated SF, but there is no threshold below which SF is not observed (that is, SF is observed in regions with \ion{H}{1} columns $<$ 10$^{21}$ cm$^{-2}$). Most recently, \citet{roychowdhury2014} found that the $\Sigma_{\rm \HI}$ $-$ $\Sigma_{\rm SFR}$ relation for a set of dwarf irregular galaxies was nearly linear. \citet{roychowdhury2015} find consistency across a range of scales (400pc and 1kpc) and galaxy types, including both low-mass galaxies and more massive spiral disks. Based on the above results, it is not trivial to anticipate where in a galaxy one will observe ongoing SF - regardless of how massive that galaxy is. Knowledge of the \ion{H}{1} properties alone is often insufficient to predict where in a given galaxy the conditions are ripe for SF. For example, \citet{krumholz2012} suggests that molecular gas is a better predictor of SF than the neutral ISM. We examine this issue from the \ion{H}{1} perspective in Section~\ref{S4.2}. In addition to the $\Sigma_{\rm gas}$ vs. $\Sigma_{\rm SFR}$ analysis, we also study the star formation efficiency (SFE), which is a useful metric when discussing where in a galaxy SF is occurring \citep{leroy2008}. Several ways of describing the SFE exist, but for consistency with other surveys we use SFE = $\Sigma_{\rm SFR} / \Sigma_{\rm gas}$ with units of yr$^{-1}$. The SFE is more useful than SFR alone to identify where conditions are conducive to SF because it is normalized by the gas mass surface density. Thus, it quantifies the local physical properties in regions where the gas is being turned into stars efficiently: regions of elevated gas surface density which have no young stars associated with them are inefficient, while regions of elevated gas surface density that show co-spatiality with young stars are efficient. Conveniently, the inverse of the SFE is the gas depletion time, which is the time required for SF to consume the gas reservoir at the present-day SFR. For a sample of low-mass galaxies, \citet{roychowdhury2014} found gas depletion timescales of $\sim$10$^{10}$ yr, an order of magnitude lower than is estimated for the outer regions of large spiral galaxies \citep{bigiel2010}. We calculate gas consumption times for our sample of galaxies in Section~\ref{S4.2}. \subsection{Low-Mass Galaxies from ALFALFA} \label{S1.2} The ALFALFA survey \citep{giovanelli2005} has produced one of the largest and most statistically useful catalogs of nearby, gas-rich galaxies to date. The final ALFALFA database will include source parameters for more than 30,000 systems. With the acquisition of data for ALFALFA now complete, a unique database exists to facilitate the study of fundamental galaxy properties across an unprecedented range of physical parameters. One particularly rich area of exploration that has been enabled by ALFALFA is a robustly-populated faint end of the \ion{H}{1} mass function \citep{martin2010}. Specifically, it is possible to identify a complete sample of gas-bearing, low-mass galaxies by matching the ALFALFA database to existing optical survey data. As introduced in \citet{cannon2011}, the ``Survey of \ion{H}{1} in Extremely Low-mass Dwarfs'' (hereafter, SHIELD) is a multi-wavelength, detailed study of the properties of ALFALFA-discovered or cataloged systems with extremely small \ion{H}{1} mass reservoirs (see Section~\ref{S2} for detailed discussion of the sample selection). Subsequent works have established the distances \citep{mcquinn2014}, the nebular abundances \citep{haurberg2015}, and the qualities of SF based on spatially resolved Hubble Space Telescope (HST) imaging \citep{mcquinn2015a}. The primary goals of SHIELD are to 1) characterize the nature of SF in very low-mass galaxies and to 2) determine what fraction of the mass in these low-mass galaxies is baryonic. In this work, we undertake a comparative study of the \ion{H}{1} gas and various tracers of recent SF in order to address goal \#1. A companion paper by \citet{mcnichols16} explores the dynamical properties of our sample galaxies in order to address goal \#2. SHIELD is one of a number of recent \ion{H}{1} surveys of dwarf galaxies using interferometric data. This list includes WHISP (The Westerbork \ion{H}{1} Survey of Irregular and Spiral Galaxies; {Swaters 2002}\nocite{swaters2002}), FIGGS (Faint Irregular Galaxies GMRT Survey; {Begum \etal\ 2008}\nocite{begum2008}), VLA-ANGST (Very Large Array Survey of ACS Nearby Galaxy Survey Treasury Galaxies; {Ott \etal\ 2012}\nocite{ott2012}), LITTLE-THINGS (Local Irregulars That Trace Luminosity Extremes in The \ion{H}{1} Nearby Galaxy Survey; {Hunter \etal\ 2012}\nocite{hunter2012}), and LVHIS (The Local Volume \ion{H}{1} Survey; {Kirby 2012}\nocite{kirby2012}). These studies have yielded valuable insights into a total of nearly two dozen systems with M$_{\rm \HI}$ $\lsim$ $10^{7}$ \msun. SHIELD adds to this relatively understudied region of parameter space by significantly increasing the number of sources with resolved \ion{H}{1} imaging. | \label{S5} SHIELD is a systematic investigation of a sample of extremely low-mass dwarf galaxies outside the Local Group. Despite the low \ion{H}{1} column densities observed in many systems, each SHIELD galaxy has a significant FUV luminosity, and we detect \halpha\ emission in all but two of them. The ability to compare multi-configuration VLA \ion{H}{1} data with SF tracers in other wavelengths allows us to examine, on a local and global scale, the SF ``law'' in these systems. We calculate $\Sigma_{\rm \HI}$ and $\Sigma_{\rm SFR}$ for all sample members and find the SFEs. We derive an index for the Kennicutt-Schmidt relation via several different methodologies. The ensemble average index using the pixel correlation mehtod gives $N \approx$ 0.68$\pm$0.04; this is in good agreement with other studies of low-mass dwarf galaxies, but is shallower than the canonical K-S relation from \citet{kennicutt1998b}. By comparing the SHIELD results to those from other major nearby galaxy surveys, we find that HI mass and UV-based SFR are strongly correlated over five orders of magnitude. We stress that any one galaxy in the sample is not representative, and that the values of $N$ vary considerably from system to system. Instead, we focus on the narratives of the individual galaxies and their distribution of gaseous and stellar components, which are complex and occasionally puzzling. The average consumption time for the sample of $\sim$2 - 10 Gyr suggests that they will consume their gas reservoir over timescales similar to those found in other dwarf galaxy surveys. At the extremely faint end of the \ion{H}{1} mass function, these systems appear to be dominated by stochastic motions in their extreme ISM. The local microphysics within the ISM of individual galaxies may govern whether or not they show signs of recent SF. Based on our data, knowledge of the \ion{H}{1} properties holds little predictive power in terms of the resulting SF characteristics. Similarly, we see ongoing or recent SF in unexpected regions of many of the SHIELD galaxies. The observed offsets between gas and stars in the galaxies could originate from tidal interactions, or the offsets might appear based on how much time has elapsed since a major SF event disrupted the central gas component. If causal relationships between atomic \ion{H}{1} gas and SF exist in galaxies in this extreme mass range (6.6 $<$ log(M$_{\rm \HI}$) $<$ 7.8), these relationships remain elusive with current data. In addition to the analysis presented here, a companion paper by \citet{mcnichols16} studies the HI gas kinematics and dynamics of the SHIELD galaxies. Two- and three-dimensional analyses are used to constrain rotational velocities. It is argued that the SHIELD galaxies span an important mass range where galaxies transition from rotational to pressure support. The sources are contextualized on the baryonic Tully-Fisher realtion. The now-complete ALFALFA catalog contains dozens of galaxies with \ion{H}{1} and stellar properties comparable to those of the 12 SHIELD galaxies studied in this work. Observations similar to the ones presented here are underway to characterize the SF properties of this statistically robust sample. \clearpage | 16 | 9 | 1609.05375 |
1609 | 1609.09647_arXiv.txt | {Low- and intermediate-mass stars lose most of their stellar mass at the end of their lives on the asymptotic giant branch (AGB). Determining gas and dust mass-loss rates (MLRs) is important in quantifying the contribution of evolved stars to the enrichment of the interstellar medium.} {Attempt to, for the first time, spectrally resolve CO thermal line emission in a small sample of AGB stars in the Large Magellanic Cloud.} {The Atacama Large Millimeter Array was used to observe 2 OH/IR stars and 4 carbon stars in the LMC in the CO J= 2-1 line.} {We present the first measurement of expansion velocities in extragalactic carbon stars. All four C-stars are detected and wind expansion velocities and stellar velocities are directly measured. Mass-loss rates are derived from modelling the spectral energy distribution and {\it Spitzer}/IRS spectrum with the DUSTY code. Gas-to-dust ratios are derived that make the predicted velocities agree with the observed ones. The expansion velocities and MLRs are compared to a Galactic sample of well-studied relatively low MLRs stars supplemented with ``extreme'' C-stars that have properties more similar to the LMC targets. Gas MLRs derived from a simple formula are significantly smaller than derived from the dust modelling, indicating an order of magnitude underestimate of the estimated CO abundance, time-variable mass loss, or that the CO intensities in LMC stars are lower than predicted by the formula derived for Galactic objects. This could be related to a stronger interstellar radiation field in the LMC. } {Although the LMC sample is small and the comparison to Galactic stars is non-trivial because of uncertainties in their distances (hence luminosities) it appears that for C stars the wind expansion velocities in the LMC are lower than in the solar neighbourhood, while the MLRs appear similar. This is in agreement with dynamical dust-driven wind models. } | Low- and intermediate-mass stars (LIMS) have initial masses of $\sim$0.8--8M$_{\odot}$, depending somewhat on metallicity. They end their lives with an intense mass-loss episode on the asymptotic giant branch (AGB). In a classical picture (Wood 1979), stellar pulsation and dust formation drive a slow, cool wind. This wind from AGB stars is one of the main sources that enrich the interstellar medium (ISM) with gas and dust. To quantify the level of enrichment and compare it to other sources, like supernovae or dust growth in the ISM, one has to determine the mass-loss rate (MLR) in gas and dust of AGB stars. Typically, the dust MLR is determined by modelling the spectral energy distribution (SED) and is especially sensitive to the infrared photometry. The gas MLR is determined by modelling the rotational-vibrational transitions of carbon monoxide (CO). The dust MLR is directly proportional to the (dust) expansion velocity of the wind, which is a priori unknown, and can not be determined from the SED fitting. Expansion velocities are known for hundreds of AGB stars in the Galaxy, through the CO thermal line emission (e.g. Kerschbaum \& Olofsson 1999, Olofsson et al.\ 2002 for M-stars, Groenewegen et al.\ 2002 for C-stars) or OH maser line for O-rich sources (see the database by Engels \& Brunzel 2015). For stars that are beyond a few kpc, determining expansion velocities becomes more difficult especially in the CO line. In part this is a sensitivity issue of the receivers and telescopes; in part the AGB population that one traces (outside the Galactic disk for example) may be constituted of stars of lower mass that may have an inherently lower MLR and thus fainter line emission. The first indication that the wind expansion velocities of AGB stars depend on environment (metallicity) came with the detection of C-stars in the Galactic Halo. Groenewegen et al. (1997) detected CO (2-1) emission in the source IRAS 12560+1656, while Lagadec et al. (2010) detected CO J= 3-2 emission in that source and five others. The expansion velocities were lower than that of C-stars in the Galactic disk, with the expansion velocity in IRAS 12560 as low as $\sim 3$ \ks. Hydrodynamical wind models for C stars by Wachter et al.\ (2008) predict that expansion velocities in the LMC are indeed about 2.2 $\pm$ 0.2 times lower than for solar metallicities, while dust-to-gas ratios are slightly larger (by a factor of $\sim$1.3), and mass-loss rates are relatively unchanged. Since maser emission is stronger than thermal emission, attempts have been made to detect OH emission in the Small and Large Magellanic Clouds (MCs). Wood et al. (1992) reported the detection in 6 AGB and RSG stars observed in the LMC and no detection in the SMC. Marshall et al. (2004) added a few detections in the LMC. The current state-of-the-art is presented by Goldman et al. (2016), adding new detections and re-analysing previous data, resulting in accurate expansion velocities for 13 OH/IR stars in the LMC. They suggest that the expansion velocity is proportional to metallicity and luminosity, $L$, as $L^{0.4}$. Recently, Matsuura et al. (2016) detected CO line emission in the bright LMC RSGs WOH G64 (one line) and IRAS 05280$-$6910 (J= 6-5 to 15-14). The data were obtained using the {\it Herschel} PACS and SPIRE instruments. The spectral resolution is insufficient to resolve the lines, but, taking the wind expansion velocity from an OH measurement, they modelled the CO line emission in IRAS 05280 and derived a MLR. It would be extremely interesting to extend this type of analysis to carbon-rich stars and to larger samples so that a meaningful comparison to Galactic objects could be made. The collecting area and small beam of the Atacama Large Millimeter Array (ALMA) is required to detect spectrally resolved CO lines in the MCs. This paper describes the first results of such a programme. The target list is presented in the next section. The ALMA observations and results are presented in Section~3. These results are discussed in Section~4 where they are compared to predictions of radiatively driven wind theory, and the results for the LMC are compared to a Galactic sample. The evolutionary status of the stars is examined with the aid of AGB stellar models. Conclusions are presented in Section~5. | The first results are presented of a programme that that aims to accurately determine gas and dust MLRs in AGB stars in the MCs. The keys to success are detection and modelling of CO thermal emission lines. In this paper we present observations of the CO J= 2-1 line of 2 OH/IR and 4 carbon stars in the LMC. The OH/IR stars are weaker than anticipated in this line, and only one OH/IR is marginally detected. The detection of all 4 C-stars in the CO J= 2-1 line allowed us to determine the expansion velocities and compare them to a sample of Galactic C-stars, including ``extreme'' C-stars that have similar large MLRs as the LMC targets. Determining the gas MLR directly and through RT modelling is deferred until the CO J= 3-2 data are in hand, and in this paper the MLR is determined from fitting the SED and {\it Spitzer}/IRS spectrum using the DUSTY code in the mode where the hydrodynamical equations of dust and gas are solved and the expansion velocity and gas MLR are predicted. These first results support the conclusions previously derived from CO observations of metal-poor C-stars in the Galactic Halo: at lower metallicity the expansion velocity in C stars is smaller, and the MLR similar, to a comparable star at solar metallicity. It must be stressed, however, that our sample is small and finding a suitable sample of comparison stars in the Galaxy is challenging. Therefore, this conclusion awaits testing with improved samples both within the Galaxy and in the Magellanic Clouds. | 16 | 9 | 1609.09647 |
1609 | 1609.02555_arXiv.txt | \vskip 3pt \noindent It has recently been shown that if the dark matter is in thermal equilibrium with a sector that is highly decoupled from the Standard Model, it can freeze-out with an acceptable relic abundance, even if the dark matter is as heavy as $\sim$1-100 PeV. In such scenarios, both the dark and visible sectors are populated after inflation, but with independent temperatures. The lightest particle in the dark sector will be generically long-lived, and can come to dominate the energy density of the universe. Upon decaying, these particles can significantly reheat the visible sector, diluting the abundance of dark matter and thus allowing for dark matter particles that are much heavier than conventional WIMPs. In this paper, we present a systematic and pedagogical treatment of the cosmological history in this class of models, emphasizing the simplest scenarios in which a dark matter candidate annihilates into hidden sector particles which then decay into visible matter through the vector, Higgs, or lepton portals. In each case, we find ample parameter space in which very heavy dark matter particles can provide an acceptable thermal relic abundance. We also discuss possible extensions of models featuring these dynamics. | \label{sec:intro} Over the past several decades, weakly interacting massive particles (WIMPs) have been the leading class of candidates for our universe's dark matter. This paradigm has been motivated primarily by the fact that a stable particle species with a weak-scale mass and interaction strength is predicted to freeze-out of thermal equilibrium in the early universe with a relic abundance that is comparable to the measured cosmological density of dark matter. As such particles are also often found within frameworks that address the electroweak hierarchy problem (including, but not limited to, weak-scale supersymmetry), this connection has become commonly known as the ``WIMP miracle''~\cite{Bertone:2016nfn}. The WIMP paradigm has motivated an expansive experimental program, consisting of direct detection, indirect detection, and collider searches. As these efforts have progressed, however, no conclusive detections have been made, and increasingly powerful bounds have been placed on dark matter's non gravitational interactions with the Standard Model (SM). Over the traditional range of WIMP masses ($\sim$10-1000 GeV), direct detection experiments now strongly constrain the dark matter's elastic scattering cross section with nuclei~\cite{Tan:2016zwf,Akerib:2015rjg,Akerib:2016vxi,Agnese:2015nto}, and astrophysical observations by gamma-ray telescopes~\cite{Hooper:2012sr,Ackermann:2015zua} and cosmic ray detectors~\cite{Bergstrom:2013jra,Giesen:2015ufa,Cirelli:2013hv} have also begun to constrain the WIMP parameter space. Although many WIMP models remain viable, it is perhaps surprising that no definitive detection of particle dark matter has yet been made. In light of this experimental situation, it has become increasingly interesting to consider dark matter scenarios beyond the conventional WIMP paradigm. In this paper, we focus on dark matter candidates with negligible couplings to the SM and that reside within a sector that is thermally decoupled from the visible matter in the early universe. In doing so, we build upon our previous recent work~\cite{Berlin:2016vnh} by considering a wider range of models and discussing their phenomenology in greater detail. Throughout this study, we assume that the visible sector, which contains the SM, is supplemented by a decoupled hidden sector, which contains the dark matter. We further assume that both sectors are thermally populated during post-inflation reheating and maintain separate temperatures throughout cosmological evolution~\cite{Allahverdi:2010xz,Adshead:2016xxj}. Although sequestered from the SM, the hidden sector may consist of many new additional particle species with sizable mutual interaction rates. In particular, it is possible that the lightest stable hidden species, $X$, freezes out via $XX \to YY$ annihilation, where $Y$ is a lighter hidden sector species that ultimately decays into SM particles. Being stable, we take $X$ to be our dark matter candidate. If the $Y$ is short-lived, it will never dominate the energy density of the universe, and will have little effect on cosmological evolution. In this regime, $X$ will freeze out with the observed dark matter abundance only if its mass and couplings are similar to those of traditional WIMPs. Although, in principle, such a scenario can be viable for a wide range of masses, constraints from perturbative unitarity typically require $m_X \lesssim \order{100}$ TeV~\cite{Griest:1989wd} (see, however, Ref.~\cite{Harigaya:2016nlg}). This bound can be circumvented, however, if the entropy of the visible sector increases appreciably after the freeze-out of $X$~\cite{Dev:2016xcp,Fornengo:2002db,Gelmini:2006pq,Kane:2015jia,Hooper:2013nia,Patwardhan:2015kga,Randall:2015xza,Reece:2015lch,Lyth:1995ka,Davoudiasl:2015vba,Cohen:2008nb,Yamanaka:2014pva}. For instance, a heavy and long-lived species in the hidden sector could come to dominate the energy density of the universe before decaying to SM particles, thereby diluting all relic abundances, including that of $X$. As we will see in Sec.~\ref{sec:decay}, the increase in the visible sector entropy from $Y$ decay scales as $\propto \tau_Y^{1/2}$, where $\tau_Y$ is the lifetime of the unstable species. Thus, for sufficiently large $\tau_Y$, it is possible to significantly dilute the abundance of $X$, thereby achieving an acceptable density of dark matter, even for masses well above the conventional limit from perturbative unitarity, $m_X \gg 100$ TeV. Long lifetimes are straightforwardly realized if the decaying particle is the lightest hidden sector state. In fact, if the hidden and visible sectors are highly decoupled, the lightest hidden sector state will automatically be long-lived, since its width relies on a coupling that is too small to sustain thermal equilibrium between the two sectors. We emphasize that this picture is relatively universal, and can be found within any model in which the dark matter freezes out through annihilations in a heavy and highly decoupled hidden sector that is populated after inflation. In contrast to scenarios in which an additional out-of-equilibrium decay is invoked solely to dilute the initial cosmological abundances of various species, dilutions of the type considered in this paper are an inevitable consequence of thermal decoupling. \begin{figure}[t] \begin{center} \includegraphics[width=0.6\textwidth]{Figures/cartoon} \caption{\label{fig:schematic} A schematic diagram of the processes that we will consider in this study. Here $X$, the dark matter candidate, annihilates into pairs of metastable hidden sector $Y$ particles. If the hidden sector is heavy and extremely decoupled from the visible sector (which contains the Standard Model), then $Y$ will be long-lived, and may eventually dominate the universe's energy density. Upon its decay into Standard Model particles, $Y$ reheats the visible universe and dilutes all particle abundances, including the relic density of $X$.} \end{center} \end{figure} The remainder of this paper is structured as follows. In Sec.~\ref{sec:thermo}, we review the early universe thermodynamics of scenarios with a decoupled hidden sector. We then discuss in detail the processes of thermal freeze-out and out-of-equilibrium decay in Secs.~\ref{sec:fo} and~\ref{sec:decay}, respectively. In Sec.~\ref{sec:Neff}, we discuss possible contributions to the effective number of neutrino species within this class of scenarios. In Sec.~\ref{sec:models}, we describe three concrete realizations of dark matter in a decoupled hidden sector, in which the hidden and visible sectors interact through the vector portal, Higgs portal, or lepton portal. Finally, we briefly summarize our results and conclusions in Sec.~\ref{sec:conclusion}. | \label{sec:conclusion} Motivated by the increasingly stringent constraints that have been placed in recent years on dark matter in the form of WIMPs, we consider in this study dark matter candidates that are part of a larger sector with no sizable interactions with the Standard Model. Such a hidden sector could very plausibly be populated after inflation, and will undergo a thermodynamic history that is independent of the visible sector (which contains the Standard Model). As the hidden sector cools, its lightest particles will become non-relativistic and may come to dominate the energy density of the universe. When these particles ultimately decay, they reheat the universe and dilute the abundances of any previously frozen-out relics, including that of the dark matter itself. This sequence of events is a generic consequence of the hidden sector's highly decoupled nature, and phenomenology of this type can be found within a wide range of theoretical frameworks. In this study, we have described in some detail the thermodynamics and cosmological evolution of models that feature a highly decoupled hidden sector. After presenting a more general discussion, we have considered three simple, representative models, in which the hidden and visible sectors interact through what are known as the vector, Higgs, and lepton portals. In each of these cases, we identify significant parameter space in which the decoupled cosmological history considered here is viably realized. Furthermore, due to the dilution that results from the decays of long-lived hidden sector particles, the dark matter can be as heavy as $\sim$1-100 PeV in these scenarios, without generating a dark matter abundance in excess of the measured value. \bigskip \bigskip \textbf{Acknowledgments.} AB is supported by the Kavli Institute for cosmological physics at the University of Chicago through grant NSF PHY-1125897. Fermilab is operated by Fermi Research Alliance, LLC, under Contract No. DE-AC02-07CH11359 with the US Department of Energy. \begin{appendix} | 16 | 9 | 1609.02555 |
1609 | 1609.02887_arXiv.txt | {To investigate the physical nature of the `nuc\-leated instability' of proto giant planets, the stability of layers in static, radiative gas spheres is analysed on the basis of Baker's standard one-zone model.} {It is shown that stability depends only upon the equations of state, the opacities and the local thermodynamic state in the layer. Stability and instability can therefore be expressed in the form of stability equations of state which are universal for a given composition.} {The stability equations of state are calculated for solar composition and are displayed in the domain $-14 \leq \lg \rho / \mathrm{[g\, cm^{-3}]} \leq 0 $, $ 8.8 \leq \lg e / \mathrm{[erg\, g^{-1}]} \leq 17.7$. These displays may be used to determine the one-zone stability of layers in stellar or planetary structure models by directly reading off the value of the stability equations for the thermodynamic state of these layers, specified by state quantities as density $\rho$, temperature $T$ or specific internal energy $e$. Regions of instability in the $(\rho,e)$-plane are described and related to the underlying microphysical processes.} {Vibrational instability is found to be a common phenomenon at temperatures lower than the second He ionisation zone. The $\kappa$-mechanism is widespread under `cool' conditions.} {} | In the \emph{nucleated instability\/} (also called core instability) hypothesis of giant planet formation, a critical mass for static core envelope protoplanets has been found. Mizuno (\cite{mizuno}) determined the critical mass of the core to be about $12 \,M_\oplus$ ($M_\oplus=5.975 \times 10^{27}\,\mathrm{g}$ is the Earth mass), which is independent of the outer boundary conditions and therefore independent of the location in the solar nebula. This critical value for the core mass corresponds closely to the cores of today's giant planets. Although no hydrodynamical study has been available many workers conjectured that a collapse or rapid contraction will ensue after accumulating the critical mass. The main motivation for this article is to investigate the stability of the static envelope at the critical mass. With this aim the local, linear stability of static radiative gas spheres is investigated on the basis of Baker's (\cite{baker}) standard one-zone model. Phenomena similar to the ones described above for giant planet formation have been found in hydrodynamical models concerning star formation where protostellar cores explode (Tscharnuter \cite{tscharnuter}, Balluch \cite{balluch}), whereas earlier studies found quasi-steady collapse flows. The similarities in the (micro)physics, i.e., constitutive relations of protostellar cores and protogiant planets serve as a further motivation for this study. | \begin{enumerate} \item The conditions for the stability of static, radiative layers in gas spheres, as described by Baker's (\cite{baker}) standard one-zone model, can be expressed as stability equations of state. These stability equations of state depend only on the local thermodynamic state of the layer. \item If the constitutive relations -- equations of state and Rosseland mean opacities -- are specified, the stability equations of state can be evaluated without specifying properties of the layer. \item For solar composition gas the $\kappa$-mechanism is working in the regions of the ice and dust features in the opacities, the $\mathrm{H}_2$ dissociation and the combined H, first He ionization zone, as indicated by vibrational instability. These regions of instability are much larger in extent and degree of instability than the second He ionization zone that drives the Cephe{\"\i}d pulsations. \end{enumerate} | 16 | 9 | 1609.02887 |
1609 | 1609.05233_arXiv.txt | {Since in situ studies and interplanetary dust collections only provide a spatially limited amount of information about the interplanetary dust properties, it is of major importance to complete these studies with properties inferred from remote observations of light scattered and emitted, with interpretation through simulations. } {Physical properties of the interplanetary dust in the near-ecliptic symmetry surface, such as the local polarization, temperature and composition, together with their heliocentric variations, may be derived from scattered and emitted light observations, giving clues to the respective contribution of the particles sources.} {A model of light scattering by a cloud of solid particles constituted by spheroidal grains and aggregates thereof is used to interpret the local light scattering data. Equilibrium temperature of the same particles allows us to interpret the temperature heliocentric variations.} {A good fit of the local polarization phase curve, $P_{\alpha}$, near 1.5~AU from the Sun is obtained for a mixture of silicates and more absorbing organics material ($\approx$40 \% in mass) and for a realistic size distribution typical of the interplanetary dust in the \unit{0.2}{\micro\metre} to \unit{200}{\micro\metre} size range. The contribution of dust particles of cometary origin is at least 20\% in mass. The same size distribution of particles gives a solar distance, $R$, dependence of the temperature in $R^{-0.45}$ different than the typical black body behavior. The heliocentric dependence of $P_{\alpha=\unit{90}{\degree}}$ is interpreted as a progressive disappearance of solid organics (such as HCN polymers or amorphous carbon) towards the Sun. } | The description of the particles constituting the interplanetary dust cloud (IDC) in terms of morphology, porosity, size distribution and complex refractive indices is a clue to their origin and evolution. Information can be retrieved through (a few) in situ studies (see e.g. Jessberger et al. \cite{ekj_ts01}) and through remote observations of the light scattering properties (brightness and polarization of solar light scattered by the dust particles in the visible domain) and emissivity (in the infrared spectrum) of the dust cloud, see e.g. Levasseur-Regourd et al. (\cite{aclr_mc99}). Photometric measurements integrate along the line of sight all the local contributions emitted and scattered by the dust. Consequently techniques of inversion, such as the nodes of lesser uncertainty method (see e.g. Dumont \& Levasseur-Regourd \cite{rd_aclr88}, Levasseur-Regourd et al. \cite{aclr_im01} and references therein) are needed to retrieve the local properties. All the values given in the following text correspond to bulk values deduced from inversion methods over elementary volumes. Light scattering numerical simulations can be used to derive physical properties of clouds of dust particles, typically of comet origin (see e.g. Levasseur-Regourd et al. \cite{aclr_tm07} and references therein). Realistic light scattering models for a distribution of particles constituted of a mixture of spheroidal grains and aggregates of small spheroids have already been used to derive information about the composition and size distribution (lower and upper cut-off, power law coefficient, proportion of absorbing and non-absorbing material and proportion of aggregates) in the case of comet Hale-Bopp dust polarimetric observations (Lasue \& Levasseur-Regourd \cite{jl_aclr06}). This study presents the results obtained by applying an irregular particles cloud model in the case of the interplanetary dust cloud observations to estimate the physical properties of the size distribution and the proportion of fluffy particles. It tentatively indicates the relative contribution of particles from cometary and asteroidal origins. In the next two paragraphs, clues to the properties of the interplanetary dust cloud and source particles are reviewed. In the last two paragraphs, the emitted light and local temperature properties of the cloud are analyzed through our model. | The physical properties of the interplanetary dust cloud in the near ecliptic symmetry surface are tentatively derived from scattered and emitted light observations. Results about the composition of the dust cloud, the size distribution and the shape of the particles are summarized below. \begin{enumerate} \item{Both silicates and (more absorbing) organics materials are necessary to explain the local polarization and temperature values retrieved from observations, as well as their variation with the solar distance.} \item{ A good fit of the polarization phase curve available near 1.5~AU is obtained for a realistic particles size distribution (with a power law $a^{-3}$ for particles with an equivalent diameter, $a$, between \unit{0.22}{\micro\metre} and \unit{20}{\micro\metre} and $a^{-4.4}$ for larger particles) and a mixture of silicates and more absorbing organics materials (between 20\% and 60 \% in mass).} \item{The upper cutoff of the size distribution is not well constrained with the above mentioned size distribution allowing the presence of rather large compact particles.} \item{The decrease of $P_{\unit{90}{\degree}}$ with the solar distance between 1.5 and 0.5~AU is interpreted as a progressive disappearance of the solid carbonaceous compounds (such as HCN polymers or amorphous carbon) towards the Sun, probably linked with the presence of an extended zone of thermal degradation.} \item{The drastic change of $P_{\unit{90}{\degree}}$ closer to the Sun between 0.5 and 0~AU could be explained by other physical processes, as for example the degradation of silicate materials or a change in the size distribution possibly favoring smaller particles towards the Sun.} \item{Unfragmented aggregates of cometary origin contribution to the interplanetary dust cloud is of at least 20\% in mass around 1.5~AU.} \item{The size distribution retrieved from the polarization fit leads to a temperature variation in $R^{-0,45}$ different from the black body behavior and closer to the observations.} \item{The variation of the temperature with the solar distance for absorbing materials is closer to the observations than the one of non absorbing materials. This behavior is mainly due to particles with a diameter smaller than \unit{2}{\micro\metre}.} \end{enumerate} | 16 | 9 | 1609.05233 |
1609 | 1609.03551.txt | Direct searches for dark matter (DM) by the LUX and PandaX-II Collaborations employing xenon-based detectors have recently come up with the most stringent limits to date on the spin-independent elastic scattering of DM off nucleons. For Higgs-portal scalar DM models, the new results have precluded any possibility of accommodating low-mass DM as suggested by the DAMA and CDMS II Si experiments utilizing other target materials, even after invoking isospin-violating DM interactions with nucleons. In the simplest model, SM+D, which is the standard model plus a real singlet scalar named darkon acting as the DM candidate, the LUX and PandaX-II limits rule out DM masses \mbox{roughly from 4 to 450 GeV}, except a small range around the resonance point at half of the Higgs mass where the interaction cross-section is near the neutrino-background floor. In the THDM\,II+D, which is the type-II two-Higgs-doublet model combined with a darkon, the region excluded in the SM+D by the direct searches can be recovered due to suppression of the DM effective interactions with nucleons at some values of the ratios of Higgs couplings to the up and down quarks, making the interactions significantly isospin-violating. However, in either model, if the 125-GeV Higgs boson is the portal between the dark and SM sectors, DM masses less than 50 GeV or so are already ruled out by the LHC constraint on the Higgs invisible decay. In the THDM\,II+D, if the heavier $CP$-even Higgs boson is the portal, theoretical restrictions from perturbativity, vacuum stability, and unitarity requirements turn out to be important instead and exclude much of the region below 100 GeV. For larger DM masses, the THDM\,II+D has plentiful parameter space that corresponds to interaction cross-sections under the neutrino-background floor and therefore is likely to be beyond the reach of future direct searches without directional sensitivity. | } Cosmological studies have led to the inference that ordinary matter makes up only about 5\% of the energy budget of the Universe, the rest being due to dark matter (26\%) and dark energy\,\,(69\%), the properties of which are largely still unknown~\cite{pdg}. Although the evidence for cosmic dark matter (DM) has been established for decades from numerous observations of its gravitational effects, the identity of its basic constituents has so far remained elusive. As the standard model (SM) of particle physics cannot account for the bulk of the DM, it is of great interest to explore various possible scenarios beyond the SM that can accommodate it. Amongst the multitudes of DM candidates that have been proposed in the literature, those classified as weakly interacting massive particles (WIMPs) are perhaps the leading favorites~\cite{pdg}. The detection of a WIMP is then essential not only for understanding the nature of the DM particle, but also for distinguishing models of new physics beyond the SM. Many different underground experiments have been and are being performed to detect WIMPs directly by looking for the signatures of nuclear recoils caused by the collisions between the DM and nucleons. The majority of these searches have so far come up empty, leading only to upper bounds on the cross section $\sigma_{\rm el}^N$ of spin-independent elastic WIMP-nucleon scattering. Experiments utilizing xenon as the target material have turned out to supply the strictest bounds to date, especially the newest ones reported separately by the LUX and PandaX-II Collaborations~\cite{lux,pandax}, under the implicit assumption that the DM interactions with the proton and neutron respect isospin symmetry. These null results are in conflict with the tentative indications of WIMP signals observed earlier at relatively low masses in the DAMA~\cite{dama} and CDMS II Si~\cite{cdmssi} measurements, which employed nonxenon target materials.\footnote{The excess events previously observed in the CoGeNT~\cite{cogent} and CRESST-II~\cite{cresst} experiments have recently been demonstrated to be entirely attributable to underestimated backgrounds instead of DM recoils~\cite{nosignal}.} A\,\,graphical comparison between the new limits on $\sigma_{\rm el}^N$ from LUX and PandaX-II and the hypothetical signal regions suggested by DAMA and CDMS II Si is presented in Fig.\,\,\ref{expt-plots}(a). It also displays the limits from a few other direct searches~\cite{Agnese:2014aze,Agnese:2015nto,Angloher:2015ewa}, which were more sensitive to lighter WIMPs, as well as the expected reaches~\cite{Cushman:2013zza} of the upcoming XENON1T~\cite{xenon1t}, DarkSide G2~\cite{dsg2}, and LZ~\cite{lz} experiments and an estimate of the WIMP discovery limit due to coherent neutrino scattering backgrounds~\cite{nubg}. Mechanisms that may reconcile the incompatible null and positive results of the WIMP DM direct searches have been suggested over the years. One of the most appealing proposals stems from the realization that the effective couplings $f_p^{}$ and $f_n^{}$ of the DM to the proton and neutron, respectively, may be very dissimilar~\cite{Kurylov:2003ra,Feng:2011vu}. If such a substantial violation of isospin symmetry occurs, the impact on the detection sensitivity to WIMP collisions can vary significantly, depending on the target material. In particular, during the collision process the DM may manifest a\,\,xenophobic behavior brought about by severe suppression of the collective coupling of the DM to xenon nuclei, but not necessarily to other nuclei~\cite{Feng:2013fyw}. This can explain why xenon-based detectors still have not discovered any DM, but DAMA and CDMS II Si perhaps did. Numerically, in the xenon case the suppression is the strongest if \,$f_n^{}/f_p^{}\simeq-0.7$\,~\cite{Feng:2011vu}. Assuming this ratio and applying it to the pertinent formulas provided in Ref.\,\cite{Feng:2011vu}, one can translate the data in Fig.\,\,\ref{expt-plots}(a) into the corresponding numbers for the spin-independent elastic WIMP-proton cross-section, $\sigma_{\rm el}^p$. The latter are plotted in Fig.\,\ref{expt-plots}(b), where the curve for DarkSide G2, which will employ an argon target, is scaled up differently from the curves for the xenon experiments including LZ. It is now evident that the conjectured signal regions of DAMA and CDMS II Si are no longer viable in light of the latest LUX and PandaX-II bounds.\footnote{If the DM-nucleon scattering is both isospin violating and inelastic, which can happen if a spin-1 particle, such as a $Z'$ boson, is the portal between the DM and SM particles, it may still be possible to accommodate the potential hint of low-mass DM from CDMS II Si and evade the limits from xenon detectors at the same time~\cite{inelastic}. The inelastic-DM approach has also been proposed to explain the DAMA anomaly~\cite{Scopel:2015eoh}.\medskip} \begin{figure}[t] \includegraphics[width=83mm]{fig_exp_sigmaelN_vs_mwimp.eps} ~ \includegraphics[width=83mm]{fig_exp_ivdm_sigmaelp_vs_mwimp.eps}\vspace{-1ex} \caption{(a) Measured upper-limits on the spin-independent elastic WIMP-nucleon cross-section at 90\% confidence level (CL) versus WIMP mass from LUX~\cite{lux}, PandaX-II~\cite{pandax}, CDMSlite~\cite{Agnese:2014aze}, SuperCDMS~\cite{Agnese:2015nto}, and CRESST~\cite{Angloher:2015ewa} in the isospin-symmetric limit. Also shown are a gray patch compatible with the DAMA Na modulation signal at the 3$\sigma$ level~\cite{Savage:2008er}, a cyan area for the possible DM hint from CDMS\,\,II\,\,Si at 90\% CL~\cite{cdmssi}, the sensitivity projections~\cite{Cushman:2013zza} of XENON1T~\cite{xenon1t} (black dotted curve), DarkSide\,\,G2~\cite{dsg2} (maroon dash-dot-dotted curve), and LZ~\cite{lz} (turquoise dash-dotted curve), and the WIMP discovery lower-limit due to coherent neutrino scattering backgrounds~\cite{nubg} (brown dashed curve). (b) The corresponding WIMP-proton cross-sections computed from (a) with isospin-violating effective WIMP couplings to the neutron and proton in the ratio \,$f_n^{}/f_p^{}=-0.7$.\label{expt-plots}} \end{figure} Since these new results have reduced further the allowed WIMP parameter space, it is of interest to investigate what implications they may have for the simplest Higgs-portal WIMP DM models and how these scenarios may be probed more stringently in the future. For definiteness, in this paper we focus on the SM+D, which is the SM minimally expanded with the addition of a\,\,real singlet scalar serving as the DM and dubbed darkon, and on its two-Higgs-doublet extension of type II, which we call THDM\,II+D.\footnote{There are earlier studies in the literature on various aspects of the SM plus singlet scalar DM, or a greater scenario containing the model, in which the scalar was real~\cite{Silveira:1985rk,sm+reald,Cline:2013gha} or complex~\cite{sm+complexd}. Two-Higgs-doublet extensions of the SM+D have also been explored previously~\cite{He:2008qm,He:2011gc,Bird:2006jd,2hdm+d,Drozd:2014yla}.} Specifically, we look at a number of constraints on these two models not only from the most recent DM direct searches, but also from LHC measurements on the gauge and Yukawa couplings of the 125-GeV Higgs boson and on its invisible decay mode, as well as from some theoretical requirements. We find that in the SM+D the darkon mass region up to {\footnotesize\,$\sim$\,}450 GeV is ruled out, except a small range near the resonant point at half of the Higgs mass where the DM-nucleon cross-section is close to the neutrino-background floor. On the other hand, in the THDM\,II+D the region excluded in the SM+D can be partially recovered because of suppression of the cross section that happens at some values of the product \,$\tan\alpha\,\tan\beta$\, or \,$\cot\alpha\,\tan\beta$,\, where $\alpha$ is the mixing angle of the $CP$-even Higgs bosons and $\tan\beta$ the ratio of vacuum expectation values (VEVs) of the Higgs doublets. The structure of the rest of the paper is as follows. We treat the SM+D in Sec.\,\ref{sec:sm+d} and the THDM\,II+D in Sec.\,\ref{sec:2hdm+d}. We summarize our results and conclude in Sec.\,\ref{conclusion}. A couple of appendices contain additional formulas and extra details. | } We have explored some of the implications of the most recent null results of WIMP DM direct searches by LUX and PandaX-II. For Higgs-portal scalar WIMP DM models, the new limits have eliminated any possibility to accommodate low-mass DM undergoing spin-independent elastic scattering off nucleons that was suggested by the potentially positive results of the DAMA and CDMS II Si experiments, even after invoking the mechanism of isospin violation in DM-nucleon interactions. We have studied particularly how the LUX and PandaX-II results probe the parameter space of the simplest Higgs-portal scalar DM models, namely the SM+D, which is the SM plus a\,\,real scalar singlet called darkon, and the THDM\,II+D, which is the two-Higgs-doublet model of type II combined with a darkon. In the THDM\,II+D we entertain the possibility that the 125-GeV Higgs boson, $h$, is the lightest one of the physical members of the scalar doublets. Our analysis takes into account various constraints from LHC data on the Yukawa \mbox{couplings of $h$}, its couplings to gauge bosons, and its invisible decay mode. Also pertinent are restrictions from oblique electroweak precision measurements and from theoretical considerations regarding perturbativity, vacuum stability, and unitarity. In the SM+D case, $h$ is the only portal between the DM and SM sectors, while in the THDM\,II+D one or both of the $CP$-even Higgs bosons, \mbox{$h$ and the heavier $H$}, can be the portals. We find that in scenarios with $h$ being the only portal the LHC information on \,$h\to\rm invisible$\, places a significant restraint on the darkon-$h$ coupling and rules out the \,$m_D^{}\le m_h^{}/2$\, region, except a small range near the resonance point \,$m_D^{}=m_h^{}/2$.\, We also find that for \,$m_D^{}>m_h^{}/2$\, in the SM+D the new LUX and PandaX-II limits exclude masses up to 450 GeV or so, but in the $h$-portal THDM\,II+D they can be recovered due to suppression of the Higgs-nucleon coupling,\,\,$g_{{\cal NN}h}^{}$, at some values of the product \,$\tan\alpha\,\tan\beta$.\, In contrast, in the THDM\,II+D scenario with $H$ being the sole portal, the \,$h\to\rm invisible$\, bound does not apply to the much heavier $H$, and the LUX and PandaX-II limits can be evaded due to suppression of $g_{{\cal NN}H}^{}$ at some values of \,$\cot\alpha\,\tan\beta$.\, However, in this case our examples demonstrate that the foregoing theoretical requirements are consequential and disallow most of the \,$m_D^{}<100$\,GeV\, region. Thus, darkon masses below \,$m_D^{}\simeq50$\,GeV\, are ruled out in the SM+D by LHC data and very likely so in the THDM\,II+D by the LHC and theoretical restrictions. For higher masses, lower parts of the dip around \,$m_D^{}=m_h^{}/2$\, in the $h$-portal cases will remain viable for the foreseeable future, and beyond the $h$-resonance area the region up to roughly 3.5, 10, and 20\,\,TeV in the SM+D will be testable by XENON1T, DarkSide G2, and LZ, respectively. For \,$m_D^{}>100$\,GeV\, in the THDM\,II+D there is generally ample parameter space that yields a\,\,darkon-nucleon cross-section below the neutrino-background floor and is therefore likely to elude direct detection experiments in the future which lack directional sensitivity. Finally, we point out that the considerable suppression of $g_{{\cal NN}\cal H}^{}$ is accompanied by $g_{pp\cal H}^{}$ and $g_{nn\cal H}^{}$ manifesting sizable isospin breaking, as illustrated in our examples. | 16 | 9 | 1609.03551 |
1609 | 1609.02908_arXiv.txt | {We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us. } \arxivnumber{1609.02908} \begin{document} | The growth of the large-scale structure in the observed Universe arises due to gravitational collapse into dark-matter dominated potentials, tempered by the expansion of the Universe. A wealth of information can be encoded in the growth rate, including constraints on the expansion history, the nature of dark energy and modified gravity \cite{Wei13,PDG14}. There are several ways of studying the growth of structure, but perhaps the oldest and highest signal-to-noise measurement comes from observations of the anisotropy in the clustering of objects in redshift surveys. Since the redshift, from which one infers distance, contains a contribution from the line-of-sight velocity the clustering of objects in redshift surveys exhibits anisotropy \cite{Kai87,Ham98,Wei13}, known as redshift-space distortions (RSD). Over the last several decades measurements of the redshift-space clustering of galaxies have become increasingly precise (for example the measurements from the recently completed BOSS survey \cite{Daw13} have percent-level uncertainties on quasi-linear scales) allowing highly precise tests of the current paradigm but also posing a significant challenge for theorists seeking to model the data. As we prepare for the next generation of surveys we need models which are able to model the redshift-space clustering of biased tracers at the percent level over a wide range of scales (to break degeneracies between parameters). In this paper we shall attempt to model the low-order moments of the redshift-space clustering signal in configuration space, using models based upon Lagrangian perturbation theory (LPT; see below) and the effective field theory of large-scale structure (EFT \cite{BNSZ12,CHS12,PajZal13,Man14,MerPaj14,CLP14,PorSenZal14,VlaWhiAvi15}). LPT is one of the oldest and most successful analytic model for studying large-scale structure, and provides a simple connection to N-body simulations and peaks theory \cite{BBKS}. EFT is a consistent method for incorporating the effects of non-perturbative physics into perturbation theory by including a number of additional terms, with free parameters, whose structure is determined by the symmetries of the theory. Our focus here will be on increasing the precision with which we can predict the clustering moments on intermediate scales ($>25\,h^{-1}$Mpc), rather than on increasing the range of scales we predict. We believe this is a more appropriate use of techniques built upon perturbation theory. For an alternative route, see Ref.~\cite{Rei14}. The outline of this paper is as follows. In the next section we review the context within which we will do our calculations: (Lagrangian) perturbation theory and the (Gaussian) streaming model. The next section describes the computation of each piece of the streaming model in terms of perturbation theory, including our bias model and the impact of small-scale physics which is not explicitly modeled. In section \ref{sec:evolution} we discuss the expected evolution of the correlation function, and the extent to which measurements in finite redshift slice can be interpreted as being at an ``effective'' redshift. We present some preliminary comparison of our results with N-body simulations in section \ref{sec:nbody}, finding that we are limited by the accuracy of the simulations. Finally we conclude in section \ref{sec:conclusions}. A number of technical steps are relegated to a series of appendices. Appendix \ref{app:GSM} reviews the derivation of the streaming model. Appendix \ref{app:fourier} reviews the Fourier-space statistics. Appendix \ref{app:derivs} details the computation of the time-derivative terms which enter in the velocity statistics. Appendix \ref{app:bias} presents a more general Lagrangian bias model which includes derivatives of the initial density field and shear terms. Appendix \ref{app:DF} compares our formalism to the distribution function formalism of Ref.~\cite{SelMcD11}. | \label{sec:conclusions} Redshift surveys by neccessity measure large-scale structure in redshift space, in which peculiar velocities sourced by large-scale gravitational potentials have induced anisotropic clustering. Measurement of these anisotropies allows us to probe the growth of large-scale structure, breaking degeneracies in cosmological distance measures and providing a key test of general relativity and the gravitational instability paradigm on quasi-linear, cosmological scales. In this paper we update earlier treatments of the Gaussian Streaming Model (GSM) and present tests against a new set of N-body simulations. We improve upon previous calculations of the ingredients in this model -- the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion -- using a Lagrangian effective field theory with an extended bias model. We show that the Lagrangian approach provides a solid framework for studying large-scale structure, and provides a simple connection to N-body simulations and peaks theory. Effective field theory techniques provide a straightforward means of incorporating the effects of non-perturbative physics into perturbation theory by including additional terms whose structure is determined by the symmetries of the theory. The expressions for the ingredients, and the bias model, are new and present the most general expressions at the given order\footnote{Code to evaluate these expressions is available at {\tt https://github.com/martinjameswhite/CLEFT\_GSM}.}. Throughout our focus has been on increasing the precision with which we can predict the clustering moments on intermediate scales ($>25\,h^{-1}$Mpc), rather than on increasing the range of scales we predict. We believe this is the most appropriate use of techniques built upon perturbation theory. Ultimately the precision of our model is limited by the neglect of 2-loop terms in the perturbative calculation, higher derivative orders in the EFT expansion, higher order terms in the bias expansion and the neglect of lightcone evolution. We find that these effects alter the predictions for the monopole and quadrupole moment of the correlation function and power spectrum at the per cent level on scales above $25-30\,h^{-1}$Mpc. The inclusion of 1-loop corrections to the Zeldovich approximation changes the clustering statistics by several per cent on large scales. The EFT terms encapsulate the effects of small-scale physics which is missing from the standard perturbative treatment. In $\xi(r)$ the primary effect is to change the width of the BAO peak and slightly decrease $\xi$ at lower $r$. The EFT terms steepen $v_{12}$ at small $r$, which is important in the streaming model in order to match the quadrupole. The EFT terms are most important for $\sigma^2$, where there is a large mismatch between the perturbative prediction and the N-body results \cite{ReiWhi11,WanReiWhi14}. The difference is very close to a constant, independent of scale and orientation, which is also the behavior of the lowest-order EFT counter term. Such an offset was included in earlier versions of the GSM as a ``finger-of-god'' term, referring to a specific type of small-scale effect. We find that a flexible bias model is at least as important as including the higher-order contributions to the evolution of clustering. The most general approach to bias is an EFT-inspired one, and reasoning purely from symmetry is highly attractive when describing the complex physics which leads to bias. We use a Lagrangian bias expansion up to the second order, including a derivative term and a shear term. This generates all the terms present in the corresponding third order Eulerian biasing expansion (see e.g.~Refs.~\cite{McDRoy09,Sen14,Mirb14,Ang15}), although the latter has more freedom coming from an additional third order bias parameter in the real space two-point statistics. Adding the third order terms in Lagrangian space would yield the same number of free parameters in both Lagrangian and Eulerian picture. We argue that using a symmetry-based approach to bias, with priors set by theory and simulations, has many benefits. In such a scheme, a Lagrangian framework has multiple advantages over an Eulerian one (\S\ref{sec:bias_philosophy}). We have compared our theoretical calculations with 4 large N-body simulations \cite{Sun16}, with a total simulated volume of $256\,h^{-3}{\rm Gpc}^3$. This volume, many times larger than accessible observationally, leads to very small statistical errors. However the simulations were run with an approximate time-stepping scheme, which limits the overall accuracy to several percent on the statistics (and scales) of relevance here. With this caveat in mind, our model performs very well when compared to N-body simulations. The model presented here achieves per cent level accuracy on the monopole and quadrupole of the correlation function and power spectrum on quasi-linear scales. This level of accuracy is likely sufficient for all upcoming surveys -- going to higher order in perturbation theory or including additional EFT terms will yield little return. In order to push to smaller scales, detailed modeling of highly-nonlinear effects are required (e.g.~Refs.~\cite{Rei14,Oku15}) which will likely increase the number of parameters dramatically for even a small increase in dynamic range. Increasing the volume, to decrease the errors at fixed scale, requires increasing the redshift range and requires modeling of the evolution of the bias (in addition to survey non-idealities). Our model works in a Lagrangian framework, with parameters that are easy to interpret within the context of the Gaussian peaks formalism or N-body simulations. Along with the LPT-based model for post-reconstruction BAO presented in \cite{Whi15a}, this formalism can be used to interpret the measurements from upcoming redshift surveys. The analytic nature of the calculation makes it possible rapidly explore changes in cosmology, and the flexible, parameterized bias model allows exploration of a wide range of effects with little effort. The analytic calculation can be used to set requirements for future grids of N-body models, both in terms of modeling the response surface for an emulator and in terms of which modes and which statistics need to be well converged. | 16 | 9 | 1609.02908 |
1609 | 1609.05227_arXiv.txt | We explore the transport of energetic particles in two-component turbulence in which the stochastic magnetic field is assumed to be a superposition of slab and two-dimensional modes. It is known that in magnetostatic slab turbulence, the motion of particles across the mean magnetic field is subdiffusive. If a two-dimensional component is added, diffusion is recovered. It was also shown before that in two-component turbulence, the slab modes do not explicitly contribute to the perpendicular diffusion coefficient. In the current paper the implicit contribution of slab modes is explored and it is shown that this contribution leads to a reduction of the perpendicular diffusion coefficient. This effect improves the agreement between simulations and analytical theory. Furthermore, the obtained results are relevant for investigations of diffusive shock acceleration. | The interaction between energetic particles and a magnetized plasma is explored analytically. Examples for energetic particles are Solar Energetic Particles (SEPs) and Cosmic Rays (CRs). If such particles move through space, their motion is usually diffusive and, therefore, a diffusive transport equation has to be used in order to describe their motion. The most important terms in such transport equations are those describing spatial diffusion along and across a mean magnetic field. Parallel and perpendicular diffusion coefficients are mostly controlled by the turbulent magnetic fields of the plasma. First treatments of perpendicular diffusion were based on quasi-linear theory (see Jokipii 1966) which can be understood as a first-order perturbation theory. However, perturbation theory is usually based on the assumption that there is a small parameter. It is often stated in the literature (see, e.g., Schlickeiser 2002) that this small parameter is the magnetic field ratio $\delta B / B_0$ (here $\delta B$ is the total turbulent field and $B_0$ is the mean magnetic field). Apart from the problem that this magnetic field ratio is usually not small in astrophysical scenarios, it was shown in the literature that a small value of $\delta B / B_0$ alone does not justify the quasi-linear approach (see, e.g., Shalchi 2009 for a detailed discussion of the problems associated with quasi-linear theory). Because quasi-linear theory is problematic, non-linear theories have been developed mainly in order to describe perpendicular diffusion. Some work was already presented in the seventies of the 20th century (see, e.g., Owens 1974). A breakthrough has been achieved by Matthaeus et al. (2003) where the so-called {\it Non-Linear Guiding Center (NLGC) theory} was presented. The latter theory agrees well with simulations for a specific turbulence model, namely a so-called two-component model in which it is assumed that the turbulence can be approximated by a superposition of slab and two-dimensional modes. However, NLGC theory does often not provide the correct result. This is in particular the case for slab turbulence, two-component turbulence with a dominant slab contribution, or three-dimensional turbulence with small Kubo numbers\footnote{The Kubo number occurs in investigations of three-dimensional turbulence and is defined as $K = (l_{\parallel} \delta B_x)/(l_{\perp} B_0)$. Here we have used characteristic lengths scales describing the correlation of the turbulent fields in the directions parallel and perpendicular with respect to the mean magnetic field. Furthermore, $\delta B_x$ is the $x$-component of the turbulent magnetic field vector and $B_0$ is the mean field.} (see, e.g., Shalchi 2006, Tautz \& Shalchi 2011, and Shalchi \& Hussein 2014). In Shalchi (2010) the {\it Unified Non-Linear Transport (UNLT) theory} was developed. Although the theory is based on some of the approximations used by Matthaeus et al. (2003), it contains a very different treatment of higher order correlations. UNLT theory uses an approach based on the CR Fokker-Planck equation in order to avoid simple approximations of such correlations. UNLT theory provides a non-linear integral equation similar compared to the NLGC result but it contains different terms in the denominator. In particular for slab and small Kubo number turbulence, NLGC and UNLT theories provide completely different results. Furthermore, UNLT theory contains the Matthaeus al. (1995) theory for field line random walk as special limit. UNLT theory provides the correct subdiffusive result for perpendicular transport in slab turbulence. Furthermore, the theory states that the slab contribution in two-component turbulence damps out subdiffusively even if a dominant two-dimensional component is added (see also Shalchi 2005 and Shalchi 2006). Therefore, slab modes do not explicitly contribute to the perpendicular diffusion coefficient. It is the purpose of the current paper to explore the implicit contribution of the slab modes to the perpendicular diffusion coefficient. The paper is organized as follows. In Sect. 2 we discuss different analytical theories for perpendicular diffusion. In Sect. 3 we developed a non-linear diffusion theory for two-component turbulence which takes into account the implicit contribution of the slab modes. In Sect. 4 we present some analytical approximations which are useful in order to simplify the new integral equation and in Sect. 5 we show the perpendicular diffusion coefficients based on different theories and compare them with each other. In Sect. 6 we summarize and conclude. Furthermore, we point out which theory should be applied for two-component and three-dimensional turbulence, respectively. | In the current paper we have revisited the problem of perpendicular diffusion of energetic particles in two-component turbulence. Whereas it was shown before that the slab modes do not explicitly contribute to the perpendicular diffusion coefficient, we explored the implicit contribution in the current paper. We have derived the modified non-linear integral equation (\ref{nlgc2}) which can be approximated by Eq. (\ref{finalapprox}). This modification should provide another improvement compared to the original NLGC theory developed in Matthaeus et al. (2003) and the extended NLGC theory of Shalchi (2006). Compared to earlier versions of the NLGC theory, the modified equations (\ref{nlgc2}) or (\ref{finalapprox}) are not more difficult to evaluate numerically. In Figs. \ref{q0l10}-\ref{q3l1} we have shown the perpendicular mean free path versus the parallel mean free path for different values of the scale ratio $l_{2D} / l_{slab}$ and different values of the energy range spectral index $q$. Both mean free paths are normalized with respect to the two-dimensional bendover scale $l_{2D}$. It can easily be seen that, in general, the implicit slab contribution reduces the perpendicular mean free path. Matthaeus et al. (2003) used $q=0$ and $l_{2D} = 0.1 l_{slab}$ in their work and they compared the original NLGC theory with test-particle simulations. They found a difference between analytical theory and simulations but this difference can be balanced out by using the correction factor $a^2$ and by setting $a^2 = 1/3$. In the current paper a possible explanation for this value is provided. The implicit contribution from the slab modes reduces the perpendicular mean free path as required to achieve agreement with simulations. The correction factor $a^2$ is no longer needed. For $q=1.5$ and $q=3$, which is in agreement with the values suggested by Matthaeus et al. (2007), we find a stronger effect. In particular for long parallel mean free paths, a strong reduction of the perpendicular mean free path can be observed. Another parameter which influences the reduction discussed here, is the scale ratio $l_{2D} / l_{slab}$. If this ratio is small, a stronger effect can be observed. For equal bendover scales, however, the perpendicular mean free path is only about a factor $2$ shorter as the one computed by using the original NLGC theory. A further theory for perpendicular diffusion was presented in Shalchi (2010) where the Unified Non-Linear Transport (UNLT) theory was developed. In the following we discuss which theory has to be used for which case. \begin{itemize} \item Solar Wind turbulence is often approximated by a slab/2D composite model which is also known as two-component turbulence. We suggest to use the extended NLGC theory with implicit slab contribution developed in the current paper for this specific turbulence model. This theory is represented by Eq. (\ref{nlgc2}) which can be well approximated by Eq. (\ref{finalapprox}). \item For full three-dimensional turbulence, the original NLGC theory, the extended theory and the approach developed in the current paper cannot be used. For this case the UNLT theory represented by Eq. (\ref{UNLT}) should provide an accurate description of perpendicular diffusion. In this case a critical parameter is the {\it Kubo number} (see Shalchi 2015 for more details). \end{itemize} The integral equation derived in the current paper should provide an accurate analytical description of perpendicular diffusion in two-component turbulence. It is straightforward to include further effects such as dynamical turbulence. In this case another term would occur in the denominator of Eq. (\ref{nlgc2}) which would be associated with the correlation time of the two-dimensional modes. The situation is more complicated, however, if there is also a dynamical turbulence effect associated with the slab modes because in this case the explicit contribution of the slab modes can be diffusive (see, e.g., Shalchi 2014). The results obtained in the current paper, and in analytical theories for perpendicular diffusion in general, are relevant for several applications: \begin{itemize} \item To understand the acceleration of particles due to turbulence (see, e.g., Lynn et al. 2014); \item For solar modulation studies (see, e.g., Alania et al. 2013, Engelbrecht \& Burger 2013, Manuel et al. 2014, and Potgieter et al. 2014); \item Particle acceleration at interplanetary shocks such as coronal mass ejection driven shocks (see, e.g., Li et al. 2012 and Wang et al. 2012); \item To describe the motion of cosmic rays in our own and in external galaxies (see, e.g., Buffie et al. 2013, Berkhuijsen et al. 2013, Heesen et al. 2014); \item To describe diffusive shock acceleration at interstellar shocks (see, e.g., Ferrand et al. 2014); \end{itemize} In particular for diffusive shock acceleration at supernova shock waves, the fact that the perpendicular mean free path becomes rigidity independent in the high energy limit, can help to explain the cosmic ray spectrum (see Ferrand et al. 2014 for more details). In the current paper we have shown that the perpendicular diffusion coefficient can even decrease with increasing rigidity in the high energy regime. To incorporate this effect in simulations of diffusive shock acceleration at interplanetary and interstellar shock waves could be important and should be subject of future work. | 16 | 9 | 1609.05227 |
1609 | 1609.00634_arXiv.txt | We present and evaluate several strategies to search for prompt, low-frequency radio emission associated with gravitational wave transients using the Murchison Widefield Array (MWA). As we are able to repoint the MWA on timescales of tens of seconds, we can search for the dispersed radio signal that has been predicted to originate along with or shortly after a neutron star-neutron star merger. We find that given the large, $600\,{\rm deg}^2$ instantaneous field-of-view of the MWA we can cover a significant fraction of the predicted gravitational wave error region, although due to the complicated geometry of the latter we only cover $>50$\% of the error region for approximately 5\% of events, and roughly 15\% of events will be located $<10\degr$ from the MWA pointing center such that they will be covered in the radio images. For optimal conditions our limiting flux density for a 10-s long transient would be 0.1\,Jy, increasing to about 1\,Jy for a wider range of events. This corresponds to luminosity limits of $10^{38-39}\,{\rm erg\,s}^{-1}$ based on expectations for the distances of the gravitational wave transients, which should be sufficient to detect or significantly constrain a range of models for prompt emission. | In 2015 September, the LIGO/Virgo Consortium (LVC) began its O1 science run that resulted in the first detection of gravitational waves \citep[][also see \citealt{ligo16b} for a second event]{ligo16}. Together with the gravitational wave (GW) analysis, the LVC sent private alerts to the electromagnetic (EM) followup community \citep{em2016,em2016b} to identify coincident electromagnetic transients (e.g., \citealt{2016arXiv160501607L,2016MNRAS.460L..40E,2016ApJ...822L...8T,2016ApJ...823L...2A,2016arXiv160503216M,2016ApJ...820L..36S,2016arXiv160203920C}). This identification is complicated by the very large uncertainty regions for the GW events: as discussed in \citet{2014ApJ...795..105S} and \citet{2014ApJ...789L...5K}, the error regions for these events can cover hundreds of square degrees (especially for the initial sensitivities of the detectors). Moreover, they need not be compact or simply connected. While identifying an EM counterpart would greatly enhance the utility of the GW signal \citep[e.g.,][]{2009astro2010S.235P,2014ApJ...795..105S,2016MNRAS.459..121C,2016arXiv160408530B} and would enable a range of new physical and astrophysical tests, it is not a simple task \citep[e.g.,][]{2014ApJ...789L...5K,2015ApJ...814...25C}. The EM counterparts span a range of models at a range of wavelengths: see \citet{2012ApJ...746...48M}, \citet{2014ApJ...795..105S}, \citet{2014ApJ...789L...5K}, and \citet{2016MNRAS.459..121C}, among other recent publications. At low radio frequencies telescopes such as the Murchison Widefield Array (MWA; \citealt{tin13}), the Low Frequency Array (LOFAR; \citealt{2013A&A...556A...2V}), and the Long Wavelength Array (LWA; \citealt{2009IEEEP..97.1421E}) have a number of advantages over optical/infrared searches: they have fields-of-view of hundreds to thousands of square degrees; unlike the optical/near-infrared sky which has a large number of transients present in every field \citep[e.g.,][]{2015ApJ...814...25C}, the radio sky is relatively quiet at these frequencies \citep{2015MNRAS.452.1254K,2015AJ....150..199T,2016MNRAS.456.2321S,rowlinson16,2016arXiv160400667P} with very few unrelated transients \citep[e.g.,][]{2016arXiv160509395H} to distract from those associated with the GW event; and many of the low-frequency facilities have no moving elements and so in principle can respond within seconds to an external trigger. While most expectations for transients associated with GW sources at radio wavelengths have concentrated on late-time radio afterglows and remnants \citep{2015ApJ...806..224M,2015MNRAS.450.1430H,2016arXiv160205529M,2016arXiv160509395H,2016arXiv160806518P}, which only peak after hundreds or thousands of days at 150\,MHz and can be quite faint (depending on the parameters of the explosion and the circum-burst medium), there are models that predict a prompt, coherent radio transient from the GW event \citep[e.g.,][]{1996A&A...312..937L,2000AA...364..655U,2010ApSS.330...13P,2013PASJ...65L..12T,2014ApJ...780L..21Z,2016ApJ...822L...7W,2016MNRAS.461.4435M} which may be related to the phenomenon of fast radio bursts (FRBs; \citealt{2007Sci...318..777L,2013Sci...341...53T}) at least some of which may be cosmological in origin \citep[][although see \citealt{2016ApJ...821L..22W,2016arXiv160304421V}]{2016arXiv160207477K}. Searches for direct connections between GW events and FRBs are proceeding largely\footnote{Even without a direct connection, current and future population studies \citep{2015MNRAS.447.2852K,2015ApJ...807...16L,2016MNRAS.455.2207R,2016arXiv160206099L} may be able to argue statistically for or against a connection \citep[e.g.,][]{2013Sci...341...53T,2016arXiv160204542Z,2016ApJ...825L..12C}.} through searches for GW events associated with individual FRBs \citep[e.g.,][]{2016arXiv160501707T} since the GW detectors have quasi-all sky sensitivity. But this strategy can be reversed: given their wide fields of view and very fast response times \citep{2015ApJ...814L..25K}, low-frequency facilities might be ideal for finding such prompt emission \citep{2016MNRAS.459..121C,2015PASA...32...46H} triggered instead by the GW signal. We then must optimize the followup procedure to maximize the prospects of a discovery without time for human-aided decision making. Strategies to aid followup have been studied in the optical/near-infrared regime \citep{2016arXiv160301689R,2015arXiv150604035C} where the signals are likely to be faint, relatively short in duration, and may be quite red \citep{2010MNRAS.406.2650M,2012ApJ...746...48M,2013ApJ...775...18B,2014MNRAS.441.3444M,2015MNRAS.450.1777K}. In the optical/near-IR the search can be aided by using prior information on host galaxies and likely distances to help reduce the search volume \citep[e.g.,][]{2016ApJ...820..136G,2016arXiv160307333S}. Strategies have also been studied in the X-ray regime \citep[e.g.,][]{2016MNRAS.455.1522E}, looking to directly probe the association between GW events and short gamma-ray bursts. In this paper we present and compare concrete strategies for low-frequency radio followup to search for prompt radio emission from a GW transient, where we use the MWA as an example to determine the likely sensitivity and success rate. Unlike in the optical/near-infrared, where a limited time window nonetheless allows limited sky coverage \citep[e.g.,][]{2015arXiv150604035C}, if we are searching for a prompt (duration $\lesssim$ms) radio signal we are limited to only a single pointing, and so we must optimize where that is with limited information. We discuss this in the context of simulated GW error regions from the first couple of years of GW observations, using two and three detectors (based on the simulated events from \citealt{2014ApJ...795..105S}). The MWA occupies a middle ground in the current generation of low-frequency arrays: it has a considerably wider field of view than the more sensitive LOFAR, but it is pointed, unlike the LWA which observes the whole (visible) sky. The MWA can respond on timescales of seconds to external triggers, which is currently not possible with LOFAR (A.~Rowlinson 2016, pers.~comm.) and which is not needed with the LWA's all-sky coverage. We discuss a search that focuses on standard imaging techniques \citep{2015AJ....150..199T,2015ApJ...814L..25K,rowlinson16} and not more rapid ``beam-formed'' data \citep[e.g.,][]{2014A&A...570A..60C,2015MNRAS.452.1254K,2015PASA...32....5T}, which, although it can be more sensitive to fast signals, is much more computationally intensive to process. | \label{sec:discuss} In the analysis above, we found that about 15\%--20\% of the events would be within the MWA's half-power point. Therefore, we would require follow-up of $\gtrsim 6$ events before we have one with a relatively sensitive observation down to luminosity limits of $\sim 10^{39}\,{\rm erg\,s}^{-1}$. Currently the predicted rates of neutron star-neutron star inspirals are 0.4--400\,${\rm yr}^{-1}$ with a mean of 40\,${\rm yr}^{-1}$ \citep{2010CQGra..27q3001A,2015ApJ...806..263D,2016LRR....19....1A}, so a single year of observing should be sufficient for one or more constraining observations if the rates are not too close to the most pessimistic case. Comparing the four strategies outlined in \S~\ref{sec:search}, we can easily reject the control strategy 1 (zenith pointing), but the remaining strategies are largely comparable in performance. Individual events may be seen better with one or the other but with the limited information available from the prompt GW triggers we cannot know which will be best in advance. Regardless of which strategy, the metrics in \S~\ref{sec:search} rely on the MWA being sensitivity-limited rather than event-limited. In principle we could have different tiles with different pointing locations, so as to cover the large LVC uncertainty region. However, the limited collecting area of the MWA drives us to point all of the tiles in a single subarray so as to achieve the most sensitive possible observation, rather than attempt to cover more of the GW error region at lower sensitivity \citep[cf.][]{2015ASPC..496..254B}. This is because, unlike in the optical regime where prompt emission from gamma-ray bursts is a known (albeit rare) phenomenon \citep[e.g.,][]{2014Sci...343...38V}, with a known luminosity function, prompt radio emission from a gamma-ray burst or a GW event has never been seen \citep{2012ApJ...757...38B,2015ApJ...814L..25K} so we do not know if shallower observations will be adequate: in the best 30\% of the cases where the MWA did cover the GW event with a reasonable sensitivity, our luminosity limits were only $\sim 1$ order of magnitude below model predictions. Splitting the MWA into subarrays would mean that all observations were less constraining. We can instead make up for the possibility of missing the GW event in a statistical sense by observing a larger number of events. At the same time the increasing performance of the GW detectors will lead to a large number of targets with improving localization. Therefore we believe it best to stick with a single array, but this will be re-evaluated as the actual successes are evaluated. Similarly, we could experiment with other observational modes like splitting our 30\,MHz bandpass into multiple sub-bands (as in \citealt{2015ApJ...814L..25K}), which could be advantageous if a bright but frequency-dependent signal is expected. Given the degree of uncertainty about these models that is unlikely to be preferred at least to start, but as we gain experience we may change our procedure. We implemented strategy 4 for the MWA during the first LIGO observing run (O1; 2015 September to 2016 January) covering the first detection, GW~150914. However, this trigger was released after a considerable delay (several days) needed for human examination of the event. Therefore we did not require any real-time decisions about strategy but instead could use multiple pointings to tile the GW error regions \citep{em2016}. We expect that as the LVC improves their internal vetting and pipelines their latency will improve to 90--120\,s after the GW event \citep{2014ApJ...795..105S,T1400054-v7} or possibly better \citep{2012ApJ...748..136C,2016MNRAS.459..121C} and this strategy will be employed. It is worth noting that the first published GW signal is from a binary black hole system \citep{ligo16}, which is not expected to have any EM signature \citep[][but see \citealt{2016arXiv160203920C}]{em2016}. The rates of similar events will likely be quite high once LIGO reaches its full design sensitivity, approaching 1/day. If this is the case then we will certainly have the opportunity to cover a sufficient number of error regions to search statistically for any associated EM emission, although the greater distances to the more massive systems will limit our sensitivity. As discussed in \citet{2015ApJ...814L..25K} and \citet{2016MNRAS.459..121C}, the expected delay of the radio signal relative to the GW transient is tens of seconds up to several minutes, based on the simulated distances of the transients and the expected extragalactic plus galactic dispersion measures. The actual time of any prompt radio signal may also be shifted by up to tens of seconds \citep[e.g.,][]{2014ApJ...780L..21Z}, potentially in either direction. Given the fast, $\approx 16\,$s response time that the MWA can achieve \citep{2015ApJ...814L..25K} we can easily repoint to catch any prompt emission as long as the GW latency improves. Overall we emphasize the need to transmit the trigger and react, as soon as possible, preferably well within 1\,min. We have demonstrated that the MWA can respond quickly to GW transients and cover a reasonable fraction of events with good sensitivity. The strategies outlined here are specifically applicable to the MWA, in that we have made use of the MWA's location and primary beam pattern in assessing the followup prospects. They can be adapted for other facilities, but there other considerations may lead to different strategies. For instance, with a considerably smaller field-of-view but better instantaneous sensitivity splitting into subarrays may be more viable. This will also evolve as new data and new models for prompt emission become available. Overall, we believe that the MWA has a good combination of field-of-view, sensitivity, and operational flexibility that enables this science: the MWA has a much larger field-of-view compared to most pointed radio telescopes \citep[e.g.,][]{2016MNRAS.459..121C,em2016}, but is more sensitive than some all-sky facilities \citep[e.g.,][]{2009IEEEP..97.1421E}. With roughly 1 year of sensitive GW observations we should be able to answer unambiguously which if any of the models for prompt emission are real. | 16 | 9 | 1609.00634 |
1609 | 1609.05157_arXiv.txt | The spatial distribution of neutral hydrogen (HI) in the Universe contains a wealth of cosmological information. The 21 cm emission line can be used to map the HI up to very high redshift and therefore reveal us something about the evolution of the large scale structures in the Universe. However little is known about the abundance and clustering properties of the HI over cosmic time. Motivated by this, we build an analytic framework where the relevant parameters that govern how the HI is distributed among dark matter halos can be fixed using observations. At the same time we provide tools to study the column density distribution function of the HI absorbers together with their clustering properties. Our formalism is the first one able to account for all observations at a single redshift, $z = 2.3$. The linear bias of the HI and the mean number density of HI sources, two main ingredients in the calculation of the signal-to-noise ratio of a cosmological survey, are then discussed in detail, also extrapolating the results to low and high redshift. We find that HI bias is relatively higher than the value reported in similar studies, but the shot noise level is always sub dominant, making the HI Power Spectrum always a high signal-to-noise measurements up to $z\simeq5$ in the limit of no instrumental noise and foreground contamination. | \label{sec:introduction} Our current understanding of the energy content of the Universe involve the presence of different components such as dark energy, dark matter, baryons or massive neutrinos. The interplay of the different constituents shape the spatial distribution of matter in the Universe. Information on the fraction that each component contributes to the overall energy budget of the Universe, together with information on the geometry and nature of the Universe initial conditions is thus embedded into the spatial distribution of matter. A way to constraint the value of the cosmological parameters is thus to measure the statistical properties of the distribution of matter in the Universe and compare them against the predictions of theoretical models. The problem resides in the fact that the distribution of matter is not directly observable. Our knowledge on it depends on the spatial distribution of tracers of it, such as galaxies, X-rays or cosmic neutral hydrogen (HI). In all cases the idea is that, on large-scales, the clustering properties of matter tracers, where perturbations are small, should resemble those of the underlying matter perturbations, modulo an overall normalization factor, which usually goes under the name of bias. Galaxy surveys such as the Sloan Digital Sky Survey\footnote{https://www.sdss3.org/surveys/boss.php} (SDSS) has mapped large regions of the sky at low-redshift and galaxy clustering measurements has been used to place tight constraints on the value of the cosmological parameters \citep[e.g.][]{Gil-Marin_2015, Alam_2016,Zhao_2016,Florien_2016a,Florien_2016b,Sanchez_2016,Grieb_2016}. The cosmic web can also be mapped with neutral hydrogen, which can be detected in the Universe either in absorption or in emission. In absorption it can be detected through the Ly$\alpha$-forest: the light from distant quasars can be absorbed by cosmic neutral hydrogen that it is located on its line of sight, producing a clear signature in their spectra. For instance, the clustering properties of the Ly$\alpha$-forest has been recently used to detect the BAO peak at $z=2.34$ \citep{Delubac_2015}. Cosmic neutral hydrogen can also be detected in emission through spectral lines such as the ${\rm H}_\alpha$ or the 21cm. In this paper we focus on the latter. The interaction between the spins of the electron and the proton induce a splitting on the hydrogen atom ground state; this is called the hyperfine structure. The wavelength of the energy difference between these two states is 21cm, while is frequency is 1420 MHz. In the post-reionization epoch, the typical temperatures of neutral hydrogen clouds range from tens to hundreds of Kelvin, much larger than the temperature different between the 2 hyperfine states, but smaller than the temperature required to excite the Ly$\alpha$ transition. Thus, in the post-reionization era neutral hydrogen clouds will have 3 out of 4 electrons in the hyperfine structure excited state, and their decay to the ground state will induce emission in terms of 21cm radiation. The 21cm emission by cosmic neutral hydrogen can be detected by radio-telescopes employing two different techniques. The first one is to detect directly the HI in galaxies (or in HI blobs \citep{Martin_2012,Villaescusa-Navarro_2016b, Burkhart_2016, Taylor_2016}); this is called a HI galaxy survey \citep{Yahya_2015, Abdalla_2015}. The second technique consists in carrying out intensity mapping observations, \ie performing low angular resolution radio-observation to measure the integrated 21cm radiation from large patches of the sky containing many galaxies, without resolving them individually \citep{Bharadwaj_2001A, Bharadwaj_2001B, Battye:2004re,McQuinn_2006, Chang_2008, Loeb_Wyithe_2008,Seo2010,Villaescusa-Navarro_2014a, Bull_2015,Santos_2015}. Each technique has its pros and cons. While a HI galaxy survey provides a catalogue with the location of galaxies (or HI clouds) from where we know very well how to extract the relevant cosmological information, the weakness of the signal would require of very powerful instruments, like the phase 2 of the Square Kilometre Array (SKA)\footnote{\url{https://www.skatelescope.org/}}, to be competitive with other surveys \citep{Bull_2015, Yahya_2015}. On the other hand, intensity mapping can be used to trace extremely large cosmological volumes but the theoretical framework requires more development and its complications (such as calibration, presence of large foregrounds, instrumental effects...etc) need to be fully understood and under control. In this paper we focus our attention on the 21cm intensity mapping technique, that given its spectroscopic nature, the large volumes it can sample and the isolation of the 21cm line \citep{Gong_2011} could revolutionize the field of cosmological observations. Current, upcoming and future instruments such as CHIME\footnote{\url{http://chime.phas.ubc.ca/}}, BINGO\footnote{\url{http://www.jb.man.ac.uk/research/BINGO/}}, ORT\footnote{\url{http://rac.ncra.tifr.res.in/}}, FAST\footnote{\url{http://fast.bao.ac.cn/en/}}, MeerKAT\footnote{\url{http://www.ska.ac.za/gallery/meerkat/}} or SKA1-MID will employ this technique to trace the large-scale structure of the Universe. In order to extract the maximum information from these surveys accurate theoretical models that model the observations are needed. Accurate predictions of the shape and amplitude of the fully non-linear 21cm power spectrum can be obtained using tools from the halo model \citep{Seljak_2000, PeacockSmith00,Scoccimarro2001, Cooray_2002}. The ingredients required are: the linear matter power spectrum, the halo mass function and halo bias, the relation between halo mass and HI mass (parametrized through the function $M_{\rm HI}(M,z)$) and the HI density profile within halos. On large, linear, scales, the HI density profile becomes irrelevant and the amplitude and shape of the signal is completely specified by the HI density parameter, $\Omega_{\rm HI}$, and by the bias of the neutral hydrogen tracer, $b_{\rm HI}$. Even if the HI field is mapped in a continuous way, the signal is coming from discrete sources, therefore estimates of the signal-to-noise from 21cm intensity mapping experiments also requires knowledge of the the effective number of tracers, in Power Spectrum analyses usually parametrized as a shot-noise term, $P_{\rm SN} = \bar{n}^{-1}$. The cosmological abundance of neutral hydrogen is known at $1.5<z<5$, from measurements of the column density distribution function (CDDF) \citep{Noterdaeme12,Zafar13,Crighton15} and at lower redshifts from the HI mass function from surveys such as HIPASS\footnote{\url{http://www.atnf.csiro.au/research/multibeam/release/}} and ALFALFA\footnote{\url{http://egg.astro.cornell.edu/index.php/}} \citep{Zwaan_2005, Braun_2012}, and within the (large) errorbars it is very slowly evolving with redshift \citep{Crighton15}. Clustering properties of HI are instead completely unknown at all redshifts\footnote{We notice that what has been measured is the clustering of HI selected galaxies, not the clustering of HI itself \citep{Martin_2012}.}, although the product $\Omega_{\rm HI}b_{\rm HI}$ has been derived from intensity mapping observations at $z\simeq0.8$ by \cite{Switzer13}. This means that we do not know which halos host which amount of neutral hydrogen at a given redshift. Hydrodynamic simulations \citep{Bird14,Villaescusa-Navarro_2014a, Rahmati15,Villaescusa-Navarro_2016b} provide some insights but their results are not conclusive, since it is hard to account with existing models for different observations, and studying the abundance and spatial distribution of HI in numerical simulations requires hydrodynamic simulations with state-of-the-art feedback models coupled with radiative transfer calculations.% \begin{figure} \includegraphics[width=.45\textwidth]{Figs/fig_bHI_n0P2_z2p3_nonoise.pdf} \caption{Top panel: linear HI bias factor as a function of the cutoff mass $M_{\rm min}$ for different values of $\alpha$. The bias of the corresponding dark matter halos is shown as a dotted line. Bottom panel: signal-to-noise ratio at $k=0.2 \kMpc$, continuous line for perfect BAO reconstruction and dashed line for 50\% reconstruction.} \label{fig:bHI} \end{figure} The closest one could get to a measurements of HI bias is the measurement from the BOSS collaboration\citep{Font-Ribera12} of the cross-correlation between the Lyman-$\alpha$ forest and the Damped-Lyman-$\alpha$ Systems (DLAs), which contain around 90\% of the all neutral hydrogen in the Universe. The quoted number for DLA bias is $b_{\rm DLA} = (2.17\pm0.2) \beta_F^{0.22}$, where $\beta_F$ is a number of order 1.5 \citep{CieplakSlosar15,Prats15}. However, as we shall see later, there is a crucial difference between the HI bias and the DLA bias, with non trivial observational consequences. The goal of this paper is to present a new analytic formalism to model the spatial distribution of cosmic neutral hydrogen in the post-reionization era that can reproduce the observations. Since the redshift evolution of the HI clustering is not constrained at all, we will fix the free parameters of our model at the single redshift where more data are available, $z_{ref}=2.3$. The measurements employed are therefore the abundance of Lyman Limit System (LLS) and DLAs from from \cite{Zafar13,Noterdaeme12} together with $\Omega_{\rm HI}$, and the DLA bias of \citep{Font-Ribera12}. We then investigate the implications of our model, in terms of the bias and the shot-noise of the HI Power Spectrum, also including estimates of the signal-to-noise ratio. Since we are interested in the cosmological signal current or future 21 cm surveys could in principle measure, as a proof of concept we do not include instrumental systematics errors as well as foregrounds contamination in our calculations. This paper is organized as follows. In Sec \ref{sec:Form} our analytical model is introduced and we define all the relevant HI quantities in a halo model fashion. Then in \ref{sub:dsigma} we describe in a novel way how to make contact with the observations and fix the free parameters of our model in a consistent manner. Sec. \ref{sec:Res} contains a number of results relevant for observations of the HI Power Spectrum at our reference redshift. Finally in Sec \ref{sec:bOfz} we speculate on redshift evolution of HI properties within our model, to both low and high redshift. We draw the main conclusions of this work in section \ref{sec:conclusions}. The cosmology used in this paper is a baseline $\Lambda$CDM cosmology from Planck 2015 \citep{Planck15}. \begin{figure} \includegraphics[width=.45\textwidth]{Figs/fig_SN_z2p3.pdf} \caption{Shot noise contribution to the HI Power Spectrum for the model specified by \eq{eq:MHI} as a function of the cutoff mass $M_{min}$ and for different values of $\alpha$. The shot noise for the corresponding halo population is shown as a dotted line.} \label{fig:SN} \end{figure} | \label{sec:conclusions} We have shown, for the first time, how to construct a consistent model for the distribution of the neutral hydrogen in the Universe, which can account for all the existing observations at $z_{ref} = 2.3$. Our model makes predictions for the bias and the shot noise of the HI Power Spectrum, and for the bias of HI absorbers with different column density. Those results could be tested with future data that would allow to further constraint the remaining freedom in the parameter space of the model. We have then computed the signal-to-noise ratio of the HI Power Spectrum at $k=0.2 \kMpc$, a scale relevant for BAO studies, and concluded that, apart from instrumental and foreground systematics, the distribution of neutral hydrogen can be a very powerful cosmological observable. Lacking observations, and therefore robust modeling, of the redshift evolution of the HI, we have made conservative assumptions for the evolution of $b_{HI}$ and $P_{SN}$, drawing conclusions at lower and higher redshift than $z_{ref}$. The net outcome is that, within our framework, the HI $P(k)$ remains a high signal-to-noise measurement up to $z\simeq5$, a result that could be relevant for future radio surveys aiming to observe the 21 cm transition on cosmological scales. | 16 | 9 | 1609.05157 |
1609 | 1609.02777_arXiv.txt | Rayleigh--B\'{e}nard convection and Taylor--Couette flow are two canonical flows that have many properties in common. We here compare the two flows in detail for parameter values where the Nusselt numbers, i.e. the thermal transport and the angular momentum transport normalized by the corresponding laminar values, coincide. We study turbulent Rayleigh--B\'{e}nard convection in air at Rayleigh number $\Ray=10^7$ and Taylor--Couette flow at shear Reynolds number $\Rey_S=2\times 10^4$ for two different mean rotation rates but the same Nusselt numbers. For individual pairwise related fields and convective currents, we compare the probability density functions normalized by the corresponding root mean square values and taken at different distances from the wall. We find one rotation number for which there is very good agreement between the mean profiles of the two corresponding quantities temperature and angular momentum. Similarly, there is good agreement between the fluctuations in temperature and velocity components. For the heat and angular momentum currents, there are differences in the fluctuations outside the boundary layers that increase with overall rotation and can be related to differences in the flow structures in the boundary layer and in the bulk. The study extends the similarities between the two flows from global quantities to local quantities and reveals the effects of rotation on the transport. | Convection in layers of fluids heated from below and cooled from above (Rayleigh--B\'enard or RB flow) and the flow between two rotating cylinders (Taylor--Couette or TC flow) are among the canonical flows in fluid mechanics. Studies of their stability properties and the manner in which the laminar profiles give way to more structured and complicated flows have provided much insight into the transition to turbulence with linear instabilities \cite{Chandrasekhar1961,Koschmieder1993}. The behavior well above the onset of turbulence has also been investigated starting with the experiments by Wendt \cite{Wendt1933}. Many different flow regimes that are not yet fully explained or explored have been described \cite{Ostilla-Monico2014b,Grossmann2016}. It was realized early on that despite the differences in the driving forces, there are many similarities, and it is helpful to draw analogies and to compare the properties of both flows \cite{Low1925}. The intimate relations between the two flows have led Busse \cite{Busse2012} to characterize them as the \textit{twins of turbulence}. A formal analogy between RB and TC flow (and pipe flow as well) was developed and described in Eckhardt et al. \cite{Eckhardt2007,Eckhardt2007a} (see also Bradshaw \cite{Bradshaw1969} for an earlier approximate relation and Dubrulle \& Hersant \cite{Dubrulle2002} for a similar analogy). The analogy identifies pairs of equations that describe the total energy dissipation and the global transport of heat or angular momentum, respectively, in the two flows. The equations allow one to relate transport properties, dimensionless parameters and other quantities, and have been used in particular to study scaling relations in fully developed turbulent flows \cite{Grossmann2016}. The similarity in the equations suggests that a more detailed comparison between the two flows should be possible. We here explore this option within direct numerical simulations (DNS). We describe the difficulties one has to overcome in identifying corresponding parameters, and present case studies where detailed comparisons are possible. In particular, we will compare the turbulent transport currents with respect to their statistical properties. Furthermore, we can relate components of the involved turbulent fields to each other and compare their statistical fluctuations at different distances from the walls. The focus of our study is on the general ideas and an illustration for a few examples, but not on a comprehensive study for all parameter values. Specifically, we will take one set of data for RB flow and compare it to TC flow cases at two different rotation numbers, which allows us to study the effect of rotation. The data are taken from well-resolved DNS of both flows at moderate Rayleigh and Reynolds numbers. The outline of the manuscript is as follows. In section~\ref{sect:relations} we present the balance equations, the numerical methods and discuss the analogy. In section~\ref{sect:reference} the choice of corresponding parameters for the comparison is explained. In section~\ref{sect:statistics} the area-averaged mean currents and their probability density functions (PDFs) as well as other pairwise related properties at different distances from the wall are analyzed. We conclude the work with a short discussion of the particular structures of the convective currents and a summary in section~\ref{sect:conclusions}. | \label{sect:conclusions} In the present work we discussed a direct comparison of the statistical properties of Rayleigh--B\'{e}nard (RB) convection and Taylor--Couette (TC) flow. The comparison is motivated by analogies of dimensionless system parameters (such as Rayleigh and Taylor numbers), the same form of the energy balances, (\ref{eps_temp}) and (\ref{eps_omega}), and the similarities in the currents of heat and angular momentum (see also references \cite{Eckhardt2007,Eckhardt2007a,Bradshaw1969,Dubrulle2002}). Our study shows that the operating point for a specific comparison between TC and RB flows can be determined by choosing corresponding values of Nusselt numbers since the Nusselt number defines the boundary layer thickness and hence the transport properties. We also find that a better characterization of TC flow can be based on the pair of shear Reynolds and rotation numbers, $(\Rey_S, R_{\Omega})$, than on Taylor and quasi-Prandtl numbers, $(\Tay, \sigma)$, since the latter do not reflect the mean rotation of the cylinders. We demonstrated that for sufficiently large shear Reynolds number $\Rey_S$, multiple TC flow cases at different rotation numbers can have the same Nusselt number as RB convection, i.e. the same amount of angular momentum is transported between the cylinders in TC flow as heat from the bottom to the top in the RB case. The comparison also shows that the case with the smaller rotation number $R_\Omega$ (case 1) provides a better agreement with RB flow than the case of larger rotation number. For this pair of flows, a remarkable agreement between mean profiles as well as probability density functions of fluctuating quantities is found. Studies of the mean profiles and the PDFs of the convective currents show that the differences between RB flow and TC flow case 1 are most pronounced in the mixing layer above the (thermal) boundary layer. They can be attributed to the strong fluctuations in this region which are connected with the detachment of plumes and other differences in the dynamics: the boundary layers in the convection case are still very close to being laminar, but in the TC system they are already turbulent. The differences should, therefore, become smaller when the boundary layers in RB become turbulent as well. The TC flow case 2, which is characterized by a larger mean rotation ($R_{\Omega}$), shows greater differences to the RB case. As a consequence of rotation, the angular velocity profile has a significant gradient in the central region, which results in a higher (lower) dissipative (convective) transport current than in the RB case. Furthermore, enhanced radial velocity fluctuations and stronger mean Taylor vortices occur for case 2 and lead to broader PDFs of the convective current away from the boundary layer, which differ from the heat flux distributions in RB flow. This demonstrates that the mean rotation determines how well the transport characteristics of TC and RB flow are comparable. The comparison presented here shows that for judiciously chosen pairs of parameters in RB and TC flow one can actually relate their transport properties in detail, both in the mean and in the fluctuations, thereby confirming the analogies between the \emph{twins of turbulence} \cite{Busse2012} for a larger set of properties. | 16 | 9 | 1609.02777 |
1609 | 1609.06681_arXiv.txt | We present the current results of the astrometric characterization of the VLT planet finder SPHERE over 2 years of on-sky operations. We first describe the criteria for the selection of the astrometric fields used for calibrating the science data: binaries, multiple systems, and stellar clusters. The analysis includes measurements of the pixel scale and the position angle with respect to the North for both near-infrared subsystems, the camera IRDIS and the integral field spectrometer IFS, as well as the distortion for the IRDIS camera. The IRDIS distortion is shown to be dominated by an anamorphism of 0.60$\pm$0.02\% between the horizontal and vertical directions of the detector, i.e. 6~mas at 1~arcsec. The anamorphism is produced by the cylindrical mirrors in the common path structure hence common to all three SPHERE science subsystems (IRDIS, IFS, and ZIMPOL), except for the relative orientation of their field of view. The current estimates of the pixel scale and North angle for IRDIS are 12.255$\pm$0.009~milliarcseconds/pixel for H2 coronagraphic images and -1.75$\pm$0.08$^{\circ}$. Analyses of the IFS data indicate a pixel scale of 7.46$\pm$0.02~milliarcseconds/pixel and a North angle of -102.18$\pm$0.13$^{\circ}$. We finally discuss plans for providing astrometric calibration to the SPHERE users outside the instrument consortium. | \label{sec:intro} % The detection and characterization of exoplanets is one of the most active research areas in modern astrophysics. Many methods are employed to address specific types of objects and/or questions. High-contrast imaging is currently the most efficient technique for probing (1) the architecture of systems with wide-separated (beyond $\sim$5--10 AU) Jovian mass planets and (2) the spectral properties of these planets\cite{Marois2008c, Lagrange2010b, Macintosh2015}\,. A key science motivation for these studies is to understand whether this population of planets is the large-separation tail of the distribution of planets discovered by radial velocity and transit surveys at shorter separations or they form a separated population with different formation mechanisms. Astrometry is critical to confirm the companionship of detected companion candidates from the comparison of the measured relative position at two separated epochs to the predicted positions under the hypothesis that they are background objects. For short-period systems, accurate astrometric monitoring is needed to constrain the orbital elements of the individual companions (e.g., period, semi-major axis, eccentricity, inclination) and the total dynamical mass hence provides insights into the dynamical properties (e.g., mean motion resonances, dynamical interactions, orbital stability). The orbital elements can be compared to predictions from different formation scenarios for substellar companions (core accretion, gravitational instability in a circumstellar disk, collapse and fragmentation of a molecular cloud) to constrain the formation mechanisms of the systems\cite{Bate2009, Raghavan2010}\,. If radial velocity measurements or astrometric motion of the central star are available, the dynamical mass of the companions can be constrained\cite{Close2005, Crepp2012, Bonnefoy2014c}\,. Dynamical mass measurements provide critical tests for atmospheric and evolutionary models for brown dwarfs and giant planets\cite{Burrows1997, Baraffe2003, 2012RSPTA.370.2765A, Spiegel2012}\,. Most of the young directly-imaged substellar companions have semi-major axis larger than a few tens of AU, so that estimates for their mass can only be inferred from their luminosity assuming possible ranges for the system age and evolutionary models. However, these estimates are strongly uncertain because the models are poorly calibrated at young ages and low masses. Detecting and measuring the orbit of young and low-mass substellar companions provide valuable benchmarks for the models. The detection and the orbital analysis of young and low-mass substellar companions are a major part of the science case for the recently commissioned planet finder SPHERE\cite{Beuzit2008} (Spectro-Polarimetric Exoplanet REsearch). The instrument includes an extreme adaptive optics system\cite{Fusco2014}\,, with a pupil stabilization control system and stress polished toric mirrors\cite{Hugot2012} to relay the beam to the coronagraphs\cite{Boccaletti2008c} and the science instruments. The science instruments are composed of the infrared dual-band imager and spectrograph IRDIS\cite{Dohlen2008a}\,, the near-infrared integral field spectrometer IFS\cite{Claudi2008}\,, and the rapid-switching visible imaging polarimeter ZIMPOL\cite{Thalmann2008}\,. SPHERE has been successfully commissioned at the Very Large Telescope from May to October 2014 and is offered to the community since April 2015. The SPHERE consortium guaranteed-time survey consists of 260 nights over 5 years, from which 200 nights are dedicated to a large census in the near-infrared of the population of young giant planets and brown dwarfs at wide orbits ($\gtrsim$5~AU). The main observing mode used for this survey consists in simultaneous observations in the YJ bands (0.95--1.35~$\mu$m, $R$\,$\sim$\,54) with IFS (field of view 1.73$''$\,$\times$1.73$''$) and in the H-band (H$_2$\,=\,1.593~$\mu$m and H$_3$\,=\,1.667~$\mu$m) with IRDIS (field of view 11$''$\,$\times$12.5$''$) in dual-band imaging mode\cite{Vigan2010}\,. A coronagraphic mask common to both instruments is used to attenuate the stellar light\cite{Boccaletti2008c}\,. Both IRDIS and IFS are operated in pupil-stabilized mode to take advantage of the angular differential imaging technique\cite{Marois2006a} to further suppress the stellar residuals in the images. High-precision relative astrometry and efficient attenuation of the stellar residuals by image post-processing techniques critically depend of a precise estimate of the location of the star behind a coronagraphic mask\cite{Marois2006b, Sivaramakrishnan2006}\,. For this purpose, a calibration image is recorded before and after a science sequence with four crosswise faint stellar replicas produced by applying a periodic modulation on the SPHERE deformable mirror\cite{Langlois2013}\,. The specifications for the SPHERE astrometric accuracy are 5 mas (goal 1 mas). Extensive tests using injections of synthetic point sources in laboratory data processed with spectral differential imaging\cite{Racine1999, Sparks2002} resulted in astrometric accuracies below 1.5--2~mas for detections at signal-to-noise ratios above 10\cite{Zurlo2014}\,. We present in this paper the current on-sky status and results of the astrometric characterization of IRDIS and IFS based on 2~years of SPHERE operations from 2014 to 2016. We describe in Sec.~\ref{sec:methodology} our criteria for the selection of the astrometric fields. We present in Sec.~\ref{sec:results} the on-sky measurements of the SPHERE optical distortion, the zeropoint angle of the SPHERE pupil in pupil-stabilized mode, and the pixel scale and true North offset for both IRDIS and IFS. We summarize our main results and briefly discuss a few prospects in Sec.~\ref{sec:conclusions}. | \label{sec:conclusions} We have presented the current on-sky results for the astrometric calibration of the SPHERE near-infrared instruments (IRDIS and IFS) based on data collected over 2~years of operations. On-sky measurements of the SPHERE+VLT optical distortion show that the optical distortion from the VLT is negligible with respect to the SPHERE optical distortion and that the main SPHERE distortion effect results in a horizontal pixel scale 0.60$\pm$0.02\% larger than the vertical pixel scale for the IRDIS camera. Then, we estimated the zeropoint angle of the SPHERE pupil in pupil-stabilized mode, which is the main observing mode used for the consortium guaranteed-time exoplanet imaging survey. This parameter is stable around an average value of $-$135.99$\pm$0.11$^{\circ}$. We measured the pixel scale for IRDIS for various filter pairs and coronagraphs as well as the true North offset from July 2014 to May 2016. For given instrument configuration and astrometric calibration field, the pixel scale has a stability over a timescale of a few months of 0.009~mas/pixel. For coronagraphic data obtained with the H2 filter, our current estimate of the pixel scale is 12.255$\pm$0.009~mas/pix. Technical tracking tests with the SPHERE internal distortion grid showed missynchronization issues between the SPHERE and VLT internal clocks. These missynchronization issues produced anomalous variations larger than 1$^{\circ}$ for the true North measurements between December 2015 and February 2016, but these issues existed since the commissioning phase. The true North deviations are clearly correlated with the derotation error produced by the clock missynchronization. The latter can be derived from the angle information in the data headers. After correcting the true North measurements for the derotation error, the statistics give a remarkable stable value of $-$1.75$\pm$0.08$^{\circ}$. For the IFS reconstructed data cubes, on-sky and internal calibration data indicate an average pixel scale value of 7.46$\pm$0.02~mas/pix and a relative orientation to the IRDIS field of view of +100.48$\pm$0.10$^{\circ}$. As part of the consortium guaranteed-time observations, we will continue to monitor the SPHERE astrometric parameters for the full survey. The public release of the GAIA data in late 2016 will provide absolute astrometric calibration for several of the SPHERE astrometric fields, which will help in improving the absolute calibration of the SPHERE data. We plan to release our consortium astrometric tool and observing procedures to ESO so that such analyses can also be carried out on a regular basis by the observatory. The results from these analyses will be made available to the SPHERE users outside the instrument consortium on a public web page. Common astrometric fields observed with various high-contrast imaging instruments (e.g., SPHERE, GPI, LMIRCam, MagAO, CHARIS) will allow for a better comparison of astrometric measurements from different instruments and a reduction of the systematic errors, which are a major issue for the determination of the orbital properties of directly-imaged companions in particular for those located at wide separations. We note that the Orion Trapezium field is very suitable to these comparisons because of its observability from both northern and southern hemispheres. | 16 | 9 | 1609.06681 |
1609 | 1609.06362_arXiv.txt | Recent studies suggest that coalescing neutron stars are subject to a fluid instability involving the nonlinear coupling of the tide to $p$-modes and $g$-modes. Its influence on the inspiral dynamics and thus the gravitational wave signal is, however, uncertain because we do not know precisely how the instability saturates. Here we construct a simple, physically motivated model of the saturation that allows us to explore the instability's impact as a function of the model parameters. We find that for plausible assumptions about the saturation, current gravitational wave detectors might miss $> 70\%$ of events if only point particle waveforms are used. Parameters such as the chirp mass, component masses, and luminosity distance might also be significantly biased. On the other hand, we find that relatively simple modifications to the point particle waveform can alleviate these problems and enhance the science that emerges from the detection of binary neutron stars. | \label{s:introduction} The detection of gravitational waves (GWs) from binary black holes (BH)~\citep{GW150914,GW151226,O1BBH} with the Laser Interferometer Gravitational-wave Observatory (LIGO)~\citep{LIGO} opens a new window to our universe and provides the first tests of strong field general relativity (GR) in vacuum~\citep{GW150914testingGR,O1BBH}. In the coming years, LIGO also expects to detect GWs from neutron stars (NSs) in coalescing binaries. Although a NS can be treated as a point particle (PP) to a first approximation, at some level tides will modify the rate of inspiral and thus the GW signal. The impact of the tidal effects are, however, uncertain. In part this is due to uncertainties in the NS equation of state, and indeed there is hope that GW observations will eventually provide precise constraints on the equation of state~\citep{Read:09, Hinderer2010, Damour:12, DelPozzo2013, Lackey2015, Agathos2015}. In addition, there are uncertainties in the tidal fluid dynamics both near the merger when matter and GR effects are strong~\citep{Read:13,Yagi:14, Favata:14} and during the long inspiral phase when the tide is weakly nonlinear \citep{Weinberg2013, Venumadhav2014, Weinberg2016}. Many previous studies considered the impact of the linear tide, implicitly assuming that nonlinear effects are negligible at GW frequencies below $\f\approx 400\,\Hz$. These include studies of the linear equilibrium tide~\citep{Read:09, Hinderer2010, Damour:12, DelPozzo2013, Lackey2015, Agathos2015} and the linear dynamical tide in nonrotating NSs~\citep{Reisenegger:94,Lai1994, Hinderer:16, Steinhoff:16, Yu:16} and rotating NSs~\citep{Ho1999,Lai:06,Flanagan:07}. The equilibrium and dynamical tide refer, respectively, to the quasistatic and resonant response of a star to a tidal field (see, e.g., \citep{Ogilvie:14}). Typically these studies conclude that linear tidal effects will be difficult to measure with current instruments without a gold-plated detection (signal-to-noise ratios $\gtrsim 50$; \cite{Read:09}) or stacked data from dozens of marginal events~\citep{DelPozzo2013, Lackey2015, Agathos2015}. Moreover, because they find that tidal effects only become significant during the late inspiral, there are proposals to test vacuum GR using waveforms from NS systems at $\f\lesssim 400$ Hz~\citep{Agathos2014}. Recently, it has been suggested that the tide is subject to a weakly nonlinear fluid instability during the early inspiral~\citep[][hereafter, VZH, W16, WAB, respectively]{Weinberg2013,Venumadhav2014,Weinberg2016}. The instability involves a nonresonant coupling between the quasistatic equilibrium tide, pressure supported {\pmode}s, and buoyancy (i.e., gravity) supported {\gmode}s. Typically, modes first become unstable at $\f \approx 50\,\Hz$ and are driven thereafter to potentially large amplitudes. This continuous transfer of energy from the orbit into the modes increases the rate of inspiral and induces an evergrowing phase shift relative to the PP waveform. Although there has been disagreement in the literature about the magnitude of the growth rates, all studies of $p$-$g$ coupling predict an instability. Furthermore, W16 find that nonstatic tidal effects (e.g., compressibility) enhance the growth rates, enabling a very large number of modes to reach significant amplitudes well before the binary merges. Studies of the $p$-$g$ instability have mainly focused on calculating the instability threshold and growth rates; they have not attempted to study its saturation in any detail. As a result, we do not know the rate at which the instability extracts energy from the orbit and thus we cannot say precisely how it will impact the GW signal. Because solving for the saturation is challenging and likely subject to uncertainties of its own, here we set a more modest goal. We construct a parametrized model of the saturation and explore the instability's impact as a function of the model parameters. Our saturation model is relatively simple, adding just three new parameters to the 15 already present in the spinning PP model. It is worth emphasizing, however, that although we believe our saturation model adequately captures the range of possibilities, without a proper saturation study we cannot be certain. The paper is structured as follows. \S~\ref{s:physical mechanism} reviews the properties of the $p$-$g$ instability and discusses the physics of its saturation and the uncertainties therein. \S~\ref{s:parameterized model} describes our parametrized model of the saturation which we use to explore the tide-induced modifications to the PP waveform. Using Bayesian methods, which we describe in \S~\ref{s:bayesian analysis}, we then study how the modified waveforms affect source detectability and parameter bias if the tidal effects are neglected (\S~\ref{s:nlgr}) and how well we can measure the tidal effects if they are included (\S~\ref{s:nlnl}). We summarize and conclude in \S~\ref{s:implications}. | \label{s:implications} By constructing a parameterized model of the saturation of the $p$-$g$ instability in coalescing binary NSs, we explored how the instability might impact GW signals for current detector sensitivities. Our model contains three parameters ($A$, $f_0$, and $n$), where $A$ and $n$ determine the magnitude and frequency dependence of the nonlinear dissipation rate $\dot{E}_{\rm NL}$, and $f_0$ is the GW frequency at which the unstable modes saturate. Applying a full Bayesian analysis, we determined as a function of $A$, $\f_0$, and $n$ the extent to which nonlinear tidal effects: (1) influence the detectability of merger events, (2) bias binary parameters such as the chirp mass $\mathcal{M}$, the mass ratio $q$, the component masses, and the luminosity distance $D_L$, and (3) can be measured. We also examined, albeit in less detail, how the instability might be confused with NS spin and generic deviations from vacuum GR when a PP model is assumed at low frequencies. We find that neglecting nonlinear tidal effects can significantly impair our ability to detect events. For example, if $A\sim10^{-7}$, $n=0$, and $f=50$ Hz, we would lose $\simeq 30\%$ of \rhonet. This means that if we neglect nonlinear tides, we would miss $1-(0.70)^3\simeq 70\%$ of NS merger events. If $A\sim 10^{-6}$, $n=0$, and $f=50$ Hz, and we neglect nonlinear tides, we would miss $\simeq 95\%$ of NS merger events. More generally, we find that nonlinear effects are detectable if $A\gtrsim 10^{-8}$. An $A\sim 10^{-8}$ yields a phase shift relative to the PP waveform of $\Delta \phi \sim 1\textrm{ radian}$ and corresponds to, e.g., $N\sim 1$ ($\sim 100$) modes with $\omega_g/\omega_0\sim 10^{-3}$ ($\sim 10^{-4}$) saturating at $E_{\rm sat}\sim 0.1 E_{\rm break}$ [see Eq. (\ref{eq:Aparam})]. Although $N$ and $E_{\rm sat}$, and therefore $A$, are highly uncertain, values as large as $A\sim 10^{-6}$ and thus $\Delta \phi \sim 10^2\textrm{ rad}$ are a possibility (see \S~\ref{s:physical mechanism} and \S~\ref{s:parameterized model}). We also found that intrinsic parameter biases can be significant if nonlinear tidal effects are neglected. For example, we found that for $A\sim \textrm{ few}\times10^{-8}$, a $1.4M_\odot-1.4M_\odot$ NS-NS binary could be strongly biased to $1.6M_\odot-1.2M_\odot$. Interestingly, at this $A$ the loss in signal \rhonet~is relatively mild ($\lesssim 10\%$) and the PP waveform model would appear to be a good match to the data, an example of a ``stealth bias.'' For larger $A$, the biases in many of the parameters tend to actually \emph{decrease} with increasing $A$ (the bias in $\mathcal{M}$ does not follow this pattern, however). Nonetheless, the quality of the PP model's match always worsens with increasing $A$. We also used \textsc{tiger} to investigate whether we can detect deviations from the PP model without knowing the precise form of the nonlinear effects. Although the evidence in favor of \textsc{tiger}'s alternative hypothesis is less than the evidence in favor of the exact nonlinear model, it does provide a significantly better match than the PP model if $A\gtrsim 10^{-8}$. This suggests that we may not need to know the precise form of the nonlinear effects in order to improve the match to the data. Moreover, it highlights the fact that neglected NS physics can produce apparent deviations from GR. For heavier systems, such as NS-BH systems, nonlinear effects are significantly less important. This is because their orbits decay faster, giving the nonlinear tides less time to modify the inspiral. Therefore, for the same $A$, $\f_0$, and $n$, their waveform phase shifts are much smaller. Assuming that we observe a cosmological population of sources, nonlinear tides may provide a way to extract distance-redshift information directly from GW waveforms without identification of an electromagnetic counterpart. This is because they provide a characteristic frequency $\f_0$ that breaks the otherwise conformal waveform. By measuring $\f_0$, we can extract the redshift directly and associate it with the corresponding $D_L$. Other studies of tidal effects have suggested similar approaches~\citep{Read2012,Mandel2014}. However, we will need to tightly constrain the possible values of $\f_0$ a priori in order to make such cosmological measurements. Our study only analyzed single events and in the future it might be interesting to consider the impact of the $p$-$g$ instability on a population of sources. Such a study would benefit greatly from first improving the theoretical constraints on $A$, $n$, and $\f_0$. A first-principles calculation of the saturation should therefore be very valuable. In addition to helping further assess the potential impact of nonlinear tides, it might also aid parameter estimation and detection pipelines by reducing the amount of parameter space that must be searched. Although a full saturation calculation would be ideal, even relatively small improvements could be useful, such as confirming the expected growth rates of the $p$-$g$ instability and more accurately determining the instability threshold and number of unstable modes. | 16 | 9 | 1609.06362 |
1609 | 1609.06154_arXiv.txt | We report on WIMP search results of the XENON100 experiment, combining three runs summing up to 477 live days from January 2010 to January 2014. Data from the first two runs were already published. A blind analysis was applied to the last run recorded between April 2013 and January 2014 prior to combining the results. The ultralow electromagnetic background of the experiment, $\sim 5 \times 10^{-3}$~events/(keV$_{\mathrm{ee}}\times$kg$\times$day) before electronic recoil rejection, together with the increased exposure of 48~kg~$\times$~yr improves the sensitivity. A profile likelihood analysis using an energy range of $(6.6-43.3)$~keV$_{\mathrm{nr}}$ sets a limit on the elastic, spin-independent WIMP-nucleon scattering cross section for WIMP masses above 8~GeV/$c^2$, with a minimum of 1.1$\times 10^{-45}$~cm$^2$ at 50~GeV/$c^2$ and 90\% confidence level. We also report updated constraints on the elastic, spin-dependent WIMP-nucleon cross sections obtained with the same data. We set upper limits on the WIMP-neutron (proton) cross section with a minimum of 2.0$\times 10^{-40}$~cm$^2$ (52$\times 10^{-40}$~cm$^2$) at a WIMP mass of 50~GeV/$c^2$, at 90\% confidence level. | Introduction} Astrophysical observations at various scales give strong evidence for the existence of a nonluminous (rarely interacting), nonbaryonic, and nonrelativistic (cold) matter component that makes up 27\% of the total mass-energy budget of the Universe, consisting of yet undetected particles whose nature remains unknown \cite{Harvey:2015hha,Ade:2015xua}. Many theories beyond the Standard Model of particle physics predict possible candidates, the most promising of which are weakly interacting massive particles (WIMPs) \cite{Jungman:1995df,Bertone:1900zza}. In this paradigm, WIMPs would interact with target nuclei of detectors placed deeply underground, shielded by the rock overburden, inducing detectable nuclear recoil (NR) signals. A plethora of experiments worldwide are devoted to observing the low-energy NRs of a few keV induced by WIMPs scattering off a nucleus~\cite{Undagoitia:2015gya}. Among these, the XENON100 experiment exploits a dual-phase (liquid-gas) xenon time projection chamber (TPC)~\cite{Aprile:2011dd}. An electric ``drift'' field of $\sim$500 V/cm is applied across the liquid xenon (LXe) volume by quasitransparent electrodes (meshes); a stronger electric ``extraction'' field of $\sim$12~kV/cm is applied in the gaseous xenon (GXe) multiplication region above the liquid-gas interface. Particles interacting in LXe create a scintillation light signal (S1) that is directly measured by 178 Hamamatsu R8520-AL photomultiplier tubes (PMTs), as well as ionization electrons that can escape the local ionization field and migrate along the drift field direction towards the top of the TPC. Those ionization electrons that reach the liquid-gas interface are extracted into the GXe and accelerated by the extraction field producing a scintillation signal (S2) that is proportional to the number of extracted ionization electrons. The S1 and S2 signal timing and S2 hit pattern are used to determine the X,Y,Z coordinates of an interaction~\cite{Aprile:2011dd}. This event-by-event 3D-position information can be used to define an optimal fiducial volume to increase the signal to background ratio. The XENON100 detector~\cite{Aprile:2011dd} features an active dark matter target of 62 kg and is installed at the Laboratori Nazionali del Gran Sasso (LNGS, Italy). Careful material selection~\cite{Aprile:2011ru} and detector design lead to very low backgrounds from electronic (ER)~\cite{Aprile:2011vb} and nuclear recoils (NR)~\cite{Aprile:2013tov}. During the operation period between 2009 and 2016, three science runs (dark matter data sets) were collected. The results of the first two runs, referred to as run~I (100.9~live days in 2010)~\cite{Aprile:2011hi,Aprile:2011ts} and run~II (224.6~live days during 2011 and 2012)~\cite{Aprile:2012nq,Aprile:2013doa} were published and provided the best constraints on the spin-independent as well as on the spin-dependent WIMP-neutron cross section at the time of publication. The final run (run~III) was taken between 2013 and 2014 (153.6 live days) and its results are published here for the first time in combination with the other two runs. In this work, several improvements to the analysis and statistical interpretation are discussed in Sec.~\ref{sec:analysis}. The results of the spin-independent (SI) and spin-dependent (SD) combined analysis of all 477 live days of XENON100 dark matter science data are presented in Sec.~\ref{sec:results}. | We present the final XENON100 spin-independent and spin-dependent results from the combined analysis of two already published science runs and a third new run, with a total exposure of 477 live days (48~kg$\times$yr) acquired between January 2010 and January 2014. Improvements to the data quality event selection were described, resulting in a reduction of background and increase in purity of the final dark matter sample. A new technique to quantify accidental coincidences was developed and implemented into the ER background model. Furthermore, the signal model is now computed analytically for S1 and S2, including more accurate modeling of all acceptances and thresholds. Finally, requiring a minimum number of detected signal quanta improves the robustness of the analysis close to the energy threshold, which is important for low WIMP masses. No evidence for dark matter is found and an upper limit of the WIMP-nucleon cross section is derived. The combination of the three science runs with the improved analysis results in a SI limit of $1.1\times10^{-45}$~cm$^2$ at a 50~GeV/$c^2$ mass and a SD neutron (proton) limit of $2.0\times10^{-40}$~cm$^2$ ($5.2\times10^{-39}$~cm$^2$) at 50~GeV/$c^2$ mass. | 16 | 9 | 1609.06154 |
1609 | 1609.04017_arXiv.txt | We report the detection of a new feature at the centre of NGC~1275 in the Perseus cluster, hosting the radio source 3C~84. This feature emerges $\sim 2$~mas ($\sim 0.8$~pc) north of the central core in recent 15 and 43~GHz VLBA images, and seems to be the counterjet to a known radio jet expanding to the south of the core. Apparently, the two jets were born through an outburst around 2005. From the ratio of the apparent lengths of the two jets from the core, we found that the jet angle to the line of sight is $\theta=65^\circ\pm 16^\circ$, which is not much different from the angle of the outer jets generated by an activity around 1959 and constrains theories on gamma-ray emission from jets. The new northern jet has a strongly inverted spectrum in contrast with the southern jet. This suggests that the central black hole is surrounded by a subparsec-scale accretion disk with the density of $\ga 10^5\rm\: cm^{-3}$. The brightness of the counterjet suggests that the disk is highly inhomogeneous. The ambient gas density in the direction of the jet is $\sim 8\rm\: cm^{-3}$ if the current jet activity is similar to the past average. | NGC~1275 is the central galaxy of the Perseus cluster. It is known as a nearby Seyfert galaxy ($z=0.0176$) and hosts the compact radio source 3C~84. Cosmic rays accelerated around the central supermassive black hole (SMBH) may be playing an important role in offsetting radiative cooling of the cool core of the cluster \citep{fuj12a,fuj13a}. The proximity of the object allows us to make detailed observations about the environment around the SMBH and its activities. Early VLBI observations showed that 3C~84 has complicated structures on a scale of pc; a mushroom-like jet is expanding southward from a bright compact core. The apparent velocity of the southern jet has been estimated to be $\sim 0.3\: c$ \citep{1982IAUS...97..291R,asa06a,lis09a}. From this velocity, it has been suggested that this expanding jet relates to an outburst in 1959 \citep[e.g.][]{nes95a}. The counterjet of this southern jet has been discovered to the north of the core \citep{ver94a,wal94a}. The ratio of the apparent distances of the two jets from the core suggests that the observing angle to the jet direction is $\sim 30^\circ$--$60^\circ$ \citep{wal94a,asa06a}. The angle between the jets and the line of sight has great importance for the gamma-ray spectrum of NGC~1275 \citep{abd09b,ale14b,tab14a}. Recently, new activity in the core has been reported. \citet{nag10a} showed that a new component (C3 in the paper) emerged in the central subparsec region of the core (C1). They indicated that this component relates to a radio outburst that began in 2005. Moreover, since the gamma-ray luminosity of NGC~1275 started to increase around 2005 \citep{dut14a}, the new component is seemingly associated with the gamma-ray activity. Since the new component is moving toward south from the core, its counterjet, if any, is expected to appear to the north of the core. In this Letter, we report the discovery of the northern counterjet. From the ratio of the apparent lengths of the southern and northern jets from the core, we estimate the inclination angle of the jets. We also discuss the environment in the vicinity of the SMBH based on the inverted spectrum of the northern jet. We adopt $H_0=70\rm\: km\: s^{-1}\: Mpc^{-1}$, $\Omega_{\rm m}=0.3$, and $\Lambda=0.7$. For these cosmological parameters, 1~mas corresponds to 0.36~pc. | We discovered a new feature $\sim 2$~mas ($\sim 0.8$~pc) north of the central core of NGC~1275 (3C~84) at 15 and 43~GHz with VLBA. This feature is considered to be the counterjet of the jet expanding southward from the core that launched around 2005. From the ratio of the lengths of the two jets, we estimated the inclination angle of the jet and found that it is $\theta=65^\circ\pm 16^\circ$, which is not much different from that of the outer old jets that launched around 1959. The northern jet has a strongly inverted spectrum, which indicates that it is absorbed by an accretion disk around the SMBH. From the brightness of the northern jet, we calculated the density of the disk and found that it is $\ga 10^5\rm\: cm^{-3}$. We also indicated that the disk may be highly inhomogeneous. Assuming that the current jet power is not much different from the past average, we derived the ambient gas density in the jet direction ($\sim 8\rm\: cm^{-3}$). | 16 | 9 | 1609.04017 |
1609 | 1609.04826_arXiv.txt | We analyze data from several studies of metal-poor stars in the Milky Way, focusing on both strong (Eu) and weak (Sr) $r$-process elements. Because these elements were injected in an explosion, we calculate the mass swept up when the blast wave first becomes radiative, yielding a lower limit for the dilution of such elements and hence a lower limit on the ejecta mass which is incorporated into the next generation of stars. Our study demonstrates that in order to explain the largest enhancements in [Eu/Fe] observed in stars at low [Fe/H] metallicities, individual $r$-process production events must synthesize a minimum of $10^{-3.5}$ \msun of $r$-process material. We also show that if the site of Mg production is the same as that of Eu, individual injection events must synthesize up to $\sim 10^{-3}$ \msun of $r$-process material. On the other hand, demanding that Sr traces Mg production results in \rp masses per event of $\sim 10^{-5 }$ \msun. This suggests that the astrophysical sites responsible for the genesis of the strong $r$-process elements need to operate at a drastically reduced rate when compared to core collapse supernovae, while the synthesis of weak \rp material is consistent with a supernova production site. | \label{sec:intro} Although the physical conditions required for \rp nucleosynthesis to occur have been understood since \citet{bbfh} and \citet{cameron1957}, the astrophysical site(s) in which those conditions are realized remains unclear. Whether enrichment has occured via Type II Supernovae \citep[SNe, e.g.][]{woosley1994}, in which the injection in a galaxy occurs frequently ($\sim 10^{-2}$ yr$^{-1}$) with low ($\sim 10^{-5}$ \msun) masses, or through neutron star mergers' \citep[NSM, e.g.][]{lattimer1974} sporadic ($\sim 10^{-5}$ yr$^{-1}$) injection of high ($\sim 10^{-2}$ \msun) masses is difficult to discern at high metallicities, as any hysteresis has been eradicated by multiple enrichment events. For this reason, metal-poor stars in the galactic halo serve as laboratories for the study of $r$-process element synthesis and can shed light on the identity of their progenitors \citep{sneden2008}. Abundance comparisons between many metal-poor halo stars suggest that the $r$-process mechanism is rather robust. Put differently, we see the same relative proportions of $r$-process elements in stars that are many billions of years different in age, hinting that this process has operated in a fairly consistent manner over the history of the Galaxy. This result has been used to constrain the specific physical conditions and nuclear properties required for the $r$-process. In the metallicity range [Fe/H] of roughly -2 to -3.5, where we are using the standard notation [X/H] = log$_{10}$(X/H) - log$_{10}$(X/H)$_\odot$, $r$-process elements have been found to exhibit large star-to-star bulk scatter in their concentrations with respect to the lighter elements albeit with a distribution that is characteristic of solar system matter. This hints at the presence of chemically inhomogeneous and unmixed gas at that epoch \citep{fields2002}. As time evolves, these localized inhomogeneities are smoothed out as more events occur and $r$-process products migrate and mix throughout the Galaxy. Recent cosmological simulations of heavy element production in a Milky Way- (MW-)like galaxy have shown the observed stellar abundances resulting from this process to be consistent with NSMs being the dominant enrichment mechanism \citep{shen2015,vandevoort2015}, but must rely on prescriptions regarding how material is mixed in the young MW and suffer from uncertainties in the delay time for NSMs. In this {\it Letter} we use simple and conservative physical arguments to show that the scatter in both strong (Eu) and weak (Sr) \rp elements at low [Fe/H] metallicities can be used to place stringent lower limits on how much $r$-process material needs to be synthesized per injection event in the early Universe. In Section \ref{sec:sn} we combine abundance data from several previous studies of MW stars and focus on Mg production to identify stars which may have formed from gas that has been enriched by a single event. In Section \ref{sec:rp} we derive lower limits on the \rp production required to explain Eu enhancements in these same stars, and also demonstrate the implications of demanding that \rp enhancements trace the Mg source. We discuss our findings and conclude in Section \ref{sec:disc}. | \label{sec:disc} By looking at metal-poor stars in the MW we are able to place strong constraints on the mass per event and hence rate of the events which have enriched them in \rp elements. As seen in Figure \ref{fig:eufe}, at least 90\% of the total \rp mass in the galaxy must have been synthesized in events that output $> 10^{-5}$ \msun of \rp material, translating to a rate of $< 10^{-2}$ yr$^{-1}$ in order to match the total \rp synthesis rate in the MW of $10^{-7}$ \msun yr$^{-1}$ \citep{cowan2004,sneden2008}. This shows that even under the most conservative assumptions core-collapse SNe are inconsistent with being the dominant progenitor of strong \rp elements in the early universe given their frequency. This analysis is in agreement with several recent arguments, as it is only in the past few years that we have been able to break the degeneracy between rate and mass per event amongst the leading theories by looking further into the history of the galaxy \citep[e.g.,][]{shen2015,ji2016a}. In addition, we have used a fiducial density of $10^{2}$ cm$^{-3}$ in our calculation of \mcool, whereas NSM are likely to occur in regions of lower density if they receive a kick from the SNe that created the pair \citep[e.g.,][]{belczynski2006,kelley2010}. From Equation \eqref{eq:mcool}, lowering the ambient density by a factor of 100 increases the mass per event by a factor of 4, implying an \rp mass of $\gtrsim 10^{-3}$ \msun per event. \begin{figure} \plotone{fig4} \caption{Total \rp mass per event required to explain the stellar abundances assuming it mixes over the same mass as the Mg as a function of metallicity. Limits for Eu are shown as {\it red} symbols while {\it black} symbols show the limits for Sr.} \label{fig:eu_sr} \end{figure} \citet{beniamini2016} have recently performed a similar analysis using ultra-faint dwarf galaxies (UFDs), assuming a gas mass for the galaxy and calculating the Eu (and hence total \rp) mass required to explain the observed stellar abundances. Their result is in agreement with ours, i.e. they find that the Eu mass per event is inconsistent with enrichment from typical core-collapse SNe given their rate, which naturally extends itself to MW stars assuming the dominant mechanism is the same in both galaxy types. This assumes the ejecta is well mixed throughout the UFD gas, an assumption which we also require at the cooling mass scale, though this is well justified as SN remnants show efficient mixing well before the cooling mass is reached \citep{lopez2011}. Though inhomogeneous mixing may take place at larger scales, this will not re-concentrate a given element. However, our analysis demands an even more conservative lower limit on the \rp mass per event, as our cooling masses are well below the fiducial $10^5$ \msun UFD gas mass. Through independent means we are able to look at both the weak and strong \rp elements and calculate the total \rp mass implied by assuming that the source which provided them also generated 0.1 \msun of Mg and scaling the \rp elements to solar abundances. We find that the implied mass per event for strong (Eu) production in most of our stars is $\gtrsim 10^{-5}$ \msun\, and up to $\approx 10^{-3}$ \msun, whereas the majority of weak (Sr) production is consistent with a mass per event of $\lesssim$ 10$^{-5}$ \msun. This implies that SNe are consistent with being the dominant source of weak \rp elements in the early universe \citep{surman2014}, and by extension that there may be two sources of \rp production, consistent with recent findings by \citet{ji2016b}. This argument does not rule out SNe with yields different from typical core-collapse, but any less common supernova must have either a Mg mass greater than 0.1 \msun(to increase the mixing mass) with a rate low enough to not overproduce the total Mg in the galaxy, or a Mg mass much less than 0.1 \msun in order to decouple the Eu production from the Mg. \begin{figure} \plotone{fig5} \caption{Inferred lower limit on \rp ejecta mass based on \mcool from Section \ref{sec:rp}. The dashed lines represent the 100 \% and 50\% values for the mass-weighted cumulative histogram as seen in Figure \ref{fig:eufe}. This argument rules out Type II SNe (purple region denotes the range of current theoretical estimates) as the dominant contributor to the r-process mass budget at low metallicities, and puts constraints on the ejecta mass required in scenarios involving magnetars (maroon region). } \label{fig:magnetar} \end{figure} The two remaining candidates for the genesis of \rp elements which do not violate these constraints are NSMs \citep[e.g.,][]{lattimer1974,rosswog1999,metzger2010,roberts2011,barnes2013,bauswein2013,grossman2014,ramirez2015} as well as jet-driven supernovae \citep[e.g.,][]{winteler2012,nishimura2015}, both of which are thought to occur less frequently and with larger mass per event, in concordance with this analysis. While we are not able to distinguish between these two, we may be able to place requirements on each scenario by varying the energy of the explosion which provided the enrichment. Figure \ref{fig:magnetar} shows how the constraints implied by our cooling mass argument change by varying the energy of the explosion. While we find that SNe are incompatible with any reasonable explosion energy, the energy implied by the spin down of a magnetar in a jet-driven SNe \citep[e.g.,][]{metzger2015} places lower limits on the mass per event of between $> 10^{-3}$ and $> 10^{-2}$ \msun. Although the data are not yet able to discern between these models, they demand a large mass per event and rate much lower than that of typical type II SNe (based on our cooling mass argument), as well as a Mg mass much greater than 0.1 \msun if the Mg is at all coupled to the Eu (based on our mixing mass argument). | 16 | 9 | 1609.04826 |
1609 | 1609.00892.txt | We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited. | Stellar evolution theory is well established especially for spherically symmetric stars, in which there is no rotation and no magnetic field. After the works of pioneers of the field~\citep{b2fh57,cameron57,hayashi61}, Henyey proposed in his seminal papers a method, which later became the defacto standard for stellar evolution calculations~\citep{henyey64}. The method is stable and capable of self-consistently incorporating various physical processes that occur in the stellar interior. It has been modified and extended a lot approximately in the last half century to accommodate rotation\citep{maeder00, woosley02}. In stellar evolution calculations, we need to obtain stellar structures consistent with, nuclear reactions (and/or molecule formations), radiative transport of energy, convective and circular motions as well as a realistic equation of state. Since the time-scale of stellar evolution is normally much longer than the dynamical time-scale, it is well approximated by series of time-independent configurations in hydrostatic equilibrium. In the presence of rotation, this is not simple. One of the difficulties is to obtain rotational equilibria for a given angular momentum distribution. What is more, however, we do not know a priori what the distribution of angular momentum looks like in the stellar interior although the problem has been studied theoretically since the 19th century by Carl Jacobi, Richard Dedekind, Peter Lejeune Dirichlet, and Bernhard Riemann to mention a few \citep{chandrasekhar}. It was in the last century that some methods to obtain rotating hydrostatic equilibria were proposed, and it was mathematically shown that cylindrical distributions of specific angular momentum are realized for EOSs, in which matter pressure is a function of density alone. This type of EOS is referred to ``{\it barotrope}"~\citep{ostriker, hachisu86}. The EOS is {\it not barotropic} in the realistic stellar interior, but {\it baroclinic} in general, i.e., pressure depends on density, entropy and chemical compositions~\footnote{For compact stars such as white dwarfs and neutron stars, the EOS may be approximately {\it barotropic}, since the temperature is negligibly low.}. Then the numerical construction of rotational equilibria becomes much more difficult compared with the case for barotropes, since the first integral of the hydrostatic equations that is available in the barotropic case no longer exists in the baroclinic case~\citep{uryu94, uryu95, roxburgh06, espinosa07, espinosa13, rieutord16}. Even if some rotational configurations are somehow obtained, it is a highly non-trivial issue how to make a sequence out of them that represents stellar evolutions appropriately. Note that in the presence of rotation fluid elements composing rotating stars could change their positions non-radially in complicated ways as the stars evolve in time even without convection. It would be highly difficult to describe such displacements of fluid elements with fluxes on a fixed numerical mesh from a Eulerian point of view, since the motions are extremely slow. The Lagrangian formulation will be hence more appropriate just as in the spherically symmetric case. And this is exactly the idea in this paper. %ȺAªð¦µÄÈ¢ÌÅí %Note that our formulation can save the numerical costs compared with the other particle-based methods to obtain the Eulerian values, e.g. pressure, density, and temperature, since We introduced in this paper a triangulated mesh with each node representing a fluid element approximately. Starting from an arbitrary reference configuration, we seek for the Lagrangian displacement for each node that gives a rotational equilibrium as a result. In so doing, the variational principle is employed. The method has its own difficulty, though. % in searching for solutions of hydrostatic equilibria; it is necessary to eliminate the gauge freedom in the displacement, otherwise, we can not identifies the solution. In this study, we introduce the Mote-Calro technique, which enables us to neglect this gauge freedom. In this paper, we construct a couple of configurations in rotational equilibrium with different angular momentum distributions in order to demonstrate the capability of our new scheme. Included in them is the so-called shellular-type rotations. It has been argued that in the stellar interior turbulence is anisotropic, operating more strongly within each isobaric surface than in its normal direction, and that a uniform rotation should be realized in the isobar as a consequence. Such a rotation law is referred to as ``shellular rotation" rather than cylindrical rotation \citep{zahn92, meynet97}. It should be stressed, however, that no rotational equilibrium with the shellular rotation was constructed numerically, not to mention analytically \footnote{The obvious exception is uniformly rotating stars.}. Very recently Fujisawa, one of the authors of this paper, has succeeded in producing some configurations with shellular-type rotation\citep{fujisawa15}. \footnote{By "shellular-type" we mean that the configuration is not perfectly but almost shellular with iso-angular-velocity surfaces being nearly aligned with isobars.} It is a nice demonstration of performance of our new scheme to reconstruct these configurations. The organization of the paper is as follows. In Section 2, we describe the formulation in detail: the Lagrangian variational principle, on which our scheme (referred to as the YFY scheme hereafter) is based, will be reviewed first; then the finite discretization on the triangulated grid will be explained and the handling of self-gravity is also mentioned; finally the minimization of the energy function with the Monte Carlo technique, which is analogous to those utilized, e.g., in nuclear physics, will be described. In Section 3, we demonstrate the nice performance of YFY scheme, constructing some rotational configurations and comparing them with the those obtained by other numerical schemes, including Fujisawa's self-consistent field scheme mentioned above. In the last section, we summarize this study and discuss possible extensions of our scheme as future works. | %---------------------- We have developed a new formulation to obtain rotational equilibria numerically. The scheme can handle not only barotropic but also baroclinic configurations, which are critically important for the application to realistic stars. Such an achievement is itself a major break through to the status quo, in which previous works are not many and, more importantly, they are all based on the Eulerian description~\citep{uryu94, uryu95, espinosa07, espinosa13, rieutord16}. Our method, on the other hand, employs the Lagrangian description just as in one-dimensional counterparts for non-rotating stars and hence stellar evolution calculations, since we can trace the potentially complex movements of each fluid element. Our formulation is based on the variational principle, in which rotational equilibria are obtained as the configurations that optimize the energy functional for given distributions of mass, specific entropy, and angular momentum on the Lagrangian coordinates. In this paper all physical quantities are discretized on triangulated grids. In order to validate our scheme, we compare the configurations obtained by our scheme with those by other Eulerian schemes: the HSCF scheme developed by Hachisu~\citep{hachisu86} for the barotropic configuration, and the FSCF scheme conceived by Fujisawa~\citep{fujisawa15} more recently for the baroclinic one. We have confirmed that all the configurations including the ones with shellular-type rotations obtained in this paper are linearly stable against axisymmetric perturbations and comply with the Bjorkness-Rosseland rule. In this comparison, we have reproduced the equilibria a shellular-type rotation, which were obtained only recently by Fujisawa although the shellular rotation is commonly assumed in the one-dimensional stellar evolution calculation with rotation being taken into account only approximately. It is found that the result obtained with the YFY scheme agree with those derived by other schemes with an error of 5 $\sim$ \%, which we think is reasonable, considering the relatively small number of nodes (489) we used in this paper. %The numerical accuracy is lowered in the regions near the surface and rotation axis, since they contribute little to the energy functional. %---- Yamada-san ---- It is then a legitimate question to ask how the accuracy is improved with the number of nodes. In order to address this issue, we have conducted additional computations, changing the node number from $\sim$ 200 to $\sim$1000, the latter of which is the maximum node number we can afford at present, since the numerical cost is proportional to $N^2$ in our currently unparallelized code, where $N$ is the node number. We find that the higher resolutions with $\sim$800 and $\sim$1000 nodes do not improve the accuracy at a recognizable level as shown in the leftmost panel of Fig.\ref{fig:ebl}. As demonstrated for the highest resolution model in the middle and rightmost panels of this figure, as the final configuration is approached, the values of energy function and virial residual repeat a sudden jump followed by a settlement to some values which satisfy our convergence criteria. This is due to the smoothing that we administer regularly to avoid the trapping by false minima (see the last part of the last section). Because of the probabilistic nature of the Monte Carlo method, the final value of the virial residual after each repetition fluctuates around the mean value. In the left panel of Fig.\ref{fig:ebl} we present these mean values and variances as dots and bars, respectively, for different node numbers. %----- FIG.27----- \begin{figure*} \hspace{-5mm} \includegraphics[width=14.pc]{./fig/fig27a.eps} \includegraphics[width=14.pc]{./fig/fig27b.eps} \includegraphics[width=14.pc]{./fig/fig27c.eps} \caption{\label{fig:ebl} (colour on-line). The range of converged virial residual for each resolution (left panel). The middle and the right panels show an example of the energy functional and the virial residual with 1073 nodes. %The converged virial residual is determined at ${\partial E}/{\partial N_i}=0$ and ${\partial V_C}/{\partial N_i}=0$. In this meaning, there are 12 types of converged values of the virial residuals in the middle and the right panels. } \end{figure*} The reason why the precision is not improved is the following: in our formulation we search for the rotational configuration that gives the lowest value to the energy functional for given mass, specific entropy and angular momentum; it is not surprising then that some nodes contribute more than others; in particular, the nodes close either to the surface or to the rotational axis are the least contributors, since they have either small densities or volumes; this means in turn that their positions are very difficult to obtain accurately; this may be understood if one scrutinizes the right panels of Figs. 2, 3, 6, 9, 10, 15, 18 as well as the lower panels of Figs. 14, 19, 20; on the hand, these nodes give contributions of the order of $10^{-4}$ to the virial residual. In principle, if the number of nodes is sufficiently large particularly in the regions of our concern, then the virial equality should be improved. The current resolutions we can afford are way too small, though, as can be understood from the figures showing the node configurations. This may be remedied if we implement the multi-layer treatment. Multi-layer treatment may be useful to improve the accuracy\footnote{Such a treatment is already employed in their scheme by Espinosa Lara and Rieutord \citep{espinosa13} and, combined with the spectral method, achieves very high accuracy. See also Kiuchi et al. \citep{kiuchi10}}, which will be also required in applying the new scheme to rotating stars in advanced evolutionary stages. %It is stressed that the our formulation can be extended to treat such multi-layer structures without any difficulties. {\bf The previous methods need to be imposed some boundary conditions between layers appropriately. We, then, need to set the boundary conditions between the layers depended on the stage of evolution. On the other hand, our method does not need. The only need to do is just to prepare the initial profiles of mass, angular momentum, entropy, and elementary fractions, and the multi-layers appear as the optimal result for the initial guesses: it does not have the concept of layers namely. } As explained earlier, the numerical error comes mainly from the regions, whose contributions to the energy functional are minor. If the multi-layer treatment is employed, these minor regions can be treated separately from the major regions. Then the minor contributions are no longer minor. The important thing is that the variational principle can be applied to each region individually, with other regions serving as fixed gravitational potentials. In order to obtain the global equilibrium, we need to find an equilibrium configuration in each region consecutively and iteratively until all these configurations do not change any longer simultaneously. In addition to the minor regions mentioned above, the central region may also need to be treated with a special care, since the nodes are rather sparse there as can be seen, e.g., in the right panel of Fig. 1. We have demonstrated that our scheme is robust, obtaining the same final configuration in equilibrium irrespective of the reference configurations assumed initially. We have also observed, on the other hand, that the Monte Carlo sweeps to get to the minimum of the energy functional are prone to be trapped by false local minima, which are generated by deformations of the numerical grid and that the smoothing should be properly administered to escape them. In order to distinguish the true minimum from a false one, the virial residual is found to be a good diagnostic. Although we have not made any attempt in this paper to reconstruct a triangulated mesh when it becomes too deformed, such re-gridding will be necessary when applying the YFY scheme to the evolution of rotating stars. %---- Ó¡s¾B ---- %The concept of our scheme is quite simple: {\it ``Find a energy minimum for optimal stellar-structures"}. We, however, find two more arts to find the solutions empirically. One is the virial residual, which is a necessary condition for the hydrostatic equilibrium. The convergence of energy is not the sufficient for the force balance because of numerical errors, e.g. the local minimum problems come from the acute triangle mesh. The another is the smoothing procedure to reduce the acute-angled triangulations grids artificially, otherwise the system will be trapped in the local energy minimum. We fix the adjacency matrix in the smoothing process in this paper, but there may be some alternatives for that. We then need to take into account the opacities to obtain a realistic atmosphere models as employed in 1D simulations. Otherwise we can not discuss the mass loss in stellar evolution calculations. The next step toward the application to the stellar evolution calculation will be to incorporate radiation transport in rotational equilibria. Unlike the previous works~\citep{uryu94, uryu95, roxburgh06, espinosa07, espinosa13, rieutord16}, we will solve time-dependent diffusion equation on the same triangulated grid, which will not be a difficult task. The meridional circulation is another important ingredient~\citep{zahn92} when considering the application of our scheme to actual rotating stars, since it is supposed to play a major role in the re-distribution of angular momentum and elements (e.g. \citealt{mathis09}). Although such motions cannot be handled directly with our scheme, they may be incorporated either as advections or as diffusions as just as in current 1D calculation. Convection is even more difficult to treat. The redistributions of angular momentum and elements as well as entropy in this case may be approximated as diffusions or advections like the meridional circulation but the real difficulty with the convection is the fact that the convectively unstable configurations do not correspond to the minimum of the energy functional but to a saddle point. A couple of ideas are currently being tested and will be reported elsewhere. Since our scheme is applicable only to axisymmetric configurations, in which the specific angular momentum is conserved in each fluid element, extension of our formalism to 3D configurations such as triaxial equilibria~\citep{tassoul78} is much beyond the scope of this paper. Possible applications of our scheme are not limited to the ordinary stars, though. They will be extended to e.g., compact stars, proto-stars and proto-planets to mention a few. Incorporation of magnetic fields and/or general relativity should be considered in due course. | 16 | 9 | 1609.00892 |
1609 | 1609.06538_arXiv.txt | \src\ is a variable (luminosity range {\rc $\sim$ 100}) ultraluminous X-ray source (ULX) proposed to host a stellar-mass black hole of less than 15~M$_{\odot}$ in a binary system with orbital period of 64~d and a 18--23~M$_{\odot}$ B9Ia companion. Within the EXTraS project we discovered pulsations at a period of $\sim$0.42~s in two \xmm\ observations of \src, during which the source was detected at $L_{\mathrm{X}}\sim2.1\times10^{39}$ and $5\times10^{39}$~\lum\ (0.3--10~keV band). These findings unambiguously demonstrate that the compact object in \src\ is a neutron star accreting at super-Eddington rates. While standard accretion models face difficulties accounting for the pulsar X-ray luminosity, the presence of a multipolar magnetic field with $B\sim$ few $\times$ 10$^{13}$\,G close to the base of the accretion column appears to be in agreement with the properties of the system. | Ultraluminous X-ray sources (ULXs) are extra-nuclear point-like X-ray objects located in nearby galaxies with X-ray luminosities exceeding the Eddington limit of $>$10$^{39}$\lum\ for a $\sim$10 M$_{\odot}$ black hole (BH). Based on their spectral and timing properties, it has been proposed (see \citealt{roberts16} for a recent review) that most ULXs are stellar-remnant black holes (with masses possibly reaching $\sim$100 M$_{\odot}$; \citealt{zampieri09,belczynski10}) accreting at super-Eddington rates. The salient ULX features revealed by \xmm\ and \nustar\ observations and supporting the scenario of super-Eddington accretion onto BHs is a downturn of the X-ray spectrum at energies of $\sim$5--10~keV and a soft excess at lower energies (\citealt{roberts16} and references therein). Despite evidences in favour of the BH nature of of the compact remnant in ULXs \citep{liu13}, there are also two notable exceptions of pulsating ULXs (PULXs) testifying to the presence of accreting neutron stars \citep{bachetti14,israel16b}. This shows that spectral properties alone are not an unambiguous way for a correct identification of the compact remnant in ULX \citep{bachetti16}. Within the framework of the EXTraS\footnote{See http://www.extras-fp7.eu/.} (Exploring the X-ray Transient and variable Sky; \citealt{deluca15}) project, we searched for coherent periodic signals in the about 290,000 time series of sources, with more than 50 counts, detected by \xmm\ in all EPIC public data. Among dozens of new X-ray pulsators found so far with periodic signals detected at high confidence ($>$4.5$\sigma$), there is \srcx\ = \srcc, also known as the ULX P13 in NGC\,7793. \src\ was first observed in 1979 by the \ein\ satellite as a bright, $L_{\mathrm{X}}\sim2\times10^{39}$~\lum\ (in the 0.3--10~keV range), X-ray stellar-like object in the nearby ($D= 3.9$~Mpc; \citealt{karachentsev03}{\rc; this distance is adopted throughout the paper}) reasonably face-on ($i= 53.7\degr$) galaxy NGC\,7793 in the Sculptor group \citep{fabbiano92}. It was also detected by \rst\ in 1992 at $L_{\mathrm{X}}\sim$$3.5\times10^{39}$~\lum\ (value extrapolated in the 0.3--10~keV band; \citealt{read99}). A \cxo\ pointing carried out in 2003 September revealed two sources at the \rst\ position of \src, separated by 2~arcsec, namely \srcc\ and CXOU J235750.9--323728 \citep{pannuti11}. The latter source is thought to be unrelated to \src\ and is more than an order of magnitude less luminous than \src\ itself. Their luminosities are $\sim$$1.2\times10^{39}$ and $\sim$$6.2\times10^{37}$~\lum, respectively. The compact object in \src\ is orbiting around a B9Ia spectral-type star of 18--23\, M$_{\odot}$ in a binary system with an orbital period of about 64 days and a moderate eccentricity $e$ of 0.3--0.4 \citep{motch14}. By modelling the strong optical and UV orbital modulation, likely arising from the heating of the donor star, a mass for the suspected BH of less than about 15~M$_{\odot}$ has been inferred for \src\ \citep{motch14}. Here we report on the discovery of coherent pulsations at a period of 0.42~s in the EPIC pn lightcurves of \srcx, with a secular first period derivative of $\dot{P}_{\mathrm{sec}}\sim - 4\times10^{-11}$~s~s$^{-1}$ (Sect.\,\ref{timing}). These findings clearly indicate that \src\ hosts an accreting neutron star (NS) in a binary system and not a stellar-mass BH as previously assumed. We discuss the nature of this new ultraluminous X-ray pulsar (Sect.\,\ref{discussion}), the third discovered so far, and also the fastest-spinning one. | \label{discussion} \citet{motch14} found that the orbital period of NGC 7793 P13 is 64~d and that the properties of the optical counterpart are consistent with those of a B9Ia supergiant companion with mass in the range $M_2 = 18$--23~M$_\odot$ and radius of \mbox{$R_2 = 50$--60~R$_\odot$}. The same authors assume that the star fills its Roche lobe, since the stellar wind from a B9Ia supergiant cannot provide the accretion rate needed to produce the maximum observed X-ray luminosity ($10^{19}$--$10^{20}$~g~s$^{-1}$, see below). All acceptable orbital solutions require a significant eccentricity ($e$=0.27--0.41). From this constraint, \citet{motch14} conclude that, at periastron, the supergiant can fill its Roche lobe for a BH companion with a mass 3.4~M$_{\odot} < $~M$_{\mathrm{BH}} < 15$~M$_{\odot}$, with the upper limit being fixed by the requirement that the Roche lobe is not too small to accommodate the star. The discovery of a pulsar in NGC 7793 P13 allows us to place an independent and even tighter constraint on the orbital eccentricity of the system. Assuming a mass $M_1 = 1.4$~M$_{\odot}$ for the NS, the Roche lobe of the companion is bigger than that for a BH. Therefore, even a B9Ia supergiant cannot fill it unless the eccentricity is $e$=0.46--0.55, so that, at periastron, the separation is sufficiently small to allow for a contact phase. Following \citet{motch14}, we assume that the mass transfer in the system proceeds on a thermal timescale $t_{\mathrm{th}}$: $ t_{\mathrm{th}} = 2.4\times 10^5 (M_2/ 20~\mathrm{M}_\odot)^2 \times (R_2/50~\mathrm{R}_\odot)^{-1} (L_2/10^4 \mathrm{L}_\odot)^{-1} \, {\rm yr} \, , \label{eq1} $ where $L_2$ is the luminosity of the companion. The mass transfer rate is then: $ {\dot M_2} \approx M_2 / t_{\mathrm{th}} = 3.7 \times 10^{21} (M_2/ 20~\mathrm{M}_\odot)^{-1} \times (R_2/50 ~\mathrm{R}_\odot) (L_2/10^4 ~\mathrm{L}_\odot) ~{\rm g~s^{-1}}. $ Owing to the large mass ratio ($q=M_2/M_1\gg1$), the evolution is expected to be non-conservative. Part of the mass is likely to be removed from the binary through hydrodynamical instabilities, although the system may possibly be stabilized by the significant mass loss of the companion \citep{fragos15}. Even considering all mass losses, ${\dot M_2}$ is so high to easily account for the accretion rate ${\dot M}$ implied by the maximum observed X-ray luminosity: $ L_{\mathrm{max}} \approx b \cdot 10^{40}~\mathrm{erg~s^{-1}},~ {\dot M} = L_{\mathrm{max}}/(\eta c^2) \approx 10^{20} b \, (0.1/\eta) \, {\rm g~s^{-1}} $, where $b$ is the beaming factor and $\eta$ the accretion efficiency (see also below). \src\ displayed a factor of $\sim${\rc 8} % flux variation {\rc in the high state (above $\sim$2$\times$10$^{39}$\lum; see Fig.\,\ref{lcurve})}, attaining a maximum isotropic luminosity of $L_{\mathrm{iso}}^{\mathrm{max}}\sim 1.6\times10^{40}$~\lum, about 100 times higher than the Eddington limit. We note that the $\sim$0.42~s pulsations were observed at the top and close to the bottom of this range, implying that accretion onto the NS took place over the entire interval of variation. \begin{figure} \vspace{-9mm} \resizebox{1.18\hsize}{!}{\includegraphics[angle=0]{Fig_nuova.pdf}} \vspace{-6mm} \caption{\label{Bfield} Accretion luminosity versus surface magnetic field constraints for \src. The solid line gives the maximum luminosity that can be produced by column-accretion onto the NS magnetic poles. The dashed line is the limit above which the energy released in the accretion disk exceeds the Eddington limit and disk thickens. Accretion is inhibited below the dot-dashed line, as the NS enters the propeller regime. Double-arrowed segments show the factor of $\sim${\rc 8} flux variation displayed by the source when pulsations were detected.% Different segments are shifted by the inverse of the beaming factor $b^{-1} = L_{\mathrm{iso}}/L_{\mathrm{acc}}$. A value of $b\sim$1/2 is found to be in agreement with the observed source properties (see text): this solution implies a dipole magnetic field of $B$$\sim${\rc 5} % $\times$$10^{12}$\,G and a multipolar field $B$$>$${\rc 8} % $$\times$$10^{13}$\,G at the base of the accretion column (dotted line).} \end{figure} In our discussion here we assume that accretion onto the NS takes place unimpeded (at least) over the above mentioned luminosity variation. The $\sim -4.0\times10^{-11}$~s~s$^{-1}$ period derivative inferred from the two one-year-apart observations during which pulsations were detected, is virtually unaffected by orbital Doppler shift given that the two \xmm\ pointings are almost at the same orbital phase (assuming P$_{orb}=$ 63.52\,d; \citealt{motch14}). NSs may attain accretion luminosities exceeding the Eddington limit by orders of magnitude if their surface magnetic field ($B$) is very high, so that electron scattering cross sections for extraordinary mode photons below the cyclotron energy $E_{\mathrm{c}} \sim 12 (B/10^{12}$\,G)~keV is much lower than the Thomson cross section. \cite{mushtukov15} show that column-accretion onto a $>10^{15}$~G magnetic pole may give rise to a luminosity of $L\sim10^{41}$~\lum. However, for a magnetic NS to accrete at a very high rate, other conditions must be met. First, the accretion flow outside the magnetosphere must take place through a disk that remains geometrically thin ({\it i.e.} height/radius ratio $<$1), such that the bulk of the flux emitted close to the bottom of the accretion column can escape. This translates into the condition that the accretion energy released in the disk down to the magnetospheric radius $r_{\mathrm{m}}$ is sub-Eddington (dashed line in Fig.\,\ref{Bfield}). An additional condition is that the NS angular velocity is smaller than the (Keplerian) angular velocity of the disk at $r_{\mathrm{m}}$, so that the drag exerted by the rotating magnetic field lines as matter enters the magnetosphere is weaker than gravity and matter can accrete onto the surface. This is equivalent to requiring that $r_{\mathrm{m}} < r_{\mathrm{cor}} $, where $r_{\mathrm{cor}} = \left(\frac{G M P^2}{4 \pi^2}\right)^{1/3}$ is the corotation radius \citep{illarionov75,stella86}. When $r_{\mathrm{m}} > r_{\mathrm{cor}}$, centrifugal forces at $r_{\mathrm{m}}$ exceed gravity and only little accretion, if any, can take place when the so-called propeller regime ensues (dot-dashed line in Fig.\,\ref{Bfield}). For \src\ to emit isotropically a maximum luminosity of $L^{\mathrm{max}}_{\mathrm{iso}}\sim 1.6 \times 10^{40}$~\lum\ according to the model of \cite{mushtukov15} the NS surface dipolar magnetic should be at least $B\sim 2 \times 10^{14}$~G. However, for such value of $B$ and $P\sim0.42$~s, accretion would be inhibited by magnetospheric drag and the NS would be deep in the propeller regime. Therefore we relax the assumption of isotropy, and consider that the NS emission is beamed by a factor $b < 1$. In this case the isotropic equivalent luminosity is $L_{\mathrm{iso}} = L_{\mathrm{acc}}/b$ and the accretion luminosity $L_{\mathrm{acc}} = GM\dot M/R$ is reduced correspondingly (here $R$ and $M$ are the NS radius and mass). We assume that the minimum (detected) isotropic luminosity of $L^{\mathrm{min}}_{\mathrm{iso}} \sim L^{\mathrm{max}}_{\mathrm{iso}}/{\rc 8} $ marks the onset of the transition from accretion to the propeller phase ({\it i.e.} $r_{\mathrm{m}} = r_{\mathrm{cor}}$) and, at the same time, require that the surface magnetic field is high enough to attain the observed luminosity range (solid line in Fig.\,\ref{Bfield}). A surface dipole field of {\rc $B\sim 2\times 10^{12}$~G} and a maximum accretion luminosity of $L_{\mathrm{acc}} \sim 10^{39}$~\lum\ are obtained, corresponding to beaming factor of $b\sim 1/15$ (note that for these parameters the disk remains geometrically thin). For a time-averaged accretion rate of $\dot M \sim 3 \times 10^{18}$~g~s$^{-1}$, as implied by this solution, we estimate the corresponding maximum spin-up rate by imposing that the matter accreting onto the NS carries the Keplerian angular momentum at $r_{\mathrm{cor}}$. This gives a maximum $\dot P = \dot{M}\ r_{\mathrm{cor}}^2P/I \sim - 1 \times 10^{-11}$~s~s$^{-1}$, four times smaller than the secular $\dot P$ derived from the data. In order to ease this problem, and by analogy with the {\rc case of NGC\,5907 ULX-1 \citep{israel16b}}, we consider the possibility that close to the NS surface (and thus the base of the accretion column) the magnetic field is dominated by higher than dipole magnetic multipoles. Close to the magnetospheric radius ($r_{\mathrm{m}} \sim 10^8$~cm) the field is virtually the dipolar by virtue of its less steep radial dependence. This is done by analogy with the case of magnetars \citep{thompson95,tiengo13}. The conditions that the accretion disk is thin for $L^{\mathrm{max}}_{\mathrm{iso}} = L^{\mathrm{max}}_{\mathrm{acc}}/b$ and that the NS is in the accretion regime for $L^{\mathrm{min}}_{\mathrm{iso}} = L^{\mathrm{min}}_{\mathrm{acc}}/b$ depend on the B-field strength at $r_{\mathrm{m}}$, where only the dipole component matters. Both conditions are satisfied for $B$ of {\rc $\sim 5 \times 10^{12}$~G} and $b \sim 1/2$. A (multipolar) $B$ $>8 \times 10^{13}$~G at the base of the accretion column would be required to give rise to corresponding maximum accretion luminosity of {\rc $L^{\mathrm{max}}_{\mathrm{acc}} =9\times 10^{39}$ \lum (dotted line in Fig.\,\ref{Bfield}). % A maximum spin-up of $\dot P \sim -7 \times 10^{-11}$~s~s$^{-1}$ is derived in this case (owing to the higher time-averaged accretion rate resulting from $b \sim 1/2$), consistent with the value inferred from the observations. For a $\sim 0.42$~s spin period we expect that the isotropic luminosity in the propeller regime is $< L^{\mathrm{min}}_{\mathrm{iso}}/90 \sim 2\times10^{37}$~\lum \citep{corbet97}, a level which is slightly below the values inferred during the 2011 \cxo\ and 2012 \xmm\ observations, to within uncertainties.} The discovery of three PULXs previously classified as stellar mass BH based on their spectral properties, strongly suggests that this class might be more numerous than suspected so far, and that other know ULXs might host an accreting NS. The large first period derivative, the intermittance of the pulsations and their relatively small pulsed fraction make their detection a difficult task. \vspace{-.5cm} | 16 | 9 | 1609.06538 |
1609 | 1609.09135_arXiv.txt | We analyse the Transit Timing Variation (TTV) measurements of a~system of two super-Earths detected as Kepler-29, in order to constrain the planets' masses and orbital parameters. A dynamical analysis of the best-fitting configurations constrains the masses to be $\sim 6$ and $\sim 5$ Earth masses for the inner and the outer planets, respectively. The analysis also reveals that the system is likely locked in the 9:7~mean motion resonance. However, a variety of orbital architectures regarding eccentricities and the relative orientation of orbits is permitted by the observations as well as by stability constraints. We attempt to find configurations preferred by the planet formation scenarios as an additional, physical constraint. We show that configurations with low eccentricities and anti-aligned apsidal lines of the orbits are a natural and most likely outcome of the convergent migration. However, we show that librations of the critical angles are not necessary for the Kepler-29 system to be dynamically resonant, and such configurations may be formed on the way of migration as well. We argue, on the other hand, that aligned configurations with $e \gtrsim 0.03$ may be not consistent with the migration scenario. | \let\thefootnote\relax\footnote{$^{\star}$Email: [email protected] (CM), [email protected] (KG), [email protected] (FP)} The \kepler{} mission has lead to the discovery of a~few hundred multiple planetary systems with super-Earth planets. Some of those systems are very compact and exhibit orbital period ratios close to small rational numbers. This may indicate their proximity to low-order mean motion resonances (MMRs) \citep[e.g.][]{Fabrycky2013}. This is not yet a fully resolved issue, since most of the \kepler{} systems are not sufficiently characterised, regarding both the planet's masses and orbital architectures. Dynamical modelling of Transit Timing Variation measurements \citep{Agol2005} or the photodynamical method \citep{Carter2011}, which account for the mutual $N$-body interactions, are common and usually the only approaches making it possible to model multiple systems in the \kepler{} sample \citep{Rowe2015,Mullally2015,Holczer2016}. A~further difficulty is a~relatively narrow time-window of observations and low signal-to-noise ratio that typically lead to weakly constrained eccentricities and longitudes of pericenter. Therefore, definite conclusions about orbital architectures of such systems are hard to derive unless {\em a priori} constraints are imposed, like requirements of dynamical stability and evolution consistent with the planetary migration. Nevertheless, the TTV method is the major technique making it possible to determine the dynamical masses, if spectroscopic measurements could not be made for faint or/and chromospherically active stars. In this paper we aim to characterise the dynamical architecture of Kepler-29 (KOI-738) planetary system detected by \cite{Fabrycky2012}. We use the TTV measurements spanning 17 quarters of \kepler{} long-cadence photometric lightcurves \citep{Rowe2015}. Kepler-29 is composed of two super-Earth planets with dynamical masses of $4.69$ and $4.16$~Earth masses, respectively \citep{JontofHutter2016}. Their stability analysis has been restricted to a relatively short-term direct $N$-body integration for a few~Myrs. We focus rather on qualitative dynamical analysis of this resonant or near-resonant system and consider the planetary migration as a possible formation scenario. The paper is structured as follows. Section~2 is devoted to the dynamical model of a co-planar Kepler-29 system constrained by the TTV measurements in \citep{Rowe2015}. We aim to obtain a comprehensive view of the parameter space with two independent optimisation methods: the Markov Chain Monte Carlo sampling as well as with genetic and evolutionary algorithms. We show the results of the stability analysis of plausible configurations with the long-term direct numerical integrations and with the fast indicator technique. We found that the planets may be in 9:7~MMR, although its presence and behaviour of critical angles, as well as the stability depend on {\em a priori} set eccentricity distribution. Different geometric configurations with librating or rotating critical angles are permitted by both the observational and dynamical constraints. Therefore, in Section~3 we attempt to construct a~global, analytic approximation of the system close to the 9:7~MMR, and to verify whether or not the best-fitting models may be formed on the way of planetary migration (Section~4). Conclusions are given in the last section. | We analysed the TTV data from \citep{Rowe2015} of the Kepler-29 system with two low-mass planets of a period ratio very close to 9/7 \citep{JontofHutter2016}. We confirmed that the masses of the planets are within a few Earth mass range, i.e., $\sim 6\,\mE$ and $\sim 5\,\mE$ for the inner and the outer planet, respectively. We demonstrated that, although the eccentricities as well as longitudes of pericenters are not well determined, the system is very likely in an exact 9:7~MMR. We found configurations with both aligned and anti-aligned apsides, that are long-term stable and fit the data equally well. The eccentricities may be as high as $0.3-0.4$ for models with aligned orbits, while for anti-aligned configurations only low eccentric orbits are allowed by the observational and stability constraints. We demonstrated that the critical angles of the resonant configurations do not necessarily librate. That implies also that the secular angle $\Delta\varpi$ may both rotate or librate, around $0$ or $\pi$. The resonant nature of such systems can be verified at the frequency maps (right-hand column of Fig.~\ref{fig:fig5}) as well as at the $(\Delta\varpi, \phi_1)$-diagrams (Fig.~\ref{fig:fig9}). The fundamental frequencies related to the mean motions are very close to the nominal value of 9/7 for the systems whose resonant angles rotate. Moreover, the evolution of the angles $\Delta\varpi$ and $\phi_1$ is correlated. \begin{figure*} \centerline{ \vbox{ \hbox{ \includegraphics[width=0.33\textwidth]{fig12a.png} \includegraphics[width=0.33\textwidth]{fig12b.png} \includegraphics[width=0.33\textwidth]{fig12c.png} } } } \caption{ Evolution of example configurations stemming from the migration simulation illustrated in Fig.~\ref{fig:fig11}, presented at the $(\Delta\varpi, \phi_1)$-diagram. The integration time is $10^5\,$yr. } \label{fig:fig12} \end{figure*} We showed that the best-fitting solutions with low eccentricities (both with aligned and anti-aligned apsides) are shifted with respect to the periodic orbits (equilibria of the averaged system) of 9:7~MMRs, and demonstrated that it is a natural outcome of the planetary migration. That holds even for configurations that lie close to the branch unstable periodic orbits for $\Delta\varpi=0$ (Fit~IV). On the other hand, we showed that configurations with $e \gtrsim 0.03$ and $\Delta\varpi \sim 0$ are unlikely to be formed on the way of migration. Systems with $e \gtrsim 0.03$ and $\Delta\varpi \sim \pi$ can form this way, but configurations of this sort do not fit the TTV observations. Therefore, we conclude that if the Kepler-29 system was formed through the smooth migration, its orbits are low eccentric $e \lesssim 0.03$, but the behaviour of $\Delta\varpi$ and the resonant angles can be hardly determined on basis of the available TTV data. | 16 | 9 | 1609.09135 |
1609 | 1609.02011_arXiv.txt | Transitional disks show a lack of excess emission at infrared wavelengths due to a large dust cavity, that is often corroborated by spatially resolved observations at $\sim$mm wavelengths. We present the first spatially resolved $\sim$mm-wavelength images of the disk around the Herbig Ae/Be star, HD~97048. Scattered light images show that the disk extends to $\approx640$~au. The ALMA data reveal a circular-symmetric dusty disk extending to $\approx350$~au, and a molecular disk traced in CO $J=3$-2 emission, extending to $\approx750$~au. The CO emission arises from a flared layer with an opening angle $\approx30\degree-40\degree$. HD~97048 is another source for which the large ($\sim$~mm-sized) dust grains are more centrally concentrated than the small ($\sim\mu$m-sized) grains and molecular gas, likely due to radial drift. The images and visibility data modeling suggest a decrement in continuum emission within $\approx50$~au, consistent with the cavity size determined from mid-infrared imaging ($34\pm4$~au). The extracted continuum intensity profiles show ring-like structures with peaks at $\approx 50$, 150, and 300~au, with associated gaps at $\approx100$ and 250~au. This structure should be confirmed in higher-resolution images (FWHM~$\approx 10-20$~au). These data confirm the classification of HD~97048 as a transitional disk that also possesses multiple ring-like structures in the dust continuum emission. Additional data are required at multiple and well-separated frequencies to fully characterize the disk structure, and thereby constrain the mechanism(s) responsible for sculpting the HD~97048 disk. | \label{introduction} Protoplanetary disks are the sites of planetary system formation. So-called {\em transitional disks} are considered a particular class of protoplanetary disk which have substantial dust cavities \cite[or gaps, see the recent review by][p.~497]{espaillat14}. The origin of dust cavities in transitional disks is much debated in the literature. Theories range from photoevaporation of dust and gas by the central star \cite[see, e.g.,][p.~475]{alexander14} to the development of {\em dead zones}, regions of low ionization which impede the angular momentum and mass transport leading to the build-up of material in a ring-like structure \citep[][]{regaly13,flock15}. A third theory is that unseen massive planets or companions in the disk create steep pressure gradients in the gas, which shepherd large dust grains into rings (so-called ``dust traps''), generating the appearance of a large cavity when imaged at (sub-)mm wavelengths \citep[][]{andrews11,pinilla12b}. Distinguishing between theories requires complementary observations of the molecular gas and imaging of the emission from both small ($\sim\mu$m) and large ($\sim$mm) dust grains \citep[see Table 2 in][p.~497]{espaillat14}. Cavities in both dust (small and large) and gas are likely created by photoevaporation whereas those created by pressure bumps (possibly triggered by planets) are devoid of large (mm) grains only, and residual gas and small dust grains may remain \citep[due to dust filtration, see, e.g.,][]{rice06}. Transitional disks were originally identified via the lack of near- to mid-infrared (IR) emission in the spectral energy distributions (SEDs) of disk-hosting stars, indicating a depletion in warm dust and hence, the presence of an inner dust cavity \citep[see, e.g.,][]{strom89}. Several transitional disks encompass Herbig Ae/Be (HAeBe) stars \citep[$T_\mathrm{eff}$, $\sim$10,000~K,][]{waters98}. HAeBe star-disk systems have been further classified by the shape of the SEDs in the mid-IR into either Group I or Group II disks; the former have a flared structure (driven by absorption of stellar UV photons) and the latter are considered to be ``flat'' disks \citep{meeus01}, within which the dust has grown to mm-sizes, has become decoupled from the gas, and has settled to the midplane \citep{dullemond04}. This scenario of the gradual depletion of small dust grains which absorbs the UV radiation necessary to trigger the flared structure has led to speculation in the literature that Group II disks may be a later evolutionary state of Group I disks \citep{dullemond04}. The advent of interferometric imaging across the wavelength range of interest has thrown doubt on this rather intuitive evolutionary scenario. High spatial-resolution imaging at long ($\gtrsim$~mm) wavelengths with ALMA, JVLA, and ATCA have revealed that grain growth can already be advanced in Group I disks ($\beta\lesssim 1$, where $F_\nu \propto \nu^{\beta + 2}$), e.g., HD~142527 \citep[][]{casassus13,casassus15}, IRS~48 \citep[][]{vandermarel13,vandermarel15}, and HD~100546 \citep[][]{pineda14,walsh14,wright15}. It should be noted that the value of $\beta$ is also sensitive to grain composition \citep{draine06}. Recent mid-IR imaging also suggests that all Group I disks are transitional in nature, and the resulting flared structure is therefore linked to the presence of the inner cavity \citep[][]{honda12,maaskant13}. Assuming the theory that massive planets are responsible for generating such cavities, perhaps primordial protoplanetary disks follow one of two evolutionary paths with the division into Group I or Group II, dependent upon the formation of a massive companion (and associated cavity) early in the disk lifetime \citep[see, e.g.,][]{currie09}. The picture is further complicated by recent mid-IR interferometric observations which suggest that several Group II HAeBe disks also exhibit evidence of inner cavities, albeit smaller than those typically seen in Group I disks \citep{menu15}. These authors hypothesize that the Group II objects are younger, and the evolution into a Group I disk follows the formation of an inner cavity. It is clear that complementary observations across the wavelength range of interest, from near-IR to (sub-)mm, are necessary to help further elucidate the evolutionary paths and states of HAeBe disks and the physical origin of the cavities observed therein. We present spatially resolved ALMA Cycle 0 observations of the Group I HAeBe star-disk system, HD~97048. The observations reveal for the first time the spatial distribution of the large ($\sim$~mm-sized) dust grains and molecular gas in this otherwise well-studied source. In Sections~\ref{hd97048}-\ref{discussion} we describe the source, the observations, present our results, and discuss the implications, respectively. | \label{discussion} \subsection{On the transitional nature of HD~97048} The data presented here support the proposed transitional nature of the disk encompassing HD~97048, with the data and extracted intensity profile showing a decrement in continuum emission within $\approx50$~au. The data also show that the molecular gas and small ($\mu$m-sized) dust grains have a larger radial extent than the large (mm-sized) dust grains (750~au versus 350~au). Better data are needed to quantify the dust depletion factor within the identified cavity. This discrepancy in radial extent between the (sub-)mm-sized dust and molecular gas may be indicative of dust evolution during the disk lifetime: as dust grains grow, they become decoupled from the gas, feel a headwind from the slightly sub-Keplerian gas, and move inwards to conserve angular momentum, a process termed {\em radial drift} \citep[see, e.g.,][]{whipple72,weidenschilling77}. This has been seen in several other disks imaged at (sub-)mm wavelengths at relatively high spatial resolution ($\lesssim$0\farcs5), including TW~Hya \citep{andrews12,andrews16,hogerheijde16}, LkCa~15 \citep{isella12}, HD~163296 \citep{isella09,degregoriomonsalvo13}, and HD~100546 \citep{pineda14,walsh14}. Sharply truncated dust disks are predicted by dust evolution models which simulate radial drift coupled with viscous gas drag \citep{birnstiel14}. \citet{birnstiel14} predict that the radius of (sub-)mm dust disks can decrease to values as low as 1/4--1/3 that of the gaseous disk by $10^{6}$ years. Such ``sharp'' outer edges are found to form quickly during early stages in the disk lifetime ($\sim10^{5}$~year) and can persist to late stages ($\sim10^{6}$~year) if the drift becomes ``self-limited,'' i.e., as dust is lost to the star, the dust-to-gas mass ratio decreases, and the maximum achievable particle size reduces \citep{birnstiel14}. HD~97048 is considered a rather young source, with an estimated age of $\approx2-3$~Myr \citep{vandenancker98,lagage06,doering07,martin-zaidi09}. The ALMA data presented here suggest a ratio for the radius of (sub-)mm-sized dust grains to that of the molecular gas of $\lesssim0.5$, if we take the radial extent of the continuum and CO line emission at face value (see the discussion in Sect.~\ref{diskradius}). This is slightly larger than that predicted by the dust evolution models at $\sim10^{6}$~year \citep{birnstiel14}. The presence of the inner cavity in the large dust grains in HD~97048 is indicative that some physical mechanism is in operation which is impeding radial drift and thus maintaining the population of large dust grains out to several hundred~au. \citet{quanz12} do not discuss any evidence of gaps and substructure in the small grain populations in existing PDI images of HD~97048. If confirmed, this likely rules out photoevaporation as the origin of the cavity in the larger dust grains; however, \citet{vanderplas09} do infer a cavity in the CO gas within the innermost 11~au using high-spectral-resolution vibrational line emission. That [OI] emission has been detected in the inner region \citep[$0.8-20$~au,][]{acke06}, further supports the idea that CO gas is photodissociated by the strong far-UV flux from the star on small scales. Alternative theories include the presence of a planet or planetary system inside the cavity which creates a pressure gradient in the gas and traps the dust in a ring-like structure external to the location of the planet(s) \citep[see, e.g.,][]{pinilla12b}. The extracted intensity profile for HD~97048 also shows the presence of rings (at $\approx50$, 150, and 300~au) with associated gaps (at $\approx100$ and 250~au). If such substructure were caused by forming planets or companions {\em within} the protoplanetary disk, then this would also help to maintain a population of large dust grains out to several hundred au and increase the ratio of the radii of the (sub-)mm-sized dust and molecular gas disks relative to that predicted by models which do not include the influence of planets. A recent reanalysis of ALMA Cycle 0 continuum emission from the disk around TW~Hya \citep{hogerheijde16} predicted the presence of one or more unseen embedded planets to explain the radial extent of (sub-)mm-sized dust grains; recent high (0\farcs3) to very high (0\farcs02) angular-resolution images of continuum emission from TW Hya confirm the presence of multiple rings and gaps which could be carved by the postulated unseen embedded planets \citep{andrews16,nomura16,tsukagoshi16}. \subsection{HD~97048 versus HD~100546: both planet-hosting disks?} HD~97048 and HD~100546 are both disk-hosting stars with a very similar spectral type. Multiple dust rings have been observed in the disk around HD~100546 with ALMA \citep{walsh14,pinilla15}, attributed to the presence of two massive companions: one orbiting within the cavity \citep[$<10$~au, e.g.,][]{acke06,brittain14,currie15} and one, likely very young object, directly imaged at $\approx50$~au \citep{currie14,currie15,quanz15}. The extracted intensity profile for HD~97048 also shows evidence of substructure with peaks in emission at $\approx50$, 150, and 300~au and gaps in emission at $\approx100$ and 250~au. The cavity size for HD~97048 as determined from these data is $\approx25$~au which corresponds to the innermost radius of the FWHM of the innermost peak in emission (see Figure~\ref{figure6}). We note here that the high signal-to-noise of the data ($\sim 1000$) coupled with data analysis conducted in the visibility domain allows the extraction of substructure from the interferometric data on size scales which are smoothed over significantly in the resulting images. In contrast with HD~100546, no observational evidence of a massive inner companion around HD~97048 yet exists, either in the disk continuum observations, or in the disk gas observations. However, elemental abundance measurements in the photosphere of HD~97048 hint that the gas-to-dust ratio of accreting material is large ($750\pm250$) compared with the canonical interstellar medium value of $\sim100$ \citep{acke04,kama15}. \citet{kama15} hypothesize that this is a potential indirect determination of the presence of unseen inner planets/companions in Group I disks: the presence of planets in an inner gap or cavity impedes the flow of dust through the gaps whereas gas can flow freely, thereby locally increasing the gas-to-dust ratio in the accreting zone. The presence of an inner companion with an appreciable mass within the dust cavity will also excite spiral density waves which may be observable with future high-spatial observations at optical wavelengths. Assuming that a single planet is responsible for clearing the inner cavity and trapping the (sub-)mm-sized dust beyond a radius of 25~au, one can estimate the mass and location of the planet \citep[see, e.g, ][]{crida06,dodsonrobinson11,pinilla12b}. \citet{pinilla12b} find that the dust accumulates at $\approx7 r_{H}$ for planets with masses of $1-3 M_\mathrm{Jup}$ and at $\approx10 r_\mathrm{H}$ for planets with mass $> 5M_\mathrm{Jup}$, where $r_\mathrm{H}$ is the Hill radius ($r_\mathrm{H} = r_p(M_p/3M_\star)^{1/3}$, where $r_p$ and $M_p$ are the radial location and mass of the planet and $M_\star$ is the stellar mass). In Figure~\ref{figure13}, the light-green shaded region highlights the range of possible planet orbital locations and masses for a sub-mm dust ring located at radii between 25 and 50~au (as suggested in the ALMA data). Also plotted are the radial ranges of the optically thick inner disk \citep[shaded gray region, $0.3-2.5$~au,][]{maaskant13}, the cavity size inferred from the ALMA data (light-green striped region, $25-50$~au, this work), and that inferred from the mid-IR imaging data \citep[dark-blue striped region, $30-38$~au,][]{maaskant13}. The dark-blue shaded region highlights the range of values when a cavity size of $34\pm4$~au is assumed (as inferred from the mid-IR data). The range of planet locations and masses is set by the size of the gap carved in the gas \citep[$\approx 5 r_H$,][]{dodsonrobinson11} and the maximum dust gap size seen in the dust evolution models \citep[$\approx 10 r_H$,][]{pinilla12b}. This simple parameterization shows that a $1~M_\mathrm{Jup}$ planet is able to create a dust trap at the required radius if it is located at $29\pm12$~au for a dust trap located between 25 and 50~au and $25\pm5$~au for a dust trap at $34\pm4$~au. However, such a low-mass planet is not able to open up a gap as wide as the full cavity inferred from both the ALMA data and the mid-IR imaging. It is more likely that a single planet has a mass $>10~M_\mathrm{Jup}$, with planet/companion masses on the order of $100~M_\mathrm{Jup}$ also possible. To date, no massive companion has been inferred from existing data on HD~97048, and no constraints on the mass of an as-yet unseen planet have been been determined \citep[see, e.g.,][]{acke06,vanderplas09,brittain14}. That the cavity inferred in HD~97048 is larger than that for HD~100546, despite the lack of constraints on the presence or otherwise of a massive inner companion, is also intriguing. Very recently, \citet{dong15} presented results from 2D hydrodynamical models in which they show that multiple (four) low-mass ($1-2M_\mathrm{Jup}$) planets can open gaps on the order of a few tens of au in the mm-sized dust grains. HD~97048 is yet another disk for which the dust emission at (sub-)mm wavelengths shows evidence of axisymmetric ring-like structures, here on spatial scales of around tens of au \citep{walsh14,alma15,andrews16,nomura16,zhang16}. We predict that this substructure will be clearly evident in images of HD~97048 at higher spatial resolution ($\approx10-20$~au, see Figure~\ref{figure14}). There remains much debate in the literature on the origin of such axisymmetric substructure in protoplanetary disks including gaps and dust traps carved by forming planets \citep[see, e.g.,][]{dipierro15,pinilla15,rosotti16}, a change in dust opacity properties at the positions of snow lines \citep[e.g.,][]{banzatti15,zhang15,guidi16,okuzumi16}, and toroidal dust traps created by hydrodynamic or magnetohydrodynamic effects \citep[see, e.g.,][]{pinilla12a,lorenaguilar15,ruge16}. To distinguish between each of the scenarios requires observations of dust emission at multiple and well-separated frequencies to determine the radial dust size and density distribution (and dust opacity index) along with emission from optically thin gas tracers to determine the gas surface density. Planets will create deep gaps in the gas surface density as well as influencing the dust \citep[note that this is dependent on the planet mass, see e.g.,][]{rosotti16}, toroidal instabilities will create much shallower features in the gas surface density, and opacity changes at snow lines will affect only the dust emission and will have no effect on the gas. We note that the ringed substructure seen here has very recently been confirmed in scattered light images of HD~97048 taken with VLT/SPHERE \citep{ginski16}. An initial (and shallow) comparison of the data sets shows remarkable coincidence between the positions of the (sub-)mm peaks and gaps and those seen in scattered light. That such structure is seen in both small ($\approx~\mu$m-sized) dust grains in the disk atmosphere and large ($\approx$~mm-sized) dust grains in the disk midplane points toward a (proto)planetary system origin; however, further data, particularly to better constrain the gas structure, are needed for confirmation. Since this paper has been accepted for publication, ALMA Cycle 2 data of HD~97048, for which longer baseline data were available and imaged with a $uv$ clip ($> 160 k\lambda$), resulted in a beam of $0\farcs48 \times 0\farcs26$ (18\degree) and resolved the inner dust cavity ($< 40-46$ au) and the bright dust ring at $\approx150$~au \citep{vanderplas16}. \begin{figure}[!h] \centering \includegraphics[width=0.5\textwidth]{./planet_tracks.pdf} \caption{Plot showing the range of possible planet locations and masses for a single planet responsible for creating a dust trap between 25 and 50~au (light-green shaded area), and at $34\pm4$~au (dark-blue-shaded area). Also shown are the size of the optically thick inner dust disk \citep[gray box,][]{maaskant13}, the cavity radius inferred from the ALMA data (light-green striped region, this work), and that inferred from mid-IR imaging \citep[dark-blue striped region,][]{maaskant13}.} \label{figure13} \end{figure} \begin{figure}[!h] \includegraphics[width=0.5\textwidth]{./convolved_intensity_50au.eps} \includegraphics[width=0.5\textwidth]{./convolved_intensity_20au.eps} \caption{Normalized flux density using the best-fit intensity profile convolved with a 50~au beam (left-hand panel) and a 20~au beam (right-hand panel).} \label{figure14} \end{figure} \subsection{HD~97048: an extremely flared disk?} The CO $J=3$-2 data show that the molecular disk around HD~97048 extends to at least the same radius as the small dust grains imaged in scattered light \citep{doering07}, confirming that the scattered light does arise from a large circumstellar disk as opposed to a remnant circumstellar envelope. The CO data suffer from missing emission at and around the source velocity which could be due to foreground absorption and/or spatial filtering of background cloud emission; however, the data quality is sufficient to constrain the source velocity ($V_\mathrm{LSRK}$) to $4.65\pm0.075$~km~s$^{-1}$. As discussed in Sect.~\ref{hd97048}, there exist limited data on emission from the outer regions of the molecular disk: most data are spatially and spectrally unresolved and probe the inner warm/hot surface layers \citep{meeus12,meeus13,fedele13,vanderwiel14}. \citet{hales14} report the detection of CO $J=3$-2 towards HD~97048 with APEX but identify the emission as arising from background material, because of an apparent offset in source velocity. Correcting the source velocity to 4.65~km~s$^{-1}$ in figure~18 in \citet{hales14} shows that the emission does indeed arise from a disk in Keplerian rotation, albeit with a red wing which is significantly stronger than the blue wing and also with significant missing emission at the source velocity (as also seen in this work). The data also show that the CO $J=3$-2 emission arises from a layer with an opening angle (relative to the midplane) of $\approx30\degree-40\degree$. This translates to a ratio, $z/r\approx0.6-0.8$ (where $z$ is the geometrical height and $r$ is the disk radius), identifying HD~97048 as one of the most flared HAeBe disks known to date in $^{12}$CO line emission, which is consistent with its SED classification as a (flared) Group I protoplanetary disk \citep{meeus01,acke10}. In comparison, \citet{rosenfeld13} derive an opening angle of $\approx15\degree$ for the $^{12}$CO-emitting surface in the disk around HD~163296 \citep[similar to that also derived by][]{degregoriomonsalvo13}. This corresponds to $z/r\approx0.3$ and is also consistent with its SED classification as a (flat) Group II protoplanetary disk \citep{meeus01}. Interestingly, \citet{bruderer12} reproduce the single-dish observations toward the Group~I disk, HD~100546, with a model which suggests that the CO $J=3$-2 emission arises from a layer deeper than that for HD~163296, at $z/r\approx0.2$. \citet{lagage06} fit an intensity profile to the $8.6~\mu$m PAH emission from HD~97048 using a power law, $z=(z_0/r_0)r^{\beta}$, where $z_0$ is the geometrical height of the emitting layer at $r_0$ and $\beta$ is the power-law index \citep[see also][]{chiang01}. They derive the following parameters: $z_0=51.3$~au and $\beta=1.26$, for a fixed $z_0=135$~au. This translates to $z/r=1.7$ at 300~au (roughly the spatial extent of the $8.6~\mu$m PAH emission), confirming that the CO J=3-2 emission arises from layer deeper in the disk than the far-UV-excited PAHs, as would be expected. Note that the PAH emission and CO $J=3$-2 line emission both arise from layers in the disk at geometrical heights several times that of the expected gas pressure scale height. \subsection{Future outlook} The data presented here are the first to spatially resolve the large disk around HD~97048 at (sub-)mm wavelengths. The data confirm the presence of a cavity in the large dust grains; however, higher spatial resolution data, ideally at multiple frequencies, are required to determine the depth of the gap in both dust and molecular gas and thus constrain the physical mechanism which is halting radial drift in the inner disk. High spatial resolution data will also shed light on the possible presence of a multiple planetary system composed of $\approx$ Jupiter-sized planets and will also confirm the multiple rings seen in the continuum emission in the current data. Finally, spatially resolved observations of multiple transitions of optically thin CO isotopologues will help to further constrain the location of the flared CO-emitting layer, and allow derivation of the temperature structure of the molecular gas. Quantification of the gas surface density will also allow further distinction between the various theories for the creation of the ring-like structures seen in the dust emission. | 16 | 9 | 1609.02011 |
1609 | 1609.07896_arXiv.txt | { M87 is one of the nearest radio galaxies with a central SMBH and a prominent relativistic jet. Due to its close distance to the observer and the large SMBH mass, the source is one of the best laboratories to obtain strong observational constraints on the theoretical models for the formation and evolution of the AGN jets. In this article, we present preliminary results from our ongoing observational study about the innermost jet of M87 at an ultra-high resolution of $\sim50\mu$as achieved by the Global Millimeter-VLBI Array (GMVA). The data obtained between 2004 and 2015 clearly show limb-brightened jets at extreme resolution and sensitivity. Our preliminary analysis reveals that the innermost jet expands in an edge-brightened cone structure (parabolic shape) but with the jet expansion profile slightly different from the outer regions of the jet. Brightness temperatures of the VLBI core obtained from cm- to mm-wavelengths show a systematic evolution, which can be interpreted as the evolution as a function of distance from the BH. We also adopt an alternative imaging algorithm, BSMEM, to test reliable imaging at higher angular resolution than provided by the standard CLEAN method (i.e. super-resolution). A demonstration with a VLBA 7mm example data set shows consistent results with a near-in-time 3mm VLBI image. Application of the method to the 2009 GMVA data yields an image with remarkable fine-scale structures that have been never imaged before. We present a brief interpretation of the complexity in the structure. } \keyword{ Galaxies: active -- Galaxies: jets -- Galaxies: individual (M87) -- Techniques: interferometric -- Techniques: image processing } \begin{document} | The giant elliptical galaxy M87 is one of the nearest radio galaxies with a distance $d$ of only $16.7 \pm 0.5$ Mpc \cite{dist} and a large Super-Massive Black Hole (SMBH) mass $M_{\rm BH}$ of $(3-6.6) \times10^{9}M_{\odot}$ (\cite{mass},\cite{mass2}), although the exact mass is still controversial. Owing to its proximity and the large BH mass, 1 milli-arcsecond (mas) on the sky plane corresponds only to $128R_{\rm sch}$ when we adopt $M_{\rm BH}=6.6\times10^{9}M_{\odot}$ (\cite{mass}), where $R_{\rm sch}$ is the Schwarzschild radius. This is the best spatial resolution achievable for any extragalactic jet-hosting system. Furthermore the M87 jet is transversely resolved and exhibits a limb-brightened structure, which contains a lot of information about the physical conditions (e.g. \cite{asada12_coll}, \cite{hsa_3mm}). The close distance, the high black hole mass, and the uniquely limb-brightened structure therefore make M87 one of the best sources to answer fundamental questions about the formation and evolution of relativistic outflows in BH-accretion systems. Accordingly, observing the inner-most region of the M87 jet with mm-VLBI is crucial to provide a connection between theoretical models and actual observations. Very Long Baseline Interferometry (VLBI) has been so far the only way that allows us to zoom in close enough to the central engine. Especially, the Global Millimeter-VLBI Array (GMVA) at 3mm resolves the innermost jet at a $50 \mu$as scale, which corresponds to a spatial scale of only $\sim 6R_{\rm sch}$. This resolution allows us to probe the geometry of the outflow near the jet launching region. Furthermore the 3mm global VLBI observations also complement the ongoing 1mm VLBI experiments (with Event Horizon Telescope; EHT), that have even higher resolving power and aim to resolve event-horizon-scale structures, but still lack high-fidelity imaging capability (e.g. \cite{eht_sci}). In this article we present preliminary results from our ongoing 3mm-VLBI observations of M87 with the GMVA. A general description of our data is given in Section 2. In Section 3 we describe the data analysis and possible interpretations. Then we give the conclusions in Section 4. | In this article we have presented our ongoing study on the innermost jet of M87 with mm-VLBI and a demonstration of super-resolution imaging using the BSMEM algorithm. Preliminary results from the analysis of our 3mm VLBI data showed a well defined, transversely expanding jet profile, significant evolution in the brightness temperature, and highest resolution image of the jet base that has ever been made. We are now analyzing details of the individual epochs along with long-term structural changes in an effort to better constrain the physical conditions. Further super-resolution imaging of the rest of the 3mm VLBI data with BSMEM is also in progress to help this goal. \vspace{6pt} | 16 | 9 | 1609.07896 |
1609 | 1609.05893_arXiv.txt | {We study the evolution of the metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized ``Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the $\delta M $ formalism for calculating the evolution of the linear tensor perturbations in anisotropic inflation models in {\it almost} the same way that the so-called $\delta N$ formula is applied to the super-horizon dynamics of the curvature perturbations. Similar to her twin formula, $\delta N$, this new method can substantially reduce the amount of calculations related to the evolution of tensor modes. However, it is not as general as $\delta N$; it is a "perturbative" formula and solves the shear only to linear order. In other words, it is restricted to weak shear limit.} | Cosmological perturbation theory is a pivotal step in finding the predictions of the early Universe models, e.g. inflation \cite{Inflation}. The success of inflationary paradigm can be addressed from three aspects, even if the linear order perturbations are considered. At the classical level, inflating background can tell us why has the early Universe been so flat and homogeneous. At the quantum level, inflaton vacuum fluctuations (the only thing that could be survived from inflation era) can explain the presence of very tiny initial inhomogeneities, as indispensable primordial seeds for large scale structure of the Universe. At the statistical point of view (the only way for checking theory by data in cosmology) simplest inflationary models predict nearly scale invariant, adiabatic and almost Gaussian statistics almost consistent with recent observations \cite{PLANCK}. Nevertheless, it is crucially important to go beyond the linear order to be able to discriminate among different cosmological models. For example, any tiny detection of the non-Gaussianity would rule out all the slow-roll inflationary models, since they predict non-Gaussianity of the order of the slow-roll parameters \cite{Maldacena:2002vr}. Amid different ways for studying Einstein equations, approximation methods are important tools in cosmology and specially in the analysis of the observed anisotropies of the Cosmic Microwave Background (CMB). A powerful approximation technique used in cosmology is the so called ``long-wavelength approximation scheme'' or ``gradient expansion''. This method has been brought up and studied by many authors in cosmology previously \cite{Lifshitz:1963ps,Belinsky:1982pk,Tomita:1972,Tomita:1975kj,Salopek:1990jq,Comer:1994np,Deruelle:1994iz,GE:2,Sasaki:1998ug,GE:III,Tanaka}. The ``quasi-isotropic'' solution of Lifshitz and Khalatnikov \cite{Lifshitz:1963ps,Belinsky:1982pk} who studied the general behavior of the space-time near the cosmological singularity, the ``anti-Newtonian'' solution of Tomita \cite{Tomita:1972,Tomita:1975kj} who investigated cosmological perturbations on super-horizon scale, and the ``long-wavelength iteration scheme'' of Salopek and Bond \cite{Salopek:1990jq} all had set up on the same approximation idea, gradient expansion. Comer et al. studied the solution of Einstein equation expanded by spatial gradient via adopting the synchronous time slice \cite{Comer:1994np}. Nonlinear perturbations near the cosmological singularity was also investigated by Deruelle and Langlois \cite{Deruelle:1994iz}. The gradient expansion scheme employs an expansion in powers of gradient operator. It is practically built upon neglecting the inhomogeneities varying over scales smaller than a smoothing scale. When the expansion is applied to the Einstein equations of motion, as the expansion parameter goes to zero, one gets a universe locally similar to the background. One important advantage of using this method is the fact that nonlinear characteristics of the dynamical equations governing the remaining perturbations are preserved. Furthermore, at first order in parameter expansion, the perturbed dynamic equations have exactly the same form as homogeneous background. In other words, the information about perturbed fields can be found through a simple ``rescaling of the background'' fields up to higher order corrections in gradient expansion. This is the essence of the so-called ``Separate Universe'' approach \cite{Wands:2000dp,Sasaki:1998ug,Lyth:2003im}. With regards to this point, $\delta N$ formalism has been developed for computing super-horizon curvature perturbations in the context of inflationary paradigm \cite{Wands:2000dp,DeltaN:II,Naruko:2012fe,Sugiyama:2012tj}. In this formalism, the long-wavelength scalar perturbations show resemblance to (; so can be absorbed in) the integrated expansion of the background geometry evaluated from some initial time $t_0$, when all relevant fields are sufficiently outside their horizon up to the end of inflation. In this work, we proceed to more general background geometries for the purpose of promoting the separate universe picture and to accommodate gravitational perturbations. Therefore, for this purpose, we follow the steps below: \begin{itemize} \item[$\bullet$] First of all we study the long-wavelength perturbations in Bianchi background in the 3+1, Arnowitt-Deser-Misner (ADM) decomposition \cite{Arnowitt:1962hi,Gourgoulhon_book}. This decomposition has been found to be more appropriate for the purpose of applying gradient expansion \cite{Sugiyama:2012tj,Lyth:2004gb,Tanaka,Naruko:2012fe,Comer:1996du}. \item[$\bullet$] Secondly, we apply the gradient expansion to the equations of motion and come up with a set of equations valid up to the first order of the gradient expansion. This set of equations are the pillars of the separate universe picture of the anisotropic inflation models. \item[$\bullet$] For the third step, we exhibit the consistent separate universe picture of the cosmological perturbation theory in the Bianchi background. We show how the similarity of the long wavelength perturbations to a background parameters changes the associated parameters. Particularly we demonstrate that the perturbed equations can be recast exactly in the form of background equations. From theoretical point of view without concerning about possible applications, we study the evolution of the super-horizon metric perturbations in a Bianchi background. \item[$\bullet$] The main step of this work is a generalization of the the so-called $\delta N$ formula, $\delta N = \psi$, to a relation applicable for tensorial degrees of freedom. Inspired by the idea of the $\delta N$ formalism, one finds that the answer lies within the geometrical shear, $\sigma_{i j}$ and anisotropic expansion of the perturbed Bianchi metric. The simplest models with non-vanishing shear are Bianchi space-times; this is essentially the reason of studying cosmological perturbation theory in anisotropic models. To put it another way, the Bianchi background is the simplest extension of the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) background capable of incorporating or admitting the tensor perturbations. \item[$\bullet$] Finally, we identify the (scalar and tensor) observable perturbations in the homogeneous background. Accordingly we exhibit the $\delta M$ formalism as a prescription for calculating non-trivial, linear tensorial modes in the similar fashion as the so called $\delta N$ formalism. \end{itemize} For the sake of clarity, we emphasize that the constant long-wavelength gravitational waves are not physical degrees of freedom in the sense that it can be gauged away at leading order in gradient expansion via a large gauge transformation likewise adiabatic scalar perturbations \cite{Bordin:2016ruc,Maldacena:2002vr}. This implies that the only meaningful tensor perturbations on super-horizon scales are the ``would-be" decaying modes which are the ones which correspond to the shear in an anisotropic universe. These modes always fade away in an expanding background unless they are sourced by non-negligible anisotropic stress. In other words, a FLRW space-time does not have any appropriate background dynamical quantity supporting the tensorial degrees of freedom. However, in the anisotropic inflation models \cite{Aniso:Inflation,Pitrou:2008gk,Pereira:2007yy,Gumrukcuoglu:2007bx}, usually the anisotropic stress show up and as a result there are a bunch of non-trivial interactions between scalar and tensor modes. This actually makes the calculations of the correlation function a cumbersome project. By employing the proposed $\delta M$ method, the calculations of the correlation functions of the perturbations astonishingly shrink. Several authors have studied the behavior of gravitational waves in Bianchi-{\it I} universe \cite{GW:BIANCHI,Gumrukcuoglu:2007bx}. It is worth emphasizing that this work is \textit{not} aimed to study the problem of the gravitational waves in a general Bianchi-{\it I} background. Instead, we exploit the Bianchi background as a suitable choice capable of incorporating tensorial degrees of freedom. This suggests that the long-wavelength tensor perturbations would redefine the integrated shear of the background metric. In standard model of cosmology, the geometry of our Universe, smoothed on large enough scales, is well described by a spatially expanding FLRW solution. The extra degrees of freedom that control the expansion may trigger a phase of anisotropic expansion (through an anisotropic tensor). The current CMB observations show that the deviation from isotropy is small \cite{Saadeh:2016sak,PLANCK}. Therefore, in a gradient expansion approach, only the ``weak shear limit'' \cite{Pontzen:2010eg,Pitrou:2015iya} in which the induced shear is small can provide good insight into the super-horizon perturbations. In order to implement this approximation, we employ a two parameter perturbation scheme \cite{Bruni:2002sma,Sopuerta:2003rg} in which besides perturbations the geometrical shear is also considered as an extra perturbative degree. Therefore in deriving the $\delta M$ formula, two expansion schemes are applied; gradient expansion, for studying long-wavelength perturbations and weak shear limit, as a limit in which the modes evolve independently and reach to FLRW Universe. A decomposition of spatial fields into scalar, vector and tensor modes lets us to identify two independent degrees of freedom which geometrically match gravitational waves ( or vector perturbations) in FLRW space-times. Our result confirms the independent evolution of these modes at linear order. In this paper we adopt a $(-+++)$ metric signature, and will use the Greek letters $(\mu,\nu,\alpha,\beta,...= 0,1,2,3)$ and the middle Latin indices $(i,j,k,l,...=1,2,3)$ to denote space-time indices (base space) and its spatial part, respectively. The rest of the paper is organized as follows: In Sec. \ref{BackGeo} we study an anisotropic model of cosmology which provides a homogeneous set up in separate universe approach. In Sec. \ref{PerGeo} we study the non-linearly perturbed Einstein equations and apply the gradient expansion to those equations. In Sec. \ref{SU}, we show that separate universe picture holds in an anisotropic universe, and discuss about the dynamics of super-horizon perturbations in FLRW limit in Sec. \ref{FlRW_limit}. A short review of $\delta N$ formula is followed by the derivation of $\delta M$ formula in Sec. \ref{deltaNM}. The conclusion and discussions are given in Sec. \ref{discussions}. Some technical details are relegated into Appendices. | \label{discussions} We have applied the gradient expansion to the evolution equations of perturbations in an anisotropic (Bianchi-{\it I}) universe. As a consequence, we came up with a consistent separate universe approach to the perturbation theory. This has been demonstrated by the form invariance of Einstein constraint and dynamical equations at long-wavelength perturbation limit. In particular, we have found how the different classes of perturbations can be absorbed in homogeneous but anisotropic background parameters. To be specific, the background geometrical shear can be redefined in such a way that absorb long-wavelength vector and tensor perturbations comparable to what the scale factor does for scalar perturbation in the standard $\delta N$ formalism. We have obtained a powerful tool called $\delta M$ formalism which relates the amplitude of spatial perturbations to the change in $M_{ij}$, which in turn is defined to measure the homogeneous changes in Euclidean metric. In particular, the change in the amplitude of a gravitational wave, with comoving wavelength $k^{-1}$, going from one time slice to another is related to variations of integrated shear $M_{\lambda}=\int_{t_0}^{t} \sigma_{\lambda} \, \mathrm{d}t'$ calculated between two initial flat and final uniform density hyper-surfaces. It should be mentioned that in contrast to its analogous $\delta N$ formula, this relation is restricted to {\it linear} perturbations on FLRW universe. Even though we started the analysis non-perturbatively, we neglected $\sigma^2$ terms in the right hand side of equations (\ref{sigma_Vert}-\ref{sigma_lambda}); this will inevitably result in a perturbative formula, which is restricted to weak shear limit. Apart from the theoretical interest in studying long-wavelength perturbations in the anisotropic background, the proposed $\delta M$ formalism is a powerful method for studying the perturbations in anisotropic inflationary models \cite{Aniso:Inflation}. Specifically, it is a tool for dealing non-trivial interaction between scalar and tensor modes showing up in anisotropic inflationary models. In a word, employing the $\delta M$ formalism substantially simplifies the calculations of the correlation functions of the linear perturbations in these models. We believe that inclusion of first order anisotropy corrections to FLRW model is accurate enough for the analysis of the observational features of an anisotropic model on the CMB. The likelihood of detecting anisotropies with higher accuracy motivates the development of different methods of computing the perturbations. | 16 | 9 | 1609.05893 |
1609 | 1609.07544_arXiv.txt | We present H{\sc i} observations of four giant low surface brightness (GLSB) galaxies UGC~1378, UGC~1922, UGC~4422 and UM~163 using the Giant Meterwave Radio Telescope (GMRT). We include H{\sc i} results on UGC~2936, UGC~6614 and Malin~2 from literature. H{\sc i} is detected from all the galaxies and the extent is roughly twice the optical size; in UM 163, H{\sc i} is detected along a broken disk encircling the optical galaxy. We combine our results with those in literature to further understand these systems. The main results are the following: (1) The peak H{\sc i} surface densities in GLSB galaxies are several times $10^{21}$ cm$^{-2}$. The H{\sc i} mass is between $0.3-4 \times 10^{10}$ M$_\odot$, dynamical mass ranges from a few times $10^{11}$ M$_\odot$ to a few times $10^{12}$ M$_\odot$. (2) The rotation curves of GLSB galaxies are flat to the outermost measured point with rotation velocities of the seven GLSB galaxies being between 225 and 432 km s$^{-1}$. (3) Recent star formation traced by near-ultraviolet emission in five GLSB galaxies in our sample appears to be located in rings around the galaxy centre. We suggest that this could be due to a stochastic burst of star formation at one location in the galaxy being propagated along a ring over a rotation period. (4) The H{\sc i} is correlated with recent star formation in five of the seven GLSB galaxies. | In the last few decades low surface brightness (LSB) galaxies have received a lot of attention. LSB galaxies are defined as disk galaxies with a central surface brightness $\mu_{B}$ $<$ 23 mag arcsec$^{-2}$ \citep{impey97} which distinguishes them from the high surface brightness (HSB) galaxies. The low surface brightness galaxies are missing in earlier optical catalogues due to sky brightness causing a strong bias against detection of objects with central surface brightness fainter than the Freeman value ($\mu_{B}$ $=$ 21.65 $\pm$ 0.35 mag arcsec$^{-2}$). The accidental discovery of the first giant LSB (GLSB) galaxy Malin-1 by \cite{bothun87} demonstrates that there might be a large number of galaxies with similar properties (\citealt{bothun90}; \citealt{sprayberry93}; \citealt{sprayberry95}; \citealt{neil2000}). Many LSB galaxies have since been identified in deep and large field survey (\citealt{schombert88}; \citealt{schombert92}; \citealt{davies94}; \citealt{schwartzenberg95}; \citealt{sprayberry95}). Surveys have revealed some LSB galaxies having disk scale lengths comparable to the Milky Way. LSB galaxies are host to a range of stellar populations, covering the entire range of H-R diagram (\citealt{zackrisson05}; \citealt{zhong08}). LSB galaxies show deficit in molecular gas \citep{schombert90} which has been detected in only a few galaxies (\citealt{das06}; \citealt{oneil00}; \citealt{das10}). LSB galaxies are very rich in H{\sc i} but have low gas surface densities and slowly rising H{\sc i} rotation curves. They have higher M$_{H{\sc I}}$/L$_{B}$ ratios as compared to HSB galaxies \citep{deblok96a}. The H{\sc i} masses are close to 10$^{9}$ M$_{\odot}$ \citep{deblok96b} and the H{\sc i} surface density are usually close to the critical density for star formation (\citealt{kennicutt89}; \citealt{vanderhulst93}; \citealt{deblok96a}). LSB galaxies comprise a significant fraction of the spiral galaxy population \citep{mcgaugh95} and hence form an important class of spiral galaxies. Some LSB spirals have been found to be larger than the normal galaxy - these have been referred to as Giant LSB galaxies. In a H{\sc i} survey of 116 LSB galaxies, selected from the \cite{bothun85} catalog, carried out using the Arecibo and Nancay telescopes, 81 LSB galaxies were detected out of which 38 have H{\sc i} mass $>10^{10}$ M$_\odot$ \citep{oneil04}. These 38 galaxies might be GLSB galaxies but this survey was done with a large telescope beam; interferometric observations are required to distinguish GLSB galaxies from HSB galaxies in the field of view. On the basis of the study to date, it is clear that LSB galaxies have some different properties compared to the HSB galaxies possibly due to different evolutionary sequence. The galaxy evolution and its star formation history are strongly correlated with the environment in which the galaxy is evolving. The effect of the environment upon bright galaxies are well studied and there are noticeable variations in galaxy properties like morphology, color and magnitude. In the present paper, we take up H{\sc i} 21cm-line study of the sample of seven GLSB galaxies, UGC~1378, UGC~1922, UGC~4422, UM~163, UGC~2936, UGC~6614 and Malin~2. This sample has been studied in the radio continuum by us in an earlier paper, \cite{mishra15}. Here, we present H{\sc i} 21cm-line observations of the first four galaxies i. e. UGC~1378, UGC~1922, UGC~4422, UM~163 and employ the results on UGC~6614, Malin~2 from \cite{pickering97} and for UGC~2936 by \cite{pickering99}. We refer to the basic properties and the parameters of the galaxies of the entire sample as given in Table 1 of \cite{mishra15}. \begin{figure*} \vspace*{50pt} \subfigure[]{\includegraphics[height=7.0cm,angle=-90]{figure.1a.ps}} \subfigure[]{\includegraphics[height=7.0cm,angle=-90]{figure.1b.ps}} \subfigure[]{\includegraphics[height=7.0cm,angle=-90]{figure.1c.ps}} \subfigure[]{\includegraphics[height=7.0cm,angle=-90]{figure.1d.ps}} \caption{Global H{\sc i} emission profiles made from the low resolution maps: (a) {\bf UGC 1378}, (b) {\bf UGC 1922}, (c) {\bf UGC 4422} and (d) {\bf UM 163} showing the double-humped profile, characteristic of rotating disks.} \label{fig:figure.1} \end{figure*} \begin{table*} \centering \begin{minipage}{100mm} \caption{GMRT Observations} \begin{tabular}{@{}lllll@{}}\hline \hline \footnotetext[1] {Flux densities from SETJY} \footnotetext[2] {Flux densities and error from GETJY} \footnotetext[3] {These data were taken with the old hardware backend at GMRT} & UGC~1378 & UGC~1922 & UGC~4422 & UM~163 \\ \hline \hline Observing dates & 30-12-11 & 31-12-11 & 29-12-11 & 28-07-06 \\ Flux calibrator(s) & 3C~48 & 3C~48 & 3C~147, 3C~286 & 3C~48, 3C~286 \\ ~~Flux density(Jy)$^{a}$ & 16.08 & 16.41 & 22.27, 14.86 & 16.31, 14.96 \\ Phase calibrator & 0217+738 & 3C 48 & 0842+185 & 2225-049 \\ ~~Flux density(Jy)$^{b}$& 2.60$\pm$0.03&16.41$\pm$0.02 &1.16$\pm$0.01 & 7.53$\pm$0.15 \\ Central frequency (MHz) & 1397 & 1362 & 1392 & 1372 \\ Central velocity (kms$^{-1}$) & 2935 & 10894 & 4330 & 10022 \\ Bandwidth (MHz) & 16 & 16 & 16 & 04 \\ t$_{source}$ (hr) & 5.5 & 6.0 & 5.5 & 5.5 \\ No. of channels & 256 & 256 & 512 & 128 \\ Channel resolution (km s$^{-1}$) & 13.8 & 14.2 & 6.9 & 6.6 \\ Synthesized beam/ & $50^{\prime\prime}\times 50^{\prime\prime}$ & $45^{\prime\prime}\times 45^{\prime\prime}$ & $45^{\prime\prime}\times 45^{\prime\prime}$ & $45^{\prime\prime}\times 45^{\prime\prime}$\\ Ang resolution&$25^{\prime\prime}\times 25^{\prime\prime}$ & $30^{\prime\prime}\times 30^{\prime\prime}$ & $30^{\prime\prime}\times 30^{\prime\prime}$ & $32^{\prime\prime}\times 32^{\prime\prime}$ \\ &$15^{\prime\prime}\times 15^{\prime\prime}$ & $15^{\prime\prime}\times 15^{\prime\prime}$& $15^{\prime\prime}\times 15^{\prime\prime}$ & $20^{\prime\prime}\times 20^{\prime\prime}$ \\ RMS noise per channel & 1.5, 1.3, 1.0 & 1.7, 1.5, 1.1 & 2.4, 2.0, 1.5 & 1.1, 1.0, 0.8$^{c}$\\ at diff. res.(mJy/beam) & & & & \\ \hline \hline \end{tabular} \end{minipage} \label{tab:lsb_obser.hi} \end{table*} | \subsection{Rotation Curves of GLSB galaxies} We have estimated the rotation curves using the AIPS task GAL on the velocity field of the galaxies and determined their H{\sc i} centres, inclination, position angle and rotation velocity. The rotation curves are obtained using the tilted ring model \citep{begeman89}. The rotation curve fitting procedure involves using the observed velocity field to derive five galaxy properties namely dynamical centre (X,Y), systemic velocity (V$_{sys}$), position angle (PA), inclination (Inc) and rotation velocity (V$_{rot}$). The velocities were averaged in elliptical annuli of width 10$^{\prime\prime}$ . The centre, PA and the Inc estimated from H{\sc i} moment 0 map were taken as initial guesses. In the first iteration we kept all the parameters free. The inclination and centre was determined for each annulus and found to be more or less similar for all annuli for UGC~1378 and UGC~4422. In the next iteration, the inclination was fixed to the average value from the first iteration. The resulting rotation curves for UGC~1378 and UGC~4422 from this exercise are shown in Figure \ref{fig:figure.7}(a) and (c). The estimated rotation velocities are 282 and 254 km s$^{-1}$. We could not fit a rotation curve to the velocity field of UM 163. The rotation curves were derived using the mid-resolution $\sim$ ($25^{\prime\prime}\times 25^{\prime\prime}$) velocity fields. The details of the fit are listed in Table \ref{tab:lsb_hiresult}. The fitting for UGC~1922 was more involved. When all the parameters were kept free then we found that the inclination and PA showed variations with radial distance from the centre of the galaxy and the resulting rotation curve is shown by stars in Figure \ref{fig:figure.7}(b). The estimated rotation velocity is very large at $\sim$ 658$\pm$42. From this run of GAL, we estimated an average value for the inclination which was 32 degrees and PA of 132 degrees which were fixed in the next iteration of GAL. This resulted in a rotation curve shown by the filled circles in Figure \ref{fig:figure.7}(b) and a rotation velocity of 588$\pm$32 km s$^{-1}$. This is also large and not commonly observed. To further check this, we derived the inclination from the observed H{\sc i} ellipticity which was 51$\pm$2 degrees. We re-ran GAL by fixing the inclination to 51 degrees and the resulting rotation curve gave a rotation velocity of 432$\pm$12 km s$^{-1}$ as shown by the filled squares in Figure \ref{fig:figure.7}(b). Although this is also large, we believe that till further observations can throw more light on this intriguing galaxy, this is the conservative estimate of the rotation velocity of UGC~1922. We believe that the rotation curve of UGC~1922 can be confirmed or otherwise if a better estimate of the inclination of the galaxy can be obtained. As noted above, if the inclination of UGC~1922 is 32 degrees then its rotation velocity comes out to be 588 km s$^{-1}$ and if it is 51 degrees it is 432 km s$^{-1}$. Nevertheless, UGC~1922 appears to be among the fastest rotating galaxies, which to the best of our knowledge are UGC 12591 (506 km s$^{-1}$; \citealt{giovanelli86}) and NGC 1961 (402 km s$^{-1}$; \citealt{courtois15}; \citealt{haan08}) as reported earlier in the literature. It is obvious that such galaxies are rare. The position angle in all galaxies showed a slow variation of about $5^{\circ}$. The rotation curves do not show any drop at large radial distance from the centre. Similarly flat rotation curves at large radial distances are also noted in UGC~2936 \citep{pickering99}, UGC~6614 and Malin~2 \citep{pickering97}. Thus all the six GLSB galaxies out of the total seven studied in radio continuum by \cite{mishra15} show a flat rotation curve to the outermost observed point - i.e. to a radial extent of about 42 kpc (220$^{\prime\prime}$), 51 kpc (70$^{\prime\prime}$) and 28 kpc (90$^{\prime\prime}$) in UGC~1378, UGC~1922 and UGC~4422 whereas the radial extent of the optical disk is 20 kpc, 44 kpc and 15 kpc respectively. Similarly a flat rotation curve is observed upto radial distances of 35 kpc in UGC 2936 \citep{pickering99}, 50 kpc in UGC~6614 and 80 kpc in Malin~2 \citep{pickering97} whereas the optical radial extent for these galaxies are 19 kpc, 21 kpc and 41 kpc. Thus, the H{\sc i} disk is roughly twice the size of the optical disk for all the GLSB galaxies and the rotation curve is flat over the detectable H{\sc i} disk. Flat rotation curves have also been observed in LSB spirals - five LSB spirals in \cite{vanderhulst93}, 19 LSB spirals in \cite{deblok96a} although we note that one of the curves appears to show a drop and eight LSB galaxies in \cite{pizzella05}. The rotation velocities of the GLSB galaxies range from 225 to 432 km s$^{-1}$. The dynamical mass estimated for the three galaxies observed here ranges from few times $10^{11}$ to few times $10^{12}$ M$_\odot$. Thus except for UM~163 where H{\sc i} is detected in a disk around the central bar of the galaxy and the line width is only about 110 km s$^{-1}$, all the GLSB galaxies are fast rotators. However we note that the LSB galaxies have lower rotation velocities between 30 and 120 km s$^{-1}$ \citep{deblok96a}. LSB galaxies seldom seem to show a drop in the rotation velocity in the outer regions as seen in the sample of six GLSB galaxies; including the sample of Pickering et al. (1997, 1999) and 24 LSB galaxies (\citealt{vanderhulst93}; \citealt{deblok96b}). One of the galaxies from the \cite{deblok96b} seems to suggest a slight fall in the rotation velocities in the outer parts. A few HSB galaxies have been found to show a drop in the rotation velocities in the outer parts of the galaxies \citep[e.g][]{honma97}. Whether this difference is significant needs to be investigated using a larger sample of LSB galaxies. \subsection{H{\sc i} properties} The peak H{\sc i} surface density estimated from the maps made with a beamsize between 25$^{\prime \prime}$ and 30$^{\prime \prime}$ is lowest at $3.3\times10^{19}$ cm$^{-2}$ for UM~163 and highest at $3.2\times10^{21}$ cm$^{-2}$ for UGC~1378. For the maps with a resolution close to 15$^{\prime \prime}$, we detect gas with peak surface densities of $7.5\times10^{21}$ cm$^{-2}$ in the centre of UGC~1378. Thus, such high surface density H{\sc i} clumps are likely to be present in LSB galaxies explaining the observed star formation. The peak surface densities detected in the six galaxies observed by \cite{vanderhulst93} at a resolution of about 25$^{\prime \prime}$ was between $5-10 \times 10^{20}$ cm$^{-2}$. For a resolution of about 22$^{\prime \prime}$, \cite{pickering99} recorded a peak surface density ranging from $4.7-8.5 \times 10^{20}$ cm$^{-2}$ for the three GLSB galaxies that they studied. All the four galaxies studied here show a hole in the centre of the H{\sc i} distribution where an active nucleus is present. The H{\sc i} is likely absorbed against this. The H{\sc i} appears to avoid the central bar as seen in both UGC~1378 and UM~163. This has been noted in HSB galaxies also. All the galaxies show some lopsidedness as seen in their integrated spectra. All the GLSB galaxies have large H{\sc i} content. The H{\sc i} mass estimated for the seven galaxies lies in the range $\sim 0.3-4\times10^{10}$ M$_{\odot}$. The H{\sc i} distribution and star formation are well-correlated for two (UGC~1922, UGC~4422) of the four galaxies studied here whereas no correlation is seen for one of the galaxies UM~163. We note that UGC~1922, UGC~4422 and UM~163 have been catalogued as members of the Low Density Contrast Extended (LDCE) groups ({\citealt{crook07}; \citealt{crook08}). UGC~4422 is also classified as member of a Lyon Galaxy Group (LGG; \citealt{garcia93}). UGC~1378 is not classified as a group member. It can be assumed that the tidal interactions in the LDCE groups are weaker than in the LGG groups. The velocity field of the four galaxies presented here appear undisturbed. The velocity field of UGC~2936 \citep{pickering99} also appears undisturbed. The kinematics of UGC~6614, which has a low inclination, shows a peculiar behaviour with the major axis of the H{\sc i} distribution being perpendicular to kinematical major axis and could be a result of a warp \citep{vanderhulst93}. We could not find information on the detailed velocity field of Malin~2. However the undistorted velocity fields of at least five galaxies support the picture of these galaxies being subjected to none or only weak tidal forces since they evolve in under-dense regions \citep{bothun93}. As pointed out by \cite{vanderhulst93} from their study of six LSB galaxies in H{\sc i}, these galaxies have normal H{\sc i} mass to light ratios and also the fraction of dynamical mass in H{\sc i}; the differences are that LSB galaxies have more extended H{\sc i} and average surface densities which are about a factor of 2 lower than in HSB spirals. LSB disks have a mean younger age compared to HSB disks as deduced from their bluish colours in the optical \citep{vanderhulst93}. The H{\sc i} mass of these LSB galaxies ($\sim 10^9$ M$_\odot$; \citealt{vanderhulst93}) is an order of magnitude lower than that of the seven GLSB galaxies ($\sim 10^{10}$ M$_\odot$) discussed here. The fraction of dynamical mass in H{\sc i} is comparable at $1-4 \%$ in GLSB galaxies and $2-9\%$ for most LSB galaxies (\citealt{vanderhulst93}; \citealt{deblok96a}). LSB galaxies follow the same Tully-Fisher (TF) relation as HSB galaxies (\citealt{zwaan95}; \citealt{mcgaugh00}; \citealt{mcgaugh05}). This implies that LSB galaxies compared to HSB galaxies of similar properties have M/L and sizes larger by factor of two. We find that out of the sample of seven GLSB galaxies discussed here six follow the TF relation. UM~163 is an outlier whose B band magnitude is similar to the other LSB galaxies but the line width is narrow. This is the galaxy in which the H{\sc i} is observed in a broken disk. \subsection{Star formation along rings} The star formation traced by the NUV and FUV emission from GALEX in the GLSB galaxies appears to indicate that recent star formation is along rings or broken rings. Several rings of NUV emission are seen in the GLSB galaxies - UGC~6614 and Malin~2 (see Figure 6, 7 in \citealt{mishra15}). Enhanced NUV emission along broken rings are visible in UGC~1922 (Figure \ref{fig:figure.3}(c)), UGC~4422 (Figure \ref{fig:figure.4}(c)) and UM~163 (Figure \ref{fig:figure.5}(c)). Out of the total seven GLSB galaxies studied by \cite{mishra15}, five galaxies show star formation along rings around the centre of the galaxies. We also examined a sample of 16 LSB galaxies whose GALEX results are presented in \cite{boissier08} to search for star formation along rings. However except for a couple of possible cases, we did not find this to be a common occurrence in that sample. This difference in GLSB galaxies and LSB galaxies could possibly indicate lack of sufficiently dense H{\sc i} gas in the smaller LSB galaxies as compared to GLSB galaxies or sensitivity of the NUV observations. While such rings have been commonly observed in both atomic gas and in optical emission in tidally interacting galaxies, their presence in relatively isolated galaxies argues for a modified explanation. One possible explanation we suggest is that a burst of star formation is spread along a ring over a rotation period for relatively isolated galaxies. The trigger of this star formation could be a weak tidal interaction or a random local perturbation in sufficiently dense neutral gas. In isolated galaxies, the perturbation would travel along the ring over a rotation period and if sufficiently dense gas is available along the ring, can trigger star formation along it. Three such rings of star formation have been seen in the isolated spiral NGC~7217 \citep{verdes95}. Since such star forming rings are also observed in galaxies subject to tidal interactions, there should be a way to distinguish between these two scenarios. If the galaxy was subject to strong tidal interactions, it can lead to gas condensing to higher densities at several locations. Subsequently star formation can be simultaneously triggered at several high density locations in a galaxy including along a ring. In this scenario, the age of the stars in the entire ring will be similar. On the other hand, in the isolated galaxy/GLSB scenario, since the differential rotation is held responsible for propagating the star formation along a ring, the stellar ages are likely to show a gradient along the ring to within a rotation period. It would be interesting to verify this by studying the stellar ages along rings in tidally interacting galaxies and in GLSB galaxies. \begin{figure} \subfigure[]{\includegraphics[height=8.5cm,angle=-90]{figure.7a.ps}} \subfigure[]{\includegraphics[height=8.5cm,angle=-90]{figure.7b.ps}} \subfigure[]{\includegraphics[height=8.5cm,angle=-90]{figure.7c.ps}} \caption{Rotation curves: {\bf (a)} UGC 1378, {\bf (b)} UGC 1922 and {\bf (c)} UGC 4422. The filled circles represent variation in V$_{rot}$ with fixed inclination and centre and stars represent variation in V$_{rot}$ with all free parameters. In UGC 1922 filled squares show V$_{rot}$ with fixed inclination (derived from ellipticity of H{\sc i} and centre.} \label{fig:figure.7} \end{figure} | 16 | 9 | 1609.07544 |
1609 | 1609.06859_arXiv.txt | We compare radio profile widths of young, energetic $\gamma$-ray-detected and non-$\gamma$-ray-detected pulsars. We find that the latter typically have wider radio profiles, with the boundary between the two samples exhibiting a dependence on the rate of rotational energy loss. We also find that within the sample of $\gamma$-ray-detected pulsars, radio profile width is correlated with both the separation of the main $\gamma$-ray peaks and the presence of narrow $\gamma$-ray components. These findings lead us to propose that these pulsars form a single population where the main factors determining $\gamma$ ray detectability are the rate of rotational energy loss and the proximity of the line of sight to the rotation axis. The expected magnetic inclination angle distribution will be different for radio pulsars with and without detectable $\gamma$ rays, naturally leading to the observed differences. Our results also suggest that the geometry of existing radio and outer-magnetosphere $\gamma$-ray emission models are at least qualitatively realistic, implying that information about the viewing geometry can be extracted from profile properties of pulsars. | \label{SectIntro} The emission of rotationally-powered pulsars is believed to ultimately be derived from the loss of rotational energy as the neutron star's rotational period increases. Observationally it is found that the pulsars which emit significant amounts of high energy (i.e. $\gamma$ ray) emission have high rates of rotational energy loss, $\dot{E}$ (e.g., \citealt{sgc+08a}). However, there are also many high-$\dot{E}$ pulsars which are as yet undetected in $\gamma$ rays \citep{aaa+13}. This raises the question of what physical factors other than $\dot{E}$ and distance may determine whether a pulsar is detectable in $\gamma$ rays. \cite{rwj15a} analysed the radio emission of a sample of $\gamma$-ray-detected (\grdd) energetic (high $\dot{E}$) pulsars detected by the \emph{Fermi} satellite's Large Area Telescope which are included in the Parkes telescope's \emph{Fermi} timing programme \citep{wjm+10}. Subsequent analysis of the magnetic inclination angle ($\alpha$) distribution \citep{rwj15b} revealed two alternative possibilities: that pulsars are born with a specific non-random $\alpha$ distribution, or that the radio beamsize depends on $\alpha$. In this paper we compare the radio profile morphologies of high-$\dot{E}$ \grd pulsars with a sample of similarly energetic, but non-$\gamma$-ray-detected (\ngdd), pulsars with the aim of investigating what, apart from $\dot{E}$, affects $\gamma$-ray detectability. \begin{figure} \centering \includegraphics[height=\hsize,angle=0]{BeamGeometryVectorGraphic.ps} \caption{\label{FigBeamGeometry}Geometry of the emission regions, using the outer gap model for the $\gamma$-ray emission as an example. The production of the $\gamma$-ray emission takes place along the pair-production front (ppf; bold lines), the position of which relative to the last open field lines is parameterised by $w$ (see $\S$~\ref{SectLargeAlpha}). The $\gamma$ rays are beamed along tangents to the ppf, resulting in a beam of emission associated with each pole (light and dark grey shaded regions for small and large $w$ respectively). The radio emission is generated on open field lines close to the stellar surface and is centred on the magnetic axis (${\bf \mu}$). The rotation axis (${\bf \Omega}$), the light cylinder (at which the corotation velocity equals the speed of light) and the null-charge surface \citep{gj69} are also shown. } \end{figure} In this paper we assume the same generic radio emission geometry as \cite{rwj15a,rwj15b}. The model (illustrated in Fig.~\ref{FigBeamGeometry}) takes the radio emission to originate close to the neutron star and to be confined to the open field line region, those magnetic dipole field lines that penetrate the light cylinder. This results in a conal beam, the opening angle of which will be sensitive to the altitude at which the emission is generated. There is some uncertainty regarding the precise structure of the radio emission within the beam. Various models have been proposed, such as the `core-cone' model \citep{ran90,ran93}, or the `patchy beam' model \citep{lm88}. However, the generic radio beam model used here is largely insensitive to the structure of the beam provided the emission extends approximately to the edges of the open field line region. An alternative to these circular beams is the `fan-beam' model \citep{mic87a,drd10,wpz+14}, in which the emission is generated in elongated subbeams arranged in a spoke-like pattern centred at the magnetic axis. We will discuss this model separately where its predictions differ from those of the core-cone and patchy beam models. In contrast to the radio emission, the $\gamma$ rays are believed to be generated at much higher (and over a much more extended range of) altitudes, close to the light cylinder (see Fig.~\ref{FigBeamGeometry}). In all currently favoured $\gamma$-ray emission models, for example the outer gap or two-pole caustic models \citep{chr86a, dr03}, the $\gamma$ rays are generated along a pair-production front (ppf) between some inner limit, such as the null-charge surface \citep{gj69}, and some outer limit. The photons are emitted along tangents to the field lines similarly to the radio emission. Detailed modelling of high-altitude $\gamma$-ray emission has been undertaken by, for example, \cite{wrw+09} and \cite{rw10}, which we use as a basis for our considerations of the $\gamma$-ray beam shape. In this paper we presume the ppf to have zero thickness for simplicity. We also note that some models of the magnetosphere (e.g., the force-free modelling of \citealt{spi06} and \citealt{cra14}) suggest that the $\gamma$-ray beam has a more complicated shape than described here. However, we believe that neither of these assumptions will make a significant qualitative difference to the conclusions of this paper. The structure of this paper is as follows: In $\S$~\ref{SectResults} we define the \grd and \ngd samples and present correlations of the radio profile width with both $\gamma$-ray detectability and $\gamma$-ray light curve morphology. In $\S$~\ref{SectPossibleExplanations} we discuss possible physical explanations for these correlations. In $\S$~\ref{SectWidthVersusEdot} we discuss the observed dependence of the radio profile width on $\dot{E}$ and consider the implications. Finally, in $\S$~\ref{SectConclusions} we summarise our findings and draw some conclusions about pulsar emission geometry. | 16 | 9 | 1609.06859 |
|
1609 | 1609.06318_arXiv.txt | Soft gravitons produced by the expansion of de Sitter can be viewed as the Nambu-Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime. We explicitly construct the associated charges, and show that acting with the charges on the vacuum creates a new state equivalent to a change in the local coordinates induced by the soft graviton. While the effect remains unobservable within the domain of a single observer where the symmetry is unbroken, this change is physical when comparing different asymptotic observers, or between a transformed and un-transformed initial state, consistent with the scale-dependent statistical anisotropies previously derived using semiclassical relations. We then compute the overlap, $\langle0| 0'\rangle$, between the unperturbed de Sitter vacuum $|0\rangle$, and the state $| 0'\rangle$ obtained by acting $\mathcal{N}$ times with the charge. We show that when $\mathcal{N}\to M_p^2/H^2$ this overlap receives order one corrections and $\langle0| 0'\rangle\to 0$, which corresponds to an infrared perturbative breakdown after a time $t_{dS} \sim M_p^2/H^3$ has elapsed, consistent with earlier arguments in the literature arguing for a perturbative breakdown on this timescale. We also discuss the generalization to inflation, and rederive the 3-point and one-loop consistency relations. | Three of the most important problems in fundamental cosmology, the quantum origin of the universe, the cosmological constant problem, and the black hole information paradox, are all believed to have to do with infrared problems in quantum gravity. Assuming that there cannot be three unrelated infrared problems of quantum gravity indicates that they must somehow be related. Thus, in addition to trying to tackle these problems individually, it makes sense to also explore their interconnection, in the hope that identifying their commonalities will shed light on what their resolutions might be. A possible connection between the cosmological constant problem and the quantum origin of the universe has been known for some time. In the landscape, the smallness of the observed cosmological constant appears as a consequence of environmental selection \cite{Weinberg:1988cp}, and eternal inflation is commonly invoked as a means of populating all false vacua and thereby realizing all possible universes\cite{hep-th/0302219, hep-th/0105097,Bousso:2000xa,Linde:1983gd}. A concrete connection between black holes and eternal inflation is so far missing, although there are many similarities between Schwarzschild and de Sitter spacetimes. On a heuristic level, they both have horizons, and there are indications of a perturbative breakdown due to the presence of infrared modes in both spacetimes\footnote{It has been suggested that this could also provide a different connection between inflation and the cosmological constant problem \cite{na-h,Polyakov:1982ug, 0709.2899, 0912.5503, Tsamis:1992sx, Tsamis:1994ca,0708.2004}, although this is not the focus of the present work.} on parametrically similar timescales \cite{hep-th/0703116, 0911.3395, 1005.1056, 1104.0002, 1109.1000, Dvali:2013eja,Dvali:2014gua}. Below we review some of the similarities between the two situations, and then in the main part of the paper, we elaborate on the connection by reanalyzing the infrared issues in de Sitter from the point of view of asymptotic symmetries, which have recently been argued to be important for the understanding of the black hole evaporation process. \subsection{Black Hole Evaporation} In order to make the connection between the dynamics of black hole evaporation and the infrared issues in de Sitter space as tight as possible, let us first review the black hole information paradox very briefly with a focus on the connection to the cosmological context. Perturbatively, one can view Hawking radiation as pairs of quantum particles created at the horizon, where one escapes to infinity and the other falls into the black hole. The escaping quantum particle is entangled with the interior quantum particle, and its entanglement entropy is \beq S_{ent} = \ln 2~. \eeq In the course of its evolution, the black hole emits $\mathcal{N}_{bh}\sim (M/M_{p})^2$ such quanta before it reaches a size of order $l_{p}$, where $M$ is the mass of the black hole, and $M_p$ and $l_p$ are the Planck mass and length respectively. At the end of its evolution it will then have an entanglement entropy \beq S_{ent} \gtrsim \mathcal{N}_{bh} \ln 2~. \eeq At this point, if the Planck sized black hole evaporates away, the external emitted particles will make up the full quantum system with an entropy given by $S_{ent}$, indicating that they are in a mixed state, despite the fact that they might have been created initially in a pure state, violating unitarity. On the other hand, a Planck sized remnant with arbitrarily high degeneracy would be a strange quantum state, with unacceptable physical consequences \cite{Giddings:1994qt,Susskind:1995da}. Assuming that both of these possibilities are unacceptable, it has been argued that the apparent paradox is a consequence of trusting perturbation theory beyond its limits of validity. Different scenarios for a non-perturbative description of black hole evaporation have been put forward (some recent examples are \cite{Mathur:2003hj,1108.2015,Giddings:2012gc,1306.0533}). In order to shed light on the problem from a different angle, it might be useful to understand the exact source of the perturbative breakdown within perturbation theory. Since we know that the black hole entropy is proportional to the horizon area, and given the symmetry between the entanglement entropy of interior versus exterior modes, it is clear that the growth in entanglement entropy has to halt when it reaches the size of the total black hole entropy and becomes decreasing as the black hole starts to evaporate, on the timescale given by the black hole half-life. At this point, information needs to start coming out of the black hole, as first argued by Page \cite{hep-th/9306083}, and the simple perturbative arguments above are therefore expected to break down. The entanglement entropy computed by the simple perturbative argument above exceeds the black hole entropy when the amount of emitted quanta is \beq \mathcal{N}_{bh} \sim S_{BH}/\ln 2 = (M/M_{p})^2/(2\ln 2)~, \eeq which is the amount of quanta emitted on the timescale of the black hole evaporation time. Using similar reasoning, it was argued in \cite{na-h} and \cite{hep-th/0703116} that we should expect a breakdown in the perturbative description of black hole evaporation on this time scale, \beq \label{tev} t_{ev} \sim R_{S} S_{BH} \sim M^3/M_p^4, \eeq when order $\mathcal{N}_{bh}$ quanta have been emitted. How would one diagnose such a perturbative breakdown? In perturbation theory, the evolution of the time-dependent perturbed quantum state of the black hole, $\left|\psi(t)\right>$ in the interacting picture, has the form \beq \left|\psi(t)\right> = T \exp\left[-i \int^t H_I(t)\right]\left|\psi\right>_0~, \eeq where $H_I$ is the interacting Hamiltonian, and $\left|\psi(t)\right>_0$ is the unperturbed state. Perturbation theory remains valid as long as the matrix elements of $\int^t H_I(t)$ remain small. It was therefore argued by Giddings in \cite{hep-th/0703116}, that if in a nice-slicing of the black hole background (where curvature is everywhere small on the spatial slices), we have \beq\label{olbh} \langle\psi(t)|\psi\rangle_0\rightarrow0 \eeq for some time $t$, then it would be an indicator that perturbation theory has broken down, and we might therefore expect this to happen on the time scale of $t_{ev}$. \subsection{Quantum Gravity in de Sitter} In de Sitter space information is not necessarily permanently lost when it recedes behind an observer's horizon. If the cosmological constant decays, as happens at the end of inflation, information will in fact reenter the horizon, and thus there is no reason to believe that the Gibbons-Hawking radiation in de Sitter space will carry information. Therefore, there is no exact analogue of the black hole information paradox in de Sitter, although the two space-times do have many similarities. An important point is that we also can associate entropy with the de Sitter horizon \beq S_{dS} = \frac{1}{4}\frac{A_{dS}}{G}= \frac{1}{8} R_{ds}^2 M_p^2~, \eeq where $R_{dS}$ is the de Sitter radius. It has been argued that this implies that the number of fundamental degrees of freedom in de Sitter, $N$, is finite \cite{hep-th/0007146} and given by $S_{dS} = \ln N$. As noted in \cite{hep-th/0106109}, this assumption clearly implies that perturbation theory must break down in de Sitter in the IR, since an infinite de Sitter space has an infinite Hilbert space in perturbation theory. During every e-fold of de Sitter expansion, $\Delta t = 1/H$, two soft (super-horizon) gravitons are emitted at the de Sitter horizon. That means that after $N_e= \ln a(t)= Ht$ e-folds of expansion, roughly $\mathcal{N}_{dS} \sim N_e$ independent quanta are emitted making up $2^{\mathcal{N}_{dS}}$ possible microstates, which exceeds $N$ when \beq \mathcal{N}_{dS} \sim S_{dS}/\ln(2)~. \eeq In fact it was argued in \cite{hep-th/0306070}, that the entropy of the emitted modes, $S_e$, can be viewed as the entanglement entropy of de Sitter, and it was further shown\footnote{See appendix A of \cite{hep-th/0306070}.} that the change in entropy per e-fold satisfies $dS_e/dN_e \gtrsim 1$, which when integrated gives \cite{hep-th/0306070,hep-th/0703116,ArkaniHamed:2007ky}, \beq S_{e} \gtrsim N_e ~. \eeq From this point of view it seems reasonable to expect that perturbation theory will break down when $S_{e} \gtrsim S_{dS}$, which happens on a time scale dimensionally equivalent to the black hole evaporation time in de Sitter \beq\label{tds} t_{dS} \sim R_{dS} S_{dS} \sim H^{-3}M_p^2\,. \eeq It is interesting that it has also been argued how a finite Hilbert space could emerge in de Sitter. If we consider the overlap between initial states and final states, $\langle i | f \rangle$, in de Sitter as a kind of ``meta observable" (similar to the ``q-observable" discussed in \cite{1104.0002}), then the matrix defined by $\langle i | f \rangle$ has infinite dimension. But it is argued that it can have finite rank if we mod out by all initial states $\langle i |$ for which $\langle i |f\rangle=0$ \cite{hep-th/0106109} (for instance by simply setting them to 0). Combining the thoughts above regarding a possible perturbative breakdown in de Sitter due to the finiteness of the Hilbert space, and the idea that finiteness shows up as $\langle i |f\rangle\to0$, it is interesting to compute an overlap like $\langle i | f \rangle$ in a finite part of de Sitter with a finite number of degrees of freedom and then see that $\langle i | f \rangle \to 0$ as we remove the IR cutoff and include more and more degrees of freedom. We then expect that once $\mathcal{N}_{dS} \sim M_p^2/H^2$ quanta has been emitted, perturbation theory will break down as a consequence of \beq \label{olds} \langle i | f \rangle \to 0 \eeq at this point. Note that this is happens naturally after the time $t_{dS}$, showing the equivalence of these two different diagnostics for the perturbative breakdown. \subsection{Diagnosing the Perturbative IR Breakdown} Given the striking similarities between the black hole information paradox and the entropy problem of de Sitter in (\ref{tev}) and (\ref{tds}), one might speculate that they are fundamentally two sides of the same problem, and we might try to diagnose the exact source of the perturbative breakdown by looking at the non-linear evolution of perturbations on timescales given by $t\sim R S$. De Sitter space enjoys many more symmetries than black holes, and therefore progress is easier here. This was done in a series of papers \cite{1005.1056,1104.0002,1109.1000}. In \cite{1005.1056}, a perturbative breakdown in cosmological correlation functions was identified on this exact timescale. In \cite{1104.0002} the physical meaning of such a perturbative breakdown was examined more carefully, and the relation between local observers and global observers was discussed. Finally in \cite{1109.1000}, the authors used the fluctuations of geodesics as a gauge invariant measure of the geometry in de Sitter, and showed that these become large, signalling breakdown of a perturbative description of the geometry, consistent with perturbative instability of de Sitter space. In fact, perturbative instability of de Sitter space and the related question of growth of perturbations during inflation has been widely discussed from many other and very different perspectives in the literature \cite{Myhrvold:1983hu,Ford:1984hs,Antoniadis:1986sb,Mukhanov:1996ak,Danielsson:2003wb,hep-th/0612138,astro-ph/0604488,0707.3377,hep-th/0605244,Garriga:2007zk,0801.1845,Urakawa:2009my,0912.2734,0912.1608,1005.3551,1008.1271,Urakawa:2010it,Byrnes:2010yc,1006.0035,1010.5327,1002.4214,1107.2712,1105.0418,Gerstenlauer:2011ti,Tanaka:2012wi,1302.3262,1302.6365,Tsamis:2013cka,1305.5705,1306.3846,1310.0367,1303.1068,Tanaka:2013caa,Frob:2014zka,1504.00894,1604.00390,1608.07237, Nacir:2016fzi, Finelli:2008zg, Finelli:2010sh}. Another point is the similarity between the expressions (\ref{olbh}) and (\ref{olds}). In the present work we will be interested in a more precise calculation of this type of overlap. We will focus on a horizon sized region, and consider the vacuum for this causal patch. As mentioned earlier, two soft gravitons will be emitted for every e-fold $\Delta t = 1/H$. Locally (within a single causal patch), the soft graviton mode can be gauged away and corresponds to a global symmetry. However, when comparing several causal patches (asymptotic observers), or between a transformed and un-transformed initial state, the symmetry is spontaneously broken, and the effect becomes physical. As noted in \cite{hep-th/0106109}, in pure de-Sitter the initial and final state should match up exactly, but when perturbations are considered that is no longer the case. Soft gravitons are then the Nambu-Goldstone bosons of the spontaneously broken symmetry. If we denote the charge generating the symmetry transformation by $Q$, then the state corresponding to adding a soft graviton to the vacuum can be obtained as $ e^{iQ}|0\rangle$. We will then show that if the state $|0'\rangle$ is obtained by acting on $|0\rangle$ with $e^{iQ}$ consecutively $\mathcal{N}$ times, corresponding to adding $\mathcal{N}$ soft gravitons, then we have for $\mathcal{N}\to \mathcal{N}_{dS}$ \beq \langle 0| 0'\rangle\to 0~. \eeq Locally, adding a soft mode corresponds to a gauge transformation that does not fall off at infinity, and $Q$ is the conserved charge associated with the large gauge transformation. However, the symmetry is spontaneously broken between different local patches, and when comparing different observers, it becomes apparent that the transformation acts nontrivially on the state. This feature is also central to recent claims relating to the black hole information paradox \cite{1601.00921}. However, on small scales, where the symmetry remains unbroken, its effect is undetectable, which is at the core of the critique in \cite{1607.03120} (See also \cite{Averin:2016hhm} of another related discussion). \subsection{Asymptotic Symmetries} It has been known for over five decades that how you view the world depends on what type of person you are \cite{Bondi:1962px,Sachs:1962wk}. By this, we are referring to the fact that the presence of a background metric breaks the full diffeomorphism symmetry of gravitational theories down to a much smaller subgroup, but which subgroup depends not only on the (asymptotic form of the) metric, but also on the asymptotic surface used to take the limiting behavior. There has recently been a resurgence in this line of thinking in the case of Minkowski space \cite{1401.7026,1411.5745}, which, according to an observer at spacelike infinity possesses Poincar\'e invariance. An observer at lightlike infinity, however, notices an enhanced symmetry group, referred to as the BvdBMS group, which also includes angle-dependent retardations known as supertranslations. This has been argued to have physical consequences, as real observers more closely resemble those at lightlike infinity in many instances. In this paper, we focus on the parallel of this discussion in de Sitter and inflationary spacetimes, which resemble de Sitter space up to slow roll corrections. Though a spatial observer would conclude that de Sitter space possesses a $SO(4,1)$ analogue of Poincar\'e symmetry, a lightlike observer would notice the symmetry group to be greatly enhanced to that of diffeomorphisms on the future boundary. These are the analogue of BvdBMS supertranslations noticed in \cite{1009.4730}, and, similar to the flat space case, possess physical consequences for observable quantities. The relation between spatial diffeomorphisms and inflationary consistency relations was noted extensively in \cite{1203.6351,1304.5527} (see also f.ex. \cite{1203.4595,Ghosh:2014kba,Kundu:2014gxa,McFadden:2014nta}), where the Noether charge was used to derive many of the previously known consistency relations, along with several novel extensions. Our work extends their analysis in three ways: first, we make the connection between the Noether charge and the Brown York charge explicit, which is important because the Brown York counterterms must be included in order to regulate both the ultraviolet and infrared divergences in the charge. Second, we single out the explicit charge from the infinite class of possible charges that corresponds to the presence of a long mode, and show that using this one recovers not only tree level consistency conditions, but also loop corrections. Lastly, we use the charge to encapsulate how the state evolves, and compute the overlap between states at two different times. From this calculation we see explicitly that the overlap is driven to zero at the Page time of de Sitter space, signalling the breakdown of the effective description. \subsection{Interpretation of the Brown-York charge} The charge allows us to encapsulate the change in the state in terms of an operator acting on the vacuum. It encodes the fact that the emission of a long wavelength graviton shifts the background coordinates by a spatial diffeomorphism. In this paper we will mostly concern ourselves with the spin two part of the graviton $\g_{ij}$ rather than the scalar $\zeta$, for two reasons: during inflation, more scalar perturbations are emitted than tensors, making the timescale for tensors to become nonperturbative the lower bound on the full system. Secondly, in de Sitter space the scalar mode is a pure gauge, so the tensor contribution will be the only one that is relevant in both cases. This is illustrated in Fig \ref{jitter} below. \begin{centering} \begin{figure*}[h] \centering \includegraphics[width=16cm]{jitter.pdf} \caption{A realization of the change in coordinates induced by the successive emission of long wavelength gravitons. Circles here represent the horizon for an observer situated at their center. Here $P_\gamma=.01$, so that each graviton emitted induces a $1\%$ deformation of the initial circles. After the Page time, which in this case corresponds to 100 e-folds, the circles are so skewed that the initial global description of the system is no longer applicable. To each local observer, however, this evolution is unobservable.} \label{jitter} \end{figure*} \end{centering} To a global observer, capable of keeping track of the entire inflated volume, the local horizons seem to jitter about stochastically, with an amplitude set by the power spectrum of gravitons. Every local observer, however, will be blissfully unaware of the extreme squeezing they experience, as they are still in a locally flat spatial region. Any ruler they could use to measure the amount of stretching in one direction relative to another would similarly adjust its length as they reorient it in various directions. As the evolution of the system approaches the Page time, however, each circle is deformed by an $\mathcal{O}(1)$ amount, a simple consequence of the Brownian nature of the deformation process. Once this happens the description in terms of the original coordinates becomes exceedingly poor. This is consistent with scale-dependent statistical anisotropies \cite{1104.0002}, the idea that de Sitter looks very anisotropic on large scales, but as one zooms in on smaller and smaller scales, it looks more and more isotropic. \subsection{Gravitational Memory} This effect is analogous to the phenomenon of gravitational memory \cite{zelpo}, where a passing gravitational wave induces a permanent displacement of neighboring freefalling observers. Many connections between the memory effect and the asymptotic symmetry group have recently been elucidated, and our work extends this connection to the inflationary setting. In flat spacetime, where the asymptotic symmetry group is the BvdBMS group, it was shown in \cite{1411.5745} that the passage of a gravitational wave out of a system induces a transformation that exactly corresponds to the gravitational memory effect that would be observed by a pair of idealized observers. This provides a physical interpretation of the transformation by relating it to a measureable quantity that may soon be observable with LIGO \cite{1605.01415}, LISA \cite{1003.3486}, and pulsar timing arrays \cite{1410.3323}. This was subsequently generalized to decelerating FLRW spacetimes in \cite{1602.02653} where it was found that because waves travelling in an expanding space have a contribution that lags behind the light cone, a readily measureable deviation from the flat space is induced. This was extended to accelerating spacetimes and de Sitter space in \cite{1509.01296,1603.00151,1606.04894}, where it was shown that the memory effect is actually enhanced by a redshift factor over the flat space case. A very insightful exposition of the relation between memory and the ASG is outlined in \cite{1507.02584}, which considers a network of superconductors arranged in a sphere surrounding a charge that subsequently escapes to infinity. The setup is arranged in such a way that the presence of the super conductors breaks the symmetry of the ground state. Since superconductors directly measure the vector potential, this induces a phase in the detectors that to each looks like a pure gauge transformation. However, when comparing the phases of the different detectors across the entire sphere it becomes clear that a physical event has taken place, as illustrated in Fig. \ref{suss}. This makes the connection with our setup most explicitly, as in the inflationary case the passage of a long wavelength graviton out of the system induces a change in the metric that to any one observer is pure gauge, but when comparing across many different observers becomes nontrivial as illustrated in Fig. \ref{pepsi}. The difference in our scenario is that while it is relatively easy to do the global comparison for charges in flat space, in the inflationary case the presence of horizons prevents any comparison between two observers from ever taking place. \begin{centering} \begin{figure*}[h] \centering \includegraphics[angle=-90,width=10cm]{memory.pdf} \caption{An illustration of the memory effect. As charges pass through the sphere, individual superconducting measurement devices register the induced vector potential as a pure gradient. However, comparison across a network of detectors would allow to reconstruct the amount of charge that has left the system.} \label{suss} \end{figure*} \end{centering} \subsection{Outline} The paper is organized as follows: In section \ref{2} we show how to construct the charge for a given long mode, and deal with various subtleties needed in its interpretation. Section \ref{3} is devoted to using the charge to compute the overlap between states at two different times, which we show goes to zero after a Page time. Section \ref{4} reproduces both the Maldacena consistency relation and the one loop correction to the two point function using our formalism, illustrating its utility. We conclude in a discussion section, and leave various technical details to the appendices. | In this paper we have demonstrated that the presence of a long mode, which is normally treated as a shift in the coordinates of all quantities to be evaluated, can equally well be thought of as changing the quantum state of the system. We found the unique shift associated with a particular long wavelength mode, and explicitly showed that calculations in this new state reproduce standard results quite readily. Furthermore, having this method of calculation in our arsenal allowed us to address aspects of the evolution of accelerating spacetimes that were somewhat inaccessible or ambiguous until now. Namely, we showed that the state changes by an order one factor after a Page time has elapsed even in de Sitter, verifying the findings of \cite{1005.1056,1104.0002,1109.1000}. Let us stress that this breakdown is in our standard method of description of the system, as someone who has arranged the initial state in a flat coordinate system would notice the global system becoming incongruously warped on this timescale. Each observer naturally gauges away these effects locally, and so this does not signify a breakdown in physically observable quantities unless the observer has access to information from many patches (or for long enough times). This regime is unamenable to our standard perturbative description, but this does not imply that a more appropriate way of organizing the description of the evolution does not exist. We will return to this point in future work. | 16 | 9 | 1609.06318 |
1609 | 1609.03826_arXiv.txt | {We present a set of 87 RAVE stars with detected solar like oscillations, observed during Campaign 1 of the K2 mission (RAVE K2-C1 sample). This dataset provides a useful benchmark for testing the gravities provided in RAVE Data Release 4 (DR4), and is key for the calibration of the RAVE Data Release 5 (DR5). The RAVE survey collected medium-resolution spectra (R=7,500) centred in the Ca II triplet (8600\AA) wavelength interval, which although being very useful for determining radial velocity and metallicity, even at low SNR, is known be affected by a \logg-\teff~degeneracy. This degeneracy is the cause of the large spread in the RAVE DR4 gravities for giants. The understanding of the trends and offsets that affects RAVE atmospheric parameters, and in particular \logg, is a crucial step in obtaining not only improved abundance measurements, but also improved distances and ages. In the present work, we use two different pipelines, GAUFRE (Valentini et al. 2013) and Sp\_Ace (Boeche \& Grebel 2016), to determine atmospheric parameters and abundances by fixing \logg~to the seismic one. Our strategy ensures highly consistent values among all stellar parameters, leading to more accurate chemical abundances. A comparison of the chemical abundances obtained here with and without the use of seismic \logg~information has shown that an underestimated (overestimated) gravity leads to an underestimated (overestimated) elemental abundance (e.g. [Mg/H] is underestimated by $\sim$0.25 dex when the gravity is underestimated by 0.5 dex). We then perform a comparison between the seismic gravities and the spectroscopic gravities presented in the RAVE DR4 catalogue, extracting a calibration for \logg~of RAVE giants in the colour interval 0.50<($J - K_S$)<0.85. Finally, we show a comparison of the distances, temperatures, extinctions (and ages) derived here for our RAVE K2-C1 sample with those derived in RAVE DR4 and DR5. DR5 performs better than DR4 thanks to the seismic calibration, although discrepancies can still be important for objects for which the difference between DR4/DR5 and seismic gravities differ by more than $\sim$0.5~dex. The method illustrated in this work will be used for analysing RAVE targets present in the other K2 campaigns, in the framework of Galactic Archaeology investigations.} | Galactic spectroscopic surveys play a key role in modern astrophysics. They provide large datasets of stellar atmospheric parameters, velocities, distances and abundances, making it possible to test modern models of Galactic dynamical and chemical evolution. RAVE \citep{Steinmetz2006}, the Gaia-ESO survey (\citealp{Gilmore2012,Randich2013}), GALAH \citep{deSilva2015}, APOGEE \citep{Majewski2015}, SEGUE \citep{Yanny2009}, and LEGUE \citep{Zhao2012} are providing stellar catalogues of several hundred thousand objects. Red giant stars are among the primary targets of spectroscopic Galactic surveys, since they are intrinsically bright and common objects and they can be observed in several components of the Milky Way. In addition, they cover a wide range in age, making it possible to reconstruct the history of our Galaxy. However, the measure of stellar atmospheric parameters (effective temperature, \Teff, and surface gravity, \logg) of red giants via spectroscopic analysis is affected by known systematics (\citealp{Morel2012, Heiter2015}). In this work we focus on the \logg~determination. It is a well-known problem in the literature that the \logg~for late type stars suffers from systematics of the order of 0.2 dex (\citealp{Morel2012, Heiter2015, Takeda2015, Takeda2016}). The causes of these systematics are numerous, and not only the different techniques adopted by different authors (e.g., ionization balance, line profile fitting). Among the culprits there are also the adoption of inaccurate line parameters (such as oscillator strenght), the assumption of Local Thermodynamical Equilibrium (LTE) and 1-D conditions, degeneracies, and noisy or ill continuum-normalised spectra. As a consequence, an inaccurate measure of the gravity can lead to inaccurate estimates of \Teff, chemical abundances, distances and stellar age, since the determinations of these quantities are linked and ultimately dependent on the \logg~estimate. With the advent of asteroseismology and thanks to the valuable observations performed using the CoRoT \citep{Baglin2006} and \kepler \citep{Borucki2010} satellites, it has been possible to derive with high precision fundamental properties of Red Giant stars, such as mass (\M) and radius (\R) by using their global seismic properties \dnu (frequency separation) and \numax (frequency of maximum oscillation power). It was immediately realised that asteroseismology could have a large impact on galactic populations studies (Miglio et al. 2009, 2013). The surface gravity determined from stellar oscillations proved to be more precise and accurate than the one derived by using only spectroscopy (\citealp{Morel2012, Hekker2013, Heiter2015}). This seismic \logg, \logg$_{\rm seismo}$, can therefore be used as a powerful tool for testing the adopted spectroscopic pipelines and, eventually, calibrating them. In the recent years, pipelines that derive atmospheric parameters and abundances, implementing the seismic gravity, have been developed too, as GAUFRE \citep{Valentini2013}. Current spectroscopic surveys are largely taking advantage of the asteroseismic techniques, by including red giants for which asteroseismology is available, in their target list. CoRoT targets are now being observed by GES as calibrators \citep{Pancino2012}, \kepler targets have been used for calibrating APOGEE \citep{Pinsonneault2014} and LAMOST \citep{Wang2016} stellar surface gravities. The first results impacting Galactic Archeology using asteroseismology coupled with spectroscopy are now starting to appear (\citealp{Chiappini2015, Martig2015, Anders2016, Anders2016b}, Valentini et al. in prep.). The Kepler K2 mission (started on June 2014, Howell et al. 2014) is the continuation of the successful \kepler space mission. In 2014, the failure of two reaction wheels made the observations of the original field not feasible any more. For this reason a new mission, K2, was conceived, planning 80-day observational runs of a set of 14 fields located along the ecliptic plane. K2 is able to detect solar-like oscillations in field red giants \citep{Stello2015} and clusters \citep{Miglio2016}, and the light curves were of sufficient quality for measuring seismic parameters. The satellite is now observing several hundreds of RAVE targets, making it now possible to obtain asteroseismic informations also for RAVE red giants (\kepler, which field was in the north hemisphere, has no common target with RAVE, and the few RAVE targets in common with CoRoT have too noisy light curves). The RAVE survey, completed in 2013, is the precursor of larger spectroscopic surveys. It provided an unprecedented view of our Galaxy, observing $\sim$ 500,000 targets in the southern hemisphere. The DR4 catalogue \citep{Kordopatis2013}, provides stellar velocities and atmospheric parameters plus metallicities, with special attention devoted to the derivation of reliable metallicities using calibration datasets. The database also contains seven element abundances (Mg, Al, Si, Ca, Ti, Fe and Ni), derived using a dedicated abundances pipeline \citep{Boeche2011}. The estimated errors in abundance, based on a comparison with reference stars, depend on the element and signal to noise ratio (hereafter SNR). For SNR>40 they range from 0.17 dex for Mg, Al and Si to 0.3 dex for Ti and Ni. The error for Fe is estimated as 0.23 dex. DR4 also provides distances, that were derived by using two different methods: via isochrone fitting \citep{Zwitter2010} and via Bayesian distance-finding with kinematic corrections \citep{Binney2013}. The later method also gives an estimate of the stellar ages, albeit with large uncertainties (see \citet{Binney2013} for a discussion). The \logg~determination is a problematic step for RAVE: its spectral interval suffers from a strong \logg-\teff~degeneracy, that causes an inaccurate \logg~measure for red giants and an offset, that causes the misplacement of the red clump of $\sim$ 0.3 dex \citep{Kordopatis2011,Kordopatis2013, Binney2013}. The main aim of this paper, as first in a series (were we will use K2 targets in common with RAVE for galactic archaeology purposes) is to show the impact of using the precise and accurate seismic gravity in the outcome temperatures and abundances of RAVE targets. We also show how the approach discussed here helps improving the RAVE stellar parameters and abundances. As shown in \citet{Bruntt2012}, \citet{Thygesen2012}, and \cite{Morel2014} asteroseismology can play an important role in this respect, as it provides precise and accurate gravities, once more helping to break remaining degeneracies. Additional improvements regarding the lifting of the degeneracy are shown in DR5 \cite{Kunder2016}, by using the new APASS photometric information, the Infra-Red Flux Method, and the \logg~calibration presented in this work. The paper is organised as follows: in Section 2, we present the RAVE targets that have been observed in K2 Campaign 1; in Section 3 we present the seismic data available for our sample; in Section 4 we describe our spectroscopic analysis strategy in order to obtain highly consistent stellar parameters and therefore accurate stellar abundances for our sample. In Section 5 we compared our results with those of RAVE DR4 for the same stars, providing a calibration for the \logg$_{\rm RAVE~DR4}$. Section 6 focus in showing how variations in \logg~impacts elements abundances, and what is the safe parameter space over which our calibration can be applied. Distances, reddening (and ages), determined via a Bayesian approach using asteroseismology and the newly determined atmospheric parameters are shown in Section 7. In this section we also provide a comparison with the values obtained in DR4 an DR5 for the same stars. In particular, DR5 has made use of the seismic analysis presented in this work. In Section 8, we summarise our results. \begin{figure} \includegraphics[width=0.99\columnwidth]{RaveField.pdf} \caption{RA-DEC position of the targets observed by K2 during Campaign 1 (grey dots), the field is centred at 11:35:46 +01:25:02 and it was observed from 30-05-2014 to 21-08-2014. Empty red circles mark the RAVE stars observed by K2, while full red circles mark the 87 RAVE targets with detected oscillations.} \label{Fig:field}% \end{figure} \begin{figure} \includegraphics[width=0.99\columnwidth]{SNRdistr.pdf} \caption{SNR distribution of the spectra of the 87 RAVE stars possessing asteroseismology.} \label{Fig:SNR}% \end{figure} | In this paper we analysed 87 RAVE stars with detected solar like oscillations, observed during Campaign 1 of the K2 mission. The use of asteroseismic \logg~ (with typical accuracy of 0.03 dex), and photometric temperature, was able to break the \logg-\teff~degeneracy that affects the RAVE wavelength interval (around CaII Triplet, especially for red giants). By comparing our measurements with those of RAVE DR4, we were able to quantify the impact of the refined gravities and effective temperature obtained here on the elemental abundances, distances, and reddening (and age) determinations for these stars.\\ Our results can be summarized as follows: \begin{itemize} \item A difference between \logg$_{\rm seismo}$ and \logg$_{\rm RAVE~DR4}$ exists. This is a consequence of the resolution and short spectral coverage of the RAVE survey, that leads to a strong \logg-\teff~degeneracy. This degeneracy had been partially solved in RAVE DR4 by adopting a decision-tree pipeline, together with a projection-method one. In this work we provide a calibration for the gravity of RAVE DR4 red giants (Eq.~\ref{Eq:corrlogg}) that is valid for giants selected in the colour interval 0.50$\leq$(J-K$_S$)$\leq$0.85. \item The difference in \logg~leads, as expected, to differences respect to the newly recomputed \teff, overall metallicity [M/H], and single element abundances. Stars with an overestimated gravity in DR4, have overestimated \teff~and metallicity. \item The change of the \logg~leads to a change of the star's luminosity, affecting distances and reddening. A correct sample of red giants, with distances in agreement with the distances derived in this work, can be selected from RAVE DR4 by applying a colour cut 0.50$\leq$(J-K$_S$)$\leq$0.85 and a very narrow cut in \logg, 2.5$\leq$\logg$\leq$2.8 dex. \end{itemize} We determined a calibration for \logg~following Eq.~\ref{Eq:corrlogg}, for photometrically selected giants in DR4. The same correction was used for the red giants in the forthcoming RAVE Data Release (DR5). In the RAVE DR5 catalogue seismically calibrated gravities were provided for a sample of red giants, photometrically selected using 0.50$\leq$(J-K$_{S}$)$_0$$\leq$0.85. These gravities appear in the ``LOGG\_SC'' column. We also recommend to recompute abundances, metallicity, abundances and distances using the calibrated \logg. The shifts introduced by a uncertain \logg~assumption may introduce artefacts, such as metal-rich or metal-poor stars, or stars with the incorrect distance or kinematics. In the RAVE DR5 catalogue this re-computation has been already performed. The nature of these trends will be further explored in the other K2 Campaigns, increasing the statistics of our calibration sample and using RAVE stars possessing asteroseismology for Galactic Archaeology investigations. Gaia will help improving the atmospheric parameters as well. The strategy developed in this work can be used for the future parameter determination, by using the \teff~and the \logg~coming from independent sources as priors (e.g. magnitude colours, parallaxes). | 16 | 9 | 1609.03826 |
1609 | 1609.04401_arXiv.txt | Intensity mapping is a promising technique for surveying the large scale structure of our Universe from $z=0$ to $z \sim 150$, using the brightness temperature field of spectral lines to directly observe previously unexplored portions of out cosmic timeline. Examples of targeted lines include the $21\,\textrm{cm}$ hyperfine transition of neutral hydrogen, rotational lines of carbon monoxide, and fine structure lines of singly ionized carbon. Recent efforts have focused on detections of the power spectrum of spatial fluctuations, but have been hindered by systematics such as foreground contamination. This has motivated the decomposition of data into Fourier modes perpendicular and parallel to the line-of-sight, which has been shown to be a particularly powerful way to diagnose systematics. However, such a method is well-defined only in the limit of a narrow-field, flat-sky approximation. This limits the sensitivity of intensity mapping experiments, as it means that wide surveys must be separately analyzed as a patchwork of smaller fields. In this paper, we develop a framework for analyzing intensity mapping data in a spherical Fourier-Bessel basis, which incorporates curved sky effects without difficulty. We use our framework to generalize a number of techniques in intensity mapping data analysis from the flat sky to the curved sky. These include visibility-based estimators for the power spectrum, treatments of interloper lines, and the ``foreground wedge" signature of spectrally smooth foregrounds. | \label{sec:Intro} {\let\thefootnote\relax\footnote{$^{\dagger}$Hubble Fellow}} \setcounter{footnote}{0} In recent years, intensity mapping has been hailed as a promising method for conducting cosmological surveys of unprecedented volume. In an intensity mapping survey, the brightness temperature of an optically thin spectral line is mapped over a three-dimensional volume, with radial distance information provided by the observed frequency (and thus redshift) of the line. By observing brightness temperature fluctuations on cosmologically relevant scales (without resolving individual sources responsible for the emission or absorption), intensity mapping provides a relatively cheap way to survey our Universe. In addition, with an appropriate choice of spectral line and a suitably designed instrument, the volume accessible to an intensity mapping survey is enormous. This allows measurements to be made over a large number of independent cosmological modes, providing highly precise constraints on both astrophysical and cosmological models. For example, intensity mapping experiments tracing the $21\,\textrm{cm}$ hyperfine transition of hydrogen can easily access $\sim 10^9$ independent modes, which is much greater than the $\sim 10^6$ accessible to the Cosmic Microwave Background, in principle unlocking a far greater portion of the available information in our observable Universe \citep{loeb_and_zaldarriaga2004,mao_et_al2008,tegmark_and_zaldarriaga2009,ma_and_scott2016,scott_et_al2016}. A large number of intensity mapping experiments are in operation, and more have been proposed. Post-reionization neutral hydrogen $21\,\textrm{cm}$ intensity mapping is being conducted by the Canadian Hydrogen Intensity Mapping Experiment \citep{bandura_et_al2014}, the Green Bank Telescope \citep{masui_et_al2013}, Tianlai telescope \citep{chen_et_al2012}, Baryon Acoustic Oscillations from Integrated Neutral Gas Observations project \citep{battye_et_al2013}, Hydrogen Intensity and Real-time Analysis eXperiment \citep{newburgh_et_al2016}, and BAORadio \citep{ansari_et_al2012}. These experiments use neutral hydrogen as a tracer of the large scale density field, with a primary scientific goal of constraining dark energy via measurements of the baryon acoustic oscillation feature from $0 < z < 4$ \citep{wyithe_et_al2008,chang_et_al2008,pober_et_al2013a}. At $z \sim 2$ to $3.5$, data from the Sloan Digital Sky Survey have been used for Ly $\alpha$ intensity mapping \citep{croft_et_al2016}. Other experiments such as the CO Power Spectrum Survey \citep{keating_et_al2015,keating_et_al2016} and the CO Mapping Array Pathfinder \citep{li_et_al2016} use CO as a tracer of molecular gas in the epoch of galaxy formation at roughly $z \sim 2$ to $3$. Using [CII] instead is the Spectroscopic Terahertz Airborne Receiver for Far-InfraRed Exploration (operating at $0.5 < z < 1.5$; \citealt{uzgil_et_al2014}), and the Tomographic Ionized carbon Mapping Experiment (operating at $5 < z < 9$; \citealt{crites_et_al2014}). The highest redshift bins of the latter encroach upon the Epoch of Reionization (EoR), when the first galaxies systematically reionized the hydrogen content of the intergalactic medium. Extending into the EoR, intensity mapping efforts are mainly focused around the $21\,\textrm{cm}$ line. The Donald C. Backer Precision Array for Probing the Epoch of Reionzation array (PAPER; \citealt{parsons_et_al2010}), the Low Frequency Array \citep{van_haarlem_et_al2013}, the Murchison Widefield Array \citep{bowman_et_al2012,tingay_et_al2013}, the Giant Metrewave Radio Telescope \citep{paciga_et_al2013}, the Long Wavelength Array (M. W. Eastwood et al., in prep.), 21 Centimeter Array \citep{huang_et_al2016,zheng_et_al2016}, and the Hydrogen Epoch of Reionization Array \citep{deboer_et_al2016} are radio interferometers that aim to use the $21\,\textrm{cm}$ line to probe the density, ionization state, and temperature of hydrogen in the range $6 < z < 13$ and beyond. The future Square Kilometre Array \citep{mellema_et_al2015} will provide yet more collecting area for $21\,\textrm{cm}$ intensity mapping to complement the aforementioned experiments. With such a large suite of instruments covering an expansive range in redshift, tremendous opportunities exist for understanding the formation of the first stars and galaxies via direct measurements of the IGM during all the relevant epochs \citep{hogan_and_rees1979,scott_and_rees1990,madau_et_al1997,tozzi_et_al2000}, as well as fundamental cosmological parameters \citep{mcquinn_et_al2006,mao_et_al2008,visbal_et_al2009,clesse_et_al2012,liu_et_al2016} and exotic phenomena such as dark matter annihilations \citep{valdes_et_al2013,evoli_et_al2014}. Despite its promise, intensity mapping is challenging, and to date the only positive detections have been tentative detections of Ly $\alpha$ at $z \sim 2$ to $3.5$ \citep{croft_et_al2016} and CO from $z\sim 2.3$ to $3.3$ \citep{keating_et_al2016}, as well as detections of HI at $z\sim 0.8$ via cross-correlation with optical galaxies \citep{chang_et_al2010,masui_et_al2013}. To realize the full potential of intensity mapping, it is necessary to overcome a large number of systematics. A prime example would be radiation from foreground astrophysical sources, which are particularly troublesome for HI intensity mapping. Especially at high redshifts, foregrounds add contaminant emission to the measurement that are orders of magnitude brighter than the cosmological signal \citep{dimatteo_et_al2002,santos_et_al2005,wang_et_al2006,deOliveiraCosta_et_al2008,sims_et_al2016}. Low frequency measurements (for instance, those targeting the $21\,\textrm{cm}$ EoR signal), are mainly contaminated by broadband foregrounds such as Galactic synchrotron emission or extragalactic point sources (whether they are bright and resolved or are part of a dim and unresolved continuum). These foregrounds are typically less dominant at the higher frequencies and are thus easier (though still challening) to handle for CO or [CII] intensity mapping experiments. However, such experiments must also contend with the problem of interloper lines, where two spectral lines of different rest wavelengths may redshift into the same observation band, leading to confusion as to which spectral line has been observed. In addition to astrophysical foregrounds, instrumental systematics must be well-controlled for a successful measurement of the cosmological signal. Among others, these systematics include beam-forming errors \citep{neben_et_al2016b}, radio frequency interference \citep{offringa_et_al2013,offringa_et_al2015,huang_et_al2016}, polarization leakage \citep{geil_et_al2011,moore_et_al2013,shaw_et_al2014b,sutinjo_et_al2015,asad_et_al2015,moore_et_al2015,kohn_et_al2016}, calibration errors \citep{newburgh_et_al2014,trott_and_wayth2016,barry_et_al2016,patil_et_al2016}, and instrumental reflections \citep{neben_et_al2016a,ewall-wice_et_al2016a,thyagarajan_et_al2016}. In this paper, we focus specifically on measurements of the power spectrum $P(k)$ of spatial fluctuations in brightness temperature, where roughly speaking, the temperature field is Fourier transformed and then squared. In diagnosing the aforementioned systematics as they pertain to spatial fluctuation experiments, it is helpful to decompose the fluctuations into modes that separate purely angular fluctuations from purely radial fluctuations from those that are a mixture of both. In recent years, for example, simulations and measured upper limits of the $21\,\textrm{cm}$ power spectrum have often been expressed as cylindrically binned power spectra. To form cylindrically binned power spectra, one begins with unbinned power spectra $P(\mathbf{k})$, where $\mathbf{k}$ is the three-dimensional wavevector of spatial Fourier modes. If the field of view is narrow, there exists a particular direction that can be identified as the line-of-sight (or radial) direction. One of the three components of $\mathbf{k}$ can then be chosen to lie along this direction and labeled $k_\parallel$ as a reminder that it is \emph{parallel} to the line-of-sight. The remaining two components---which we arbitrarily designate $k_x$ and $k_y$ in this paper---describe transverse (i.e., angular fluctuations), and have a magnitude $k_\perp \equiv \sqrt{k_x^2 + k_y^2}$. Binning $P(\mathbf{k})$ along contours of constant $k_\perp$ gives $P(k_\perp, k_\parallel)$, the cylindrically binned power spectrum. Expressing the power spectrum as a function of $k_\perp$ and $k_\parallel$ is a powerful diagnostic exercise because intensity mapping surveys probe line-of-sight fluctuations in a fundamentally different way than the way they probe angular fluctuations. Systematics are therefore usually anisotropic and have distinct signatures on the $k_\perp$-$k_\parallel$ plane \citep{morales_and_hewitt2004}. For example, cable reflections and bandpass calibration errors tend to appear as features parallel to the $k_\parallel$ axis \citep{dillon_et_al2015,ewall-wice_et_al2016b,jacobs_et_al2016}. Thus, the cylindrically binned power spectrum is a useful intermediate quantity to compute before one performs a final binning along constant $k \equiv \sqrt{k_\perp^2 + k_\parallel^2}$ to give an isotropic power spectrum $P(k)$. The diagnostic capability of $P(k_\perp, k_\parallel)$ is particularly apparent when considering foregrounds. Assuming that they are spectrally smooth, foregrounds preferentially contaminate low $k_\parallel$ modes, since $k_\parallel$ is the Fourier conjugate to line-of-sight distance, which is probed by the frequency spectrum in intensity mapping experiments. The situation is more complicated for the (large) subset of intensity mapping measurements that are performed on interferometers. Interferometers are inherently chromatic in nature, causing intrinsically smooth spectrum foregrounds to acquire spectral structure, which results in leakage to higher $k_\parallel$ modes. Even this leakage, however, has been shown in recent years to have a predictable ``wedge" signature on the $k_\perp$-$k_\parallel$ plane, limiting the contaminated region to a triangular-shaped region at high $k_\perp$ and low $k_\parallel$ \citep{Datta2010,Vedantham2012,Morales2012,Parsons_et_al2012b,Trott2012,Thyagarajan2013,pober_et_al2013b,dillon_et_al2014,Hazelton2013,Thyagarajan_et_al2015a,Thyagarajan_et_al2015b,liu_et_al2014a,liu_et_al2014b,chapman_et_al2016,pober_et_al2016,seo_and_hirata2016,jensen_et_al2016,kohn_et_al2016}. In fact, the foreground wedge is considered sufficiently robust that some instruments have been designed around it \citep{pober_et_al2014,deboer_et_al2016,dillon_et_al2016,neben_et_al2016a,ewall-wice_et_al2016a,thyagarajan_et_al2016}, implicitly pursuing a strategy of foreground avoidance where the power spectrum can be measured in relatively uncontaminated Fourier modes outside the wedge. This mitigates the need for extremely detailed models of the foregrounds, providing a conservative path towards early detections of the power spectrum. Despite its utility, the $k_\perp$-$k_\parallel$ power spectrum is limited in that it is ultimately a quantity that is only well-defined in the flat-sky, narrow field-of-view limit, where a single line-of-sight direction can be unambiguously defined. For surveys with wide fields of view, different portions of the survey have different lines of sight that point in different directions with respect to a cosmological reference frame. Note that this is a separate problem from that of wide-field imaging: even if one's imaging software does not make any flat-sky approximations (so that the resulting images of emission within the survey volume are undistorted by any wide-field effects), the act of forming a power spectrum on a $k_\perp$-$k_\parallel$ invokes a narrow-field approximation. If one insists on forming $P(k_\perp, k_\parallel)$ as a diagnostic, the simplest way to do so is to split up the survey into multiple small patches that are individually small enough to warrant a narrow-field assumption. A separate power spectrum can then be formed from each patch by squaring the Fourier mode amplitudes, and the resulting collection of power spectra can then be averaged together. While correct, such a ``square-then-average" procedure results in lower signal-to-noise than a hypothetical ``average-then-square" procedure whereby a single power spectrum is formed out of the entire survey. The latter allows the spatial modes of a survey to be averaged together coherently, which allows instrumental noise to be averaged down very quickly. Roughly speaking, if $N$ patches of sky are averaged in a coherent fashion to constrain a particular spatial mode, the noise on the measured mode amplitude averages down as $1/\sqrt{N}$. Squaring this amplitude to form a power spectrum then results in a quicker $1/N$ scaling of noise. In contrast, a ``square-then-average" method combines $N$ independent pieces of information after squaring, and thus the power spectrum noise scales more slowly\footnote{In \citet{parsons_et_al2016} it was shown that in specialized situations it is possible to pre-filter visibility data from an interferometer to recover some of the loss of sensitivity from a square-then-average approach. However, such an approach does not recover large scale angular modes from a wide field of view.} as $1/\sqrt{N}$. The result is a less sensitive statistic, whether for the diagnosis of systematics or for a cosmological measurement. To be fair, one could recover the lost sensitivity by also computing all cross-correlations between a series of small overlapping patches. However, the necessary geometric adjustments for such high precision mosaicking will likely be computationally wasteful, and it quickly becomes preferable to adopt an approach that incorporates the curved sky from the beginning. In this paper, we rectify the shortcomings of the $k_\perp$-$k_\parallel$ plane by introducing an alternative that is well-defined in the wide-field limit. Rather than expanding sky emission in a basis of rectilinear Fourier modes, we propose a spherical Fourier-Bessel basis. In this basis, the sky brightness temperature $T(\mathbf{r})$ of a survey (where $\mathbf{r}$ is the comoving position) is expressed in terms of $\overline{T}_{\ell m} (k)$, defined as\footnote{ It is an unfortunate coincidence that the spherical harmonic indices are typically denoted by $\ell$ and $m$ in the cosmological literature, while in radio astronomy they are reserved for the direction cosines from zenith in the east-west and north-south directions, respectively. In this paper, $\ell$ and $m$ will always represent spherical harmonic indices, and never direction cosines.} \begin{equation} \label{eq:TellmEverything} \overline{T}_{\ell m} (k) \equiv \sqrt{\frac{2}{\pi}} \int \! d\Omega dr\, r^2 j_\ell (kr) Y_{\ell m}^* (\rhat) T(\mathbf{r}), \end{equation} where $k$ is the \emph{total} wavenumber, $\ell$ and $m$ are the spherical harmonic indices, $Y_{\ell m}$ denotes the corresponding spherical harmonic, $r \equiv | \mathbf{r}|$ is the radial distance, $\mathbf{\hat{r}} \equiv \mathbf{r} / r$ is the angular direction unit vector\footnote{In this paper, we use hats for two different purposes. When placed above a vector (e.g., with $\rhat$), the hat indicates that the vector is a unit vector. When placed above a scalar (e.g., with $\widehat{P}$), the hat indicates an estimator of the hatless quantity.}, and $j_\ell$ is the $\ell$th order spherical Bessel function of the first kind. The quantity $P(k_\perp, k_\parallel)$ is replaced by the analogous quantity $S_\ell (k)$, the spherical harmonic power spectrum, which roughly takes the form \begin{equation} \label{eq:Sellkrough} S_\ell (k) \propto \frac{1}{2 \ell + 1} \sum_{m = -\ell}^\ell |\overline{T}_{\ell m} (k)|^2, \end{equation} where the sum over $m$ is analogous to the binning of $k_x$ and $k_y$ into $k_\perp$, and a more rigorous definition (with constants of proportionality) will be defined in Section \ref{sec:SphericalPspecFormalism}. Instead of the $k_\perp$-$k_\parallel$ plane, power spectrum measurements are now expressed on an $\ell$-$k$ plane. Now, we will show in Section \ref{sec:SphericalPspecFormalism} that in the limit of a translationally invariant cosmological field, $S_\ell (k)$ reduces to $P(k)$. Therefore, just as $P(k_\perp, k_\parallel)$ can be averaged along contours of constant $k$ to form $P(k)$ once systematic effects are under control, the same can be done for $S_\ell (k)$ to form $P(k)$ by averaging over all values of $\ell$ for a particular $k$. Spherical Fourier-Bessel methods have been explored in the past within the galaxy survey literature \citep{binney_quinn1991,lahav_et_al1994,fisher_et_al1994,fisher_et_al1995,heavens_taylor1995,zaroubi_et_al1995,castro_et_al2005,leistedt_et_al2012,rassat_refregier2012,shapiro_et_al2012,pratten_munshi2013,yoo_desjacques2013}. In this paper, we build upon these methods and present a framework for implementing them in an analysis of intensity mapping data. We emphasize the way in which intensity mapping surveys have unique geometric properties, and how these properties affect spherical Fourier-Bessel methods. For instance, we pay special attention to the fact that particularly for the highest redshift observations, intensity mapping experiments probe survey volumes that are radially compressed but angularly expansive (as illustrated in Figure \ref{fig:surveyGeom}). In harmonic space, this expectation is reversed, and there is excellent spatial resolution along the line-of-sight (since high spectral resolution is relatively easy to achieve), but poor angular resolution. In addition to addressing these geometric peculiarities, we also show how interferometric data can be analyzed with spherical Fourier-Bessel methods. Importantly, we find that the foregrounds again appear as a wedge in interferometric measurements of $S_\ell (k)$, which suggests that the $\ell$-$k$ plane is at least as powerful a diagnostic tool as the $k_\perp$-$k_\parallel$ plane, particularly given the signal-to-noise advantages discussed above.\footnote{This does not, of course, preclude the examination of systematics in other spaces. For example, though cable reflections may have well-defined signatures on the $k_\perp$-$k_\parallel$ or $\ell$-$k$ planes, they are an example of a systematic that can (and should) also be diagnosed in spaces appropriate for raw data coming off an instrument.} \begin{figure}[!] \centering \includegraphics[width=0.35\textwidth,trim=2.0cm 1.2cm 0.8cm 0.5cm,clip]{surveyGeom.pdf} \caption{A typical geometry for an intensity mapping survey. The observer is located in the middle, and the thin pink ring denotes the survey's coverage. Particularly at high redshifts (such as those relevant to Epoch of Reionization $21\,\textrm{cm}$ measurements), the cosmological scalings of Section \ref{sec:Notation} typically result in surveys where the median comoving radial distance $r_0$ is much larger than the total radial extent $\Delta r_\textrm{survey}$, i.e., thin-shell surveys. Additionally, most intensity mapping surveys have much higher spectral/radial resolution than they do angular resolution.} \label{fig:surveyGeom} \end{figure} The rest of this paper is organized as follows. In Section \ref{sec:Notation} we establish notational conventions for this paper. Section \ref{sec:SphericalPspecFormalism} introduces spherical Fourier-Bessel methods for power spectrum estimation, with the complication of finite surveys (in both the angular and spectral directions) the subject of Section \ref{sec:FiniteVolume}. In Section \ref{sec:Foregrounds} we compute the signature of smooth spectrum foregrounds on the $\ell$-$k$ plane. Interloper lines are explored in Section \ref{sec:Interlopers}. A framework for interferometric power spectrum estimation using spherical Fourier-Bessel methods (which includes a derivation of the foreground wedge) is presented in Section \ref{sec:Interferometry}. To build intuition, we develop a parallel series of flat-sky, narrow field-of-view expressions in a series of Appendices. Our conclusions are summarized in Section \ref{sec:Conclusions}. Because of the large number of mathematical quantities defined in this paper, we provide a glossary of important symbols for the reader's convenience in Table \ref{tab:Definitions}. \begin{table*} \caption{\label{tab:Definitions}Glossary of important mathematical quantities. The ``context" column gives equation references, typically either their defining equation or their first appearance in the text.} \begin{ruledtabular} \begin{tabular}{lll} Quantity & Meaning/Definition & Context \\ \hline $\mathbf{r}$ & Comoving position & Section \ref{sec:Intro} \\ $\mathbf{\hat{r}}$ & Angular direction unit vector & Section \ref{sec:Intro} \\ $\mathbf{r}_\perp$ & Comoving transverse distance & Eq. \eqref{eq:AngularConversion} \\ $r(\nu)$ or $r_\nu$ & Comoving radial distance & Eq. \eqref{eq:ComovingDistDef} \\ $s(r)$ & Incorrect radial distance assumed for true radial distance $r$ due to interloper lines & Eq. \eqref{sec:Interlopers} \\ $\nu(r)$ or $\nu_r$ & Observed frequency of radio emission & Section \ref{sec:Notation} \\ $\alpha$ & Linearized conversion factor between frequency and radial comoving distance & Eq. \eqref{eq:AlphaConversion} \\ $ \boldsymbol \theta$ & Sky image angle & Eq. \eqref{eq:AngularConversion} \\ $\mathbf{k}$ & Wavevector of rectilinear spatial Fourier modes & Section \ref{sec:Intro} \\ $k_\perp$ & Magnitude of wavevector components perpendicular to line of sight & Section \ref{sec:Intro} \\ $k_\parallel$ & Magnitude of wavevector components parallel to line of sight & Section \ref{sec:Intro} \\ $k$ & Total wavenumber/wavevector magnitude of rectilinear spatial Fourier modes & Section \ref{sec:Intro} \\ $\phi(\mathbf{r})$& Survey volume selection function & Section \ref{sec:FiniteVolume} \\ $\phi(r)$ & Radial survey profile or survey volume selection function assuming full-sky covarage & Section \ref{sec:FiniteVolume} \\ $\Phi(r)$ & Radial survey profile centered on radial midpoint of survey & Section \ref{sec:MostlyRadialNoInterferometry} \\ $T(\mathbf{r})$ or $T(\rhat, \nu)$ & Sky temperature in configuration space & Eq. \eqref{eq:TellmEverything} \\ $ \overline{T}_{\ell m} (k)$ & Sky temperature in spherical Fourier-Bessel space & Eq. \eqref{eq:TellmEverything} \\ $ \overline{T}_{\ell m}^\textrm{meas} (k)$ & Estimated sky temperature in spherical Fourier-Bessel space for finite-volume surveys & Eq. \eqref{eq:Tellm^meas} \\ $\widetilde{T} (\mathbf{k})$ & Sky temperature in rectilinear Fourier space & Eq. \eqref{eq:RectilinearPspecDef} \\ $\kappa (\nu)$ & Frequency spectrum of foreground contaminants & Eq. \eqref{eq:qellk} \\ $q_\ell (k)$ & Frequency spectrum of foreground contaminants in radial spherical Bessel basis & Eq. \eqref{eq:qellk}\\ $a_{\ell m} (\nu)$ & Sky temperature in frequency/spherical harmonic space & Eq. \eqref{eq:SHTdef} \\ $Y_{\ell m} $ & Spherical harmonic function & Section \ref{sec:SphericalPspecFormalism} \\ $\psi_{\ell m} (k; \rhat, \nu)$ & Spherical Fourier-Bessel basis function in configuration space & Eq. \eqref{eq:BasisFcts} \\ $j_\ell (kr) $ & $\ell$th order spherical Bessel function of the first kind & Section \ref{sec:SphericalPspecFormalism} \\ $C_\ell$ & Angular power spectrum & Section \ref{sec:RotationalInvarianceOnly} \\ $P(\mathbf{k})$ & Brightness temperature power spectrum & Section \ref{sec:Intro} \\ $P(k_\perp, k_\parallel)$ & Brightness temperature power spectrum, assuming cylindrical symmetry & Section \ref{sec:Intro} \\ $P(k)$ & Brightness temperature power spectrum, assuming isotropy & Eq. \eqref{eq:RectilinearPspecDef} \\ $S_\ell (k) $ & Spherical harmonic power spectrum & Eq. \eqref{eq:SlkDef} \\ $ \mathbf{b}$ & Interferometer baseline vector & Section \ref{sec:Interferometry} \\ $\tau$ & Interferometric time delay & Eq. \eqref{eq:DelayDef} \\ $V(\mathbf{b}, \nu)$ & Interferometric visibility & Eq. \eqref{eq:VisDef} \\ $\widetilde{V}(\mathbf{b}, \tau)$ & Interferometric visibility in delay space & Eq. \eqref{eq:DelayDef} \\ $A(\rhat, \nu)$ & Primary beam of receiving elements of interferometer & Eq. \eqref{eq:VisDef}\\ $B(\rhat, \nu)$ & Rescaled primary beam & Eq. \eqref{eq:Bdef} \\ $\overline{B^2}(\theta) $ & Squared primary beam profile, averaged azimuthally about a baseline vector & Eq. \eqref{eq:FinalWedgeEq} \\ $\gamma (\nu)$ & Delay transform tapering function & Eq. \eqref{eq:DelayDef} \\ $f_{\ell m} (\mathbf{b}, \nu)$ & Response of baseline $\mathbf{b}$ at frequency $\nu$ to unit perturbation of spherical harmonic mode $Y_{\ell m}$ & Eq. \eqref{eq:flm} \\ $g_{\ell m} (\mathbf{b}, \tau)$ & Response of baseline $\mathbf{b}$ at delay $\tau$ to unit perturbation of spherical harmonic mode $Y_{\ell m}$ & Eq. \eqref{eq:glm} \\ $W_\ell (k; \mathbf{b}, \tau)$ & Spherical harmonic power spectrum window function for a single baseline delay-based & Eq. \eqref{eq:DelayWindowFcts} \\ & power spectrum estimate & \\ $\Theta(\nu)$ & Re-centered frequency profile of the foregrounds as seen in the data, with finite bandwidth & Section \ref{sec:CurvedSkyWedge} \\ & and tapering effects & \\ $D(\mathbf{r})$ & Survey volume selection function including primary beam, bandwidth, and data analysis & Appendix \ref{sec:RectilinearInterferometerPspecNorm} \\ & tapering effects& \\ \end{tabular} \end{ruledtabular} \end{table*} | \label{sec:Conclusions} In this paper, we have established a framework for analyzing intensity mapping data using spherical Fourier-Bessel techniques. Such techniques easily incorporate the wide-field nature of many intensity mapping surveys, obviating the need to split up one's field into several approximately flat fields during analysis. This builds sensitivity for science measurements as well as diagnostic tests, and additionally provides access to the largest angular scales on the sky. Adapting spherical Fourier-Bessel techniques from galaxy surveys requires one to pay special attention to the unique properties of intensity mapping. For example, we saw in Figure \ref{fig:surveyGeom} that intensity mapping surveys (particularly those that operate at high redshifts) tend to be compressed in the radial direction and have very fine radial resolution compared to angular resolution. Intensity mapping experiments must also contend with extremely bright foregrounds that overwhelm the cosmological signals of interest. A successful spherical Fourier-Bessel analysis framework must demonstrate that it is able to deal with such systematics at least as well as traditional rectilinear Fourier techniques can. This paper demonstrates that spherical Fourier-Bessel modes are indeed a suitable basis for intensity mapping analyses. Focusing on power spectrum measurements, in Section \ref{sec:FiniteVolume} we proposed that the cylindrically binned power spectrum $P(k_\perp, k_\parallel)$ be replaced by the spherical harmonic power spectrum $S_\ell (k)$. The quantity $S_\ell (k)$ is conveniently defined so that a weighted average of it over different $\ell$ values yields the spherically binned cosmological power spectrum $P(k)$. At the same time, by splitting up the measured power spectrum into a function of $\ell$ and $k$, angular fluctuations are separated from arbitrarily oriented spatial fluctuations. This separation of fluctuations into angular and non-angular modes provides a powerful diagnostic for systematics. This has historically been the motivation for viewing the power spectrum as a function of $k_\perp$ and $k_\parallel$, and $S_\ell (k)$ preserves this crucial property of $P(k_\perp, k_\parallel)$. Of course, this is not to say that the data should not also be examined in bases like $(\mathbf{b}, \tau)$ that are more closely related to the actual instrument's measurement \citep{Vedantham2012,Parsons_et_al2012b}. Doing so is particularly valuable prior to the squaring of the data to form power spectra, and both approaches can and should be used. Chief amongst the systematics that may be discerningly diagnosed on the $k_\perp$-$k_\parallel$ plane are astrophysical foregrounds. Foregrounds are expected to have localized signatures in $P(k_\perp, k_\parallel)$, facilitating their removal. We have shown in this paper that the same is true for $S_\ell (k)$. For non-interferometric intensity mapping surveys, we have shown that the spectrally smooth nature of foregrounds results in their being sequestered at low $k$, and that interloper lines can be detected using $S_\ell (k)$ just as easily as they can be using $P(k_\perp, k_\parallel)$. For interferometric surveys, foregrounds tend to limited to a wedge-like feature on the $k_\perp$-$k_\parallel$ plane. Foregrounds are limited to a similar wedge on the $\ell$-$k$ plane. This suggests that $S_\ell(k)$ is just as capable a diagnostic quantity as $P(k_\perp, k_\parallel)$ for intensity mapping surveys, while simultaneously discarding unwarranted flat-sky approximations seen in previous papers. Another attractive property of our spherical Fourier-Bessel formulation is that many of the relevant formulae derived in this paper (such as the equation delineating the boundary of the foreground wedge) are very similar to their flat-sky counterparts. Intuition for the behavior of $P(k_\perp, k_\parallel)$ that has been built up in the prior literature is thus almost entirely transferrable to $S_\ell (k)$. Our framework may be generalized in several ways in future work. For instance, we have thus far neglected to describe redshift space distortions, although the spherical formalism that we espouse here should be particularly well-suited for the purpose (C. J. Schmit et al., in prep.). A crucial area of investigation will be to determine whether cosmological redshift space distortions interfere with the signature of interloper lines. Another area of future development would be the incorporation of light-cone effects, since it has been shown that cosmological evolution cannot be neglected over the survey volume of a typical intensity mapping survey \citep{barkana_and_loeb2006,datta_et_al2012,datta_et_al2014,laplante_et_al2014,zawada_et_al2014,ghara_et_al2015}. For now, however, this paper points to the promise of spherical Fourier-Bessel techniques for rigorous data analysis, providing yet another powerful diagnostic tool in the continuing progress of intensity mapping towards surveying an unprecedentedly large volume of our observable Universe. | 16 | 9 | 1609.04401 |
1609 | 1609.09502_arXiv.txt | We recently developed a procedure to recognize $\gamma$-ray blazar candidates within the positional uncertainty regions of the unidentified/unassociated $\gamma$-ray sources (UGSs). Such procedure was based on the discovery that \fer\ blazars show peculiar infrared colors. However, to confirm the real nature of the selected candidates, optical spectroscopic data are necessary. Thus, we performed an extensive archival search for spectra available in the literature in parallel with an optical spectroscopic campaign aimed to reveal and confirm the nature of the selected $\gamma$-ray blazar candidates. Here, we first search for optical spectra of a selected sample of $\gamma$-ray blazar candidates that can be potential counterparts of UGSs using the Sloan Digital Sky Survey (SDSS DR12). This search enables us to update the archival search carried out to date. We also describe the state-of-art and the future perspectives of our campaign to discover previously unknown $\gamma$-ray blazars. | \label{sec:intro} The first observations performed with the Energetic Gamma Ray Experiment Telescope \citep[EGRET;][]{thompson93} revealed that the largest fraction of sources detected in the MeV-GeV energy range were unidentified/unassociated. According to the latest versions of the 3$^{rd}$ EGRET \citep[][]{hartman99,casandjian08} source catalog, the fraction of $\gamma$-ray objects with an unknown origin is $\sim$60\%. This is mostly due to the large positional uncertainties of the $\gamma$-ray sources being up to an order of magnitude greater than those at lower energies. Thus, the association of $\gamma$-ray sources with their low energy counterparts is one of the most demanding task for modern $\gamma$-ray astronomy \citep[see e.g.,][]{thompson08,massaro12a,review}. The study of the unidentified/unassociated $\gamma$-ray sources (UGSs) was set as one of the major scientific goals of the \fer\ mission \citep{atwood09}. Thanks to the major improvements achieved in the source localization with the Large Area Telescope (LAT) on board of \fer, the ``source association task'' has been greatly simplified. This was also due to the improvements of statistical methods used to search for low energy counterparts of \fer\ detected objects \citep[see e.g.,][]{abdo10a,abdo10b}. Difficulties on the source association in $\gamma$-rays is partially mitigated by another aspect: the largest fraction of known $\gamma$-ray emitters is associated with the rarest class of active galaxies: the blazars. In the \fer-Large Area Telescope (LAT) third source catalog \citep[3FGL;][]{acero15} blazars constitute about 36\% of the \fer\ sources. Blazars are generally divided in two classes on the basis of the equivalent width (EW) of their optical spectral features \citep[see e.g.,][]{stickel91}. When presenting featureless spectra or with emission/absorption lines with EW$<$5\AA\ they are classified as BL Lac objects, while those showing quasar-like optical spectra coupled with a flat radio spectrum are known as flat spectrum radio quasars \citep[FSRQ; see also][for more details on the blazar properties]{urry95}. Following the nomenclature proposed in the multifrequency catalog of Blazars \citep[\bzcat;][]{massaro15b}, we indicate the former class as BZB while the latter one as BZQ. We also considered the blazar of galaxy type (indicated as BZG), according to the definition presented in the latest release of the \bzcat\ catalog\footnote{http://www.asdc.asi.it/bzcat/} \citep{massaro09}, being sources whose multifrequency emission exhibits some properties of blazars but appears dominated by the host galaxy contribution in the optical-ultraviolet energy range \citep{massaro12b,massaro14}. Across all the releases of the \fer-LAT source catalogs, the fraction of UGSs does not seem to decrease significantly. In the First \fer-LAT source catalog \citep[1FGL][]{abdo10a} there were 630 out of 1451 unassociated \fer\ objects (i.e., $\sim$43\%), fraction that decreases to 34\% in the Second \fer-LAT source catalog \citep[2FGL][]{nolan12} then being $\sim$33\% in the 3FGL. This is in agreement with the fact that even as more distant and/or less luminous sources are found, the UGS fraction remains about the same. This indicates that, even eight years after the launch of \fer, unveiling the UGS nature is still an unsolved issue. According to the 3FGL analysis the second largest population is constituted by the blazar candidates of uncertain type (BCUs) defined in the 3FGL and in the Third Catalog of Active Galactic Nuclei Detected by the \fer-LAT \citep[3LAC;][see following sections for additional details]{ackermann15a}. This corresponds to a revised definition of the previous $\gamma$-ray source class of active galaxies of uncertain type (AGUs) \citep[see e.g., the First and the Second Catalog of Active Galactic Nuclei Detected by the \fer-LAT, 1LAC and 2LAC, respectively][]{abdo10b,ackermann11}. BCUs are most probably all blazars \citep[see e.g.,][]{massaro12c,crespo16c,chiaro16}, but the lack of spectroscopic information does not permit us to confirm their nature. Follow up observations aiming to search for the potential counterparts of the UGSs and to confirm BCUs have been carried out in the radio \citep[e.g.,][]{kovalev09,hovatta12,petrov13,hovatta14,schinzel15}, even below 1GHz \citep{ugs3,ugs6,mwabl}, in the sub millimeter ranges \citep{giommi12,lopez13} and in the X-rays with \swf\ \citep[e.g.,][]{mirabal09,paggi13,takeuchi13,stroh13,acero13} as well as with \chn\ and \suz\ \citep[e.g.,][]{maeda11,cheung12,kataoka12,takahashi12}. Additional archival analyses were also carried out using multifrequency surveys and catalogs \citep[see e.g.,][]{cowperthwaite13,BATcan,blarch}. Using the \wse\ all-sky survey \citep{wright10}, we showed that in the IR color-color diagrams the $\gamma$-ray blazars, dominated by non-thermal emission, lie in a distinct region well separated from that occupied by other extragalactic sources \citep{paper1,paper2,connect}. On the basis of this discovery, we built new procedures to recognize $\gamma$-ray blazar candidates lying within the positional uncertainty regions of the UGSs \citep{ugs1,ugs2,wibrals}. Then in 2012 we started an optical spectroscopic campaign to confirm the nature of both $\gamma$-ray blazar candidates selected according to our IR procedure, UGS potential counterparts and BCUs associated in the \fer\ catalogs. All the spectroscopic observations collected during our campaign are already published \citep[see e.g.,][]{paggi14,massaro15c,landoni15,ricci15,crespo16a,crespo16b}. During our campaign we also continuously searched in the optical databases to exclude targets for which an optical spectrum became recently available (see e.g., Massaro et al. 2014, Massaro et al. 2015a, \'Alvarez Crespo et al. 2016c, for the spectra of the Sloan Digital Sky Survey, SDSS, DR12 and of the Six-degree-Field Galaxy Survey, 6dFGS). In the present paper we aim to present the state-of-art of our {\it hunt} for $\gamma$-ray blazar candidates. Scientific objectives of the current analysis can be summarized as follows: \begin{enumerate} \item searching for optical spectra of radio sources that could be potential counterparts of 3FGL UGSs lying in the SDSS footprint; \item presenting an overview of the results of our optical spectroscopic campaign achieved to date; \item discussing on the future perspectives towards the preparation of the 4FGL catalog. \end{enumerate} The paper is organized as follows. In \S~\ref{sec:new} we described our search for radio sources having a blazar-like optical spectrum and lying within the positional uncertainty region of the UGSs in the footprint of the SDSS. Then \S~\ref{sec:state} and \S~\ref{sec:summary} are devoted to present results and the summary of our optical spectroscopic campaign, respectively. Finally in \S~\ref{sec:future} we speculate on future perspectives towards a better understanding of the unknown $\gamma$-ray sky. We used cgs units unless stated otherwise through the whole paper, and spectral indices, $\alpha$, are defined by flux density, S$_{\nu}\propto\nu^{-\alpha}$ considering sources with a flat spectrum when $\alpha<$0.5. \begin{table*}[!ht] \tiny \caption{Summary of source details for the eleven blazars found within the sample of UGSs lying in the SDSS footprint (See \S~\ref{sec:new} for more details).} \label{tab:new} \begin{tabular}{|lllllllll|} \hline 3FGL & SDSS & \wse\ & class & $z$ & 1FGL & 2FGL & 1FHL & BZCAT \\ name & name & name & & & name & name & name & name \\ \hline \hline J0158.6+0102 & J015852.77+010132.9 & J015852.76+010132.9 & bzb & 0.0 & & J0158.4+0107 & & 5BZU J0158+0101\\ J0234.2-0629 & J023410.30-062825.7 & J023410.28-062825.8 & bzb & 0.0 & & & \\ J1103.3+5239 & J110249.84+525012.6 & J110249.86+525012.6 & bzq & 0.68984 & & & \\ J1105.7+4427 & J110544.28+442830.4 & J110544.29+442830.6 & bzb & 0.74641 & & & \\ J1129.0+3758 & J112904.78+375844.6 & J112904.78+375844.6 & bzb & 0.0 & J1129.3+3757 & J1129.5+3758 & \\ J1301.5+3333 & J130129.14+333700.3 & J130129.16+333700.2 & bzq & 1.00826 & & J1301.6+3331 & & 5BZQ J1301+3337\\ % J1330.4+5641 & J133040.69+565520.1 & J133040.67+565520.1 & bzb & 0.0 & & & & 5BZB J1330+5655\\ J1411.1+3717 & J141130.56+372245.5 & J141130.51+372246.4 & bzb & 0.0 & & & \\ J1731.9+5428 & J173340.32+542636.8 & J173340.31+542636.7 & bzb & 0.0 & & J1730.8+5427 & \\ J2145.5+1007 & J214530.19+100605.4 & J214530.19+100605.5 & bzb & 0.0 & & & \\ J2223.3+0103 & J222329.57+010226.6 & J222329.57+010226.7 & bzb & 0.0 & J2223.3+0103 & J2223.4+0104 & J2223.4+0104 & 5BZB J2223+0102\\ % \hline \end{tabular}\\ Column description: (1) name reported in the Third \fer-LAT source catalog (3FGL); (2) SDSS name; (3) \wse\ name; (4) Spectroscopic class; (5) redshift; (6) name in the First \fer-LAT source catalog (1FGL); (7) name in the Second \fer-LAT source catalog (2FGL); (8) name in the First Fermi-LAT Catalog of Sources above 10 GeV (1FHL); (9) \bzcat\ name. \end{table*} | \label{sec:summary} The \wse\ all-sky survey \citep{wright10} allowed us to distinguish $\gamma$-ray emitting blazars from other extragalactic sources. On the basis of the mid-IR colors we developed a set of procedures to select potential counterparts of the UGSs and to recognize blazar candidates within the AGUs and the BCUs listed in the \fer\ catalogs. Motivated by preliminary results of our IR selection, we carried out an optical spectroscopic campaign aiming to verify the blazar-like nature of UGS potential counterparts As secondary goal we also obtained a classification for AGUs and BCUs present in the \fer\ catalogs. During our campaign we collected and analyzed 223 unique spectra and the major results achieved are summarized as follows. \begin{enumerate} \item The largest fraction of pointed targets are classified as BZBs (i.e., 173/223). This strongly suggests that \fer\ survey is extremely useful to discover new BZBs and confirms that these are one of most elusive class of active galaxies. \item We obtained 49 certain redshifts for the blazars observed thanks to the presence of emission/absorption lines or only absorption features due to intervening systems. \item We discovered a handful of transitional sources: blazars with a different spectrum available in the literature and thus classified differently. \item During our campaign we found two BL Lac objects without radio counterparts in the major radio surveys \citep{paggi14,ricci15}. This discovery could open new scenarios on the blazar phenomenon and could potentially make the $\gamma$-ray association task more challenging since a large fraction of the \fer\ associations come from radio surveys/catalogs. \item Within the sample of newly discovered BL Lacs with a $z$ estimate, presented in Section~\ref{sec:new}, it is worth noting that one of them lie above redshift $z=$0.7 (this occurs only for 11 BL Lacs from the \bzcat\ listed in the \fer\ catalogs). \end{enumerate} Given the small number of QSOs found during our campaign (i.e., $\sim$4\%) in addition to a handful of unpublished spectra that did not have enough signal-to-noise ratio to clearly classify the observed targets, our results strongly supports the reliability of our IR selection method \citep[see][for more details]{dabrusco16}. Finally, we emphasize that results obtained thanks to our campaign were used to classify the sources listed in the latest release of the \fer\ catalogs \citep[i.e., 3FGL, 3LAC and 2FHL][]{ackermann16} as well as to increase those in the \bzcat. | 16 | 9 | 1609.09502 |
1609 | 1609.00423_arXiv.txt | We present optical UBVRI zenith night sky brightness measurements collected on eighteen nights during 2013--2016 and SQM measurements obtained daily over twenty months during 2014--2016 at the Observatorio Astron\'omico Nacional on the Sierra San Pedro M\'artir (OAN-SPM) in M\'exico. The UBVRI data is based upon CCD images obtained with the 0.84\,m and 2.12\,m telescopes, while the SQM data is obtained with a high-sensitivity, low-cost photometer. The typical moonless night sky brightness at zenith averaged over the whole period is U = 22.68, B = 23.10, V = 21.84, R = 21.04, I = 19.36, and SQM = 21.88 $\mathrm{mag\,arcsec^{-2}}$, once corrected for zodiacal light. We find no seasonal variation of the night sky brightness measured with the SQM. The typical night sky brightness values found at OAN-SPM are similar to those reported for other astronomical dark sites at a similar phase of the solar cycle. We find a trend of decreasing night sky brightness with decreasing solar activity during period of the observations. This trend implies that the sky has become darker by $\Delta U =$0.7, $\Delta B =$0.5, $\Delta V =$0.3, $\Delta R =$0.5 mag arcsec$^{-2}$ since early 2014 due to the present solar cycle. | The Observatorio Astron\'omico Nacional San Pedro M\'artir (hereafter OAN-SPM) is located on the top of Sierra San Pedro M\'artir in Baja California, M\'exico (2800\,m, +31$^{\circ}$\,02''\, 40'\, N, 115$^{\circ}$\,28''\, 00'\, W). The site excels in sky clarity with, in recent decades, approximately 70\% and 80\% photometric and spectroscopic time, respectively \citep{2007RMxAC..31...47T}. The median seeing measured at zenith at 5000\AA\ varies from 0.''50 to 0''.79 (\citealp{1998RMxAA..34...47E}; \citealp{2003RMxAC..19...37M}; \citealp{2009PASP..121.1151S}; \citealp{2012MNRAS.426..635S}). Atmospheric extinction is typically 0.13\,mag airmass$^{-1}$ in V band (\citealp{2001RMxAA..37..187S}). Due to these excellent atmospheric conditions and favorable location away from large urban areas, the OAN-SPM is an excellent site for optical and infrared facilities. \\ Among the most important parameters that define the quality of an observing site it is the night sky brightness (NSB). This parameter has been extensively studied by several authors (\citealp{1975PASP...87..869K}; \citealp{1988PASP..100..496W}; \citealp{1989PASP..101..707P}; \citealp{1987PASP...99..887K}; \citealp{1995A&AS..112...99L}; \citealp{1996A&AS..119..153M}; \citealp{2003A&A...400.1183P} and references therein), starting with the pioneering work by \citet{1928RSPSA.119...11R}. In the following, we will concentrate on optical wavelengths only.\\ The NSB is the integrated light from two main kinds of sources: natural and artificial. Among the sources of natural origin are airglow (recombination of molecules heated by Sun UV radiation during daytime), aurorae, zodiacal light (sunlight scattered from interplanetary dust), diffuse galactic light (from faint unresolved stars in our Galaxy), and the extragalactic background (due to distant, faint unresolved galaxies). The airglow and aurorae, which originate in the Earth's atmosphere, depend upon the site and time of the observation, while the other three do not. The source of artificial light is mainly street lighting, with an increasing contribution from electronic billboards and other luminous advertising media. This contribution, also known as light pollution, is amenable to monitoring through long-term campaigns of the variation in the night sky brightness (\citealp{1979PASP...91..530S}; \citealp{1988PASP..100..496W}; \citealp{1975PASP...87..869K}; \citealp{1987PASP...99..887K}; \citealp{1989PASP..101..707P}; \citealp{1995A&AS..112...99L}).\\ In Fig.~\ref{fig:cities} we show the cities and towns near the OAN-SPM. The cities of Ensenada and Tijuana lie between 150 and 230\,km NW of OAN-SPM and have populations of 480,000 and 1.6 million people, respectively. The city of San Diego lies 260\,km distant, also to the NW, with a population of 1.3 million people. An estimate of the contribution to the NSB due to light from nearby cities can be obtained using the model of \citet{1989PASP..101..306G}, which provides an approximate light-pollution contribution expected from different sources. The combined contribution of Ensenada, Tijuana and San Diego to the sky brightness at the OAN-SPM is estimated to be less than 0.08\,mag at a zenith distance of 45$^{\circ}$. To the Northeast, at an average distance of 185\,km, the cities of Mexicali, Yuma, and San Luis R\'\i o Colorado, with a combined population of 1.3 million contribute with 0.04\,mag. Other cities like San Felipe and San Quint\'\i n, which are nearer to the observatory ($\sim$60\,km), but less populated ($\sim$17\,000 and 10\,000 people) contribute $<$0.01\,mag each. In Baja California, state lighting ordinances that took effect starting in 2006 in the municipality of Ensenada and statewide in 2010 include light pollution among the environmental disturbances to be controlled. Among its goals, this legislation seeks to reduce or at least minimize the light pollution, even with the constant growth of its cities.\\ \begin{figure*} \begin{center} \includegraphics[width=0.80\textwidth]{f1.eps} \caption{Night map showing nearby cities and their approximate distances to OAN-SPM. The cross indicates the location of the OAN-SPM. Bright areas indicate street lights as seen from space. Credit: Google maps and NightEarth.com with data provided by NASA.} \label{fig:cities} \end{center} \end{figure*} In the present paper we report UBVRI sky brightness measurements obtained on eighteen moonless nights during 2013 to 2016 and SQM sky brightness measurements collected daily during 2014 to 2016. As far as we are aware, these data constitute the largest homogeneous data set available for the OAN-SPM. The SQM data set is continuously accumulating and it will provide an unprecedented opportunity to investigate the long-term evolution of the night sky at the OAN-SPM. In Sect.~\ref{sec:observ}, we present our observation procedures and reduction techniques. The results are presented in Sect.~\ref{sec:results}, while, in Sect.~\ref{sec:discuss}, we consider the variation of the NSB as a function of the solar activity and compare our measurements with other dark sites. Finally, in Sect.~\ref{sec:concl}, we present our conclusions. | \label{sec:concl} We obtained UBVRI photometry of the night sky brightness (NSB) during 18 nights from 2013 to 2016 and SQM measurements on a daily basis from 2014 to 2016 at the Observatorio Astron\'omico Nacional on the Sierra San Pedro M\'artir (OAN-SPM). We have taken into account contributions to the sky brightness due to zodiacal light and have excluded observations at low galactic latitudes in order to compare our data to those obtained at other sites. We find no clear trend of the NSB as a function of time after twilight. The dispersion of NSB measurements over the course of a night is typically 0.2\,mag, based upon our SQM data. \\ We investigate the long term variations of the NSB and its correlation with solar activity. We find a trend of decreasing NSB with decreasing solar activity in the UBVR and SQM bands, though the trend is statistically robust only for the UB and SQM bands, perhaps due to too few data points in the VR bands. \\ We compare the NSB at the OAN-SPM with measurements made elsewhere and find that the NSB at the OAN-SPM is comparable to that of other observing sites. When comparing data from different observatories, we find a strong correlation between the NSB and the solar flux at the time the measurements were made, which can be useful to estimate the expected increase in the NSB due to solar actvity for any site. The variation in the NSB due to solar activity can be as high as 0.6 and 0.9\,mag (B and V bands) from the maximum (250 sfu) to the minimum (60 sfu) of the solar cycle. The NSB data presented here should be useful for long-term monitoring of the quality of OAN-SPM site, which remains one of the darkest sites in use and for future large telescope facilities.\\ | 16 | 9 | 1609.00423 |
1609 | 1609.05030_arXiv.txt | { Electron cyclotron resonant scattering features (CRSFs) are observed as absorption-like lines in the spectra of X-ray pulsars. A significant fraction of the computing time for Monte Carlo simulations of these quantum mechanical features is spent on the calculation of the mean free path for each individual photon before scattering, since it involves a complex numerical integration over the scattering cross section and the (thermal) velocity distribution of the scattering electrons. } { We aim to numerically calculate interpolation tables which can be used in CRSF simulations to sample the mean free path of the scattering photon and the momentum of the scattering electron. The tables also contain all the information required for sampling the scattering electron's final spin. } { The tables were calculated using an adaptive Simpson integration scheme. The energy and angle grids were refined until a prescribed accuracy is reached. The tables are used by our simulation code to produce artificial CRSF spectra. The electron momenta sampled during these simulations were analyzed and justified using theoretically determined boundaries. } { We present a complete set of tables suited for mean free path calculations of Monte Carlo simulations of the cyclotron scattering process for conditions expected in typical X-ray pulsar accretion columns ($0.01 \le B/B_{\mathrm{crit}} \le 0.12$, where $B_\mathrm{crit}=4.413\times 10^{13}\,\mathrm{G}$, and $3\,\mathrm{keV} \le k_\mathrm{B} T \le 15\,\mathrm{keV}$). The sampling of the tables is chosen such that the results have an estimated relative error of at most $1/15$ for all points in the grid. The tables are available online. } {} | \label{sec:intro} Cyclotron resonant scattering features (CRSFs, often also called ``cyclotron lines'') have been measured in numerous accreting X-ray pulsars and are the only direct way to measure a neutron star's magnetic field. They result from the interaction of photons with electrons in the presence of strong B-fields approaching the critical field strength, \begin{equation}\label{eq:B_crit} B_\mathrm{crit}= \frac{m_e^2 c^3}{e\hbar} = 4.413\times 10^{13}\,\mathrm{G}\,, \end{equation} where $m_e$ is the electron rest mass, $e$ its charge, and $c$ the speed of light. Their positions can be estimated as $\sim$$n\,E_\mathrm{cyc}\;(n=1, 2, 3,\ldots)$ using the 12-B-12 rule, $E_\mathrm{cyc} \approx 12 B_{12}\,\mathrm{keV}$, with the B-field strength $B_{12}$ given in units of $10^{12}\,G$. Cyclotron lines have their origin in transitions of electrons between different Landau levels, which are the discrete energy states an electron can occupy within such a strong magnetic field. The electrons are quantized perpendicular to the field and therefore give rise to quantum mechanical absorption and resonant scattering processes altering the spectral and spatial distribution of the participating photons. The probability for an interaction to occur is given by the corresponding cyclotron cross section. In the course of simulating this process with Monte Carlo (MC) methods, these cross sections can be used to sample the mean free path of a photon within such a medium. We have separated this core issue from the larger simulation code to allow for an efficient simulation of any complex X-ray pulsar geometry based on precalculated tables of the mean free path. In the following we describe the calculation method and usage of these mean free path interpolation tables and discuss how the sampling of electron parallel momenta influences the formation of CRSFs. In Sect.~\ref{sec:tables} we discuss the necessity of mean free path interpolation tables and their usage and introduce their computation and the interpolation mechanism. In Sect.~\ref{sec:momentum} we explain the importance of the sampling of the electron parallel momentum. In particular we illustrate the connection between cyclotron resonances and the corresponding behavior of the sampled electron parallel momenta, since the understanding of these parameters is essential for the application of the Monte Carlo code to generate synthetic spectra. Many more applications can be envisioned, including the simulation of the influence of cyclotron scattering on the electrons, or the overall accretion geometry. Here, we restrict ourselves to the discussion of the mean free path interpolation tables. Their motivation and application is described against the background of Monte Carlo simulation of cyclotron lines. The description and application of the full MC scattering code, which has been written with the prime goal of imprinting cyclotron lines on the continuum emission of astronomical X-ray sources, and which includes a working fit model, will be the subject of a forthcoming publication \citep[hereafter paper II]{schwarm16b}. Compared to previous MC simulations, it allows for much more complex physical scenarios, the exploration of which is the goal of this series of papers. | For accelerating Monte Carlo simulations of cyclotron lines we replaced the most time consuming part -- that is the calculation of the photon mean free path -- with a tabular interpolation scheme. These tables store the mean free paths of photons for different incident angles and energies. The partial results necessary for interpolating the electron momentum after a mean free path has been drawn from the exponential probability distribution, and the spin dependent results, are saved as well. The electronic tables described here are available online. This interpolation scheme is used to generate synthetic cyclotron line spectra using our MC simulation code. It enables us to simulate much more complex physical scenarios than previous works. As an example, we have investigated the application of the momentum sampling. | 16 | 9 | 1609.05030 |
1609 | 1609.08959_arXiv.txt | { In this paper, we consider two case examples of Dirac-Born-Infeld (DBI) generalizations of canonical large-field inflation models, characterized by a reduced sound speed, $c_{S} < 1$. The reduced speed of sound lowers the tensor-scalar ratio, improving the fit of the models to the data, but increases the equilateral-mode non-Gaussianity, $f^\mathrm{equil.}_\mathrm{NL}$, which the latest results from the Planck satellite constrain by a new upper bound. We examine constraints on these models in light of the most recent Planck and BICEP/Keck results, and find that they have a greatly decreased window of viability. The upper bound on $f^\mathrm{equil.}_\mathrm{NL}$ corresponds to a lower bound on the sound speed and a corresponding lower bound on the tensor-scalar ratio of $r \sim 0.01$, so that near-future Cosmic Microwave Background observations may be capable of ruling out entire classes of DBI inflation models. The result is, however, not universal: infrared-type DBI inflation models, where the speed of sound increases with time, are not subject to the bound. } | Inflationary cosmology \cite{Starobinsky:1980te,Sato:1981ds,Sato:1980yn,Kazanas:1980tx,Guth:1980zm,Linde:1981mu,Albrecht:1982wi} remains a uniquely successful phenomenological framework for understanding the origins of the universe, making quantitative predictions which current data strongly support \cite{Spergel:2006hy,Alabidi:2006qa,Seljak:2006bg,Kinney:2006qm,Martin:2006rs}. Inflation relates the evolution of the universe to one or more scalar \textit{inflaton} fields, the properties of which dictate the dynamics of the period of rapidly accelerating expansion which terminates locally in a period of reheating, followed by radiation-dominated expansion. The specific form of the potential for the inflaton field or fields is unknown, but different choices of potential result in different values for cosmological parameters, which are distinguishable by observation \cite{Dodelson:1997hr,Kinney:1998md}. Recent data, in particular the Planck measurement of Cosmic Microwave Background (CMB) anisotropy and polarization \cite{Ade:2015lrj,Ade:2015xua,Aghanim:2015xee} and the BICEP/Keck measurement of CMB polarization \cite{Ade:2015fwj} now place strong constraints on the inflationary parameter space, and falsify many previously viable inflationary potentials, including some of the simplest and most theoretically attractive models. A particular class of models now known to be in conflict with CMB data is so-called ``large-field'' potentials, canonical scalar field models with field excursion during inflation $\Delta\phi \geq M_{\rm P}$, where $M_{\rm P} \equiv m_{\rm Pl} / \sqrt{8 \pi}$ is the reduced Planck mass. Such models predict a tensor scalar ratio $r \sim O(0.1)$ \cite{Lyth:1996im}, which conflicts with an upper bound from CMB data of $r < 0.066$ \cite{Kinney:2016qyl}. This is a result of the steepness of the potential, with \begin{equation} r = 16 \epsilon, \end{equation} where $\epsilon$ is a parameter related to the equation of state during inflation, and is set by the first derivative of the potential during slow-roll inflation, \begin{equation} \epsilon \equiv \frac{3}{2}\left(\frac{p}{\rho} + 1\right) \simeq \frac{M_{\rm P}^2}{2} \left(\frac{V'\left(\phi\right)}{V\left(\phi\right)}\right)^2, \end{equation} where a prime represents a derivative with respect to the field $\phi$. Large-field models generically have potentials steep enough that $\epsilon \sim O(0.01)$, resulting in the overproduction of tensors. An example is a quadratic potential, $V\left(\phi\right) = m^2 \phi^2$, which produces tensor/scalar ratio $r \sim 0.15$, and is therefore ruled out by Planck/BICEP/Keck \cite{Kinney:2016qyl}. (Previous work \cite{Baumann:2014cja,Palma:2014faa,Zavala:2014bda,Gobbetti:2015cya} has considered the effect of a {\it lower bound} on $r$ on the speed of sound inflationary model building. In this paper, we consider the effect of an {\it upper bound}, consistent with current constraints.) The simplest way to reconcile single-field inflation with CMB data is to choose ``small-field'' potentials, for which $\Delta\phi \ll M_{\rm P}$ during inflation. An example is hilltop-type inflation models \cite{Kohri:2007gq,Martin:2013tda,Barenboim:2013wra,Coone:2015fha,Huang:2015cke,Vennin:2015egh,Barenboim:2016mmw}, for which $V'\left(\phi\right) \rightarrow 0$ near the inflationary fixed-point and $r \ll 0.1$, or plateau-type models such as Starobinsky inflation \cite{Starobinsky:1980te,Kehagias:2013mya}. Warm Inflation, which occurs in the presence of a thermal bath, may also reconcile large-field models with data \cite{Bastero-Gil:2016qru}. Another, less-studied alternative is to consider non-canonical generalizations of large-field inflation models \cite{Kinney:2007ag,Tzirakis:2008qy}. If we take a general non-canonical Lagrangian ${\mathcal L}\left(X,\phi\right)$, where \begin{equation} X \equiv \frac{1}{2} g^{\mu\nu}\partial_\mu \phi \partial_\nu\phi \end{equation} is the standard canonical kinetic term, the speed of sound is no longer generically equal to the speed of light, but is given by \begin{equation} c_S^2 = \frac{{\mathcal L}_X}{{\mathcal L}_X + 2 X {\mathcal L}_{XX}}, \end{equation} where a subscript indicates a derivative, ${\mathcal L}_X \equiv \delta {\mathcal L} / \delta X$. This affects inflationary observables, in particular the tensor/scalar ratio, which generalizes for non-canonical Lagrangians to \begin{equation} r = r = 16 \epsilon c_S^{\left(1+\epsilon\right)/\left(1-\epsilon\right)}, \end{equation} so that, for $c_S \ll 1$, tensors are suppressed even for large $\epsilon$, and large-field models can be made consistent with CMB limits \cite{Tzirakis:2008qy} despite the steepness of the potential. Tensor suppression from non-canonical kinetic terms comes at a price, however. A small sound speed generates equilateral-mode non-Gaussianity in CMB fluctuations, with \begin{equation} f^{\rm equil.}_{\rm NL} \propto \frac{1}{c_S^2}. \end{equation} The Planck CMB data place a strong {\it upper bound} on non-Gaussianity, with a $1\sigma$ constraint on the equilateral mode of \cite{Ade:2015ava} \begin{equation} f^{\rm equil.}_{\rm NL} = -4 \pm 43. \end{equation} This means that there is a limit on how much tensor suppression can be achieved before violating the bound on non-Gaussianity, since smaller $c_S$ means larger $f^{\rm equil.}_{\rm NL}$ \cite{Baumann:2014cja}. In this paper, we revisit calculations of tensor suppression from non-canonical terms in power-law inflation \cite{Kinney:2007ag} and ``isokinetic'' generalizations of quadratic large-field inflation models \cite{Tzirakis:2008qy}, and derive new lower bounds on the tensor/scalar ratios for these cases. We find that the ultraviolet-type Dirac-Born-Infeld (DBI) models and isokinetic models are compatible with Planck bounds on both $r$ and $f^{\rm equil.}_{\rm NL}$ in both cases, but with a lower bound on the tensor/scalar ratio of $r \sim 0.01$, a figure within reach of near-future CMB experiments. Thus, next-generation CMB observations may rule out not only canonical large-field models, but classes of non-canonical generalization as well. Infrared-type DBI models are not subject to the bound. The paper is organized as follows: In Sec. \ref{sec:Review}, we review canonical scalar field theories for inflation as described by the useful horizon flow formalism \cite{Kinney:2002qn}, and the generalization of the flow equations to non-canonical theories \cite{Peiris:2007gz}. In Sec. \ref{sec:PowerLaw} we discuss observational limits on non-canonical generalizations of power-law inflation models, in Sec. \ref{sec:Isokinetic} we discuss the corresponding limits on isokinetic generalizations to quadratic large-field models, and in Section \ref{sec:SlowRoll} we discuss the general slow-roll case. Section \ref{sec:Conclusions} presents summary and conclusions. | \label{sec:Conclusions} In this paper, we have considered non-canonical generalizations to large-field inflation models, which generically overproduce tensors and are inconsistent with CMB constraints. Non-canonical Lagrangians are characterized by a sound speed $c_S < 1$, which results in suppression of the tensor/scalar ratio, allowing models which overproduce tensors to be brought into agreement with current constraints. We first considered non-canonical generalizations of the Power-Law inflation scenario, which is exactly solvable in both canonical and non-canonical versions. We next considered the non-canonical generalization of the simplest ``chaotic" inflation scenario with potential $V(\phi)=m^2\phi^2$, for which the field evolves with a near-constant velocity $\dot{\phi}$, called ``isokinetic'' inflation. We found that for both of these cases, the current $2\sigma$ upper bounds on $f^\mathrm{equil.}_\mathrm{NL}$ creates a {\it lower bound} on $r$ of order $0.01$, creating a narrow window of potential viability for the models. In the power-law case, the bound only applies to ultraviolet-type DBI inflation, for which the slow roll parameter $s < 0$, and the brane evolves {\it toward} the tip of the Klebanov-Strassler throat. While such models are allowed by the Planck data alone, Planck combined with constraints from perturbative unitarity \cite{Baumann:2015nta} rule them out altogether. The original DBI model of Silverstein and Tong, for example, is of this type, with $s = - 2 \epsilon$ \cite{Silverstein:2003hf}. Other versions of the power-law DBI inflation, however, survive, in particular the infrared-type DBI models, for which $s > 0$ \cite{Chen:2004gc,Chen:2005ad}, and the brane evolves {\it away from} the tip of the throat. In this case, there is no lower bound on the parameter $\epsilon$ and therefore no lower bound on $r$, despite the lower bound on the sound speed $c_S$. A tensor/scalar ratio $r \sim 0.01$ is within range of near-future Cosmic Microwave Background experiments, so that a lack of detection of tensor modes will not only rule out large-field models in their canonical form, but broad classes of non-canonical generalizations as well. | 16 | 9 | 1609.08959 |
1609 | 1609.04170_arXiv.txt | We test one-zone synchrotron self-Compton (SSC) models with high-quality multiwavelength spectral energy distribution (SED) data of Mrk 421. We use Markov chain Monte Carlo (MCMC) technique to fit twelve day-scale SEDs of Mrk 421 with one-zone SSC models. Three types of electron energy distribution (EED), a log-parabola (LP) EED, a power-law log-parabola (PLLP) EED and a broken power-law (BPL) EED, are assumed in fits. We find that the one-zone SSC model with the PLLP EED provides successful fits to all the twelve SEDs. However, the one-zone SSC model with the LP and BPL EEDs fail to provide acceptable fits to the highest energy X-ray data or GeV data in several states. We therefore conclude that the one-zone SSC model works well in explaining the SEDs of Mrk 421, and the PLLP EED is preferred over the LP and BPL EEDs for Mrk 421 during the flare in March 2010. We derive magnetic field $B'\sim0.01$\ G, Doppler factor $\delta_{\rm D}\sim$30--50, and the curvature parameter of EED $r\sim1$--$10$ in the model with the PLLP EED. The evolutions of model parameters are explored. The physical implications of our results are discussed. | Blazars are a class of radio-loud active galactic nuclei (AGN) whose jets point to Earth. Blazar emission extends from MHz radio frequencies to TeV gamma-ray energies. Their spectral energy distributions (SEDs) have two bumps, one peaking at infrared to X-rays, and the other peaking in gamma-ray energies. It is believed that the low-energy bump is the synchrotron emission from high-energy electrons in the jet. The origin of the high-energy bump is still under debate. Leptonic models and hadronic models have been proposed to explain the origin of the high-energy bump. In the leptonic models, the high-energy bump is the inverse-Compton emission from high-energy electrons scattering low-energy photons \citep[e.g.,][]{Dermer93,Sikora1994}. In the hadronic models, the high-energy bump is the synchrotron emissions radiated by high-energy protons or secondary particles produced in proton-photon interactions \citep[e.g.,][]{Mannheim,mucke2001,bottcher13}. For high-synchrotron-peaked (HSP) BL Lac objects whose synchrotron peak frequency is greater than $10^{15}\ $Hz \citep{Abdo10}, a one-zone leptonic synchrotron-self Compton (SSC) model usually provides excellent fits to their SEDs \citep{Abdo11a,Abdo11b,Man,zhang12,Yan14,Zhou14}. Mrk 421 and Mrk 501 are two of the closest (the redshift $z=0.031$ and $z=0.034$ respectively) and brightest TeV HSPs. Many multiwavelength monitoring campaigns for the two typical HSPs have been organized to study their broadband SEDs \citep[e.g.,][]{Abdo11b,Aleksi15,Balokovic,Bartoli,Furniss}. We recently notice that new extensive broadband data seem to challenge the one-one SSC model for HSPs. \citet{Shukla} constructed the simultaneous SEDs of Mrk 501 from observations during 2011. They claimed that a one-zone SSC model cannot explain the SED of Mrk 501 during 2011 April-May, due to the hard {\it Fermi}-LAT spectrum. \citet{Furniss} reported the simultaneous broadband observations of Mrk 501 between 2013 April 1 and August 10, including the first {\it NuSTAR} observations, and modelled the SEDs with a one-zone SSC model. Looking at their modelling results, one can see that the one-zone SSC model cannot reproduce the highest TeV data. \citet{Balokovic} presented the simultaneous broadband observations of Mrk 421 taken in 2013 January-March, and they modelled these SEDs with a one-zone SSC model. One can see that the SSC model is inconsistent with the GeV-TeV spectrum obtained during 2013 January 15. Mrk 421 was observed at multiwavelengthes for 13 consecutive days during March 2010, and its simultaneous SEDs with unprecedented wavelength coverage from radio frequencies to GeV-TeV energies were built \citep{Aleksi15}. \citet{Aleksi15} found that in several states the one-zone SSC model does not matches the observed data. In order to match the data, \citet{Shukla} and \citet{Aleksi15} developed a two-zone SSC model for Mrk 501 and Mrk 421. Although several examples that challenge the one-zone SSC model for Mrk 421 and Mrk 501 are summarized above, one cannot exclude the one-zone SSC model for the two typical HSPs. In our view a key point is missing, i.e., the above studies dot not perform searching for parameter space, and therefore the modelling result may not be the best-fit result. It is important to find convinced evidence for the failures of one-zone SSC model for HSPs. It will motivate us to develop new models, and to find new emission mechanisms, which has a big impact on our understandings of the blazar jet physics. As mentioned above, \citet{Aleksi15} reported the day-scale SEDs of Mrk 421 during a flare state in March 2010. These SEDs have unprecedented wavelength coverage. We adopt these high-quality SEDs to test the one-zone SSC model. Given that we do not know the electron energy distribution (EED) in the emission region, we assume three kinds of EED, i.e., a log-parabola (LP) EED, a power-law log-parabola (PLLP) EED and a broken power-law (BPL) EED. The Markov chain Monte Carlo (MCMC) technique is used to search high-dimension parameter space, and to obtain the best-fit result. Throughout this paper, the cosmology with $H_0=71\rm \ km\ s^{-1}\ Mpc^{-3}$, $\Omega_{\rm m}=0.27$, and $\Omega_{\Lambda}=0.73$ is adopted. | Taking advantage of the MCMC technique \citep{Yan13,Yan151}, we test the one-zone SSC models for Mrk 421 using the high-quality SEDs with unprecedented data coverage reported in \citet{Aleksi15}. According to the fitting results, we conclude that the one-zone SSC model still works well in explaining the broadband SEDs. There is no evidence of a second leptonic/hadronic emission component. Furthermore, our study rules out the LP and BPL EEDs for Mrk 421, and supports the PLLP EED. We determine the magnetic field $B'\sim0.01\ $G and the radius of blob $R'_{\rm b}\sim[5-8]\times10^{16}\ $cm in the PLLP model. The curvature in electron distribution is related to second-order Fermi acceleration theory \citep[e.g.,][]{Becker06,Massaro6,sp08,Tramacere11,Yan12,Asano14}. Second-order processes broaden the injected electron distribution, and introduce a curvature into the energy distribution. Our results that the EED in the jet of Mrk 421 is the PLLP EED implies a scenario combining the first- and second-order Fermi acceleration processes, in which a power-law distribution of particles injected downstream of a shock into a turbulent region where the second-order Fermi acceleration processes broaden the distribution, and then the PLLP EED is formed. The curvature of PLLP EED $r$ in MJD 55265 and MJD 55266 is extremely large, so that the EED is very close to a single power-law distribution. This may be due to the cooling effect \citep{Tramacere11}. The evolution of model parameters can reveal the information of physical processes \citep[e.g.,][]{Yan13,Yan16}. We find that the cut-off energy $\g'_{\rm c}$ in the PLLP EED increases with the EED's curvature $r$. \citet{Tramacere11} have shown that the curvature $r$ is inversely proportional to the momentum diffusion coefficient when acceleration is dominated over cooling; and $r$ quickly increases once the cooling becomes relevant. The evolution of $\g'_{\rm c}$ with $r$ (Fig.~\ref{g-c}) hints that the radiative cooling of electrons become relevant and the EED approaches the equilibrium between acceleration and cooling. Moreover, the trend of $\nu^{\rm pk}_{\rm s} - b_{\rm s}$ we derived (Fig.~\ref{rv}; using the relation $b_{\rm s}\simeq r/5$) is different from the inverse correlation found in optical-X-ray data analysis on HSPs \citep[e.g.,][]{Massaro6,MassaroE,Tramacere07,Tramacere09}. The inverse correlation between $\nu^{\rm pk}_{\rm s}$ and $b_{\rm s}$ may imply an acceleration-dominated scenario \citep{Tramacere11}. From our resutls, one can see that the evolution of $\nu^{\rm pk}_{\rm s} - b_{\rm s}$ is the direct representation of the evolution of $\g'_{\rm c} - r$ in the observable space. \citet{Yan13} analyzed two SEDs of Mrk 421, respectively, in a quiescent state \citep{Abdo11b} and in a giant TeV flare \citep{Shukla12}, and found that the EED in the TeV flare is the PLLP. The 12 SEDs analyzed in this work are obtained in a X-ray and TeV flare state in March 2010 \citep{Aleksi15}. It seems that the PLLP EED that involves the first- and second-order Fermi acceleration processes works in the flare state of Mrk 421, and the cooling timescale of electrons with $\g'_{\rm c}$ may be close to the acceleration timescale. The physical mechanism in quiescent states of Mrk 421 is worth a systematical investigation in a separate study. As a last remark, we would like to note that an alternative model to explain the SEDs is the leptonic-hadronic model. \citet{Petropouloua} explained the 13 SEDs in \citet{Aleksi15} well with a one-zone leptonic-hadronic model. They derived $B'=5\ $G and $\delta_{\rm D}\sim20$, which are different from those derived in the leptonic model. The hadronic model is attractive, since it predicts high-energy neutrinos. To distinguish the leptonic model from the hadronic model is not only important for understanding the jet physics, but also important for resolving the origin of the high-energy cosmic neutrinos, however, it is still very difficult for now. | 16 | 9 | 1609.04170 |
1609 | 1609.03566_arXiv.txt | We propose a new method to probe the Warm Hot Intergalactic Medium (WHIM) beyond the virial radius ($R_{200}$) of a cluster of galaxies, where X-ray observations are not easily achievable. In this method, we use dispersion measures (DMs) of Fast Radio Bursts (FRBs) that appear behind the cluster and the Sunyaev-Zel'dovich (SZ) effect towards the cluster. The DMs reflect the density of the intracluster medium (ICM) including the WHIM. If we observe a sufficient number of FRBs in the direction of the cluster, we can derive the density profile from the DMs. Similarly, we can derive the pressure profile from the SZ effect. By combining the density and the pressure profiles, the temperature profile can be obtained. Based on mock observations of nearby clusters, we find that the density of the WHIM can be determined even at $> 2\: R_{\rm 200}$ from the cluster center when FRB observations with the Square Kilometre Array (SKA) become available. The temperature can be derived out to $r\sim 1.5\: R_{\rm 200}$, and the radius is limited by the current sensitivity of SZ observations. | \label{sec:intro} It has been predicted that a diffuse warm hot intergalactic medium (WHIM) at temperatures $T\sim 10^5$--$10^7$~K contains $\sim $50\% of the baryons in the universe at low redshifts \citep[e.g.][]{1999ApJ...514....1C,2001ApJ...552..473D}. Although a number of surveys have been conducted to constrain the WHIM \citep[e.g.][]{2005Natur.433..495N,2007PASJ...59S.339T,fuj08b,2008ApJ...679..194D,2008ApJS..177...39T}, they have detected only a fraction of the predicted amount of the WHIM. Some of the WHIM is expected to exist in the outskirts of galaxy clusters. This WHIM gradually falls into the clusters and is heated at accretion shocks \citep[e.g.][]{ryu03a}. Thus, we can understand the process in which the WHIM turns into the hot intracluster medium (ICM) in the clusters by exploring the WHIM in this region. The outskirts of clusters have been investigated in X-rays especially with {\it Suzaku} (e.g. \citealt{fuj08b,rei09a,2009MNRAS.395..657G,2010ApJ...714..423K,2010PASJ...62..371H,2011PASJ...63S1019A,sim11a,2012MNRAS.422.3503W,2012PASJ...64...95S,2013ApJ...766...90I,2016ApJ...829...49W}, see a recent review by \citealt{rei13a}). Many of these observations show that the entropy of the ICM in the outskirts of massive clusters is smaller than that predicted by numerical simulations (e.g. \citealt{voi05a} but see \citealt{eck13a}), which may indicate that the heating is less effective than expected \citep[e.g.][]{2009ApJ...707.1141W,fuj13b}. Unfortunately, the X-ray observations are limited to $r\lesssim R_{200}$, where $R_{200}$ is the radius at which the cluster density is 200 times the critical density at that redshift and is often regarded as the virial radius of the cluster \citep[e.g.][]{nav96a}. In order to understand the heating process, observations of the WHIM at $r\gtrsim R_{200}$ are crucial. Although the signatures of the (thermal) Sunyaev-Zel'dovich (SZ) effect \citep{1972CoASP...4..173S} have been detected at $r\gtrsim R_{200}$ for a number of clusters \citep{pla13d,pla15b,pla15a}, it gives us only the information on the pressure profiles, and the density and the temperature profiles are not obtained separately. Fast Radio Bursts (FRBs) are bright, unresolved, millisecond signals. Although their origin is not clear, their large dispersion measures (DMs) suggest that they are extragalactic \citep{2007Sci...318..777L,2012MNRAS.425L..71K,2013Sci...341...53T,2014ApJ...790..101S,2014ApJ...792...19B,2015ApJ...799L...5R,2015MNRAS.447..246P,mas15b}. It has been proposed that the DMs of transient objects such as gamma-ray bursts (GRBs) and FRBs can be used to probe the WHIM along the line of sight \citep{2003ApJ...598L..79I,2004MNRAS.348..999I}. In this study, we propose a new idea to explore the WHIM by combining the DMs of FRBs and the SZ effect. We show that this method will reveal the properties of the WHIM at $r\gtrsim R_{200}$ when observations of FRBs with the Square Kilometre Array (SKA) become available. We use $H_0=70\:\rm km\: s^{-1}\: Mpc^{-1}$, $\Omega_m=0.3$, and $\Omega_\Lambda=0.7$. | We have proposed a new method to observe the ICM including WHIM in the outskirts of galaxy clusters. In this method, DMs of numerous FRBs and the SZ effect are combined. Since the DMs and the SZ effect give information on the ICM density and pressure, respectively, we can estimate the temperature of the ICM from them. From mock observations of a massive cluster with SKA1-MID and {\it Planck}, we showed that the ICM density could be determined even at $> 2\: R_{200}$, while the temperature profile could be derived out to $\sim 1.5\: R_{200}$, and this maximum radius is limited by the current sensitivity of the SZ observations \citep{pla13a,pla13d}. We find that the low-$\ell$ excess ($\ell\lesssim 50$) in the {\em Planck} noise power spectrum $P_{\ell,\mathrm{noise}}$ due to residual foreground contamination \citep{pla15a} has a non-negligible impact on the simulated $y$ errors in the cluster outskirts. Hence, it will be important in cluster outskirt studies to reduce the level of foreground contamination in $y$ maps at large angular scales. The combination of our method and X-ray observations can be useful. For example, clumpiness of the ICM could be studied. The ICM density and temperature have been obtained for the interior ($\lesssim R_{200}$) of many clusters especially with {\it Suzaku} \citep[e.g.][]{rei13a}. The X-ray surface brightness of a cluster is represented by \begin{equation} S_X\propto \int^{\infty}_{-\infty} n_{\rm ICM}^2 dL\:, \end{equation} if the weak temperature dependence is ignored. The density dependence ($n_{\rm ICM}^2$) is different from that for the DM ($n_{\rm ICM}$) in equation~(\ref{eq:DMICMorg}). This means that if the ICM is moderately clumpy on a small scale that cannot be resolved by X-ray telescopes, $S_X$ will be higher than that for smoothly distributed ICM with the same mass. This does not happen for the DM, which is not dependent on the clumpiness for a given column density. Thus, $n_{\rm ICM}$ determined by X-ray observations is systematically higher than that determined by DM observations. Note that while the $y$ parameter depends linearly on $n_{\rm ICM}$ as does the DM (equation~(\ref{eq:y})), its behavior may be different from that of the DM. For example, if the clump size is relatively large and the ICM is in pressure equilibrium on that scale, the DM values depend on whether the line-of-sight to a FRB crosses one or more clumps because the column density fluctuates, while the $y$ parameter is not much affected by the clumping. The large-scale structure filaments that connect clusters are also expected to have the WHIM \citep{1999ApJ...514....1C}, although it is difficult to detect the SZ effect toward them because they are usually located at $r\gg R_{\rm 200}$. However, the typical density of a particular filament can be obtained if a sufficient number of FRBs are detected toward the filament and their DMs are measured. Here the location of the filament can be inferred from galaxy distributions. One problem is that the density $n_{\rm fil}$ is degenerate with the depth of the filament along the line of sight $L_{\rm fil}$, because ${\rm DM_{fil}}\propto n_{\rm fil}L_{\rm fil}$ assuming that $n_{\rm fil}$ is constant. However, this degeneracy can be resolved by an observation of line emissions from the filament. For example, the WHIM is expected to radiate O{\small VII} and O{\small VIII} line emissions \citep{yos03a}, and the line surface brightness varies as $S_{\rm L}\propto n_{\rm fil}^2 L_{\rm fil}$. Thus, the density can be derived as $n_{\rm fil}\propto S_{\rm L}/{\rm DM_{fil}}$. The oxygen lines could be observed with {\it DIOS} \citep{2015arXiv150308405O} and {\it Athena}\footnote{http://www.the-athena-x-ray-observatory.eu/} in the future. In the future, the efficiency of FRB searches may dramatically improve. If FRBs are found to be bright at lower frequencies, they can be detected with SKA1-LOW, which has a huge FOV ($20.77 \rm\: deg^{-2}$ at 110~MHz; \citealt{dew16a}). When SKA2 becomes available, the sensitivity will increase by a factor of 10 compared with SKA1\footnote{http://astronomers.skatelescope.org/ska2/}, which means that the required exposure time will be significantly reduced. Moreover, if the origin of the dispersion, $\sigma_{\rm DM}^2$, is revealed, its influence on the error, $\delta{\rm \langle DM\rangle_{ICM}}$ (equation~(\ref{eq:dDMICM})), can be decreased by considering an appropriate correction based on this knowledge. For example, if the DMs of FRBs vary with the distance and the positions of the hosts are known well enough to get a redshift, the distance dependence can be removed. This could greatly reduce the uncertainty of the DM values, and make the errors in our method much smaller. Although we have focused on individual cluster measurements, this method can be readily generalized to study a stacked ensemble of high-redshift clusters or group-sized systems. The Canadian Hydrogen Intensity Mapping Experiment\footnote{http://chime.phas.ubc.ca/} and The Next Generation Very Large Array\footnote{https://science.nrao.edu/futures/ngvla} may also be useful for this study. | 16 | 9 | 1609.03566 |
1609 | 1609.04941_arXiv.txt | We find that the ratio $r_{\mu e}$ of the muon to the electromagnetic component of an extended air shower at the ground level provides an indirect measure of the depth $X_{\rm max}$ of the shower maximum. This result, obtained with the air-shower code AIRES, is independent of the hadronic model used in the simulation. We show that the value of $r_{\mu e}$ in a particular shower discriminates its proton or iron nature with a 98\% efficiency. We also show that the eventual production of {\it forward} heavy quarks inside the shower may introduce anomalous values of $r_{\mu e}$ in isolated events. | Ultrahigh energy comic rays (CRs) enter the atmosphere with energies above $10^{9}\; {\rm GeV} = 1\; {\rm EeV}$. The precise determination of their composition, direction of arrival and energy provides valuable information about their astrophysical sources and about the medium that they have traveled through on their way to the Earth. In addition, their collisions with air nuclei probe QCD in a regime never tested at colliders. The center of mass energy $\sqrt{2Em_N}$ when the primary CR or the leading hadron inside an extensive air shower (EAS) hits an atmospheric nucleon is $14$ TeV for $E=10^8$ GeV, the nominal energy at the LHC. Beyond that point collisions occur in uncharted territory. The complementarity between air-shower and collider observations does not refer only to the energy involved in the collisions, but also to the kinematic regions that are accessible in each type of experiments. At colliders the detectors capable of particle identification do not cover the ultraforward region, too close to the beampipe. This region includes the {\it spectator} degrees of freedom in the projectile, which carry a large fraction of the incident energy after the collision. It turns out that the details there can be relevant to the longitudinal development of EASs. The production of forward heavy hadrons \cite{Brodsky:1980pb}, for example, is a possibility frequently entertained in the literature that is difficult to test at colliders \cite{Lykasov:2012hf}. Air-shower observatories with surface detectors able to separate the muon from the electromagnetic (EM) signals, like the Pierre Auger Observatory \cite{AugerOriginal} will after its projected upgrade \cite{AugerUpgrade}, offer new oportunities in the characterization of EASs. In this paper we show that the ratio of these two signals at the ground level defines a model-independent observable very strongly correlated with the atmospheric slant depth of the shower maximum and sensitive to possible anomalies introduced by forward heavy quarks. | The possibility to separate the muon and the EM components in the surface detectors at CR observatories seems essential both to fully characterize the shower and also to {\it tune} the Monte Carlo codes used to simulate ultrahigh-energy events. Here we have discussed a new observable, the ratio $r_{\mu e}$ between the two components, that correlates with $X_{\rm max}$ with an uncertainty of around $\pm 10$ g/cm$^2$ for iron nuclei or $\pm 40$ g/cm$^2$ for protons. A precise analysis of the spectrum and the composition of ultrahigh energy CRs relies very strongly on simulations, and this observable could provide a crucial consistency check. In particular, it could give a surprisingly effective discriminant in composition analyses. One important issue currently being discussed \cite{Aab:2015bza} is the possible under-prediction of the muon signal by basically all hadronic simulators. This would suggest a correction towards a higher multiplicity in hadron collisions: a larger number of less energetic pions inside the shower implies a stronger muon signal (number of muons) with the same EM signal (energy in electrons and photons). Obviously, if the {\it muon problem} is confirmed after the upgrade of the Auger observatory and the hadronic models are modified, their prediction for $r_{\mu e}$ will change accordingly. The analysis with the {\it wrong} simulators presented here would then be biased, and our determination of $X_{\rm max}$ from $r_{\mu e}$ would have a {\it systematic} error. The only way to identify and correct this bias would be to compare $X^{\mu e}_{\rm max}$ with the $X_{\rm max}$ provided by the fluorescence detectors in hybrid events. It is then interesting that such comparison can be used to quantify the suspected muon problem of current simulations. Our analyses based on SIBYLL and QGSjetII show that the relation between $X_{\rm max}$ and $r_{\mu e}$ is very stable and model independent. It is crucial that we compare showers at the same distance depth from the maximum ({\it i.e.}, same value of $X_{\rm grd}-X_{\rm max}$), which minimizes the shower to shower fluctuations. Our results also reflect that the fluctuations and the model dependencies in the muon and the EM components of a shower are correlated, {\it i.e.}, if $r_{\mu e} = x/y$ with $x=n_\mu$ and $y=E_{\rm em}/(0.5\;{\rm GeV})$, then $\Delta r_{\mu e} \ll \sqrt{ \left( \Delta x/y \right)^2 + \left( \Delta y\;x/y^2 \right)^2 }$. We have argued that only the production of very energetic {\it forward} heavy hadrons could introduce anomalies. In particular, we have identified reductions in the value of $r_{\mu e}$ caused {\it (i)} by the decay of these hadrons deep in the atmosphere in proton showers of intermediate inclination ($50^\circ < \theta <60^\circ$), and {\it (ii)} by stochastic energy depositions near the ground coming from very energetic muons in inclined showers ($\theta > 65^\circ$). These muons would be created high in the atmosphere through semileptonic decays of charm and bottom hadrons. Therefore, we conclude that $r_{\mu e}$ may be a key observable to characterize EASs, determine the nature of the CR primary, and even in the search for the elusive forward heavy hadrons. | 16 | 9 | 1609.04941 |
1609 | 1609.08168_arXiv.txt | In the weak field regime, gravitational waves can be considered as being made up of collisionless, relativistic tensor modes that travel along null geodesics of the perturbed background metric. We work in this geometric optics picture to calculate the anisotropies in gravitational wave backgrounds resulting from astrophysical and cosmological sources. Our formalism yields expressions for the angular power spectrum of the anisotropies. We show how the anisotropies are sourced by intrinsic, Doppler, Sachs-Wolfe, and Integrated Sachs-Wolfe terms in analogy with Cosmic Microwave Background photons. | 16 | 9 | 1609.08168 |
||
1609 | 1609.03799_arXiv.txt | The vertical structure of stationary thin accretion discs is calculated from the energy balance equation with heat generation due to microscopic ion viscosity $\eta$ and electron heat conductivity $\kappa$, both depending on temperature. In the optically thin discs it is found that for the heat conductivity increasing with temperature, the vertical temperature gradient exceeds the adiabatic value at some height, suggesting convective instability in the upper disc layer. There is a critical Prandtl number, $\Pr=4/9$, above which a Keplerian disc become fully convective. The vertical density distribution of optically thin laminar accretion discs as found from the hydrostatic equilibrium equation cannot be generally described by a polytrope but in the case of constant viscosity and heat conductivity. In the optically thick discs with radiation heat transfer, the vertical disc structure is found to be convectively stable for both absorption dominated and scattering dominated opacities, unless a very steep dependence of the viscosity coefficient on temperature is assumed. A polytropic-like structure in this case is found for Thomson scattering dominated opacity. | \label{intro} The origin of angular momentum transfer in accretion discs is the key issue in accretion disc theory. The standard accretion disc theory \citep{1973SvA....16..756S,1973A&A....24..337S,1981ARA&A..19..137P} assumes that turbulent viscosity, which can be parametrized by the dimensionless parameter $\alpha$, can be responsible for the observed high mass accretion rate in compact X-ray sources, protoplanetary discs and in other astrophysical objects. From purely hydrodynamic point of view, Keplerian flows are stable against small perturbations according to the classical Rayleigh criterion, and various mechanisms giving rise to turbulence in Keplerian accretion discs have been discussed. For example, magnetorotational instability \citep{1991ApJ...376..214B,1998RvMP...70....1B} is thought to be responsible for turbulence in various astrophysical discs. Recently, in an attempt to search for purely hydrodynamic mechanisms of turbulence in shear flows, we have revisited the problem of turbulence appearance in thin Keplerian discs from small perturbations in non-ideal fluids with microscopic transport coefficients \citep[viscosity and heat conductivity;][]{2015MNRAS.448.3707S,2015MNRAS.451.3995S,2016arXiv160304878M}. By modal analysis, we have found that both in the simplest Boussinesq and anelastic approximations of hydrodynamic equations, unstable axially symmetric modes can appear in the shear accretion flows, which may serve as seeds for turbulence even in the absence of dynamically significant magnetic fields. In addition to traditional modal analysis of small perturbations, non-modal analysis of transient perturbations can be a powerful tool for searching for possible mechanisms of hydrodynamic turbulence in accretion flows \citep[e.g.][]{2015PhyU...58.1031R}. In the modal analysis of perturbations in thin accretion discs, equations for small variations of dynamical variables (density, velocity, pressure) are formulated as a boundary value problem against a given background, which should be solution of unperturbed hydrodynamic equations. In \citet{2015MNRAS.451.3995S} this problem was solved using a priori postulated polytropic vertical structure of the disc. Earlier it was conjectured \citep[e.g.][]{1998A&AT...15..193K} that the vertical structure of stationary accretion $\alpha$-discs can admit an effective polytropic description. However, it is far from being obvious that this is the case if the microscopic transport coefficients (instead of the effective turbulent viscosity prescription) are used in hydrodynamic equations. The purpose of this paper is to find solution of vertical structure of stationary shear accretion flows with microscopic transport coefficients --- dynamic ion viscosity $\eta$ and heat conductivity $\kappa$, which can be characterized by a dimensionless Prandtl number $\Pr$. The ion viscosity in hot accretion disc was considered already by \citet{1978AcA....28..253P} and was shown to be able to provide, in some cases, sufficiently high mass accretion rate through the disc. However, \citet{1978AcA....28..253P} did not calculate the vertical disc structure. In Section \ref{s:Sect2}, we find such a solution for optically thin laminar discs and show that with standard microscopic transport coefficients, for a given Prandtl number a convectively unstable layer appear near the upper boundary of the disc, which can encompass the total disc height if the Prandtl number exceeds some critical value ($4/9$ for a Keplerian disc). The possibility of thermal convection in accretion discs was found earlier in shear-box calculations and discussed in the context of outward angular momentum transfer by \cite{2010MNRAS.404L..64L}. In Section \ref{s:rad}, we consider the vertical disc structure with ion viscosity and radiative energy transfer, pertinent to optically thick accretion discs. Here, for completeness, we also calculate the vertical structure of the standard turbulized $\alpha$-discs. The knowledge of the vertical structure of such discs, in turn, is needed to calculate their radial structure, which is usually done by averaging accretion disc equations over the disc thickness. The optically thick discs with heat generation due to microscopic ion viscosity and radiation heat transfer are found to be convectively stable for both absorption dominated (Kramer's opacity) and scattering dominated (Thomson opacity) cases. | In this paper we have calculated the vertical structure of steady-state thin Keplerian accretion discs. The microscopic ion viscosity is assumed to be the only source of heat generation. We considered two cases of vertical energy transfer --- due to electron heat conductivity in the optically thin discs and due to radiation conductivity in the optically thick discs. In the optically thin case, if the microscopic transport coefficients are functions of temperature only, the vertical temperature distribution can be calculated from the energy balance equation. Assuming power-law dependence of these coefficients on temperature~\eqref{eq.kappa}, \eqref{eq.eta}, we solved the energy balance equation~\eqref{eq.difeq} to obtain the vertical temperature gradient~\eqref{eq.u}. If the surface temperature is small enough, the temperature gradient~\eqref{eq.u} exceeds the adiabatic value at some point, suggesting the appearance of an upper convective layer. If the Prandtl number exceeds some critical value, $\Pr \geq \Pr_\mathrm{crit}$, the entire disc become convectively unstable. For Keplerian discs $\Pr_\mathrm{crit}=4/9$. Solution~\eqref{eq.x_t} also enabled us to calculate the vertical density distribution from the hydrostatic equation, which turned out to be non-polytropic in general case. However, in the special case of constant transport coefficients in a fully laminar disc (at $\Pr<\Pr_\mathrm{crit}$) the vertical density distribution is polytropic. For optically thick stationary Keplerian thin discs with radiative energy transfer, the vertical structure is calculated from system of equations~\eqref{eq.Pis} supplemented with eight boundary conditions (see Section~\ref{s:boundcond}). Two boundary conditions for temperature are set at the photosphere, location of which is found for two opacity laws --- absorption dominated atmosphere (Section~\ref{s:absorption}) and Thomson scattering dominated atmosphere (Section~\ref{s:scattering}). For completeness, we calculate the vertical structure of standard $\alpha$-discs, which was earlier considered by \citet{1998A&AT...15..193K}. These discs are found to be convectively stable (see Fig.~\ref{fig.alpha}). Their vertical structure generally cannot be described by a polytrope. Optically thick Keplerian discs with ion viscosity and electron heat conductivity are found to be convectively stable for both opacity laws. A polytropic-like structure with polytrope index $n\approx 5/2$ is recovered for discs with Thomson scattering dominated atmospheres (see Fig.~\ref{fig.ion}, right-hand panels). The four dimensionless parameters $\Pi_{1..4}$ of the vertical disc structure determined from the solution of equations~\eqref{eq.Pis} are needed to calculate the radial disc structure \citep{2007ARep...51..549S}. The appearance of convection in laminar Keplerian discs can cause turbulence (see, e.g., \cite{2010MNRAS.404L..64L}), which is required for efficient angular momentum transfer. In the convectively stable cases, the vertical structure of laminar flows calculated in this paper can be used as a background solution for further analysis of evolution of small hydrodynamic perturbations, which will be considered elsewhere. | 16 | 9 | 1609.03799 |
1609 | 1609.04346_arXiv.txt | We report the discovery of a new ultra-faint dwarf satellite companion of the Milky Way based on the early survey data from the Hyper Suprime-Cam Subaru Strategic Program. This new satellite, Virgo~I, which is located in the constellation of Virgo, has been identified as a statistically significant (5.5$\sigma$) spatial overdensity of star-like objects with a well-defined main sequence and red giant branch in their color-magnitude diagram. The significance of this overdensity increases to 10.8$\sigma$ when the relevant isochrone filter is adopted for the search. Based on the distribution of the stars around the likely main sequence turn-off at $r \sim 24$ mag, the distance to Virgo~I is estimated as 87~kpc, and its most likely absolute magnitude calculated from a Monte Carlo analysis is $M_V = -0.8 \pm 0.9$~mag. This stellar system has an extended spatial distribution with a half-light radius of 38$^{+12}_{-11}$~pc, which clearly distinguishes it from a globular cluster with comparable luminosity. Thus, Virgo~I is one of the faintest dwarf satellites known and is located beyond the reach of the Sloan Digital Sky Survey. This demonstrates the power of this survey program to identify very faint dwarf satellites. This discovery of Virgo~I is based only on about 100 square degrees of data, thus a large number of faint dwarf satellites are likely to exist in the outer halo of the Milky Way. | Dwarf spheroidal galaxies (dSphs) associated with the Milky Way (MW) and Andromeda galaxies provide important constraints on the role of dark matter in galaxy formation and evolution. Indeed, these faint stellar systems are largely dominated by dark matter with mass-to-luminosity ratios of 10 to 1000 or even larger in fainter systems, based on their stellar dynamics \citep{Gilmore2007,Simon2007}. Thus, the basic properties of dSphs, such as their total number and spatial distributions inside a host halo like the MW, provide useful constraints on dark matter on small scales, in particular the nature and evolution of cold dark matter (CDM) in a $\Lambda$ dominated universe. One of the tensions between theory and observation is the missing satellite problem: the theory predicts a much larger number of subhalos in a MW-like halo than the observed number of satellite galaxies \citep{Klypin1999,Moore1999}. Solutions to this problem are to consider other types of dark matter than CDM \citep[e.g.,][]{Maccio2010} or to invoke baryonic physics \citep[e.g.,][]{Sawala2016}. Another possibility is that we have seen only a fraction of all the satellites associated with the MW due to various observational biases \citep{Tollerud2008}. Motivated by this, a systematic search for new dSphs has been made based on large survey programs, such as the Sloan Digital Sky Survey (SDSS) \citep{York2000} and the Dark Energy Survey (DES) \citep{Abbott2016}. SDSS discovered 15 ultra-faint dwarf galaxies (UFDs) with $M_V \gsim -8$ mag \citep[e.g.,][]{Willman2005,Sakamoto2006,Belokurov2006}, and DES recently reported the discovery of many more candidate UFDs in the south \citep[e.g.,][]{Bechtol2015,Koposov2015,Drlica-Wagner2015}. These discoveries are consistent with the work by \citet{Tollerud2008}, anticipating that there exists a large number of yet unidentified dwarf satellites in the MW halo, especially in its outer parts. This paper reports the discovery of a new faint dwarf satellite in the MW, in the course of the Subaru Strategic Program (SSP) using Hyper Suprime-Cam (HSC). HSC is a new prime-focus camera on the Subaru telescope with a 1.5~deg diameter field of view \citep{Miyazaki2012}, which thus allows us to survey a large volume of the MW halo out to a large distance from the Sun, where a systematic search for new satellites has not yet been undertaken. \begin{figure*}[t!] \centering \includegraphics[width=120mm]{fig1.eps} \caption{ Left panel: the spatial distribution of the sources classified as stars with $i < 24.5$ mag and $g-r<1.0$, covering one square degree centered on the candidate overdensity of stars. The star counts are in bins of $0^{\circ}.05 \times 0^{\circ}.05$. Right panel: the plot for the sources classified as galaxies with $i < 24.5$ mag and $g-r<1.0$. Note that there is no overdensity at the center of this plot. } \label{fig: space} \end{figure*} \begin{figure*}[t!] \centering \includegraphics[width=150mm]{fig2.eps} \caption{ The spatial distribution of the stars around the overdensity (upper panels, where $\Delta\alpha$ and $\Delta\delta$ are the relative offsets in celestial coordinates) and their distribution in the $g-r$ vs. $r$ CMD (lower panels). Panel (a): spatial distribution of the sources classified as stars with $i < 24.5$ mag and $g-r<1.0$. Red circles denote annuli with radii $=2'$, $6'$, and $6'.33$ from the center. There is an overdensity around the field center with statistical significance of 5.5$\sigma$. Panel (b): the same as (a) but for the stars passing the isochrone filter shown in panel (d). The statistical significance of the overdensity, 10.8$\sigma$, is higher than in panel (a). Panel (c): CMD for the stars at $r < 2'$, where the error bars show a typical measurement error in color at each $r$ magnitude. Panel (d): the same as (c) but including an isochrone (red line) for an old, metal-poor system [age of 13~Gyr and metallicity of [M$/$H]$=-2.2$ at a distance modulus of $(m-M)_0 = 19.7$ mag]. The shaded area covers both the typical photometric error and likely intrinsic dispersion of the CMD in star clusters. Panel (e): the same as (c) but for field stars at $6' < r < 6'.33$, which has the same solid angle. Note the absence of a main sequence turn-off. } \label{fig: space_cmd} \end{figure*} | We have identified a new ultra-faint dwarf satellite of the MW, Virgo~I, in the constellation of Virgo. The satellite is located at a heliocentric distance of 87~kpc and its absolute magnitude in the $V$ band is estimated as $M_V = -0.8 \pm 0.9$ mag, which is comparable to or fainter than that of the faintest dwarf satellite, Segue~1. The half-light radius of Virgo~I is estimated to be $\sim 38$ pc, significantly larger than globular clusters with the same luminosity, suggesting that it is a dwarf galaxy. To set further constraints on Virgo~I, follow-up spectroscopic studies of bright RGB stars will be useful to investigate their membership and to determine the chemical and dynamical properties in this dwarf satellite. Virgo~I is located beyond the reach of the SDSS: its limiting magnitude of $r = 22.2$ implies that the completeness radius beyond which a faint dwarf galaxy like Virgo~I will not be detected \citep{Tollerud2008} is 28~kpc. With Subaru/HSC, this completeness radius for Virgo~I is estimated as 89~kpc, if we adopt the limiting $i$-band magnitude of 24.5 mag combined with a typical $(r-i)$ color of $\simeq 0.2$. Thus, Virgo~I with $D = 87^{+13}_{-8}$ kpc is located just at the edge where Subaru/HSC can reach. We therefore expect the presence of yet unidentified faint satellites in the outer parts of the MW halo as the HSC survey continues. Deep imaging surveys for these faint and distant satellites are indeed important to get further insights into their true number and thus the nature of dark matter on small scales. | 16 | 9 | 1609.04346 |
1609 | 1609.04808.txt | Hot, Dust-Obscured Galaxies (Hot DOGs), selected from the {\it WISE} all sky infrared survey, host some of the most powerful Active Galactic Nuclei (AGN) known, and might represent an important stage in the evolution of galaxies. Most known Hot DOGs are at $z> 1.5$, due in part to a strong bias against identifying them at lower redshift related to the selection criteria. We present a new selection method that identifies 153 Hot DOG candidates at $z\sim 1$, where they are significantly brighter and easier to study. We validate this approach by measuring a redshift $z=1.009$, and an SED similar to higher redshift Hot DOGs for one of these objects, WISE\,J1036+0449 ($L_{\rm\,Bol}\simeq 8\times 10^{46}\rm\,erg\,s^{-1}$), using data from Keck/LRIS and NIRSPEC, SDSS, and CSO. We find evidence of a broadened component in Mg\,{\sc ii}, which, if due to the gravitational potential of the supermassive black hole, would imply a black hole mass of $M_{\rm\,BH}\simeq 2 \times 10^8 M_{\odot}$, and an Eddington ratio of $\lambda_{\rm\,Edd}\simeq 2.7$. WISE\,J1036+0449 is the first Hot DOG detected by {\it NuSTAR}, and the observations show that the source is heavily obscured, with a column density of $N_{\rm\,H}\simeq(2-15)\times10^{23}\rm\,cm^{-2}$. The source has an intrinsic 2--10\,keV luminosity of $\sim 6\times 10^{44}\rm\,erg\,s^{-1}$, a value significantly lower than that expected from the mid-infrared/X-ray correlation. We also find that the other Hot DOGs observed by X-ray facilities show a similar deficiency of X-ray flux. We discuss the origin of the X-ray weakness and the absorption properties of Hot DOGs. Hot DOGs at $z\lesssim1$ could be excellent laboratories to probe the characteristics of the accretion flow and of the X-ray emitting plasma at extreme values of the Eddington ratio. | \setcounter{footnote}{0} Supermassive black holes (SMBHs) are known to reside at the centers of most galaxies (e.g., \citealp{Kormendy:1995hc,Magorrian:1998tg,Tremaine:2002qa}), and are believed to play an important role in the evolution of their host galaxies during an active phase in which they accrete matter (e.g., \citealp{Ferrarese:2000ij,Gebhardt:2000bs,Kormendy:2013mj}). During such phases, they are observed as Active Galactic Nuclei (AGN). In the most luminous AGN, accretion is likely triggered by major galaxy mergers (e.g., \citealp{Treister:2012fk}). An important stage in the life-cycle of SMBHs is believed to happen during a dust-enshrouded phase, when SMBHs accrete most of their mass, before blowing out the material (e.g., \citealp{Martinez-Sansigre:2005lh}, \citealp{Glikman:2007ys}, \citealp{Urrutia:2008vn}, \citealp{LaMassa:2016ly}) and evolving into a blue unobscured source (e.g., \citealp{Hopkins:2006fv}). During this obscured phase the system is expected to be extremely bright in the infrared (IR). The first objects with these characteristics were discovered in large numbers by the {\it Infrared Astronomical Satellite} ({\it IRAS}), and are called luminous [$L_{\rm\,IR}(8-1000\,\mu\rm\,m)=10^{11}-10^{12}$ $L_{\odot}$] and ultra-luminous ($L_{\rm\,IR}= 10^{12}-10^{13 }$ $L_{\odot}$) infrared galaxies (LIRGs and ULIRGs, respectively; e.g., \citealp{Sanders:1996uq}, \citealp{Farrah:2003mi}, \citealp{Lonsdale:2006fu}, \citealp{Imanishi:2007pi}, \citealp{Veilleux:2009ff}). Subsequently, submillimeter galaxies (SMGs; e.g., \citealp{Blain:2002dz,Alexander:2005fu,Casey:2014kl}) at $z\sim 2-4$ were discovered at longer wavelengths, while {\it Spitzer} surveys identified a population of Dust-Obscured Galaxies at $z\sim 2$ (DOGs; e.g., \citealp{Yan:2007dq,Dey:2008cr,Fiore:2009nx}, see also \citealp{Toba:2015uq} and \citealp{Toba:2016fk} for studies of DOGs selected using other facilities). More recently, the {\it Wide-field Infrared Survey Explorer} satellite ({\it WISE}, \citealp{Wright:2010fk}) has surveyed the whole sky in four mid-infrared (mid-IR) bands, discovering new populations of hyper-luminous ($L_{\rm\,IR} = 10^{13}-10^{14}$ $L_{\odot}$; e.g., \citealp{Eisenhardt:2012ve,Wu:2014,Hainline:2014wa}) and extremely luminous ($L_{\rm\,IR} > 10^{14} L_{\odot}$; \citealp{Tsai:2015qf}) infrared galaxies (HyLIRGs and ELIRGs, respectively). This was accomplished by selecting objects that are faint or undetected in the $W1$ (3.4\,$\mu$m) and $W2$ (4.6\,$\mu$m) bands, but bright in the $W3$ (12\,$\mu$m) and $W4$ (22\,$\mu$m) bands. Overall $\sim 1000$ of these sources were discovered across the entire extragalactic sky (i.e., $\sim 1$ per 30 deg$^2$) \citep{Eisenhardt:2012ve}. Spectroscopic redshifts for $115$ ``$W1W2$-dropouts'' are currently available \citep{Assef:2015zr}, and most of these objects are at $z \gtrsim 1.5$, with the current highest redshift being $z = 4.601$ (\citealp{Tsai:2015qf,Diaz-Santos:2016ly}). These sources are typically optically faint, and their IR spectral energy distributions (SEDs) peak at rest-frame $\lambda\sim 20\,\mu$m, implying dust hotter ($T\gg 60$\,K) than in ULIRGs, SMGs or DOGs. They are therefore referred to as Hot, Dust-Obscured Galaxies (Hot DOGs; \citealp{Wu:2012bh}). It has been shown that for these ELIRGs the 1--20$\mu$m luminosity is always larger than the infrared luminosity above 20$\mu$m \citep{Tsai:2015qf}. The lack of a far-IR peak in their SEDs implies that the dominant energy sources are luminous heavily obscured AGNs and not extreme starbursts \citep{Wu:2012bh,Tsai:2015qf}. {\it Hubble Space Telescope} and Keck/NIRC2 observations of Hot DOGs show strong lensing is unlikely \citep{Eisenhardt:2012ve,Wu:2014,Tsai:2015qf,Fan:2016sf}, while X-ray studies (\citealp{Stern:2014kx,Assef:2016qf,Piconcelli:2015uq}, this work) show that they contain very powerful AGN. The number density of Hot DOGs is comparable to that of type 1 AGN with similar luminosities at redshifts $2<z<4$ \citep{Stern:2014kx,Assef:2015zr}. The most-luminous known galaxy in the Universe, WISE\,J2246-0526 ($L_{\rm\,bol}=3.5\times 10^{14} L_{\odot}$, \citealp{Tsai:2015qf}), is a Hot DOG. Recent ALMA observations of this object have found evidence wide velocity spread, consistent with strong turbulence or isotropic outflows, which implies that the system is blowing out its interstellar medium, and might be in the process of becoming an unobscured quasar \citep{Diaz-Santos:2016ly}. Hot DOGs might therefore represent a key phase in the evolution of AGN. \begin{figure*}[t!] \centering \begin{minipage}[!b]{.48\textwidth} \centering \fbox{\includegraphics[width=8.5cm]{nustar_image.ps}}\end{minipage} \begin{minipage}[!b]{.48\textwidth} \centering \fbox{\includegraphics[width=8.5cm]{XRTimage.ps}}\end{minipage} \begin{minipage}[!b]{.48\textwidth} \centering \fbox{\includegraphics[width=8.5cm]{sdss_rband.ps}}\end{minipage} \begin{minipage}[!b]{.48\textwidth} \centering \fbox{\includegraphics[width=8.5cm]{w1image.ps}}\end{minipage} \begin{minipage}[!b]{.48\textwidth} \centering \fbox{\includegraphics[width=8.5cm]{w2image.ps}}\end{minipage} \begin{minipage}[!b]{.48\textwidth} \centering \fbox{\includegraphics[width=8.5cm]{w3image.ps}}\end{minipage} \begin{minipage}[!b]{.48\textwidth} \centering \fbox{\includegraphics[width=8.5cm]{w4image.ps}}\end{minipage} \begin{minipage}[!b]{.48\textwidth} \centering \fbox{\includegraphics[width=8.5cm]{cso_sn_image.ps}}\end{minipage} \begin{minipage}[t]{\textwidth} \caption{Images of the field around WISE\,J1036+0449 from the hard X-rays to the far-IR. From the top to the bottom, the panels show the images obtained by {\it NuSTAR} FPMA (3--24\,keV), {\it Swift}/XRT (0.3--10\,keV), SDSS $r$-band (6231\AA), {\it WISE} band 1 ($3.4\,\mu$m), band 2 ($4.6\,\mu$m), band 3 ($12\,\mu$m) and band 4 ($22\,\mu$m), and by CSO ($350\,\mu$m). The {\it NuSTAR} image was obtained by combining the three observations, as described in Section\,\ref{sect:specAnalysis}, and was smoothed with a Gaussian kernel of radius 12 pixels. The SDSS image was smoothed with a Gaussian kernel of radius 2 pixels. The CSO image shows the signal-to-noise ratio per pixel. The crosses show the position of WISE\,J1036+0449, while the circles in the bottom right the size of the beam. In all images North is up and East is left.} \label{fig:images} \end{minipage} \end{figure*} In AGN, much of the X-ray emission is produced in a compact region very close to the SMBH ($\lesssim 10\,r_{\rm\,G}$; \citealp{Zoghbi:2012uq,De-Marco:2013fk} --- where $r_{\rm\,G}=G\,M_{\rm\,BH}/c^2$ is the gravitational radius of the SMBH). X-ray observations are therefore a potent tool to infer the line-of-sight column density to the central engine ($N_{\rm\,H}$). The relation between the bolometric and X-ray output of Hot DOGs also sheds light on the physical conditions of the X-ray emitting plasma. Hot DOGs are therefore excellent laboratories for probing the structure of the accretion flow at the highest luminosities, although they are not yet well-studied in the X-ray band, with only a handful having been observed by X-ray facilities to date. \citet{Stern:2014kx} reported on two Hot DOGs observed with {\it NuSTAR} and {\it XMM-Newton}, plus an additional source observed only by {\it XMM-Newton}. All three targets are at $z\sim 2$. Neither target observed by {\it NuSTAR} yielded a significant detection, while two of the three objects were faintly detected by {\it XMM-Newton}, implying that the sources are either X-ray weak or heavily obscured by column densities $N_{\rm H}\gg 10^{24}~\rm cm^{-2}$. Similar results were obtained by \citet{Piconcelli:2015uq}, who studied a 40~ks {\it{XMM-Newton}} spectrum of WISE\,J1835+4355, a Hot DOG at $z= 2.298$, and found $N_{\rm H}\gg 10^{23}~\rm cm^{-2}$, with the source likely being reflection dominated (Zappacosta et al., in prep.). Recently, \citet{Assef:2016qf} found evidence of similar levels of obscuration in the X-rays for another Hot DOG, WISE\,J0204--0506 ($z= 2.100$), using a serendipitous off-axis {\it Chandra} observation (160~ks exposure). \begin{figure*} \begin{center} \epsscale{0.75} \plotone{lris_spec.v3.eps} \caption{UV/optical spectrum of \sname, obtained with the LRIS instrument at the Keck Observatory. See $\S$\ref{sect:Opticalspec} for details.} \label{fg:lris_spec} \end{center} \end{figure*} To constrain better the X-ray absorption of Hot DOGs, and hence their intrinsic X-ray luminosities, it is necessary to obtain reliable detections at $E\gtrsim 10\rm\,keV$, where their emission is less affected by neutral gas absorption (e.g., \citealp{Lansbury:2015dq}, \citealp{Annuar:2015qf}, \citealp{Puccetti:2016zr}, \citealp{Tanimoto:2016vn}, \citealp{Ricci:2016kq,Ricci:2016fk}). The simplest way to do this is to observe brighter, lower-redshift sources. However, \citet{Assef:2015zr} show that the number of Hot DOGs at such redshift is very small, in part due to an inherent bias in their selection function, with fast space density evolution also a likely contributing factor. Furthermore, Hot DOGs that happen to be at lower redshifts are biased toward being much less luminous than their higher redshift counterparts due, at least in part, to the strict requirements of the selection function on the $W1$ flux. A new selection technique, as discussed in the following section, allows identification of a significant population of Hot DOGs at $z\sim 1$ (Assef et al. in prep.). We report here on the study of one of these new objects, WISE\,J103648.31+044951.0 (WISE\,J1036+0449). In this paper, we show that the SED of WISE\,J1036+0449 at z=1.009 peaks in the mid IR, similarly to Hot DOGs at higher redshift. Exploiting three {\it NuSTAR} observations, we are able to constrain the line-of-sight column density and its intrinsic X-ray luminosity. WISE\,J1036+0449 is one of the closest Hot DOGs known ($z=1.009$) and, given its relative proximity, it could become an important case study of this interesting population of AGN. The paper is structured as follows. In $\S$\ref{sect:selection} we describe the selection method, and show that the SED of WISE\,J1036+0449 is consistent with those of other Hot DOGs. In $\S$\ref{Sect:data_analysis} and $\S$\ref{sect:specAnalysis} we report on the X-ray observations available and on the X-ray spectral analysis, respectively. In $\S$\ref{sect:discussion} we discuss the possible intrinsic X-ray weakness of Hot DOGs and their absorption properties, while in $\S$\ref{sect:conclusion} we report our conclusions. Throughout the paper we use Vega magnitudes and adopt standard cosmological parameters ($H_{0}=70\rm\,km\,s^{-1}\,Mpc^{-1}$, $\Omega_{\mathrm{m}}=0.3$, $\Omega_{\Lambda}=0.7$). Unless otherwise stated, all uncertainties are quoted at the 90\% confidence level. | \label{sect:conclusion} We reported here on the multi-wavelength study of WISE\,J1036+0449, the first Hot DOG detected by {\it NuSTAR}. The source was selected using new selection criteria that identify Hot DOGs at lower redshifts than previously discovered. We report below the main findings of our work. \begin{itemize} \item The redshift of WISE\,J1036+0449 is $z=1.009$. The SED of the source is extremely similar to those of Hot DOGs at $z\sim 2$ (Fig.\,\ref{fig:SED}), validating the new method to select Hot DOGs at $z\simeq 1$. \item The source is detected in the X-ray band, which confirms the presence of a powerful AGN. We found that the source is obscured [$N_{\rm\,H}\simeq(2-15)\times10^{23}\rm\,cm^{-2}$], with a column density consistent with that of the bulk of the Hot DOG population. \item If the broadening of the Mg\,{\sc ii} line is due to the gravitational field of the SMBH, then the black hole mass is $M_{\rm\,BH}\simeq 2 \times 10^8 M_{\odot}$ and the Eddington ratio $\lambda_{\rm\,Edd}\simeq 2.7$. \item The intrinsic 2--10\,keV luminosity of WISE\,J1036+0449 [$\log (L_{2-10\rm\,keV}/\rm erg\,s^{-1})\sim44.80$] is considerably lower than the value expected from the mid-IR/X-ray luminosity correlation, considering its $6\,\mu$m luminosity [$\log (L_{6\rm\,\mu m}/\rm erg\,s^{-1})\sim46.61$], and the 2--10\,keV bolometric correction is $\kappa_{\mathrm{x}}\simeq 130$. Other Hot DOGs are fainter than expected in the X-ray band (Fig.\,\ref{fig:lxvslmir_stern}), which might imply that X-ray weakness is a common characteristic of extremely luminous AGN. X-ray weakness might either be related to significantly larger values of $\lambda_{\rm\,Edd}$ (and therefore of $\kappa_{\mathrm{x}}$ and $\alpha_{\rm\,OX}$), and/or to the disruption of the X-ray corona caused by outflowing material. An alternative explanation is that Hot DOGs are significantly more obscured than what is inferred by current studies based on X-ray spectroscopy and on the analysis of the SED. \end{itemize} Future X-ray observations of Hot DOGs at $z\lesssim 1$ will be extremely important to understand whether these objects are intrinsically X-ray weak and to shed light on the conditions of the X-ray emitting plasma around SMBHs at the highest luminosities and accretion rates. | 16 | 9 | 1609.04808 |
1609 | 1609.08732_arXiv.txt | The spectrum of a quasar contains important information about its properties. Thus, it can be expected that two quasars with similar spectra will have similar properties, but just how similar has not before been quantified. Here we compare the ultraviolet spectra of a sample of 5553 quasars from Data Release 7 of the Sloan Digital Sky Survey, focusing on the $1350$ \AA \ $\leq \lambda \leq 2900$ \AA \ rest-frame region which contains prominent emission lines from \SiIV, O IV], \CIV, \CIII, and \MgII\ species. We use principal component analysis to determine the dominant components of spectral variation, as well as to quantitatively measure spectral similarity. As suggested by both the Baldwin effect and modified Baldwin effect, quasars with similar spectra have similar properties: bolometric luminosity, Eddington fraction, and black hole mass. The latter two quantities are calculated from the luminosity in conjunction with spectral features, and the variation between quasars with virtually identical spectra (which we call doppelgangers) is driven by the variance in the luminosity plus measurement uncertainties. In the doppelgangers the luminosity differences show 1$\sigma$ uncertainties of 57\% (or 0.63 magnitudes) and $\sim$70\% 1$\sigma$ uncertainties for mass and Eddington fraction. Much of the difference in luminosities may be attributable to time lags between the spectral lines and the continuum. Furthermore, we find that suggestions that the mostly highly accreting quasars should be better standard candles than other quasars are not bourne out for doppelgangers. Finally, we discuss the implications for using quasars as cosmological probes and the nature of the first two spectral principal components. | Baldwin (1977) reported the inverse correlation between the equivalent width (EW) of the C IV $\lambda$1549 emission line and the continuum emission. This empirical relationship, now known as the Baldwin effect, was of interest for several reasons. The fact that the line emission does not scale linearly with the underlying continuum suggests intriguing astrophysics (e.g., Mushotsky \& Ferland 1984; Netzer 1985; Wandel 1999). More practically, a way to predict the continuum luminosity independent of redshift opened up the possibility of calibrating quasars as cosmological probes (e.g., Baldwin et al. 1978; Wampler et al. 1984). The scatter in the Baldwin effect has unfortunately proven too large to let the relationship be of practical use for cosmology, at least with existing samples despite their now impressive size (e.g., Bian et al. 2012). There are other correlations of interest relating quasar spectra and their physical properties. For instance, the modified Baldwin effect is an inverse correlation between EW C IV and the Eddington fraction, L$_{bol}$/L$_{Edd}$ (e.g., Baskin \& Laor 2004; Shemmer et al. 2008; Shemmer \& Lieber 2015), generally stronger and more significant than the Baldwin effect itself. Quasar masses are routinely estimated from single-epoch spectra using the velocity width of broad emission lines in combination with the continuum luminosity (Vestergaard \& Peterson 2006; Vestergaard \& Osmer 2009, and others). Other parameters also leave their mark on the ultraviolet quasar spectrum, such as the orientation to the line of sight (e.g., Vestergaard 2002; Runnoe et al. 2014) and metallicity (e.g., Hamman \& Ferland 1999). We must also be mindful of other issues, such as line-of-sight gas and dust that can redden spectra, or leave the imprints of absorption lines, which can complicate the measurement and interpretation of spectra. Theoretically, the emitted quasar continuum and emission-line spectrum critically depend on parameters like the luminosity, which is related to the spectral energy distribution and ionizing continuum (e.g., Just et al. 2007). The central black hole mass drives the kinematics of the broad-line region or BLR and the resulting observed line profiles (Peterson \& Wandel 1999). The Eddington fraction depends on both the luminosity and the mass. There are other factors, such as the specific geometries, quantities, and physical conditions of the line-emitting gas that are also important and may have significant variance from quasar to quasar, even if their underlying fundamental properties like black hole mass, accretion rate, and luminosity are the same. It would be useful to quantify this variance statistically and learn to what extent an ultraviolet spectrum can be used to predict general quasar properties. Traditionally, through the Baldwin effect and modified Baldwin effect, crude measurements like EW C IV have been used to predict luminosity and the Eddington fraction. Modern computing allows spectra to be characterized in much more sophisticated ways than the equivalent width of a single line, and large data sets like the Sloan Digital Sky Survey (SDSS) and its quasar catalogs (e.g., Schneider et al. 2010) permit much more varied and extensive statistical comparisons. There exist quasars with essentially identical ultraviolet spectra, to within differences associated with noise and absorption features, which we will refer to as doppelgangers. We ask the question: how similar are the physical properties of quasar doppelgangers with nearly identical ultraviolet spectra? We explicitly note that the black hole mass and the Eddington fraction are calculated using the continuum luminosity and the velocity widths of broad emission lines. Therefore, for doppelganger pairs, any observed differences in these properties can be attributed to differences in luminosity plus spectral measurement uncertainties. Luminosity then is the observable parameter driving all the differences in doppelganger pair properties. We will consider each quasar property empirically but interpret our results in a self-consistent way in which luminosity variation is primary. In this paper, we use the technique of spectral principal component analysis (SPCA) to reconstruct quasar spectra without significant noise or absorption features, and to use their component weights to characterize how similar different spectra actually are. In \S 2, we describe our sample selection, data, and SPCA approach. In \S 3, we describe our analyses and results, examining how well very similar ultraviolet spectra can on average predict luminosity, the Eddington fraction L$_{bol}$/L$_{Edd}$, and black hole mass in quasars, as well as the special case of high Eddington fraction objects, which have been proposed to have more similar luminosities, thus potentially making them usable as cosmological probes. We furthermore discuss our first two spectral principal components, which dominate the object-to-object spectral variation, what they physically represent, and how they correlate with quasar properties. Finally, in \S 4 we discuss the implications of our results for cosmology and quasar astrophysics, along with outstanding sources of scatter, and in \S 5 summarize our general conclusions. Throughout this paper, in order to be consistent with Shen et al. (2011), hereafter S11, we use cosmological parameters $\Omega_{\Lambda}$ = 0.7, $\Omega_{m}$ = 0.3, and H$_{0}$=70 km s$^{-1}$ Mpc$^{-1}$. | There exist quasars with extremely similar ultraviolet spectra, and the more similar the spectra, the more similar on average the luminosity. The similarity in luminosity given similar spectra with similar broad line velocity widths also results in similar Eddington fraction and black hole mass. The similarity in luminosity only approaches 50\% in the mean, however, and can be as large as factors of several in individual pairings. Our findings identify the quantitative limits of using quasars as standard candles based on ultraviolet spectra alone, as well as the limits of our current parameter estimation techniques. Our spectral principal component analysis (SPCA) recovers the same first principal component seen in previous work, which primarily has strong effects on the C IV emission-line profile in the ultraviolet, and furthermore appears to have a strong contribution to the Baldwin effect. Our second principal component appears likely to be consistent with orientation effects and also contributes to the Baldwin effect. This study shows that when quasars match well spectroscopically there is general agreement in their luminosities, i.e., quasar emission lines in certain cases do indeed show correlation with luminosity. The most well-matched quasars can be calibrated to predict luminosity and hence test luminosity distance. This supports previous arguments for the potential to use quasars for high-redshift cosmology, but that potential is not yet realized with current samples. An approach such as ours, using quasar doppelgangers, appears promising for cosmological studies, approaching supernova precision. Deeper flux limits at high redshift will be advantageous. | 16 | 9 | 1609.08732 |
1609 | 1609.09322_arXiv.txt | {\textit{Aims} { Black holes (BHs) surrounded by accretion disks are present in the Universe at different scales of masses, from microquasars up to the active galactic nuclei (AGNs). Since the work of Shakura and Sunyaev (1973) and their $\alpha$-disk model, various prescriptions for the heat-production rate are used to describe the accretion process. The current picture remains ad hoc due the complexity of the magnetic field action. In addition, accretion disks at high Eddington rates can be radiation-pressure dominated and, according to some of the heating prescriptions, thermally unstable. The observational verification of their resulting variability patterns may shed light on both the role of radiation pressure and magnetic fields in the accretion process.} \\ \textit{Methods} { We compute the structure and time evolution of an accretion disk, using the code GLADIS (which models the global accretion disk instability). We supplement this model with a modified viscosity prescription, which can to some extent describe the magnetisation of the disk. We study the results for a large grid of models, to cover the whole parameter space, and we derive conclusions separately for different scales of black hole masses, which are characteristic for various types of cosmic sources. We show the dependencies between the flare or outburst duration, its amplitude, and period, on the accretion rate and viscosity scaling. } \\ \textit{Results} { We present the results for the three grids of models, designed for different black hole systems (X-ray binaries, intermediate mass black holes, and galaxy centres). We show that if the heating rate in the accretion disk grows more rapidly with the total pressure and temperature, the instability results in longer and sharper flares. In general, we confirm that the disks around the supermassive black holes are more radiation-pressure dominated and present relatively brighter bursts. Our method can also be used as an independent tool for the black hole mass determination, which we confront now for the intermediate black hole in the source HLX-1. We reproduce the light curve of the HLX-1 source. We also compare the duration times of the model flares with the ages and bolometric luminosities of AGNs. } \\ \textit{Conclusions} { With our modelling, we justify the modified $\mu$-prescription for the stress tensor $\tau_{\rm r \phi}$ in the accretion flow in microquasars. The discovery of the Ultraluminous X-ray source HLX-1, claimed to be an intermediate black hole, gives further support to this result. The exact value of the $\mu$ parameter, as fitted to the observed light curves, may be treated as a proxy for the magnetic field strength in the accretion flow in particular sources, or their states.}} | \label{sect:intro} Accretion disks are ubiquitous in the astrophysical black holes (BHs) environment, and populate a large number of known sources. Black hole masses range from stellar mass black holes in X-ray binaries, through intermediate mass black holes (IMBHs), up to the supermassive blackholes in quasars and active galaxy centers (Active Galactic Nuclei, AGNs). The geometrically thin, optically thick accretion disk that is described by the theory of Shakura and Sunyaev is probably most relevant for the high/soft spectral states of black hole X-ray binaries, as well as for some active galaxies, such as Narrow Line Seyfert 1s and numerous radio quiet quasars \citep{brandt1997,peterson2000,foschini2015}. The basic theory of a geometrically thin stationary accretion is based on the simple albeit powerful $\alpha$ prescription for the viscosity in the accreting plasma, introduced by \citet{1973A&A....24..337S}. This simple scaling of viscous stress with pressure is also reproduced in the more recent numerical simulations of magnetised plasmas \citep{HiroseKrolikStone,2013ApJ...778...65J, Mishra2016}. However, the latter are still not capable of modelling the global dynamics, time variability, and radiation emitted in the cosmic sources, and hence cannot be directly adopted to fit the observations. The global models, however, must go beyond the stationary model, as the time-dependent effects connected with non-stationary accretion are clearly important. In particular, a number of observational facts support the idea of a cyclic activity in the high-accretion-rate sources. One of the best studied examples is the microquasar GRS 1915+105, which in some spectral states exhibits cyclic flares of its X-ray luminosity, well fitted to the limit cycle oscillations of an accretion disk on timescales of tens or hundreds of seconds \citet{GRS1997Taam,GRS2000Belloni,GRS2011Neilsen}. Those heartbeat states are known since 1997, when the first XTE PCA observations of this source were published \citep{GRS1997Taam}, while recently yet another microquasar of that type, IGR J17091-3624, was discovered \citep{Revnivtsev,Kuulkers,Capitanio09}; heartbeat states were also found for this source \citep{Altamirano11a,Capitanio12,Pahari14,Janiuk2015}. Furthermore, a sample of sources proposed in \citet{Janiuk2011} was suggested to undergo luminosity oscillations, possibly induced by the non-linear dynamics of the emitting gas. This suggestion was confirmed by the recurrence analysis of the observed time series, presented in \citet{Sukova2016}. One possible driver of the non-linear process in the accretion disk is its thermal and viscous oscillation induced by the radiation pressure term; it can be dominant for high enough accretion rates in the innermost regions of the accretion disk, which are the hottest. The timescales of such oscillations depend on the black hole mass, and are on the order of tens to hundreds of seconds for stellar mass BH systems. For a typical supermassive black hole of $10^{8} $M$_{\odot}$, the process would require timescales of hundreds of years. Therefore, in active galactic nuclei (AGNs) we cannot observe the evolution under the radiation pressure instability directly. Nevertheless, statistical studies may shed some light on the sources' evolution. For instance, the Giga-Hertz Peaked quasars \citep{Czerny2009} have very compact sizes, which would directly imply their ages. In the case of a limit-cycle kind of evolution, these sources would in fact not be very young, but `reactivated'. Another observational hint is the shape of distortions or discontinuities in the radio structures. These structures may reflect the history of the central power source of a quasar, which has been through subsequent phases of activity and quiescence. An exemplary source of that kind, quasar FIRST J164311.3+315618, was studied in \citet{Kunert2011}, and found to exhibit multiple radio structures. Another class of objects, which are claimed to contain the BH accretion disk, are the Ultraluminous X-ray sources (ULXs). ULXs are a class of sources that have a luminosity larger than the Eddington one for the heaviest stellar-mass objects ($ > 10^{40}$ ergs s$^{-1}$). Therefore, ULXs are frequently claimed to contain accreting black holes with masses larger than the most massive stars and lower than AGNs ($10^3 - 10^6 M_{\odot}$ intermediate-mass black holes, IMBHs). An example object in this class is HLX-1, which is possibly the best known candidate for an IMBH \citep{Farrell2009,Lasota2011HLX,Servillat2011,Godet2012}. This source is located near the spiral galaxy ESO 243-49 \citep{Wiersema2010HLX,Soria2013} with peak luminosity exceeding $10^{42}$ erg s$^{-1}$. HLX-1 also exhibits periodic limit-cycle oscillations. During seven years of observations of its X-Ray variability, six significant bursts lasting a few tens of days have been noticed. The mass of the black hole inside HLX-1 is estimated at about $10^4 - 10^5 M_{\odot}$ \citep{Straub2014HLX}. In this work, we investigate a broad range of theoretical models of radiation-pressure-driven flares and prepare the results for easy confrontation with observational data. The appearance of the radiation pressure instability in hot parts of accretion disks can lead to significant outburst for all scales of the black hole mass. Temperature and heat production rate determine the outburst frequency and shape. Different effective prescriptions for turbulent viscosity affect the instability range and the outburst properties. Thus, by confronting the model predictions with observed flares, we can put constraints on those built-in assumptions. The attractiveness of the radiation pressure instability as a mechanism to explain various phenomena across the whole black hole mass scale has been outlined by \citet{Wu2016}. In the present paper we expand this work by making a systematic study showing how the model parameters modify the local stability curve and global disk behaviour. We expand the parameter space of the model and identify the key parameters characterising the data. We develop a convenient way to compare the models to the data by providing simple fits to model predictions for the parameters directly measurable from the data. This approach makes the dependence of the models on the parameters much more clear, and it allows for much easier comparison of the model with observational data. | \label{sect:discussion} In this work, we studied the accretion disk instability induced by the dominant radiation pressure, with the use of the generalised prescription for the stress tensor. We adopted a power-law dependence, with an index $\mu$, to describe the contribution of the radiation pressure to the heat production. In other words, the strength of the radiation pressure instability deepens with growing $\mu$. We computed a large grid of time-dependent models of accretion disks, parameterised by the black hole mass, and mass accretion rate. We used the values of these parameters, which are characteristic for the microquasars, intermediate black holes, or AGN. One of our key findings is that this model can be directly applicable for determination of the black hole mass and accretion rate values, for example, for the Ultraluminous X-ray source HLX-1, and possibly also for other sources. We also found that the critical accretion rate, for which the thermal instability appears, decreases with growing $\mu$ (see Figure \ref{fig:sa}). Also, the amplitudes of the flares of accretion disks in AGN are larger than the amplitudes of flares in microquasars and in IMBHs. The flare period grows monotonously with its amplitude, for any value of mass (see Figure \ref{fig:sap}). The outburst width remains in a well-defined relationship with its amplitude (see Figure \ref{fig:sas}). We also found that there is a significant negative correlation between $\mu$ and the ratio of the flare duration to the variability period, $\Delta$. On the other hand, the dependence between the outburst amplitude $A$ and the mass accretion rate $\dot{m}$ is non-linear and complicated. Our results present different variability modes (Figures \ref{fig:ifl} and \ref{fig:iou}). The flickering mode is presented in Fig. \ref{fig:ifl}. In this mode the relative amplitude is small, and flares repeat after one another. In the burst mode the amplitude is large, and the maximum luminosity can be hundreds of times greater than minimal. An exemplary light curve is shown in Fig. \ref{fig:iou}. In this mode we observe long separation between the flares (i.e. an extended low luminosity state), dominated by the diffusive phenomena. A slow rise of the luminosity is the characteristic property of the disk instability model. \begin{table} \begin{tabular}{|c|c|c|c|c|c|c|} \hline {\bf Source} & {\bf ID} & {\bf P} & {\bf A} & {\bf $\Delta$} & {\bf $\frac{M}{M_\odot} (\frac{\alpha}{0.02})^{1.88}$} & {\bf $\mu$}* \\ \hline IGR & $\nu_{I} $ & $45$s & $2.5$ & $0.15$ & $6.38$ & $0.717$ \\ \hline IGR & $\rho_{I A}$ & $30$s & $3.5$ & $0.3$ & $3.52$ & $0.634$ \\ \hline IGR & $\rho_{I B}$ & $30$s & $4$ & $0.4$ & $3.198$ & $0.589$ \\ \hline GRS & $\nu_{G} $ & $90$s & $4$ & $0.1$ & $8.31$ & $0.763$ \\ \hline GRS & $\rho_{G A} $ & $45$s & $5$ & $0.25$ & $3.87$ & $0.661$ \\ \hline GRS & $\rho_{G B} $ & $40$s & $4.5$ & $0.4$ & $3.77$ & $0.583$ \\ \hline HLX & - & $400$d & $2.5$ & $0.14$ & $1.88 \times 10^5$ & $0.534$ \\ \hline\hline AGN${*}$ & - & $10^5$y & $100$ & $0.1$ & $1.6 \times 10^8$ & $0.515$ \\ \hline \end{tabular} \caption{Characteristic quantities of the RXTE PCA light curves for Galactic sources presented in \citep{Altamirano11a} (columns $4,5,6$) supplemented with HLX and AGNs, and estimations of the {$mass-\alpha$ relations} and magnetisation of sources (columns $7,8$). {\bf Notation:} IGR = IGR J17091, GRS = GRS1915, HLX = HLX-1, AGN - typical value for the sample of AGNs presented in \citep{Czerny2009}. The OBSIDs of the ligth curves are as follows: $\nu_{I} =96420-01-05-00$ ( $\nu$ state), $\rho_{I A} =96420-01-06-00$ ({ $\rho$ state}), $ \rho_{I B} = 96420-01-07-00$({ $\rho$ state}) ,$\nu_{G} =10408-01-40-00$ ( $\nu$ state) , $\rho_{G A} = 20402-01-34-00$ ({ $\nu$ state}) and $\rho_{G B} = 93791-01-02-00$ ({ $\rho$ state}), * - Values for a typical AGN.} \label{tab:deter} \end{table} \subsection{Mass - $\alpha$ relation} \label{sect:ma} Since the thermal and viscous timescales strongly depend on $\alpha$, which has only ad-hoc character \citep{King2012} and does not constitute any fundamental physical quantity, $\alpha$ is the parameter describing development of the MHD turbulence in the accretion disk. Thus $\alpha$ should, to some extent, vary depending on the source source and its state; for example, the value of $\alpha$ for the AGN accretion disks can differ from its value for the disks in X-ray binaries. In Fig. $\ref{fig:lca}$ we present different light curve shapes for six different values of $\alpha$. In Fig. $\ref{fig:oa}$ we present the dependence of the light curve observables on $\alpha$. \begin{figure} \includegraphics[width=\columnwidth]{all.png} \caption{Light curves for six different values of $\alpha$ for $M = 10 M_{\odot}$, $\dot{m} = 0.64$, and $\mu = 0.6$. } \label{fig:lca} \end{figure} \begin{figure} \includegraphics[width=\columnwidth]{alphaaps.png} \caption{Dependence between the $\alpha$ parameter and observables for $M = 10 M_{\odot}$, $\dot{m} = 0.64$, and $\mu = 0.6$ for $\alpha \in [0.01:0.32]$.} \label{fig:oa} \end{figure} { The formulae describing fits in Fig. $\ref{fig:oa}$ are as follows:} \begin{equation} \log O_X = b_X \log \alpha + c_X \label{eq:ox} ,\end{equation} { where $O_X = A$, P$ $[in seconds], or $\Delta$. The coefficients are as follows $b_A = 2.25 \pm 0.11$, $c_A = 0.85 \pm 0.05$, $b_P = -0.3 \pm 0.05$, $c_P = 1.85 \pm 0.07$, $b_{\Delta} = -0.29 \pm 0.03$, $c_{\Delta} = -0.87 \pm 0.05$. According to Eqs. $(\ref{eq:massestimation})$ and $(\ref{eq:muestimation})$ we obtain from Eq. $(\ref{eq:ox})$ the following: } \begin{equation} M [M_\odot] = 0.45 P[s]^{0.87} A^{-0.72} (\frac{\alpha}{0.02})^{1.88}, \label{eq:mea} \end{equation} \begin{equation} \mu = 3/7 + \frac{- \log \Delta + 0.87 \log (\frac{\alpha}{0.02})}{1.49 + 1.04 \log P - 0.864 \log A}. \label{eq:muea} \end{equation} \subsection{Radiation pressure instability in microquasars} Quantitatively, our numerical computations, as well as the fitting formula (\ref{eq:20160713}), give the adequate description of the characteristic `heartbeat' oscillations of the two known microquasars: GRS 1915+105, and IGR 17091-324. Their profiles resemble those observed in the so-called $\rho$ state of these sources, as found, for example, on 27th May, 1997 \citep{Pahari14}. For the microquasar IGR J17091, the period of the observed variability is less than $50$s, as observed in the most regular heartbeat cases, that is, in the $\rho$ and $\nu$ states \citep{AltamiranoBelloni2011}. The $\nu$ class is the second most regular variability class after $\rho$, much more regular than any of the other ten classes described in \citet{GRS2000Belloni} ($\alpha$, $\beta$,$\gamma$, $\delta$, $\theta$, $\kappa$, $\lambda$,$\mu$, $\phi$, $\chi$). The $\rho$ state is sometimes described as `extremely regular' \citep{GRS2000Belloni}, with a period of about $60-120$ seconds for the case of GRS1915. The class $\nu$ includes typical Quasi-Periodic Oscillations with relative amplitude large than $2$ and a period of $10-100$s. We apply the results of the current work to model the heartbeat states qualitatively. Eqs. $(\ref{eq:20160713})$ and $(\ref{eq:deltammu})$ allow us to determine the values of BH masses for the accretion disks and the $\mu$ parameter. The results are given in Table \ref{tab:deter}. For the $\rho$-type light curves we can estimate the $mass-\alpha$ $(\frac{M}{M_\odot} (\frac{\alpha}{0.02})^{-1.88})$ parameter of IGR J17091-3624 at the level of $3.2-3.5$ and GRS 1915+105 at the level of $3.7-3.9$. $\mu = 0.58 - 0.63$ for the IGR J17091-3624 and $0.58 - 0.66$ for the $GRS1915,$ respectively. From the $\nu$-type light curves we get significantly larger values of $M-\alpha$ parameters and $\mu$s. Our model thus works properly for the periodic and regular oscillations, which are produced in the accretion disk for a broad range of parameters, if only the instability appears. Irregular variability states $\alpha$, $\beta$, $\lambda$ and $\mu$ should be regarded as results of other physical processes. The explanation of class $\kappa$ of the microquasar GRS 1915 variable state, \citep{GRS2000Belloni} which presents modulated QPOs, seems to be on the border of applicability. In general, the method is correct for estimation of the order of magnitude, although not perfect for exact determination of the parameters due to the nonlinearity of the model. For this paper we assumed a constant value of $\alpha = 0.02$ which could not be true for all values of masses. For a source with known mass, such as GRS1915 \citep{Greiner2001,Steeghs2013}, we can use previous estimations as a limitation for the value of $\alpha$, as presented in Section \ref{tab:6}. \citet{Steeghs2013} estimated the mass of GRS1915 at the level $10.1 \pm 0.6 M_\odot$. From the high-frequency QPO comparison method used by \citet{Rebusco2012} we know the GRS/IGR mass ratio, which is at the level of 2.4. Combining the results of \citet{Rebusco2012} and later the GRS1915 mass estimation from \citet{Steeghs2013}, for the IGR J17091 we get $M = 4.2 \pm 0.25 M_{\odot}$. Results of \citet{IyerNandi2015} suggest the probable mass range of IGR J17091 is between $8.7$ and $15.6 M_{\odot}$. \begin{table} \begin{tabular}{|c|c|c|c|c|} \hline {\bf source} & {\bf ID} & {\bf *$\mathcal{M}$} & $\frac{M}{M_\odot}$ & $\alpha$ \\ \hline IGR & $\nu_{I} $ & $6.38$ & $3.95 - 4.45$** & $0.0155 - 0.0165$ \\ \hline IGR & $\rho_{I A}$ & $3.52$ & $3.95 - 4.45$** & $0.0213 - 0.0227$ \\ \hline IGR & $\rho_{I B}$ & $3.198$ & $3.95 - 4.45$** & $0.0223 - 0.0238$ \\ \hline IGR & $\nu_{I} $ & $6.38$ & $8.7 - 15.6$*** & $0.0235 - 0.0321$ \\ \hline IGR & $\rho_{I A}$ & $3.52$ & $8.7 - 15.6$*** & $0.0323 - 0.0441$ \\ \hline IGR & $\rho_{I B}$ & $3.198$ & $8.7 - 15.6$*** & $0.0330 - 0.0446$ \\ \hline GRS & $\nu_{G} $ & $8.31$ & $9.5 - 10.7$ & $0.0214 - 0.0228$ \\ \hline GRS & $\rho_{G A} $ & $3.87$ & $9.5 - 10.7$ & $0.0322 - 0.0343$ \\ \hline GRS & $\rho_{G B} $ & $3.77$ & $9.5 - 10.7$ & $0.0327 -0.0348$ \\ \hline \end{tabular} \label{tab:6} \caption{{Determination of $\alpha$ values based on the known IGR and GRS mass values \citep{Rebusco2012,Steeghs2013,IyerNandi2015} and mass-$\alpha$ relation presented in Table $\ref{tab:deter}$. Descriptions of the sources, their states and OBSIDs are presented in Table $\ref{tab:deter}.$ * - Mass - $\alpha$ factor $(\frac{M}{M_\odot} (\frac{\alpha}{0.02})^{-1.88})$. ** - IGR mass estimation from \citet{Rebusco2012} and \citep{Steeghs2013} *** - IGR mass estimation from \citet{IyerNandi2015}.}} \end{table} {From Tables \ref{tab:deter} and \ref{tab:6} we conclude the possible dependence between $\alpha$ and the variability state or the source type. For the $\nu$ state of IGR we found $\alpha \approx 0.0155 - 0.0165$, for the $\rho$ state of this source $\alpha \approx 0.021 -0.024$, for the $\nu$ state of GRS $\alpha \approx 0.021 - 0.023$ and for the $\rho$ state of GRS $\alpha \approx 0.032 -0.035$.} {Those values can change if we assume the BHs spin, which can be near to extreme in the case of GRS1915 \citep{Done2004} and very low, even retrograde in the case of IGR J17091 \citep{Rao2012}.} In our current model we neglect the presence of the accretion disk corona. {If we follow the mass estimation done by \citet{IyerNandi2015}, we get quite a consistent model for both microquasars' $\nu$ and $\rho$ variability states - $\alpha \approx 0.023$ for the $\nu$ state and $\alpha \approx 0.033$ the $\rho$ state, if only we assume the mass of IGR at the level of $9-10 M_{\odot}$, that is, close to the lower limit from results of \citet{IyerNandi2015}.} {We get the above results under the assumption of negligible influence of coronal emission on the light curve.} According to \citet{2006MNRAS.372..728M}, power fraction $f$ emitted by the corona is given by following formula: % \begin{equation} f = \sqrt{\alpha} \Bigg[ \frac{P}{P_{\rm gas}} \Bigg]^{1 - \mu}. \end{equation} For our model with $\alpha = 0.02$, the values of $f$ are low, where $f = 0.141 (\frac{P}{P_{\rm gas}})^{1-\mu}$, which for the values of $\mu$ investigated in the paper fulfills the inequality of $0.0125 < f < 0.141$, if we assume a threshold maximal value of the gas-to-total pressure rate $\beta = \frac{P_{\rm gas}}{P}$ from Eq.(~\ref{eq:muszusz}). According to the fact that the (\textit{heartbeat}) states are strongly radiation-pressure dominated and the coronal emission rate is lower for lower values of the $\mu$ parameter, (which are more likely to reproduce the observational data), we can regard the coronal emission as negligible. \subsection{Disk instability in supermassive black holes} \label{wykresy:a} In the scenario of radiation pressure instability, with a considerable supply of accreting matter, the outbursts should repeat regularly every $10^4-10^6$ years \citep{Czerny2009}. From the grid of models performed in \citep{Czerny2009}, done for $\mu = 0.5$ ($\tau_{ r \phi} = \alpha \sqrt{P P_{\rm gas}}$) and $10^7 M_\odot < M < 3 \times 10^9$, they obtained the following formula expressing correlation between the duration time, $\alpha$ parameter and bolometric luminosity $L_{\rm bol}$: \begin{equation} \log (\frac{T_{\rm dur}}{\rm yr}) \approx 1.25 \log (\frac{L}{{\rm erg s}^{-1}}) + 0.38 \log (\frac{\alpha}{0.02}) + 1.25 \log K - 53.6 \label{eq:duration} \end{equation} which, for the special case $\alpha = 0.02$ and neglecting the bolometric correction, has the following form: \begin{equation} \log \frac{L_{\rm bol}}{ {\rm erg s}^{-1}} = 0.8 \log (T_{\rm dur}/s) + 42.88. \label{eq:durationa} \end{equation} The formula $(\ref{eq:durationa})$ also found its confirmation in observational data for different scales of BH masses, as presented in Fig. \ref{fig:13}. This applies despite the assumption of $\mu = 0.5$ since the expected dependence on $\mu$ is weak. If we combine Eqs. (\ref{eq:20160713}) and (\ref{eq:deltammu}), we get: \begin{equation} \log (T_{\rm dur}/s) = (1.15 - 1.2(\mu - 3/7)) \log M + 0.83 \log A - 1.9\mu + 0.83. \label{eq:160824} \end{equation} From Fig. \ref{fig:13} we can suggest the approximate dependence \begin{equation} \log A = 0.4 \log M + 0.25 \label{eq:160824a} ,\end{equation} since for the same model input parameters (e.g. $\log \dot{m} = -0.2$, $\alpha = 0.02$ and $\mu = 0.56$) the amplitude could be even a hundred times larger for the case of AGNs than for microquasars. Combining Eqs. (\ref{eq:160824}) and (\ref{eq:160824a}) and adopting $L_{bol} = \dot{m} L_{Edd, \odot}$ where $L_{Edd, \odot} = 1.26 \times 10^{38}$erg s$^{-1}$, we get: \begin{equation} \log (T_{\rm dur}/yr) = (1.91 - 1.2 \mu )(\log L- \log L_{edd \odot} - \log \dot{m} ) - 6.68. \label{eq:160824b} \end{equation} { The Eq. (\ref{eq:160824b}) can be inverted: \begin{equation} \log L = \frac{1}{1.91 - 1.2 \mu} \log (T_{\rm dur}/yr)+ 37.1 + \frac{6.68}{1.91 - 1.2 \mu} + \log \frac{\dot{m}}{0.1}. \label{eq:56} \end{equation} The above Equation is a generalised version of the results from \citet{Czerny2009} and \citet{Wu2016}. \begin{figure} \includegraphics[width=\columnwidth]{fig13.png} \caption{Correlation between the bolometric luminosity and the outburst duration for different-scale BHs. Thick lines represent the best fit from \citet{Wu2016}, and the prediction from \citet{Czerny2009}. Thin lines represent Eq. (\ref{eq:56}) for several different values of $\mu$, assuming $\dot{m} = 0.1$.} \label{fig:13} \end{figure} In Fig. \ref{fig:13} we present the observational points from \citet{Wu2016}, and the theoretical lines as a result from Eq. (\ref{eq:56}) for several values of $\mu$. We assumed that the Eddington accretion rate and the accretion efficiency are roughly independent for different BH masses. The proportionality coefficient in Eq.~\ref{eq:duration} changes from 1.25 to $1.91 - 1.2 \mu$, that is, 1.19 for $\mu = 0.6$. For most of the known AGNs, except for the Low Luminosity AGNs, their luminosity in Eddington units is over $0.02$ \citep{AGN2006Hardy}, and the sources remain in their soft state, so the radiation pressure instability model should apply. The weak sources claimed to be AGNs, such as NGC4395 and NGC4258 \citep{LasotaNGC42,FilippenkoNGC43} are claimed to be in the hard state, being not described accurately by the accretion disk model of Shakura-Sunyaev. It should be possible to study the evolution of those sources statistically. Based on the known masses, accretion rates, and timescales for AGN, the luminosity distribution for the samples of AGN with similar masses or accretion rates can be acquired. This should allow us to reproduce an average light curve for a range of masses and accretion rates for a survey of the known AGNs \citep{Wu2009}. The averaged light curve for a big ensemble of AGN will help us to provide expected luminosity distributions or luminosity-mass, luminosity-duration relations for the AGNs existing in the universe. However, high-amplitude outbursts may complicate the study since the detection of the sources between the flares may be strongly biased as the sources become very dim. Existence of the likely value of $\mu \approx 0.6$, proven by comparison of Eqs. (\ref{eq:duration}) and (\ref{eq:160824b}), could also help in mass determination of newly discovered objects. Another interesting situation comprises the so-called Changing-Look-AGN, such as IC751 \citep{ricci2016}. Although most AGN have a variability timescale on the order of thousands of years, the shape of model light curves (sharp and rapid luminosity increases) could suggest that, for some cases, luminosity changes can be observed. \subsection{Explanation of the HLX-1 light curve irregularity} \label{sect:irreg} The light curve of HLX-1, presented in the upper panel of Fig. \ref{fig:hlxobs}, despite very regular values of peak luminosity ($\log \frac{L}{{\rm erg s}^{-1}}$ between $42.5$ and $42.6$), presents significant variability of the flare duration. According to our model, for any constant input parameter (mass, Eddington rate, $\alpha$ and $\mu$), period, duration, and amplitude should remain constant. To our knowledge, the only explanation for such a phenomenon is variation in the input parameters. The variability of the central object mass is too faint (approx. $10^{-8}$ per one cycle for any accreting source) to be visible. The variability of $\dot{m}$ is possible, bearing in mind the fact that accretion rate of HLX-1 (order of $10^{-3} M_\odot$ per one duty cycle) can be significantly disturbed by the tidal disruption of the minor bodies such as planets with mass ranging from $10^{-6} M_\odot$ to $10^{-3} M_\odot$. A detailed description of this process can be found in \citet{EvansKochanek1989} and \citet{DelSanto14} presented its application for the case of phenomena inside the globular clusters. The Eddingtion rate $\dot{m}$ is a global parameter, strongly connected with the accretion disk neighbourhood ($\dot{m}$ can change rapidly in the case of tidal disruption). In contradiction, $\mu$ and $\alpha$ are the local parameters approaching the MHD turbulence. As $\alpha$ can be connected with the rate of the typical velocity of turbulent movement to the sound speed \citep{1973A&A....24..337S}, $\mu$ can represent the magnetisation of the disk, as shown by the Eq. (\ref{eq:mumagnetic}). In the HLX-1 observation, out of the four observables, only the $\Delta$ parameter was changing significantly between different flares. According to Eq. $(\ref{eq:muea})$ this follows from changing $\mu$. Specifically, the growth of $\mu$ from $0.48$ to $0.56$ is responsible for $\Delta$ decreasing from $0.4$ to $0.1$ . According to those results, $\mu$ was growing during the sampling time, which can be explained by a decrease in disk magnetisation. \subsection{Conclusions} \label{sect:discconc} We propose a possible application of the modified viscosity model as a description of a regular variability pattern (heartbeat states) of black hole accretion disks for the microquasars, IMBHs and AGNs. The model works for optically thick, geometrically thin disks and determines the range and scale of the radiation pressure instability. The parameter $\mu$, which describes viscosity, can reproduce a possibly stabilising influence of the strong magnetic field in the accretion disk. Nonlinearity of the models causes appearance of different modes of the disk state (stable disk, flickering, outbursts). Thanks to the computation of computing a large grid of models we are able to present quantitative estimations for the variability periods and amplitudes, and our model light curves reproduce several different variability patterns. Also, many observables, such as, $L$, $P$, $A$, and $\Delta$, can be used directly to determine the physical parameters, like $\alpha$, $\mu$, $M$, and $\dot{m}$. Finally, our model can be successfully applied to the mass and accretion rate determination for the intermediate black hole HLX-1 at the level of $1.9 \times 10^5 $M$_\odot$ and $0.09 - 0.18$ respectively, updating the result from \citet{Wu2016}. The prospects of further applications to microquasars and AGNs are promising. | 16 | 9 | 1609.09322 |
1609 | 1609.09114_arXiv.txt | We perform the first systematic study on how dynamical stellar tides and general relativistic (GR) effects affect the dynamics and outcomes of binary-single interactions. For this, we have constructed an N-body code that includes tides in the affine approximation, where stars are modeled as self-similar ellipsoidal polytropes, and GR corrections using the commonly-used post-Newtonian formalism. Using this numerical formalism, we are able resolve the leading effect from tides and GR across several orders of magnitude in both stellar radius and initial target binary separation. We find that the main effect from tides is the formation of two-body tidal captures that form during the chaotic and resonant evolution of the triple system. The two stars undergoing the capture spiral in and merge. The inclusion of tides can thus lead to an increase on the stellar coalescence rate. We also develop an analytical framework for calculating the cross section of tidal inspirals between any pair of objects with similar mass. From our analytical and numerical estimates we find that the rate of tidal inspirals relative to collisions increases as the initial semi-major axis of the target binary increases and the radius of the interacting tidal objects decreases. The largest effect is therefore found for triple systems hosting white dwarfs and neutron stars. In this case, we find the rate of highly eccentric white dwarf - neutron star mergers to likely be dominated by tidal inspirals. While tidal inspirals occur rarely, we note that they can give rise to a plethora of thermonuclear transients such as Ca-rich transients. | Stars in dense stellar systems evolve very differently than those in the solar neighborhood. In an environment of extreme stellar density, like a globular cluster (GC), close encounters between stars are frequent \citep{Heggie:1975uy, Hut:1983js, Hut:1983by, 1992PASP..104..981H, Hut:1993gs, Heggie:1993hi}. Binary-single dynamical encounters, which occur when a single star passes close to a binary and perturbs it, are particularly likely. These encounters are much more frequent than single-single stellar encounters because the orbit of the binary acts as a net -- sweeping passing single stars into periods of resonant triple-object interactivity which are characterized by the formation and dissolution of temporary binary pairings. As such, binary-single interactions are responsible for shaping the populations of close binaries in dense clusters \citep{Heggie:1975uy, 1991ASPC...13..324M, 1992PASP..104..981H, Baumgardt:2002eb, 2005ASPC..328..231I, 2005MNRAS.358..572I, 2009ApJ...707.1533F, 2014A&A...561A..11V}. Because the energy and momentum are randomized during these chaotic triple interactions, very close passages between pairs of objects are possible \citep[e.g.,][]{1985ApJ...298..502H, 1986ApJ...306..552M, 2006tbp..book.....V}. During close passages deviations in the dynamics from the behavior of point masses in the limit of Newtonian gravity can become apparent. \cite{2014ApJ...784...71S} studied the modification of binary-single dynamics by the inclusion of gravitational wave (GW) energy losses. This work showed a counterintuitive result: passages close enough to modify the dynamics are actually most common in systems involving {\em wide} target binaries. We typically associate general relativistic corrections with being most important in compact systems, but \cite{2014ApJ...784...71S} show that the likelihood of generating a very close encounter actually rises as the target binary widens because its larger cross section sweeps in the most perturbing stars. This paper focuses on stellar tides, another commonly neglected physical ingredient in the full $N$-body equation of motion of stars. Stellar tides can be excited in close passages and much like gravitational radiation, the amplitude of tidally-excited oscillations is very sensitive to the passage distance between two objects. Tides play a role in stellar dynamics when stars are sufficiently close that there is an appreciable difference in gravitational force across the object radius. The relative tidal force scales to leading order as $(R/r)^3$ for a perturber at distance $r$ from a star with radius $R$. The associated energy transfer has a much steeper dependence on $r$ \citep[][which we refer as PT for the rest of the paper]{1977ApJ...213..183P}. Thus tides can become important when objects come within a few stellar radii of each other. Previous work on how dynamical tides might affect GC evolution has mostly been related to the role of binaries that are formed through two-body tidal captures \citep{1975MNRAS.172P..15F, 1977ApJ...213..183P, 1986ApJ...310..176L, 1987ApJ...318..261M}. These "two-body" binaries have been suggested to, for example, help reverse the contraction of GC core collapse long before binaries formed by pure "three-body" interactions are created \citep{1983Natur.305..506K, 1985IAUS..113..347O, 1986ApJ...306..552M}. Tidally formed binaries also have potentially observable consequences and were initially suggested to explain GC X-ray sources \citep{1975MNRAS.172P..15F, 1975ApJ...199L.143C}. Numerical modeling and observations have shown that few-body interactions must play a role not only in the formation and disruption of X-ray binaries \citep{1983Natur.301..587H, 2003ApJ...591L.131P, Pooley:2006ef, 2010ApJ...717..948I, Ivanova:2013tw, 2014A&A...561A..11V}, but of all compact binaries in dense stellar systems \citep[e.g.,][]{Sigurdsson:1993jz, Sigurdsson:1995gh, 2006MNRAS.372.1043I, Ivanova:2008jx}. This further includes compact neutron star binaries which are believed to be the progenitors of short gamma-ray bursts \citep[SGRBs;][]{Grindlay:2006ef,Lee:2010ina}. Other distinct features of dynamically formed binaries include high eccentricity at merger, which can give rise to a rich variety of electromagnetic and GW signatures for black holes and neutron stars \citep{2011ApJ...737L...5S, East:2012hg, Gold:2012jg, East:2012es, East:2013iy, 2014ApJ...784...71S}. The role of dynamical encounters has been further linked to the observed distribution of pulsars \citep{2005ASPC..328..147C, 2013IAUS..291..243F, 2014A&A...561A..11V}. In particular, the observed population of single millisecond-pulsars (MSPs) in GCs suggests that few-body interactions must happen frequently with outcomes that both assemble and disrupt compact binaries \citep{2013IAUS..291..243F, 2014A&A...561A..11V}. Few-body interactions involving two or more stars are also likely to result in stellar mergers \citep{Fregeau:2004fj}. The remnants of such mergers have been proposed to partially explain the observed population of so-called blue stragglers \citep[BSs;][]{1953AJ.....58...61S}. However, the leading formation mechanism of BSs is still under debate \citep[e.g.,][]{2011MNRAS.416.1410L, 2013MNRAS.428..897L, 2015ebss.book..295K}, with formation mechanisms ranging from isolated mass transfer \citep{2011Natur.478..356G} to secular dynamics \citep{2009ApJ...697.1048P} and resonant few-body interactions \citep{Fregeau:2004fj}. Despite the clear importance of few-body interactions in shaping the distributions of binaries and singles, no systematic study has been done of how tidal effects might affect the outcomes. The nature of tidal encounters also remains uncertain. In fact, simulations and semi-analytical models indicate that a tidally formed binary may lead to a merger rather than a stable binary \citep{1992ApJ...385..604K, 1993PASP..105..973R}, a concern that was also raised in the original paper by \cite{1975MNRAS.172P..15F}. The evolution of the tidal capture itself has been studied using different analytical prescriptions: \cite{Mardling:1995hx, Mardling:1995it} showed using a linear mode analysis that if one takes into account the evolving oscillatory state of the stars on the orbital evolution, tidal captures are likely to undergo quasiperiodic or even random walk behavior. Similar behavior has also been discussed and seen in work related to the non-linear affine model developed by \citet{1985MNRAS.212...23C} and \citet{Luminet:1986cha}, further studied by e.g. \cite{1992ApJ...385..604K}, \citet{1993ApJS...88..205L,1994ApJ...423..344L,1994ApJ...420..811L, 1994ApJ...437..742L} and \citet{1995ApJ...443..705L}, and later generalized by \citet{2001ApJ...549..467I} and \citet{2003MNRAS.338..147I}. Non-linear mode couplings could therefore play a role in the problem of a tidal encounter since the mode excitation spectrum of the star determines the dynamical evolution at subsequent passages. The outcome is therefore intimately linked to the problem of how the energy is dissipated during the evolution, which remains an open question \citep[e.g.,][]{2014ARA&A..52..171O}. GC simulations including approximations of tidal effects have been performed \citep{Mardling:2001dl}, but to our knowledge, there is little systematic study of how dynamical tides play a role in few-body systems. Earlier works, particularly by \citet{1985ApJ...298..502H} and \citet{1986ApJ...306..552M}, have discussed the effect of tides and finite sizes. However, their results are based on point-particle simulations and the few-body systems they study are not evolved consistently with tides. Recent studies by, e.g., \cite{2010MNRAS.402..105G} have modeled a few binary-single interactions using smoothed particle hydrodynamics (SPH). However, their limited sample mainly consists of very hard target binaries due to the heavy computational cost of SPH simulations, and are therefore not representative for the wide distribution of binary-single interactions that are known to occur in dense stellar systems. The first clear insight about how tides might affect binary-single interactions in general, was given by \citet{1992ApJ...385..604K}, who correctly suggested that tidal effects in three-body interactions will lead to two-body tidal captures during the chaotic evolution of the triple system. Furthermore, \citet{1992ApJ...385..604K} imagined that these tidally formed binaries probably have an orbital distribution different from those formed by two-body captures in the field. In our work we study close three-body encounters using an $N$-body prescription where the orbital dynamics is evolved consistently with both tides and GR. We show that the main effect of including tides is the formation of two-body tidal captures during the three-body evolution, in agreement with earlier predictions by \citet{1992ApJ...385..604K}. Using both numerical and analytical arguments we illustrate that the relative rate of these tidal captures increases as the radius of the tidal object decreases relative to the size of the initial target binary. In the astrophysical context, tides therefore show the largest effect when the perturbed object is a white dwarf. Our analysis of the role of tides in binary-single dynamics proceeds as follows. We discuss the general properties of binary-single encounters and build some intuition for the possible role of tides in shaping these encounters in Section \ref{sec:Binary-Single Interactions and Tidal effects}. In Section \ref{sec: N-body with Tides and GR: Numerical Methods} we describe a numerical formalism for including tidal excitation in $N$-body encounters by treating stars as compressible ellipsoids. In Section \ref{sec: Numerical Scattering Results} we describe results of scattering experiments of large numbers of binary-single encounters. In Section \ref{sec:Analytical Models} we derive analytical relationships to interpret the dependence of these results on stellar type and binary properties. Finally, in Section \ref{sec:Discussion} we discussed our findings while our conclusions are presented in Section \ref{sec:Conclusion}. | \label{sec:Conclusion} We present the first systematic study of how dynamical tides affect the interaction and relative outcomes in binary-single interactions. From performing a large set of binary-single scatterings using an $N$-body code that includes tides and GR, we find that the inclusion of tides leads to a population of tidal captures which are occurring during the chaotic evolution of the triple interaction. We denote these captures \emph{tidal inspirals}, partly due to their similarity with the GW inspirals studied in \citep{2014ApJ...784...71S}. We confirm with analytical models that the rate of tidal inspirals relative to the classical sticky star collision rate increases with $(a_{0}/R)$, as a result, tides show the largest effect for widely separated binaries. Since the upper limit on $a_{0}$ is set by the HB limit, which scales linearly with mass $m$, we conclude that the compactness $m/R$ of the tidal object is the key factor for determining if tides play a significant role or not in a given cluster environment: a larger compactness leads to more tidal inspirals relative to collisions. As a result of these scalings, we find that the only tidal object which is compact enough to have tidal inspirals dominating over collisions in a typical GC environment is a WD. We further conclude that tides, from a dynamical perspective, do not seem to effect the dense stellar system as a whole, as otherwise speculated in several previous studies \citep[e.g.][]{Fregeau:2004fj} -- although stellar finite sizes do matter through collisions and dynamical kicks \citep{1986ApJ...306..552M}. However, the inclusion of tides and GWs leads to a rare, but highly interesting population of eccentric binaries. The high eccentricity likely results in unique EM and GW signals. While highly eccentric binaries can be created in single-single captures, it was illustrated in \cite{2014ApJ...784...71S} that the binary-single channel is likely the dominant formation path. These observations motivate further dynamical studies on few-body interactions involving especially WDs and COs, as well as hydrodynamical studies on the outcome of highly eccentric captures. While our estimated inspiral rate involving a heavy WD (1.2$M_{\odot}$) is still modest, we do expect the rate to be significantly higher for lower mass WDs simply because they are more vulnerable to tidal deformations. We are currently working on the analytical prescriptions for unequal mass encounters. | 16 | 9 | 1609.09114 |
1609 | 1609.00035_arXiv.txt | The inner regions of the solar corona from 1-2.5 Rsun are poorly sampled both from the ground and space telescopes. A solar eclipse reduces the sky scattered background intensity by a factor of about 10,000 and opens a window to view this region directly. The goal of the Citizen {\it Continental-America Telescopic Eclipse} (CATE) Experiment is to take a 90-minute time sequence of calibrated white light images of this coronal region using 60 identical telescopes spread from Oregon to South Carolina during the 21 August 2017 total solar eclipse. Observations that can address questions of coronal dynamics in this region can be collected with rather modest telescope equipment, but the large dynamic range of the coronal brightness requires careful camera control. The instruments used for test runs on the Faroe Islands in 2015 and at five sites in Indonesia in 2016 are described. Intensity calibration of the coronal images is done and compared with previous eclipse measurements from November \& Koutchmy (1996) and Bazin et al. (2015). The change of coronal brightness with distance from the Sun seen in the 2016 eclipse agrees with observations from the 1991 eclipse but differ substantially from the 2010 eclipse. The 2015 observations agree with 2016 and 1991 solar radii near the Sun, but are fainter at larger distances. Problems encountered during these test runs are discussed as well the solutions which will be implemented for the 2017 eclipse experiment. | The path of totality of a solar eclipse will cross over 10 million homes in the USA during the late morning and early afternoon on Monday 21 August 2017. Tens of millions more people will travel to view the total eclipse and hundreds of millions more will directly view the partial eclipse. Using broadcasts hundreds of millions of people will watch the total eclipse, from school children through senior citizens. From one location during the 2017 eclipse the corona will only be revealed for about 2.5 minutes; this short time does not allow detailed study of slower changes in the corona (Lites et al., 1999). From the moment the lunar shadow touches Oregon until it leaves South Carolina 90 minutes of time will elapse. The Citizen {\it Continental-America Telescopic Eclipse} (CATE) Experiment will use 60 identical telescopes positioned across the country to image the solar corona. The CATE goal is to collect calibrated white-light image of the solar corona from about $1~R_{sun}$ to $2~R_{sun}$ with about 2 arcsecond pixels every 10 seconds continuously for 90 minutes. Using data from the Spartan 201-01 mission in 1993, Fisher and Guhathakurta (1995) measured white light polar plumes above the northern and southern solar coronal hole. These plumes extended from the lower limit of the occulting disk at $R=1.25~R_{sun}$ up to over $5~R_{sun}$ Simultaneous ground-based measurements from Mauna Loa suggested that the plumes extended down to $R=1.16~R_{sun}$. The directions of the plumes, while appearing roughly radial, did not intersect the center of the solar disk but rather seemed to originate at higher latitudes. Later work by DeForest and Gurman (1998) traced these structures down to magnetic features at the solar poles using SOHO EIT 171A data, and measured a size of between 3-5 arcsec. The CATE data will measure these structures in white light with 2 arcsec pixels to very low heights of $R=1.05~R_{sun}$, and out to the edge of the field-of-view at $2~R_{sun}$. Using simultaneous magnetograms from other telescopes, these polar plume structures can be traced using the continuum signal from coronal electron density enhancements back to the Sun with better resolution than previous studies. At solar minimum structures called polar plumes are clearly visible above the magnetic north and south poles of the Sun. These regions have been found to be very dynamic. DeForest and Gurman (1998) used SOHO EIT 171A observations to observe outwardly moving density enhancements traveling at 75-150 km/s velocity, showing brightness changes of 5 to 10\%, and displaying periodicity at 10-15 minute periods. Cranmer (2004) estimated 3 to 15\% variations in the electron density in these events. Using UVCS observations at two alternating heights in the corona $R=1.9~R_{sun}$ and $2.1~R_{sun}$), Ofman et al (2000) found quasi-periodic variations of 5 to 10\% in polarized brightness traveling radially at 210 km/s with periods between 6.5 and 10.5 minutes. Morgan et al (2004) used Lyman alpha data out to $2.2~R_{sun}$ to find oscillations with 7 to 8 minute periods. With SUMER disk observations of Ne VIII emission, Gupta et al (2012) found 5-10\% intensity oscillations traveling at 60 km/s with a period of 14.5 minutes. From eclipse observations, Pasachoff (2009) found changes in the corona above the southern solar pole. But since this observation used only two images taken 19 minutes apart, it is difficult to find systematic radial motion. With 540 images taken at 10 second cadence across 90 minutes, the CATE data will have direct applications to the study of polar plume dynamics. Periodicities at the 15 minute time scale will be fully sampled, and the velocities and accelerations of these events will be measured from $R=1.05~R_{sun}$ out to at least $2~R_{sun}$. The CATE data will be sensitive to transverse velocities of roughly 0.8 to 145 km/sec (3pix/90 min to 1 pix/10 sec) and will easily measure these events. In addition to showing polar plumes, the solar minimum corona which will be seen during the 2017 total solar eclipse will likely show several prominences. The interaction of the hot corona with the cold prominence plasma has been studied recently. With the Hinode SOT instrument Berger et al (2007) show upwardly moving hot gas parcels, thought to be Rayleigh-Taylor instabilities in the prominences. Typical sizes which were observed were about 2250 km, and these features showed upward speeds of roughly 20 km/s. Using lower resolution white-light images of the hot coronal plasma, Druckmuller et al (2014) examined a static structure observed near a prominence called a smoke ring. The authors speculate that these structures are related to the RT instabilities seen in prominences. The CATE data will reveal and motions of these new coronal structures during the 90 minutes of the eclipse, and will have a transverse velocity sensitivity that covers the expected 20km/s motion. The CATE observations may reveal how the instabilities seen in prominences interact with the hot corona and produce density enhancements or depletions such as these smoke rings. In preparation for the 2017 CATE experiment, two test runs have been completed at the total solar eclipses in 2015 and 2016. Equipment similar to the 2017 instrument was used in each case by citizen scientists and first-time eclipse observers. We describe the results of these tests and plans for the 2017 experiment in the following paper. | 16 | 9 | 1609.00035 |
|
1609 | 1609.01802_arXiv.txt | We consider torsional oscillations that are trapped in a layer of spherical-hole (bubble) nuclear structure, which is expected to occur in the deepest region of the inner crust of a neutron star. Because this layer intervenes between the phase of slab nuclei and the outer core of uniform nuclear matter, torsional oscillations in the bubble phase can be excited separately from usual crustal torsional oscillations. We find from eigenmode analyses for various models of the equation of state of uniform nuclear matter that the fundamental frequencies of such oscillations are almost independent of the incompressibility of symmetric nuclear matter, but strongly depend on the slope parameter of the nuclear symmetry energy $L$. Although the frequencies are also sensitive to the entrainment effect, i.e., what portion of nucleons outside bubbles contribute to the oscillations, by having such a portion fixed, we can successfully fit the calculated fundamental frequencies of torsional oscillations in the bubble phase inside a star of specific mass and radius as a function of $L$. By comparing the resultant fitting formula to the frequencies of quasi-periodic oscillations (QPOs) observed from the soft-gamma repeaters, we find that each of the observed low-frequency QPOs can be identified either as a torsional oscillation in the bubble phase or as a usual crustal oscillation, given generally accepted values of $L$ for all the stellar models considered here. | \label{sec:I} Neutron star crusts, which are composed of inhomogeneous neutron-rich nuclear matter embedded in a roughly uniform neutralizing background of electrons, can be unique laboratories to provide us with simultaneous manifestations of superfluids, liquid crystals, and solids. This is because nuclear matter at subnuclear densities and sufficiently low temperatures can exhibit various mixed phases of a liquid composed of protons and neutrons and a neutron gas as a result of the combined effect of the tensor, isoscalar part of the nuclear force and the Coulomb interaction, while keeping both the liquid and the gas in a superfluid state thanks to the central, isovector part of the nuclear force \citep{PR1995}. The crustal region, which is located in the outer part of a neutron star, is observationally more relevant than the inner part, namely, the core region, because of the closer distance to the star's magnetosphere and surface, from which electromagnetic emission occurs. From the viewpoint of condensed matter physics, however, the deeper, the more interesting. In fact, roughly spherical nuclei (liquid part), which are predicted to form a body-centered cubic (bcc) lattice at relatively low densities, are considered to fuse into rod-like nuclei in a gas of neutrons when the spherical nuclei become so closely packed as to be almost unstable with respect to quadrupolar deformations. As the density increases further, it is expected that the shape of the liquid part in the crust changes from spherical to cylindrical (rod), slab, cylindrical-hole (tube), and spherical-hole (bubble) structures until matter becomes uniform \citep{LRP1993,O1993}. The rod, slab, tube, and bubble structures are often referred to as nuclear pasta. Since the spherical and bubble phases are solids while the cylindrical, slab, and cylindrical-hole phases are liquid crystals, possible observations of global free oscillations from neutron stars could be useful for obtaining information about elastic and superfluid properties of neutron star interiors \citep{PA2012}. This technique is known as asteroseismology, which is essentially the same as seismology in the case of the Earth and helioseismology in the case of the Sun. In fact, it has been suggested that the neutron star's properties such as the mass and radius, the equation of state (EOS) of matter therein, and the magnetic properties would be possible to obtain via the spectra of the star's oscillations (see, e.g., \cite{VH1995}). Neutron star asteroseimology is unique in the sense that in addition to electromagnetic waves, gravitational waves radiating from the star are expected to provide us with information about the star's global oscillations \citep{AK1996,STM2001,SKH2004,SYMT2011,DGKK2013}. Direct gravitational wave detections from neutron stars, which have yet to be done, would be highly promising in the near future. Meanwhile, there are X-ray observational evidences for neutron star oscillations. In fact, quasi-periodic oscillations (QPOs) were discovered in the X-ray afterglow of giant flares from soft-gamma repeaters (SGRs) \citep{I2005,SW2005,SW2006,QPO2}, which are supposed to be strongly magnetized neutron stars \citep{K1998,H1999}. Although there are still many uncertainties in understanding of the mechanism of the giant flares and the subsequent QPOs, it is generally accepted that the QPOs arise from global oscillations of the neutron stars. The observed QPO frequencies are in the range of tens Hz up to kHz, while typical frequencies of neutron star acoustic oscillations are around kHz \citep{VH1995}. Particularly, identification of the QPO frequencies lower than $\sim 100$ Hz is not straightforward but could significantly constrain the possible origin of the QPOs. Basically, candidates for the corresponding global oscillations are crustal torsional oscillations, magnetic oscillations, and coupled oscillations between these two. Global magnetic oscillations in neutron stars depend crucially on the magnetic field strength and structure therein \citep{GCFMS2013}, but those are still poorly known, particularly in superconducting materials, as well as the EOS for matter in the core. In order to avoid such uncertainties, in this paper we simply consider the observed low-lying QPOs as crustal torsional oscillations. In fact, within such identifications, one can obtain information about the crustal properties by fitting the calculated eigenfrequencies to the observed QPO frequencies \citep{SA2007,SW2009,GNJL2011,SNIO2012,SNIO2013a,SNIO2013b,S2014,S2016,SIO2016}. Because of the success in accurately reproducing all the QPO frequencies, this kind of approach might well play the role of a canonical model for the low-lying QPOs from SGRs. There is nevertheless a serious caveat: To obtain the shear modulus that is consistent with the QPO frequencies, one requires a significantly large value of the parameter $L$ that characterizes the density dependence of the symmetry energy of nuclear matter, as compared with what various nuclear observables suggest. So far, several calculations of the eigenfrequencies of crustal torsional oscillations have been done by including the effect of superfluidity, but the effect of the possible existence of the pasta structure has been neglected in most of such calculations; an artificial shear modulus has been at most taken into consideration for the pasta phases \citep{S2011,PP2016}. Since the crystalline structure in the bubble phase is presumably the same as that in the low density region composed of spherical nuclei, however, one can likewise calculate the eigenfrequencies of the torsional oscillations in the bubble phase. As we shall see, furthermore, the smectic-A liquid-crystalline properties in the phase with slab-shaped nuclei \citep{PP1998} do not allow torsional shear oscillations to occur in linear analysis, which leads to the conclusion that the torsional oscillations in the bubble phase can be excited separately from those in the low density regime. Bearing this in mind, we search for a better fitting to the observed low-lying QPO frequencies while keeping the value of $L$ reasonable. In Sec.\ \ref{sec:II} the equilibrium configuration of a neutron star crust is constructed. Section \ref{sec:III} is devoted to eigenmode analyses of torsional shear oscillations within the bubble phase. The resultant eigenfrequencies are compared with the observed QPO frequencies in Sec.\ \ref{sec:IV}. Concluding remarks are given in Sec.\ \ref{sec:V}. We use units in which $c=G=1$, where $c$ and $G$ denote the speed of light and the gravitational constant, respectively. | \label{sec:V} In summary, we have examined torsional oscillations in the bubble phase located just above the crust-core boundary of neutron stars. The corresponding eigenfrequencies of the fundamental modes have been calculated for various models of the crust EOS, for various values of the star's mass and radius, as well as for various values of the participant ratio that reflects the entrainment effect, i.e., what portion of nucleons outside the bubbles comove with the oscillating bubbles. The resultant eigenfrequencies in the bubble phase are appreciably higher than the ones in the phase of spherical nuclei. This feature allows one to search for the possibility of reproducing the low-lying QPO frequencies observed from SGRs by appropriately identifying the low-lying QPOs either as a torsional oscillation in the bubble phase or as a usual crustal oscillation in the phase of spherical nuclei, as well as by keeping the value of $L$ reasonable. By simplified calculations, we have succeeded in finding out such a possibility. To make better estimates, however, many questions remain. It would be significant to examine the entrainment effect in the bubble phase based on band calculations \citep{Chamel2012}. For completeness, possible coupling with propagating shear modes in the cylindrical, slab, and cylindrical-hole phases should be allowed for. Magnetic fields, shell and pairing effects on bubbles, electron screening, polycrystalline nature, etc.\ have been also ignored, but would play a role in modifying the eigenfrequencies in the bubbles phase. This work was supported in part by Grants-in-Aid for Scientific Research on Innovative Areas through No.\ 15H00843 and No.\ 24105008 provided by MEXT and by Grant-in-Aid for Young Scientists (B) through No.\ 26800133 provided by JSPS. | 16 | 9 | 1609.01802 |
1609 | 1609.01519_arXiv.txt | We present a novel approach for analysing radial velocity data that combines two features: all the planets are searched at once and the algorithm is fast. This is achieved by utilizing compressed sensing techniques, which are modified to be compatible with the Gaussian processes framework. The resulting tool can be used like a Lomb-Scargle periodogram and has the same aspect but with much fewer peaks due to aliasing. The method is applied to five systems with published radial velocity data sets: HD 69830, HD 10180, 55 Cnc, GJ 876 and a simulated very active star. The results are fully compatible with previous analysis, though obtained more straightforwardly. We further show that 55 Cnc e and f could have been respectively detected and suspected in early measurements from the Lick observatory and Hobby-Eberly Telescope available in 2004, and that frequencies due to dynamical interactions in GJ 876 can be seen. | \subsection{Overview} Determining the content of radial velocity data is a challenging task. There might be several companions to the star, unpredictable instrumental effects as well as astrophysical jitter. Fitting separately the different features of the model might distort the residual and prevent from finding small planets, as pointed out for instance by~\cite{angladaescude2010,tuomi2012}. There might even be cases where, due to aliasing and noise, the tallest peak of the periodogram is a spurious one while being statistically significant. To overcome those issues, recent approaches privilege the fitting of the whole model at once. In those cases, the usual framework is the maximization of an \textit{a posteriori} probability distribution. In order to avoid being trapped in a suboptimal solution, random searches such as Monte Carlo Markov Chain (MCMC) methods or genetic algorithm are used~\citep[e.g.][]{gregory2011,segransan2011}. The goal of this paper is to suggest an alternative method using convex optimization, therefore offering a unique minimum and faster algorithms. To do so, we will not try to find directly the orbital parameters of the planets but to unveil the true spectrum of the underlying continuous signal, which is equivalent. The power spectrum is often estimated with a Lomb-Scargle periodogram~\citep{ lomb1976,scargle} or generalizations~\citep{ferrazmello1981,cumming1999,zechmeister}. However, as said above the estimation of the power spectrum with one frequency at a time has severe drawbacks. To improve the estimate, we introduce an \textit{a priori} information: the representation of exoplanetary signal in the Fourier domain is sparse. In other words, the number of sine functions needed to represent the signal is small compared to the number of observations. The Keplerian models are not the only ones to verify this assumptions, stable planetary systems are quasi-periodic as well~\citep[e.g.][]{laskar1993}. By doing so, the periodogram can be efficiently cleaned (see figures~\ref{hd69830},\ref{hd10180},\ref{rvsurvey55cnc},\ref{rvsurvey_gj876},\ref{rvsurvey_challenge}). The field of signal processing devoted to the study of sparse signals is often referred to as ``Compressed Sensing'' or ``Compressive Sampling''~\citep{donoho2006_2, candes2006} -- though it is sometimes restricted to sampling strategies based on sparsity of the signal. The related methods show very good performances and are backed up by solid theoretical results. For instance, Compressed Sensing techniques allow to recover exactly a spectrum while sampling it at a much lower rate than the Nyquist frequency~\citep{mishali2008, tropp2009}. Its use was advocated to improve the scientific data transmission in space-based astronomy~\citep{bobin2008}. Sparse recovery techniques are also used in image processing~\cite[e.g.][]{starck2005}. It seems relevant to add to that list a few techniques developed by astronomers to retrieve harmonics in a signal. In the next section, we show that even though the term ``sparsity" is not explicitly used~\citep[except in][]{bourguignon2007}, some of the existing techniques have an equivalent in the Compressed Sensing literature. After those remarks on our framework, the paper is organized as follows: in section~\ref{methods}, the theoretical background and the associated algorithms are presented. Section~\ref{implementation} presents in detail the procedure we developed for analysing radial velocity data. This one is applied section~\ref{results} to simulated observations and four real radial velocity data sets: HD 69830, HD 10180, 55 Cnc and GJ 876 and to a simulated very active star. The performance of the method is discussed section~\ref{discussion} and conclusions are drawn section~\ref{conclusion}. \subsection{Previous work} \label{previouswork} The goal of this paper is to devise a method to efficiently analyse radial velocity data. As it builds upon the retrieval of harmonics, the discussion will focus on spectral synthesis of unevenly sampled data~\citep[see][for surveys]{kay1981,schwarzenberg1998,babustoica2010}. First let us consider the methods that are efficient to spot one harmonic at a time. The first statistical analysis is given by~\cite{schuster1898}. However, the statistical properties of Schuster's periodogram only hold when the measurements are equispaced in time. When this is not the case, one can use Lomb-Scargle periodogram~\citep{lomb1976,scargle} or its generalisation consisting in adding a constant to the model~\citep{ ferrazmello1981,cumming1999,reegen2007, zechmeister}. More recently,~\cite{mortier2015} derived a Bayesian periodogram associated to the maximum of an \textit{a posteriori} distribution. Also, \cite{cumming2004} and~\cite{otoole2009} define the Keplerian periodogram, which measures the $\chi^2$ of residuals after the fit of a Keplerian curve. One can remark that ``Keplerian'' vectors defined by $P,e,\omega$ and $M_0$ form a family of vectors in which the sparsity of exoplanetary signals is enhanced. These methods can be applied iteratively to retrieve several harmonics. In the context of radial velocity data processing, one searches for the peak of maximum power, then the corresponding signal is subtracted and the search is performed again. This procedure is very close to CLEAN~\citep{roberts1987}, which relies on the same principle of maximum correlation and subtraction. One of the first general algorithm exploiting sparsity of a signal in a given set of vectors~\citep[Matching Pursuit,][]{mallatzhang1993} relies on the same iterative process. This method was formerly known as Forward Stepwise Regression~\citep[e.g.][]{bellman1975}. To limit the effects of error propagation in the residuals, one can use the Orthogonal Matching Pursuit algorithm~\citep{pati1993,troppgilbert2007}. In that case, when an harmonic is found to have maximum correlation with the residuals, it is not directly subtracted. The next residual is computed as the original signal minus the fit of all the frequencies found so far. The CLEANest algorithm~\citep{foster1995}, and Frequency Map Analysis~\citep{laskar1988,laskar1992,laskar1993,laskar2003}, though developped earlier, are particular cases of this algorithm. To analyse radial velocity data, \cite{baluev2009} and \cite{angladaescude2012} introduce what they call respectively the ``residual periodogram'' and the ``recursive periodogram'', which can be seen as pushing that logic one step further. The principle is to re-fit at each trial frequency the previous Keplerian signals plus a sine at the considered frequency. Besides the matching pursuit procedures, there are two other popular algorithms in the Compressed Sensing literature: convex relaxations~\citep[e.g.][]{tibshirani1994,chen1998, starck2005} and iteratively re-weighted least squares (IRWLS)~\citep[e.g.][]{focuss,donoho2006_2,candesromberg2006,daubechies2010}. In the context of astronomy, \cite{bourguignon2007} implements a convex relaxation method using $\ell_1$ norm weighting (see equation~\eqref{lpnorm}) to find periodicity in unevenly sampled signals and \cite{babu2010} presents an IRWLS algorithm named IAA to analyse radial velocity. The methods presented above are apparently very different, yet they can be viewed as a way to bypass the brute force minimization of \begin{equation} \arg \min \limits_{K,\omega,\phi} \quad \sum\limits_{i=1}^{m} \left(y(t_i)-\sum\limits_{j=1}^k K_j\cos (\omega_j t_i+\phi_j) \right)^2 \label{p1} \end{equation} where $y(t)$ is a vector made of $m$ measurements, and $x^\star = \arg \min f(x)$ denotes the element such that $f(x^\star)=\min f(x)$ for a function $f$. This problem is very similar to ``best $k$-term approximation'', and its link to compressed sensing has been studied in~\cite{cohen2009} in the noise-free case. Solving that problem is suggested by~\cite{baluev2013} under the name of ``multi-frequency periodograms''. However, finding that minimum by discretizing the values of $(K_j,\omega_j,\phi_j)_{j=1..k}$ depends exponentially on the number of parameters, and the multi-frequency periodograms could hardly handle more than three or four sines with conventional methods. However, with parallel progamming on GPUs one can handle up to $\approx$25 frequencies depending on the number of measurements~\citep{baluev2013_freqdecomposer}. \cite{jenkins2014} explicitly mentions the above problem and suggests a tree-like algorithm to explore the frequency space. They analyse GJ 876 with their procedure and find six significant harmonics, which we confirm section~\ref{gj876_sixsines}. Let us mention that searching for a few sources of periodicity in a signal is not always done with the Fourier space. When the shape of the repeating signal or the noise structure are not well known, other tests might be more robust. A large part of those methods consists in computing the autocorrelation function or folding the data at a certain period and look for correlation. See \cite{engelbrecht2013} for a survey or~\cite{zucker2015,zucker2016} in the context of radial velocity measurements. Finally, we point out that the use of the sparsity of the signal is not specific to Compressed Sensing. The number of planets in a model is often selected via likelihood ratio tests. A model with an additional planet must yield a significant improvement of the evidence. In general the model with $k+1$ planets $\mathcal{M}_{k+1}$ is selected over a model with $k$ planet if $\rm{Pr}\{y(t) | \mathcal{M}_{k+1}\}/\rm{Pr}\{y(t)|\mathcal{M}_{k}\}$ is greater than 150~\citep[see][]{tuomi2014}, $y(t)$ being the observations. Indeed, adding more parameters to the model automatically decreases the $\chi^2$ of the residuals. Putting a minimum improvement of the $\chi^2$ acts against overly complicated models. The discussion above points that searching planets one after another is already in the compressed sensing paradigm: this iterative procedure is close to the orthogonal matching pursuit algorithm. \cite{donoho2006} shows that for a wide range of signals, this algorithm is outperformed by $\ell_1$ relaxation methods. Does this claim still applies to radial velocity signals ? In this paper, this question is not treated in full generality, but we show the interest of $\ell_1$ relaxation on several examples. To address that question more directly, it is shown appendix~\ref{appendix_wrongpeak} that in some cases, the tallest peak of the periodogram is spurious but $\ell_1$ minimization prevents from being mislead. | \label{conclusion} The aim of the present paper was to produce a tool for analysing radial velocity that can be used as the periodogram but without having to estimate the frequencies iteratively. To do so, we used the theory of Compressed Sensing, adapted for handling correlated noise, and went through the following steps: \begin{enumerate} \item Selecting a family of normalized vectors where the signal is represented by a small number of coefficients. \item Approximating a solution to~\eqref{ANDNwlambda}; for example by discretizing the dictionary, and ensuring the grid spacing is consistent with the noise power (see eq~\eqref{omegabound}) then solving~\eqref{BPDNepsilonw} with SPGL1 and take the average power. The introduction of the weight matrix $W$ accounts for correlated Gaussian noises. \item Estimating the detection significance, which we do by computing subsequent FAPs of the models with an increasing number of planets. \end{enumerate} We showed that the published planets for each systems could be seen directly on the same graph, and that taking into account the possible correlations in the noise could make a signal appear. This was established in the case of radial velocity data but the method could be adapted to other types of measurements, such as astrometric observations. The use of the Basis Pursuit/$\ell_1$-periodogram we suggest is as follows. This method can be used as a first guess to see if the signal is sparse or not, in that extent it constitutes an evaluation of the difficulty of the system and possibly a short-cut to the solution. It can bring attention to signal features that are hidden in the classical periodogram, which can still be used for an analysis ``by hand''. Secondly, for confirming the planetary nature of a system we advocate to use in a second time statistical hypothesis testing. The perspective for future work are two-fold. First, we saw that the algorithm itself could be improved. Also, there might be significance tests more robust than the FAP and the effect of introducing a weight matrix $W$ must be studied into more depth. Secondly, let us recall that our method uses an \textit{a priori} information, that is the sparsity of the signal, but still does not handle all the information we have. To improve the technique we wish to broaden its field of application by: \begin{itemize} \item Adapting the method for very eccentric orbits, through the addition of Keplerian vectors to the dictionary for example. \item Using precise models of the noise, especially magnetic activity, granulation, p-modes. Possibly include an adaptive estimation of the noise, especially one could extend the dictionary to wavelets. \item Handling several types of measurements at once (e.g. radial velocity, astrometry and photometry). \end{itemize} | 16 | 9 | 1609.01519 |
1609 | 1609.03807_arXiv.txt | We present a new, semi-analytic framework for estimating the level of residuals present in CMB maps derived from multi-frequency Cosmic Microwave Background (CMB) data and forecasting their impact on cosmological parameters. The data are assumed to contain non-negligible signals of astrophysical and/or Galactic origin, which we clean using parametric component separation technique. We account for discrepancies between the foreground model assumed during the separation procedure and the true one, allowing for differences in scaling laws and/or their spatial variations. Our estimates and their uncertainties include both systematic and statistical effects and are averaged over the instrumental noise and CMB signal realizations. The framework can be further extended to account self-consistently for existing uncertainties in the foreground models. We demonstrate and validate the framework on simple study cases which aim at estimating the tensor-to-scalar ratio, $r$. The proposed approach is computationally efficient permitting an investigation of hundreds of set-ups and foreground models on a single CPU. | Forecasting performance of current and future CMB experiments is a necessary step in conception, design and optimization of their hardware as well as operations. Ideally, a forecasting procedure should be both reliable and efficient permitting scrutiny of broad swaths of parameter space in order to quickly zoom on a limited subset of the most promising configurations. This subset should be small enough to facilitate their further, more detailed investigation, typically employing numerical simulations, which while permitting a higher level of realism and detail are significantly more time and resource consuming. Reliable forecasting for high precision CMB experiments is difficult due to the presence of the non-CMB signals, which unavoidably contribute to the measurements registered by the CMB instruments. Indeed, the multi-frequency observations from the Planck and WMAP satellites indicate that foreground emissions originating from our Galaxy or extra-galactic sources represent a major contaminant, e.g.,~\cite{Gold2011, PlanckXX2015,Krach2016}, which current and future CMB polarization experiments will have to deal explicitly with. Methods employed for this purpose will thus have to ensure precision matching sensitivity envisaged for these forthcoming efforts and set by very ambitious science goals, which the CMB community world-wide is preparing to address. These goals include a detection and a characterization of the B-mode signal over a broad range of angular scales with a special emphasis on its large angular scale part, which is thought to be generated by primordial gravity waves present in the early Universe. The key parameter in this latter case is the so-called tensor-to-scalar ratio, $r$, and for concreteness in the following we will couch our presentation as targeting constraints on this parameter. The approach we introduce is however fully general and generalization to other parameters is straightforward. The standard CMB forecasting tools are ill-adapted to tackle cases with non-negligible foreground contributions. Their impact is therefore often either modelled or assessed by some simplified means either in respect to estimating the residuals or their impact on the detection of $r$, e.g.,~\cite{Snowmass2015a, Verde2006, Amblard2007, dunkley2009, bonaldi2011, creminelli2015, Krach2016, Kogut2016}. Alternately, the issue is investigated with help of numerical simulations, which are typically computationally heavy and thus only allow for a limited number of studied cases~\cite{Katayama2011,Remazeilles2016, Alonso2016}. Against this background, Errard et al (2011)~\cite{Errard2011} has proposed a semi-analytic framework, which attempts to propagate strictly statistical uncertainties incurred as a result of a component separation procedure to the final estimate of $r$. Their component separation of choice is a maximum likelihood parametric component separation approach~\cite{brandt1994, 2006ApJ...641..665E, Stompor2009}, which assumes a parametrization of the frequency scalings for each considered sky component. Though self-consistent this approach is only capable of dealing with the statistical uncertainties and therefore its conclusions are limited in their validity and the results should be interpreted with caution. Specifically, this approach requires that the parametrization assumed for the frequency scaling of the sky components is sufficiently flexible and general that the actual frequency scaling laws of the true sky signals is included as its special case. Nonetheless, the framework has proven to be helpful in enabling studies of numerous experimental set-ups in a uniform fashion~\cite{Errard2012, Errard2015}, providing useful insights and intuitions and informing multiple instrument designs. In this work we develop a framework capable of accounting for differences between these two sky signal models. As in~\cite{Errard2011}, we assume that the components are separated with help of the parametric component separation technique and we estimate by semi-analytic means both the bias and statistical uncertainty, which are both present whenever the two sky models do not match. This can be either due to differences in the frequency scaling laws for some of the components or their spatial variability. The framework also permits incorporating the uncertainty related to our ignorance of the foreground signals and/or shortcomings of our models. The bias and statistical uncertainties are then propagated to the second step of the procedure, where their impact on $r$ is calculated. The new approach is equivalent to that of Errard et al (2011)~\cite{Errard2011}, if the sky model and the true sky are consistent, and in this sense it extends and completes this earlier work. We present the formalism in Sect.~\ref{sect:Framework} and demonstrate and validate it in Sect.~\ref{sect:applic}. We leave a thorough investigation of different experimental set-ups and foreground models for future work. For convenience, we define symbols most commonly used in this paper in Table I. \begin{table*}[htb!] \caption{Notations} \centering \label{table:notations} \resizebox{15cm}{!}{ \hspace{-2cm} \begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c|c} \hline \hline symbols & $\mathbf{d}$ & $\mathbf{\hat{s}}$ & $\bd{n}$, $\bd{N}$ & $\bd{\hat d}$ & $\mathbf{\hat A}$ & $p$ & $k$ &$\beta$ & $\mathbf{A}$ & $\mathbf{s}$ & $\mathbf{\bar m}_p$ & $\mathbf{r}_p$, $\mathbf{r}^{\rm cmb} (\beta)$, ${C}^{\rm res}_{\ell}$& $\mathbf{\hat f}_p$, $\mathbf{F}_{p k}$, ${\cal F}_\ell^{\rm fore} $\\ \hline \multirow{3}{*}{definition} & set of observed & true sky & noise, & true sky & true mixing & sky& frequency & spectral & model & model sky & noiseless & noiseless & foregrounds \\ & multi-frequency &noiseless & covariance & component & matrix &pixel &channel & parameters & mixing &component & estimates of & residuals & signal \\ & maps & signal & & amplitudes & & & & &matrix & amplitudes &the components & & \\ \hline \hline \end{tabular}} \end{table*} | In this work we have proposed a semi-analytic approach suitable for realistic forecasting of constraints, which can be set on the cosmological parameters by multi-frequency CMB experiments in the presence of complex foreground contaminations. The derived constraints are averaged over the instrumental noise and CMB realizations and consist of the estimates of the most likely values of the parameters as well as of their dispersion. The method assumes that the foregrounds are cleaned using a pixel-based, parametric, maximum likelihood component separation approach, however it does not require that the parametric model assumed for the separation process matches the true one for any set of parameter values. If the mismatch is indeed present, the estimated scaling laws will differ from the actual sky ones in a systematic way. This leads to foreground residuals, both systematic and statistical, which will be present in the cleaned CMB map. In our approach we first estimate both these residuals and subsequently incorporate them in the pixel-based cosmological parameter likelihood, which we use to set constraints on cosmological parameters. The constraints derived in this way therefore include both biases as well as statistical uncertainty. In this sense our method generalizes previous efforts of the similar kind~\cite{Errard2011, Errard2012, Errard2015}. We have validated the method in the case of pixel-independent scaling laws and white pixel-domain noise, however, the presented algebraic framework is flexible enough to allow for spatial variation of the foreground scaling for both the true and modelled signals as well as some other real life effects. Furthermore, we also note that the proposed formalism permits incorporating any uncertainties in the foreground modelling in the final forecasts. This could be a potentially very handy feature if broad families of the foreground models need to be investigated. We leave detailed studies of those cases for future work. In the cases studied in this work, we have found that even a rather minor mismatch, say of $\sim 1$\%, between the true and assumed scaling laws over a broad range of frequencies can lead to substantial biases of the estimated value of the tensor-to-ratio parameter, $r$, if its true value is as low as $10^{-3}$. This emphasizes two things: (1) importance of accurate and realistic modelling of the underlying foreground signals in ensuring that the obtained forecasts are realistic; (2) importance of suitably chosen, parametric scaling models. In this work, for the demonstration purposes, we have adopted rather simple models in both these instances. In particular, we have employed a simple, two-parameter scaling model for the separation stage and thus have not explored all the constraining power of the considered observation, which allows for a significantly larger number of the spectral parameters. For these reasons the results shown here should not be seen as a fair evaluation of the performance of the assumed instrumental set-up but rather merely as indicative of more qualitative effects and dependences one may expect in such circumstances. Again we leave exhaustive explorations of this kind to future work. Our approach, though clearly more involved and complex than that of~\cite{Errard2011, Errard2012, Errard2015}, retains the speed and efficiency of these previous, simplified techniques, while permitting to attain a higher level of realism. Indeed, all the numerical computations scale linearly with the high-$\ell$ cut-off, $\ell_{max}$, allowing the calculation to be conducted efficiently even for high-resolution experimental set-ups. Consequently, the method is very well-suited for optimizations of experimental set-ups and forecasting their performance, in particular whenever large parameter space of experimental characteristics needs to be considered. Equally importantly, this approach also allows for a direct exploration of a large number of viable foreground models, thus enabling investigations of robustness of the predictions with respect to details of the foreground modelling -- a key feature given our present ignorance about the polarized foreground emissions in the microwave band and the impact of the assumed foreground models on the derived predictions. In all these aspects, the proposed approach is complementary to a more thorough but also more resource demanding, fully-fledged, end-to-end analysis of the realistic simulations. \\ | 16 | 9 | 1609.03807 |
1609 | 1609.08324_arXiv.txt | Magnetic fields on the surface of the Sun and stars in general imprint or modify the polarization state of the electromagnetic radiation that is leaving from the star. The inference of solar/stellar magnetic fields is performed by detecting, studying and modeling polarized light from the target star. In this review we present an overview of techniques that are used to study the atmosphere of the Sun, and particularly those that allow to infer magnetic fields. We have combined a small selection of theory on polarized radiative transfer, inversion techniques and we discuss a number of results from chromospheric inversions. | 16 | 9 | 1609.08324 |
||
1609 | 1609.01205_arXiv.txt | Primordial Black Holes (PBHs) might have formed in the early Universe as a consequence of the collapse of density fluctuations with an amplitude above a critical value $\delta_{c}$: the formation threshold. Although for a radiation-dominated Universe $\delta_{c}$ remains constant, if the Universe experiences some dust-like phases (e.g. phase transitions) $\delta_{c}$ might decrease, improving the chances of PBH formation. We studied the evolution of $\delta_{c}$ during the QCD phase transition epoch within three different models: Bag Model (BM), Lattice Fit Model (LFM), and Crossover Model (CM). We found that the reduction on the background value of $\delta_{c}$ can be as high as $77\%$ (BM), which might imply a $\sim10^{-10}$ probability of PBHs forming at the QCD epoch. | \label{sec:Introduction} Primordial Black Holes (PBHs) may have formed in the early Universe as a consequence of the collapse of density fluctuations \citep[e.g.][]{1971MNRAS.152...75H, 1974MNRAS.168..399C, 1975ApJ...201....1C, 1979A&A....80..104N, 2001IJMPD..10..927P, 2010RAA....10..495K}. They might even be directly detectable within our neighboorhood \citep[][]{2014MNRAS.441.2878S}. During inflation, fluctuations of quantum origin are stretched to scales much larger than the cosmological horizon~$R_H$ at the time $t$ when they were produced ($R_{H}(t)=c/H(t)$, with $H(t)$ the Hubble parameter). Once a physical wavelength becomes larger than $R_{H}$, it is causally disconnected from physical processes. The inflationary era is followed, respectively, by radiation-dominated and matter-dominated epochs during which these fluctuations can re-enter the cosmological horizon~\citep[e.g.][]{2006ARNPS..56..441B}. For a given physical scale $k$, the horizon crossing time $t_{k}$ (i.e. the instant when that scale re-enters $R_{H}$) is conventionally defined by \citep[e.g.][]{2003PhRvD..67b4024B,2002PhRvD..65b4008B} \begin{equation} \label{horizon crossing} ck=a(t_{k})H(t_{k}) \end{equation} where $a(t)$ represents the scale factor. The collapse that gives rise to the formation of a PBH is now possible but only if the amplitude of the density fluctuation ($\delta$) is larger than a specific threshold value $\delta_{c}$. In this case the expansion of the overdense region will, eventually, come to a halt, followed by its collapse. The majority of the PBHs formed at a particular epoch have masses within the order of the horizon mass, $M_{H}$, at that epoch \citep[e.g.][]{2003LNP...631..301C} given by \begin{equation} \label{horizon-mass} M_{H}(t)\sim 10^{15}\left(\frac{t}{10^{-23}\mathrm{~s}}\right)\mathrm{~g}. \end{equation} However, in the case of perturbations with $\delta$ only slightly larger than the critical value, $\delta_c$, the PBH masses rather obey the scaling law \citep[][]{1999PhRvD..59l4013N} \begin{equation} \label{scaling-law} M_{PBH}\propto M_{H}\left(\delta-\delta_{c}\right)^{\gamma} \end{equation} where $\gamma\approx 0.36$ in the case of a radiation-dominated Universe. This power law scaling has been found to hold down to $(\delta-\delta_{c})\sim 10^{-10}$ \citep[][]{2009CQGra..26w5001M,2013CQGra..30n5009M}. The probability that a fluctuation crossing the horizon at some instant $t_{k}$ has of collapsing and forming a PBH can be written as \citep[e.g.][]{green2015} \begin{equation} \label{Bringmann_et_al_2001_eq5} \beta(t_{k})=\frac{1}{\sqrt{2\pi}\sigma(t_{k})}\int_{\delta_{c}}^{\infty} \exp\left(-\frac{\delta^{2}}{2\sigma^{2}(t_{k})}\right)d\delta \end{equation} where $\sigma^{2}(t_{k})$ is the mass variance at horizon crossing. \citet[][]{1975ApJ...201....1C}, based on a simplified model of an overdense collapsing region, found $\delta_{c}=1/3$ for a radiation-dominated Universe. In more recent years the threshold $\delta_{c}$ has been extensively investigated by numerical simulations in PBH formation, in particular by numerically solving relativistic hydrodynamical equations \citep[see e.g.][]{2005CQGra..22.1405M}. Although \citet[][]{1999PhRvD..59l4013N} reported the value $\delta_{c}\simeq 0.7$ in the case of a radiation-dominated expanding Universe, this was later revised to $\delta_{c}\simeq 0.43 - 0.47$ \cite[][]{2005CQGra..22.1405M, 2007CQGra..24.1405P, 2009CQGra..26w5001M, 2013PhRvD..88h4051H, 2013CQGra..30n5009M}. Usually $\delta_{c}$ is constant throught the radiation-dominated epoch, the exception occurring during cosmological phase transitions, when the value of $\delta_{c}$ decreases (as a consequence of the decrease of the sound speed). This is relevant, since a lower value of $\delta_{c}$ favours PBH production \citep[e.g.][]{2003LNP...631..301C}. The Standard Model of Particle Physics (SMPP) predicts: (i) the Electroweak (EW) phase transition at temperatures of $\sim 100\mathrm{~GeV}$, responsible for the spontaneous breaking of the EW symmetry \citep[e.g.][]{2006Natur.443..675A} and (ii) the Quantum Chromodynamics (QCD) phase transition at $170\mathrm{~MeV}$ \citep[e.g.][]{2002PhRvD..66g4507A, 2005PhRvD..71c4504B, 2006PhLB..643...46A} related to the spontaneous breaking of the chiral symmetry of the QCD when quarks and gluons become confined in hadrons. At very high temperatures ($T> 172.5\mathrm{~GeV}$) all the particles of the SMPP contribute to the effective number of degrees of freedom giving g(T)=106.75 \citep[e.g.][]{2006JPhG...33....1Y, sobrinho2011}. As the expansion of the Universe goes on, the temperature decreases and, by the temperature of the QCD transition, with the Universe consisting on a Quark-Gluon Plasma (QGP), we have $g_{QGP}=61.75$. At the end of the QCD transition, when the Universe becomes an Hadronic Gas (HG), we reach $g_{HG}=17.25$ \citep[e.g.][]{2012PhRvD..86a0001B}. The aim of this paper is to study the behaviour of $\delta_{c}$ during the QCD phase transition. The paper is organized as follows: after reviewing, in Section \ref{sec:The early Universe}, some key aspects concerning the early Universe and the QCD phase transition we derive, in Section \ref{sec:delta_c QCD}, new results for $\delta_{c}$ considering three different models: the Bag Model (BM), the Lattice Fit Model (LFM), and the Crossover Model (CM). In Section \ref{sec:discussion} we conclude with a general discussion. We have considered, for the radiation-dominated phase of the Universe, the lowest accepted value of $\delta_{c}=0.43$, which corresponds to the Mexican-Hat perturbation profile, a very representative one. Table \ref{tabela-inicial} (Section~\ref{sec:The early Universe}) sums up key observational and derived parameters that we used throughout this paper. \begin{table*} \caption[]{Observational and derived (the last three) parameters used in our calculations: {\bf (1)} nomenclature; {\bf (2)} description (HG --- Hadronic Gas; QGP --- Quark-Gluon Plasma); {\bf (3)} numerical value (BM --- Bag Model; LFM --- Lattice Fit Model); {\bf (4)} reference, if any: [1] \citet[][]{2014A&A...571A..16P}; [2] \citet[][]{2013ApJS..208...20B}; [3]~\citet[][]{2002PhRvD..66g4507A, 2005PhRvD..71c4504B, 2006PhLB..643...46A} [4] \citet[][]{2012PhRvD..86a0001B}. \label{tabela-inicial} } \center \begin{tabular}{lp{10cm}lc} \hline {\bf (1)} & {\bf (2)} & {\bf (3)} & {\bf (4)} \\ \hline $t_{0}$ & Age of the Universe & $4.36\times10^{17}$~s & [1]\\ $T_{0}$ & Cosmic Microwave Background Temperature & 2.72548~K & [2]\\ $H_{0}$ & Present day value of the Hubble Parameter $H(t)$& $67.3\mathrm{~kms}^{-1}\mathrm{Mpc}^{-1}$ & [1]\\ $\Omega_{\Lambda}$ & Dark energy density parameter & 0.685 & [1] \\ $t_{\Lambda}$ & Age of the Universe at matter-$\Lambda$ equality (when the expansion starts to accelerate); equals $2/(3H_0)$ & $3.06\times10^{17}\mathrm{~s}$ & ---\\ $z_{eq}$ & Redshift at matter-radiation equality & 3391 & [1]\\ $t_{eq}$ & Age of the Universe at matter-radiation equality (from equation (\ref{scale factor matter}), considering that $a_{m}(t_{eq})=(1+z_{eq})^{-1}$) & $2.37\times10^{12}\mathrm{~s}$ & --- \\ $T_{c}$ & The temperature of the Universe at the QCD phase transition & 170~MeV & [3]\\ $g_{QGP}$ & Degrees of freedom for the QGP Universe & 61.75 & [4]\\ $g_{HG}$ & Degrees of freedom for the HG Universe & 17.25 & [4]\\ $t_{+}$ & Age of the Universe at the end of the QCD phase transition & $1.2\times10^{-4}\mathrm{~s}$~(BM, LFM) & Section \ref{sec:delta_c QCD}\\ $t_{-}$ & Age of the Universe at the begining of the QCD phase transition & $6.2\times10^{-5}\mathrm{~s}$~(BM) & Section \ref{sec:delta_c QCD}\\ & & $9.5\times10^{-5}\mathrm{~s}$~(LFM) & Section \ref{sec:delta_c QCD}\\ \hline \hline \end{tabular} \end{table*} | \label{sec:discussion} In order for the collapse of an overdense region in the early Universe forming a PBH, we must have $\delta_k > \delta_c$ where $\delta_k$ is the amplitude of the density fluctuation perturbation and $\delta_c$ a critical value which is related to the particular perturbation profile shape. We chose to work with $\delta_{c}=0.43$ since it corresponds to the representative Mexican-hat perturbation profile. Although the value of $\delta_{c}$ remains constant during the radiation-dominated epoch, it can experience important reductions during cosmological phase transitions, which lead to a higher probability $\beta(t_k)$ of forming PBHs. In particular, at the QCD phase transition $\sim 1$~M$_{\odot}$ PBHs might be formed \citep[][]{2010PhRvD..81j4019C}, even if only constituting a small fraction of the dark halo objets \citep[e.g.][]{2007A&A...469..387T}, they are not completely ruled out. A population of even smaller PBHs might also have formed, according to the scaling law given by equation (\ref{scaling-law}). In this paper we explored the behaviour of $\delta_{c}$ during the QCD phase transition under three diferent models: Bag Model (BM), Crossover Model (CM), and Lattice Fit Model (LFM) and obtained reductions of $20\%$ (CM), $65\%$ (LFM), and $77\%$ (BM) -- cf.~Table~\ref{delta-c-min}. Assuming, for example, $\sigma^{2}(t_{k})=2.3 \times 10^{-4}$ \citep[cf.][]{sobrinho2011} we get, for a radiation-dominated Universe ($\delta_{c}=0.43$), $\beta(t_{k})\sim 10^{-177}$ (equation \ref{Bringmann_et_al_2001_eq5}), a negligible value. Our new results, however, show that $\delta_c$ can get as low as 0.097 (BM; Table~\ref{delta-c-min}), which implies the much higher probability of $\beta(t_k)\sim 10^{-10}$, which lies very close to the observational constraints at the QCD epoch \citep[cf.][]{2010PhRvD..81j4019C}. Although the BM is the one that offers the best prospects as regards PBH formation, even in the case of the CM (a much smoother event: compare Figures \ref{sobrinho2007_QCD_BagModel_deltac_t} and \ref{sobrinho2007_QCD_crossover_total}) an important contribution to PBH formation is still expectable. Assuming, for example, $\sigma^{2}(t_{k})=2.0 \times 10^{-3}$ we get $\beta(t_k)\sim 10^{-14}$. Our next step will be to find an appropriate expression for the mass variance at horizon crossing, so that we might estimate the fraction of the Universe going into PBHs during the QCD epoch and, consequently, their cosmological density. This might be very relevant towards understanding the dark matter halo build-up in the Galaxy and in other galaxies. | 16 | 9 | 1609.01205 |
1609 | 1609.03813_arXiv.txt | {} {Most models identify the X-ray bright North Polar Spur (NPS) with a hot interstellar (IS) bubble in the Sco-Cen star-forming region at $\simeq$130 pc. An opposite view considers the NPS as a distant structure associated with Galactic nuclear outflows. Constraints on the NPS distance can be obtained by comparing the foreground IS gas column inferred from X-ray absorption to the distribution of gas and dust along the line of sight. Absorbing columns towards shadowing molecular clouds simultaneously constrain the CO-H$_{2}$ conversion factor.} {We derived the columns of X-ray absorbing matter N$_{Habs}$ from spectral fitting of dedicated XMM-Newton observations towards the NPS southern terminus (l$^{II}\simeq29\fdeg$, b$^{II}\simeq+5$ to $+11\fdeg$). The distribution of the IS matter was obtained from absorption lines in stellar spectra, 3D dust maps and emission data, including high spatial resolution CO measurements recorded for this purpose.} {N$_{Habs}$ varies from $\simeq$ 4.3 to $\simeq$ 1.3 x 10$^{21}$ cm$^{-2}$ along the 19 fields. Relationships between X-ray brightness, absorbing column and hardness ratio demonstrate a brightness decrease with latitude governed by increasing absorption. The comparison with absorption data, local and large-scale dust maps rules out a NPS near side closer than 300 pc. The correlation between N$_{Habs}$ and the reddening increases with the sightline length from 300 pc to 4 kpc and is the tightest with Planck $\tau_{353GHz}$-based reddening, suggesting a much larger distance. N(H)/E(B-V)$_{\tau}$ $\simeq$ 4.1 x 10$^{21}$ cm$^{-2}$ mag$^{-1}$, close to Fermi-Planck determinations. N$_{Habs}$ absolute values are compatible with HI-CO clouds at -5 $\leq$ V$_{LSR}$ $\leq$ +25 to +45 km s$^{-1}$ and a NPS potentially far beyond the Local Arm. A shadow cast by a b=+9$\fdeg$ molecular cloud constrains X$_{CO}$ in that direction to $\leq$ 1.0 x 10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s. The average X$_{CO}$ over the fields is $\leq$ 0.75 x 10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s.} {} | The North Polar Spur is one of the best known features in radio continuum and diffuse soft X-ray background maps. It is seen as a $\simeq$ $15^\circ$ wide arc that runs with varying intensity from $l,b\sim25^\circ,20^\circ$ to $330^\circ,75^\circ$ \citep[e.g.,][]{Brown60,Bowyer68}. As surveys of the diffuse background expanded it was seen to be one of the most prominent features of the entire sky, although it was joined by a wide region of diffuse emission in the general direction of the Galactic center both above and below the Galactic plane, the {\it X-ray bulge} \citep{Snowden95, Snowden97}. Radio Loop I \citep{Berkhuijsen71,Haslam82} lies next to the NPS, and appears to bound the NPS. Both are also seen in polarized radio emission and in total-intensity and polarized microwave emission \citep{Sofue79, Sun14, Vidal14, PlanckXXV15}. Filaments and arcs seen in HI and extending up to +85\fdeg northern galactic latitude are also spatially associated with the Loop I and the NPS \citep{Colomb80,Kalberla05}. The NPS/Loop I is detected at GeV energies \citep{Casandjian09, Ackermann14}, presumably due to inverse-Compton scattering of starlight by the energetic electrons, combined with pion decay emission from the cold border. Using Loop I to outline a small circle on the sky it was then assumed that the NPS was the limb-brightened edge of a superbubble with a radius of $\simeq100$pc centered on the Sco-Cen OB association at $\sim130$~pc, with the Sco-Cen OB association easily creating and powering the superbubble with both stellar winds and supernovae \citep{deGeus92,Egger95}. The size and high latitude extent of the Loop I strongly suggests its proximity, and indeed measured distances to the HI arcs, either from stellar light polarization \citep{Heiles00}, or from absorption studies \citep{Puspi12} are on the order of 100 pc. The HI shells are thought to be shock-compressed ISM at the periphery of the Loop I/NPS expanding structure. Sophisticated models of time-dependent evolution of the ISM under the action of winds and supernovae are able to reproduce the Loop I structure and its interaction with the cavity surrounding the Sun (the Local Bubble, or LB), and most of the observations \citep{deAvillez05, Breitschwerdt06}. A different interpretation of the NPS enhancement has been defended over the years \citep{Sofue74,Sofue94,Sofue00}, based on several arguments on the geometry and difficulties in adjusting SNR models to the radio continuum, X-ray and HI measurements. According to the author, NPS/Loop I better traces a shock front propagating through the Galactic halo, having originated from an intense explosion and/or a starburst at the galactic center, of energy 3 x 10$^{56}$ ergs and about 15 million years ago. While the shock can mimic the radio and X-ray North Polar Spur, the post-shock high-temperature gas may also explain the observed X-ray bulge around the Galactic center. More recently, \cite{BlandHawthorn03} uncovered a 200 pc wide bipolar structure at the Galactic Center at mid-infrared wavelengths, likely associated with a bursting episode. Interestingly, they also showed that a large scale structure extrapolated from the central region and extending up to the halo could be seen from the Sun as a Loop despite being open-ended, provided it is wider than the solar galactocentric radius, and suggested that the \cite{Snowden97} X-ray bulge observed at 0.5-2.0 keV reveals this bipolar structure. Finally, the existence of Galactic nuclear activity and associated large-scale structures has been spectacularly demonstrated with the discovery of the gigantic $\gamma$-ray bubbles in the high energy {\it Fermi}-LAT data \citep{Su10}. The Fermi bubbles (FBs) and concentric structures at their feet in the Galactic Plane are also seen in total-intensity or polarized radio and microwave emission \citep{Carretti13}, their inner parts are close to the X-ray bulge (see Fig. 6 from \cite{Casandjian15F}) and their edges seem to parallel bright arcs in the 1.5-2 keV ROSAT maps (see Fig. 20 from \cite{Su10}). Following the discovery several models have been proposed for the FBs: one class of scenarios considers a recent, short, AGN-type outburst activity while other models consider less energetic, long duration Galactic wind models maintained by supernovae. In the former (latter) case the $\gamma$-ray emission is mainly of leptonic (hadronic) origin (see, e.g., \cite{Crocker15} and \cite{Sarkar15} for further discussion and description of their analytical and numerical Galactic wind models). Outside the bubbles, \cite{Su10} also identify larger gamma-ray structures, the so-called {\it inner arc} that seems to border the low latitude portion of the northern bubble at galactic longitude +20$\fdeg$, and the {\it outer arc} at +25-;+30$\fdeg$. Both are seen in polarized microwave emission, and the {\it inner arc} is clearly considered as a galactic center feature. The {\it outer arc}, which is very similar to the inner arc, seems to parallel the low latitude part of the NPS (see Fig. 2 of \citep{Su10}). Based on these geometrical arguments, \cite{Su10} considered the possibility that Loop I and the northern outer arc are parts of the relics of previous bubbles. On the other hand, while there are other X-ray arcs in the vicinity of the Galactic center, there are no structures similar to the NPS either in the northern Galactic hemisphere on the other side of the FB or at all in the south. This would require a rather asymmetric origin mechanism. The implications of the two scenarios in terms of Galactic nuclear activity, its temporal variability and outflow interaction with the halo are drastically different, and today the NPS distance and the link between NPS/Loop I and the Galactic Center are still a matter of debate. \cite{PlanckXXV15} extensively discuss the NPS-Loop I characteristics and origin based on Planck-WMAP polarization, and list the various constraints on their distance. As noted by the authors, new evidence for a distance greater than the traditional value of 130 pc has been published. \cite{Wolleben07} showed that the radio emission from Loop I is strongly depolarized below 30$\fdeg$ latitude and attributed this depolarization to fluctuations in the foreground Faraday depth. The required path length beyond the Local Bubble is above 70 pc, which places the front face of the loop beyond the Sco-Cen association. More recently \cite{Puspitarini14} failed to identify in 3D maps of the nearby IS dust \citep{Lallement14} a large cavity that could potentially be filled with hot gas and produce the NPS emission, contrary to other X-ray enhancements that have cavity counterparts. Instead, they suggested that the near side of the NPS source is located beyond 200 pc. \cite{Sofue15} used the X-ray absorption pattern and inferred that the source is beyond the Aquila Rift main dense part, i.e. again beyond the Sco-Cen association (but see section 2). On the other hand, \cite{PlanckXXV15} concluded based on geometrical arguments and the Planck polarization maps that the NPS is not associated with the Galactic Center. Here we address the question of the NPS distance by means of a detailed comparison between the columns of interstellar gas that are located in front of the NPS source and absorb its X-ray emission, and the distribution with distance of the IS matter derived from stellar absorption data. The former information is obtained by means of spectral fitting of new, dedicated X-ray observations, and the latter from dedicated ground-based spectroscopic data and published dust maps. We complement this study by additional comparisons between X-ray absorption and IS emission data. Dedicated CO measurements at high spatial resolution were performed for this purpose. In section 2 we describe the new XMM-Newton data and their spectral analysis. In section 3 we present the ground-based optical data and compare them as well as 3D reddening maps with the X-ray absorbing columns deduced from the XMM fitting results. In section 4 we present the new CO data and compare X-ray absorbing columns with line-of-sight IS dust and gas based on emission data. In section 5 we summarize the comparisons and draw conclusions. | The southern terminus of the X-ray NPS has been analyzed with unprecedented detail and spatial resolution by means of a dedicated series of XMM-Newton measurements. Spectral fitting to the whole dataset provided the X-ray absorbing columns of IS gas in 19 directions spanning a Galactic latitude interval of 5.5 degrees at l$\simeq29$$\fdeg$. The absorbing columns vary from 1.3 to 4.3 x 10$^{21}$ cm$^{-2}$ between b=+11$\fdeg$.1 and b=+5$\fdeg$.6. A shadowing cloud visible in CO maps is clearly detected at b= $\simeq$+9$\fdeg$. Such measurements allowed for the first time a detailed comparison with tracers of the IS dust gas and gas distribution, both distance-limited data and total LOS emission-based data, in particular a dedicated radio $^{12}$CO high resolution survey and ground-based absorption measurements in support to the XMM program. We have obtained the following results: 1) There is compelling evidence from surface brightnesses, hardness ratios and absorbing columns that the southern terminus of the North Spur is fully absorption bounded and consequently that the source extends farther toward the Plane. 2) For the three stars located in the XMM fields, estimated IS gas columns N$_{Habs}$ deduced from absorption lines are below the X-ray absorbing columns, implying a first minimum distance to the NPS inner boundary of 260 pc. 3) The set of target stars was used to validate local dust maps in the NPS area and to estimate the integrated reddening along the XMM directions up to 300 pc. Reddenings are converted into gas columns that are compared with N$_{Habs}$ for the 19 XMM fields. This comparison shows that the distance to the X-ray source front is definitely beyond 300 pc. 4) Independently, the comparison with the larger scale Pan-STARRS (PS) 3D dust maps \citep{Green15} also implies a minimal distance to the NPS of 300 pc, in agreement with evidence from recent studies based on other X-ray data, 3D tomography of dust or radio polarization \citep{Sofue15,Puspitarini14,Wolleben07}. The comparison favours a larger distance, and uncertainties on the calibrations and the conversion factors allow for as much as 4 kpc. As a matter of fact, the low amount of reddening between 600 pc and 4 kpc (see Fig \ref{LOS_ALL_NH}) precludes a precise upper limit. On the other hand, a large distance is independently favoured by the intercomparison of the correlations between N$_{Habs}$ and the PS color excesses at various distances. As a matter of fact, the correlation improves by increasing the sightline length from 400 pc to 4 kpc. Part of the effect may be linked to the improved statistics of the PS measure, however, and more work is needed to disentangle the two effects. 5) The absorbing column N$_{Habs}$ latitude profile deduced from the X-ray spectral fitting is found to correlate more tightly with the reddening deduced from Planck dust optical depths than with any distance-limited reddening, suggesting that the emission originates beyond a very large fraction of the matter the Planck emission is tracing, i.e. potentially several kpc away. In terms of absolute values, the correspondence between the X-ray absorbing columns and Planck $\tau_{353GHz}$-based reddenings results in N(H)/E(B-V) = 4.1 cm$^{-2}$ mag$^{-1}$, a value that matches well recent determinations from Fermi and Planck data joint analyses \citep{PlanckFermi15}. 6) The existence of a shadowing molecular cloud at b=+9$\fdeg$ allows the use of the X-ray absorbing columns and emission data to constrain the CO-H$_{2}$ conversion factor X$_{CO}$ below 1.0 x 10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s. 7) The combination of X-ray absorbing columns and emission data for the entire XMM path constrains the average X$_{CO}$ below 0.75 x 10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s, with the most probable value as low as 0.6 10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s. Such values are unusually low, but X$_{CO}$ factors comprised between 0.6 and 1.1 10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s have been recently derived from combined Fermi-Planck studies of local clouds \citep{PlanckFermi15, Remy15}. 8) Absolute values of X-ray absorbing columns and their latitude profiles are compatible with HI and CO based columns of gas at -5 $\leq$ V$_{LSR}$ $\leq$ +25 to +45 km s$^{-1}$, with the broadest interval being favoured. The large uncertainty on the velocity interval of the gas absorbing the NPS is due to the very limited amount of gas at positive velocities between +25 and +45 km s$^{-1}$. According to kinematical models of Galactic rotation (e.g. \cite{Vallee08}), at l=+29$\fdeg$ the radial velocity of the Sagittarius Arm gas is on the order of +20,+30 km s$^{-1}$), resulting in a potential location of the NPS in front of or beyond this Arm depending on the actual Sagittarius velocity range, with the latter case being more likely. Because there is a very small additional amount of gas faster than +45 km s$^{-1}$, a larger (positive) interval and a subsequent even more distant NPS can not be precluded. However, as discussed in section 4, more work is needed to understand the observed discrepancies and reduce the systematic uncertainties on the absorption profiles before a precise distance can be determined. The minimum distance to the NPS derived from this study definitely demonstrates the absence of link with the nearby Sco-Cen star-forming region. The high probability of a much larger NPS distance that comes out from comparisons with dust and gas absorption and emission raises one more time the question of a possible link between the Spur and outflows from the inner Galaxy (Fermi bubbles, Galactic wind). \cite{PlanckXXV15} disfavor such a link based on the identification of northern and southern polarized emission structures with Loop I secondary arcs and the following geometrical arguments: - the strong North-South asymmetry of the NPS, - the absence of a pinched structure symmetric about the Galactic plane, - the absence of a trace of any interaction between NPS/Loop I and the Fermi bubbles. However, it can be argued that NPS-Loop I and the Fermi bubbles may trace completely distinct episodes of nuclear activity, in which case geometrical arguments become weaker. Refined analyses of the XMM spectra should help constraining further the NPS characteristics. Although absorbing columns are not expected to vary significantly after relaxation of the constraints on the component parameters that have been imposed here, allowance for departures from thermal emission, for non-solar ion abundances and abundance ratios, as well as the inclusion of a dedicated modeling of the heliospheric charge-exchange emission should all together put stronger constraints on the emission mechanisms. This is beyond the scope of the present work, mainly devoted to comparisons with existing IS data. From the ISM distribution point of view, hopefully future 3D mapping of Galactic clouds and their distance and velocity assignments should allow to take larger benefit from the present study and better constrain the NPS source location. In particular, future measurements with Gaia should better constrain the cloud distribution from both parallax data and improved reddening estimates. In particular, accurate measurements of Sagittarius gas velocities should allow to use our results in a more definitive way. Thanks to Gaia too, young star associations in the Inner Galaxy that may give rise to a giant super-bubble and a structure similar to NPS-Loop I should also be identified and located. On the longer term, high sensitivity, spectral and spatial resolution Athena X-ray spectra \citep{Athena13} are expected to shed additional light on the NPS spectral characteristics and the nature of its source. | 16 | 9 | 1609.03813 |
1609 | 1609.04434_arXiv.txt | {The discovery by the Large Area Telescope on board {\em Fermi} of variable $\gamma$-ray emission from radio-loud narrow-line Seyfert 1 (NLSy1) galaxies revealed the presence of a possible third class of Active Galactic Nuclei (AGN) with relativistic jets in addition to blazars and radio galaxies. Considering that NLSy1 are usually hosted in spiral galaxies, this finding poses intriguing questions about the nature of these objects and the formation of relativistic jets. We report on a systematic investigation of the $\gamma$-ray properties of a sample of radio-loud NLSy1, including the detection of new objects, using 7 years of {\em Fermi}-LAT data with the new Pass 8 event-level analysis. In addition we discuss the radio-to-very-high-energy properties of the $\gamma$-ray emitting NLSy1, their host galaxy, and black hole mass in the context of the blazar scenario and the unification of relativistic jets at different~scales.} \keyword{galaxies: nuclei; galaxies: jets; galaxies: Seyfert; gamma-rays: general} \conferencetitle{Blazars through Sharp Multi-Wavelength Eyes} \begin{document} | Since its launch on 11 June 2008, the {\em Fermi Gamma-ray Space Telescope} has opened a new era in high-energy astrophysics. The primary instrument on board {\em Fermi}, the Large Area Telescope~(LAT), is a~pair-conversion telescope covering the energy range from $\sim$20 MeV up to $\sim$1 TeV with unprecedented sensitivity and effective area~\cite{atwood09}. One of the major scientific goals of the {\it Fermi} mission is to investigate the high-energy emission in Active Galactic Nuclei (AGN) in order to understand the mechanisms by which the particles are accelerated and the precise site of the $\gamma$-ray emission. The combination of deep and fairly uniform exposure over two orbits ($\sim$90 min), very good angular resolution, and stable response of the LAT has allowed the production of the most sensitive, best-resolved survey of the $\gamma$-ray sky. Before the launch of the {\em Fermi} satellite only two classes of AGN were known to generate strong relativistic jets, and therefore to emit up to the $\gamma$-ray energy range: blazars and radio galaxies, both hosted in giant elliptical galaxies \cite{blandford78}. The first 4 years of observation by {\em Fermi}-LAT confirmed that the extragalactic $\gamma$-ray sky is dominated by blazars, with only a few radio galaxies detected \cite{acero15}. The~discovery by {\em Fermi}-LAT of variable $\gamma$-ray emission from a few radio-loud narrow-line Seyfert 1 (NLSy1) galaxies revealed the presence of a possible third class of AGN with relativistic jets \cite{abdo2009a,abdo2009b}. NLSy1 are a class of AGN identified by \cite{osterbrock85} and characterized by their optical properties: narrow permitted emission lines (FWHM (H$\beta$) $<$ 2000 km $\cdot$ s$^{-1}$), flux ratio [OIII]/H$\beta$ $<$ 3, and a bump due to Fe II (e.g., \cite{pogge00}). They also exhibit strong X-ray variability, steep X-ray spectra, substantial soft X-ray excess and relatively high luminosity (e.g., \cite{grupe10}). These characteristics seem to point to systems with smaller masses of the central black hole (BH; 10$^6$--10$^8$ M$_\odot$) and higher accretion rates (close to or above the Eddington limit) with respect to blazars and radio galaxies. NLSy1 are generally radio-quiet (radio-loudness $R$ $<$ 10), with only a small fraction ($<$ 7$\%$; \cite{komossa06}) classified as radio-loud. Objects with higher values of radio-loudness ($R$ $>$ 100) are even more sparse ($\sim$2.5\%), while $\sim$15$\%$ of quasars are~radio-loud. Considering that NLSy1 are usually hosted in spiral galaxies, their detection in $\gamma$-rays poses intriguing questions about the nature of these sources, the production of relativistic jets, and the mechanisms of high-energy emission. In this paper we discuss the radio to $\gamma$-ray properties of relativistic jets in NLSy1 galaxies. In Section \ref{section 2}, we report the results of the LAT data analysis of a sample of NLSy1 over 7 years of {\em Fermi} observation, and discuss the $\gamma$-ray properties of NLSy1. In Sections \ref{section 3}-- \ref{section 5} we discuss the X-ray, infrared-to-UV, and radio properties, respectively, of the $\gamma$-ray NLSy1. Results about the modelling of the broad-band spectral energy distribution (SED) of $\gamma$-ray emitting NLSy1 are presentented in Section~\ref{section 6}. In Section \ref{section 7} we discuss about BH mass measurements, host galaxies, and the jet formation for these sources. Throughout the paper the photon indices are parameterized as $dN/dE \propto E^{-\Gamma_{\nu}}$, where $\Gamma_{\nu}$ is the photon index in the different energy bands. We adopt a $\Lambda$ cold dark matter cosmology with $H_0$ = 71 km $\cdot$ s$^{-1}$ $\cdot$ Mpc$^{-1}$, $\Omega_{\Lambda} = 0.73$, and $\Omega_{\rm m} = 0.27$ \cite{komatsu11}. | 16 | 9 | 1609.04434 |
|
1609 | 1609.03022_arXiv.txt | We consider a head-on collision of two massive particles that move in the equatorial plane of an extremal Kerr black hole, which results in the production of two massless particles. Focusing on a typical case, where both of the colliding particles have zero angular momenta, we show that a massless particle produced in such a collision can escape to infinity with arbitrarily large energy in the near-horizon limit of the collision point. Furthermore, if we assume that the emission of the produced massless particles is isotropic in the center-of-mass frame but confined to the equatorial plane, the escape probability of the produced massless particle approaches $5/12$ and almost all escaping massless particles have arbitrarily large energy at infinity and an impact parameter approaching $2GM/c^2$, where $M$ is the mass of the black hole. | 16 | 9 | 1609.03022 |
||
1609 | 1609.00717.txt | \label{sec:intro} %=================================================================% Current and next generation CMB and galaxy surveys, such as eBOSS~\cite{Dawson:2015wdb}, LSST~\cite{Abell:2009aa}, DESI~\cite{Levi:2013gra} and Euclid~\cite{Refregier:2010ss}, SPT~\cite{Ruhl:2004kv} and ACT~\cite{Thornton:2016wjq}, will measure the statistical distribution of cosmological large-scale structures with percent/sub-percent precision~\cite{Percival:2013awa}. In order to fully exploit these cosmological data, it is important to be able to have a way to make theoretical predictions with comparable or better accuracy. While in the last couple of decades numerical simulations have been the main tool to predict the clustering of large scale structures, in the last few years the advent of the so-called Effective Field Theory of Large Scale Structures (EFTofLSS)~\cite{Baumann:2010tm,Carrasco:2012cv,Porto:2013qua,Senatore:2014via} has allowed the development of an analytic approach that is able to predict the Large Scale Structure (LSS) correlation functions with exquisite precision in the so-called mildly non-linear regime, where density fluctuations are still safely smaller than one~\cite{Baumann:2010tm,Carrasco:2012cv,Porto:2013qua,Senatore:2014via,Carrasco:2013sva,Carrasco:2013mua,Pajer:2013jj,Carroll:2013oxa,Mercolli:2013bsa,Angulo:2014tfa,Baldauf:2014qfa,Senatore:2014eva,Senatore:2014vja,Lewandowski:2014rca,Mirbabayi:2014zca,Foreman:2015uva,Angulo:2015eqa,McQuinn:2015tva,Assassi:2015jqa,Baldauf:2015tla,Baldauf:2015xfa,Foreman:2015lca,Baldauf:2015aha,Baldauf:2015zga,Bertolini:2015fya,Bertolini:2016bmt,Assassi:2015fma,Lewandowski:2015ziq,Cataneo:2016suz,Bertolini:2016hxg}. In particular, the EFTofLSS has been applied to the description of the dark matter two-point function~\cite{Carrasco:2012cv,Senatore:2014via,Carrasco:2013mua,Foreman:2015lca,Baldauf:2015aha}, three-point function~\cite{Angulo:2014tfa,Baldauf:2014qfa}, four-point function (which includes the covariance of the power spectrum)~\cite{Bertolini:2015fya,Bertolini:2016bmt}; to the dark matter momentum power spectrum~\cite{Senatore:2014via,Baldauf:2015aha}, to the displacement field~\cite{Baldauf:2014qfa}; and to the vorticity slope~\cite{Carrasco:2013mua,Hahn:2014lca}. The effects of baryons on the power spectrum have been incorporated in~\cite{Lewandowski:2014rca}. The extension of the EFTofLSS to biased tracers has been carried out in~\cite{Senatore:2014vja}, and the predictions compared to data for the power spectrum and bispectrum in~\cite{Angulo:2015eqa}. Redshift space distortions~\cite{Senatore:2014vja,Lewandowski:2015ziq}, and the impact of primordial non-Gaussianity on large scale structure observables~\cite{Angulo:2015eqa,Assassi:2015jqa,Assassi:2015fma,Lewandowski:2015ziq} have also been recently included. Fast implementations of the predictions of the EFTofLSS to efficiently explore their dependence on various cosmological parameters have been recently developed in~\cite{Cataneo:2016suz}, with public codes available at the following website~\footnote{\website}. This paper will focus on the EFTofLSS when applied to biased tracers, such as halos or galaxies. In particular, we will focus on tracers which are highly massive, and therefore highly biased. In the EFTofLSS biased tracers are represented as a functional of the second derivatives of the gravitational fields, of matter fields, such as dark matter (denoted by the subscript ${}_c$) or baryons (denoted by the subscript ${}_b$), of stochastic terms $\epsilon$, and of spatial derivatives, as well as of the parameters of the background cosmology, such as $\Omega_{dm}$, as well as of all other parameters that determine the laws of nature, such as the electron mass $m_e$, and in general of all terms allowed by general covariance. All of these terms need to be evaluated on the past light cone of the spacetime point of interest. Schematically, we have the tremendous expression~\cite{Senatore:2014vja} \be\label{eq:euler_bias_0} \delta_M(\vec x,t)= f\left(\left.\{\d_i\d_j \phi(\vec x',t'), \delta_b, \d_j v_c^i(\vec x',t'), \frac{\d^i}{\km},\epsilon(\vec x',t'), \ldots,\Omega_c, \ldots, m_e,\ldots\}\right|_{\rm on \ past\ lightcone}\right)\ , \ee If we are interested in spatial fluctuations of this quantity, we realize that only the fluctuating fields in (\ref{eq:euler_bias_0}) carry spatial dependence. If we are interested in long wavelength perturbations, the fluctuations are small, and we can Taylor expand (\ref{eq:euler_bias_0}) to drastically simplify it and obtain, schematically, \bea\label{eq:euler_bias_2} &&\delta_M(\vec x,t)\simeq \int^t dt'\; H(t')\; \left[ \sum_{j=c,b} \bar c_{\d^2\phi,j}(t,t')\; \delta_j(\xfl,t') \right.\\ \nonumber &&\quad+\sum_{j=c,b} \bar c_{\d_i v^i,j}(t,t') \; \frac{\d_i v^i_j(\xfl,t')}{H(t')}+\bar c_{\d_i \d_j \phi \d^i \d^j \phi}(t,t') \;\frac{\d_i\d_j \phi(\xfl, t')}{H(t')^2}\frac{ \d^i \d^j \phi(\xfl,t')}{H(t')^2} + \ldots\\\nonumber &&\quad+ \bar c_{\epsilon}(t,t')\;\epsilon(\xfl,t')+\bar c_{\epsilon\d^2\phi}(t,t') \;\epsilon(\xfl,t')\frac{\d^2\phi(\xfl,t')}{H(t')^2}+ \ldots \\ \nonumber &&\left.\quad+ \bar c_{\d^4\phi}(t,t') \;\frac{\d^2_{x_{\rm fl}}}{\km^2}\frac{\d^2\phi(\xfl,t')}{H(t')^2}+\dots\ \right] . \eea Here $\bar c_{\ldots}(t,t')$ are dimensionless kernels with support of order one Hubble time and with size of order one, $\xfl$ represents the location at time $t'$ of the fluid element that at time $t$ is at location ${\bf x}$, and the scale~$\km$ here is the comoving wavenumber enclosing the mass of an object~\cite{Senatore:2014eva} (we defer to later in the text for more explicit definitions). How to include the effect of baryons for biased tracers was introduced in~\cite{Angulo:2015eqa,Schmidt:2016coo}, which of course required first to understand that baryons can be treated as an effective fluid-like system similar to dark matter, which was done in~\cite{Lewandowski:2014rca}. In the presence of primordial non-Gaussianities~\cite{Angulo:2015eqa,Assassi:2015jqa,Assassi:2015fma,Lewandowski:2015ziq} the tracer fields depend on additional fields, $\tilde\phi(\xfl(t,t_{\rm in}),t_{\rm in})^{i_1,\ldots ,i_n}$, that can be formed out of the gravitational field, multiplied by some power $\alpha$ of the long wavenumber of interest, $k_L^\alpha$, with $0\leq \alpha\leq 2$, and potentially by some additional factor associated to the angle of $\vec k_L$, and then divided by the transfer function $T(k)$ of the primordial fluctuations. Notice also the peculiar value of the coordinates $(\xfl(t,t_{\rm in}),t_{\rm in})$ at which this field needs to be evaluated. We will neglect the effect of baryons and primordial non-Gaussianities for the rest of this paper, though all what we describe can be trivially extended to include these cases. The time integrals over unknown kernels that appear in~(\ref{eq:euler_bias_2}) might make it seem not a very useful expression. However, the structure of the perturbative solutions comes to our help. In perturbation theory, the solution at a given order is the sum of products of a function of time, approximately equal to the a power of the linear growth factor, times a function of wavenumber. Therefore, by plugging in (\ref{eq:euler_bias_2}) the perturbative solution, we can formally evaluate the time integrals to obtain an expression where each term in perturbation theory is multiplied by his own bias. Schematically, we have~\cite{Senatore:2014vja} \bea\label{eq:euler_bias_4_intro} && \delta_h(\bold{k}, t) = \nonumber \\ && \quad = c_{\delta, 1}(t) \delta^{(1)}(\bold{k}, t) + c_{\delta, 2}(t) \delta^{(2)}(\bold{k}, t) + c_{\delta, 3}(t) \delta^{(3)}(\bold{k}, t) + c_{\delta, 3_{c_s}}(t) \delta^{(3)}_{c_s}(\bold{k}, t) +\ldots \nonumber \\ \nn && \qquad + [c_{\delta, 1}(t) - c_{\delta, 2}(t)] \left[\partial_i \delta^{(1)} \frac{\partial^i}{\partial^2} \theta^{(1)} \right]_{\bold{k}}(t) + [c_{\delta, 2}(t) - c_{\delta, 3}(t)] \left[\partial_i \delta^{(2)} \frac{\partial^i}{\partial^2} \theta^{(1)} \right]_{\bold{k}}(t) +\ldots\\ && \qquad+ \bar c_{\d^4\phi}(t,t') \;\frac{\d^2_{x}}{\km^2}\delta ^{(1)}+\dots\ . \eea After the renormalization is performed, the loop expansion, completed by the insertion of the relevant higher order bias coefficients, amounts to an expansion in the parameters that control the dark matter expansion: $\epsilon_{\delta<}$ and $\epsilon_{s>}$~\cite{Porto:2013qua,Senatore:2014via}. These are defined as \bea &&\epsilon_{s >} =k^2 \int_k^\infty \frac{d^3k' }{ (2 \pi)^3} \frac{P_{11}(k') }{ k'^2}\ , \qquad \epsilon_{\delta <} = \int^k_0 \frac{d^3k' }{ (2 \pi)^3} P_{11}(k')\ , \eea where $P_{11}(k)$ is the dark matter power spectrum. $\epsilon_{s >} $ represents the displacement due to short wavelength modes, while $\epsilon_{\delta <}$ represents the tidal force due to long wavelength modes. Both of these scale proportionally to $k/\knl$. For simplicity, we will refer to $\epsilon_{\delta<}$ and $\epsilon_{s>}$ with the common symbol of $\epsilon_{\delta}$. In the Eulerian treatment we expand also in displacement due to long wavelength modes $\epsilon_{s<}= (k\, \delta s_<)^2$, where~\footnote{For IR-safe quantities, the relevant parameters is~\cite{Senatore:2014via} \be\label{eq:epssafe} \epsilon_{s_<}^{\rm safe} =k^2 \int_{k_{\rm bao}}^k \frac{d^3k' }{ (2 \pi)^3} \frac{P_{11}(k') }{ k'^2}\ , \ee where $k_{\rm bao}$ is the wavenumber associated to the inverse of the bao peak length. } \bea \epsilon_{s_<} &=&k^2 \int_0^k \frac{d^3k' }{ (2 \pi)^3} \frac{P_{11}(k') }{ k'^2}\ . \eea As described in~\cite{Senatore:2014via}, $\epsilon_{s<}$ is of order one for the $k$'s of interest, and therefore one cannot Taylor expand in this parameter. However, as explained in~\cite{Senatore:2014via,Angulo:2014tfa,Lewandowski:2014rca} for dark matter and baryons, and in~\cite{Senatore:2014vja,Angulo:2015eqa} for redshift space distorsions, one can resum exactly in this parameter. Instead, the expansion in higher derivative bias coefficients corresponds to an expansion in \be \epsilon_M\sim\left(\frac{k}{\km}\right)^2\ . \ee Finally, the expansion in stochastic bias terms offers yet another parametric dependence, since $\langle\epsilon^2\rangle\sim \frac{1}{\bar n_M}$, with $\bar n_M$ being the number density of the population of biased tracers under consideration. Schematically, we therefore have the following perturbative expansion for biased tracers~\cite{Senatore:2014vja,Angulo:2015eqa} \bea\label{eq:dark_galaxy_galaxy_expansion} &&\langle\delta_M(k)\delta_M(k)\rangle'\sim c_{\delta} \left\{ \underbrace{\left[1+\left(\frac{k}{\km}\right)^2+\ldots\right]}_\text{Bias Derivative Expansion: $k/k_M$}\times \underbrace{\left[1+\epsilon_{\delta<}+\ldots\right]}_\text{Matter Loop Expansions: $\epsilon_{\delta}$}\times \ P_{11}(k) \right\} \\ \nonumber &&\left. +\underbrace{\left[1+\left(\frac{k}{\km}\right)^2+\ldots\right]}_\text{Stochastic Bias Derivative Expansion: $k/k_M$}\times \underbrace{c_{\delta}\left[1+\epsilon_{\delta<}+\ldots\right]}_\text{Mixed Matter Stochastic Bias Expansion: $\epsilon_{\delta}$}\times \underbrace{\frac{1}{\bar n_M}}_\text{Stochastic Bias: $1/\bar n_M$} \right. \ . \eea Of the above perturbative expression, we still need to explain how the bias coefficients appear, which was not specified in~\cite{Senatore:2014vja,Angulo:2015eqa}. We have put only one common factor in front of the expansion that is not proportional to the stochastic terms. Often in the community, it is assumed that the bias coefficients $c_n$, such as $c_{\delta^n}$, multiplying terms of order $(\delta^{(1)})^n$ in~(\ref{eq:euler_bias_4_intro}) go as $c_{n}\sim (c_{1})^n$. Instead, as we describe in this paper, we find neither very strong justification nor evidence in the fitting to the data of such a behavior. We rather find that all bias coefficients are of comparable order, as expressed in~(\ref{eq:dark_galaxy_galaxy_expansion}): $c_{n}\sim c_{1}$. The consistent perturbative expansion of (\ref{eq:dark_galaxy_galaxy_expansion}) was compared with simulation data on several statistic of halos in~\cite{Angulo:2015eqa}. In particular, in~\cite{Angulo:2015eqa} measurements of the halo-halo and halo-matter two point functions, and of the matter-matter-halo, the matter-halo-halo and halo-halo-halo three point functions for three different mass populations were matched to the predictions of the EFTofLSS. There, it was found that the EFTofLSS allows for a much improved match between theory and simulations. However, in the same paper~\cite{Angulo:2015eqa} it was found that the predictions for tracers characterized by a smaller mass performed better than the ones for more massive tracers. A look at expression~(\ref{eq:dark_galaxy_galaxy_expansion}) easily explains this fact. In fact, predictions in~\cite{Angulo:2015eqa} were made at one loop for the two-point functions and at tree level for the three-point functions. Performing the calculations at the same loop order for all the tracers means performing the calculation at the same order in $\epsdl$ for all the tracers. Since the more massive is the tracers, the smaller is $k_M$, if one does not include higher derivative terms for more massive tracers, then the predictions for these more massive tracers are doomed to fail at lower wavenumber. Viceversa, a prediction of the perturbative expansion in the EFTofLSS in eq.~(\ref{eq:dark_galaxy_galaxy_expansion}) is that, given a calculation at a given loop order, by solely adding higher derivative terms, the predictions for the tracers of all masses should fail approximately at the same wavenumber, when the common theoretical error from the next order in $\epsdl$ is the dominant error for all the tracers. The only reason for failing at different wavenumbers is the fact that there is an additional source of theoretical error that comes from the fact that the size of the bias coefficient might depend on the tracer. Once the error due to $k/k_M$ is made negligible, the theoretical error scales as $c (\epsilon_{\delta})^m \sim c (k/\knl)^{m(3+n)}$, where $m$ is the perturbative order of the calculation, and we took $\epsilon_\delta\sim (k/\knl)^{3+n}$, with $n\sim -1.7$ being that approximate slope of the power spectrum at the $k$ of interest. Therefore, we have that, if we threshold on a given error $\epsilon_{\rm error}$, this occurs at wavenumber $k \propto c^{-\frac{1}{m(3+n)}} $. In this expression, we see that the dependence on the tracer is simply relegated to the factor $c^{-\frac{1}{m(3+n)}}$, which, as the perturbative order $m$ in made higher, becomes smaller and smaller. The purpose of this paper is to check the correctness of this prediction. First, we will add higher derivative operators for the bins associated to more massive halos, and we will indeed find that the predictions now fail approximately at the same wavenumber for all tracers. We have that the power spectra in \cite{Angulo:2015eqa} were computed to one-loop order, which correspond to order $\epsilon_{\delta} + \epsilon_M \epsilon_{\delta} + \epsilon_{\delta}^2$. The $\epsilon_M \epsilon_{\delta}$ part comes from the leading linear higher derivative term $\frac{\d^2}{k_M^2} \delta$, which was already included in \cite{Angulo:2015eqa}. The next leading term in $\epsilon_M$ scale as $\epsilon_M^2 \epsilon_{\delta}$, which is potentially larger than $\epsilon_M \epsilon_{\delta}^2$. The order of the terms we will add to the power spectra will therefore be $\epsilon_M^2 \epsilon_{\delta}$. Instead, the bispectra were computed at tree level with no higher derivative terms. This corresponds to order $\epsilon_{\delta}^2$. We will therefore limit ourselves to add the higher derivative terms that contribute to order $\epsilon_M \epsilon_{\delta}^2$. We can estimate the importance of the higher derivative terms by comparing the two expansion parameters $\left( k/k_M \right)^2$ and $\left( k/k_{\rm NL} \right)^{3+n}$ at different values of $k$. To do so, we use the approximate values $k_{\rm NL} \approx 4.6 \, h \, {\rm Mpc}^{-1}$ and $n \approx -1.7$, which are valid for a regime where $k \lesssim 0.25 \, h \, {\rm Mpc}^{-1}$, \cite{Carrasco:2013mua}. For~$k_M$, we use the rough estimate $k_M \sim 2 \pi \left( \frac{4 \pi}{3} \frac{\rho_{b,0}}{M_{\rm halo}} \right)^{1/3}$, where $\rho_{b,0} \simeq 2.6 \cdot 10^{-24} {\rm g}/{\rm m^3}$ is the background density of the universe. Notice that $k_M$ depends on the mass of the halo, that is why the higher derivative terms are important to predict the clustering of very high mass halos. In this work, the halos are separated into four bins, (Bin0, Bin1, Bin2, Bin3), according to their mass, from the lightest to the heaviest. The mass of the halos for each bin is given in \cite{Okumura:2012xh}. Table \ref{tb:kmvalue} presents the estimates for $k_M$ and the ratios $\left( k/k_M \right)^2$ for two different values of $k$ for each bin. These estimates are very rough, and should be taken at the order of magnitude level, but they already highlight the fact that the higher derivative terms are far more important for Bin2 and Bin3 than for Bin0 and Bin1, which explained why Bin2 was not matching the data up to the same maximum wavenumber $k_{\rm max}$ as Bin0 and Bin1 in \cite{Angulo:2015eqa}. Also we see that for Bin2 and Bin3 the order of magnitude of the higher derivative terms is comparable with the one of the perturbative expansion. Though very rough, these estimates encourage us to add the higher derivative terms. \begin{table*}[t!] \caption{The first line presents approximate values of $k_M$ for each mass bin. To compute those values, we use $k_M \sim 2 \pi \left( \frac{4 \pi}{3} \frac{\rho_{b,0}}{M} \right)^{1/3}$, with $M$ being the mass of the bin. The numerical values of the mass of the bins are given in \cite{Okumura:2012xh}. $\rho_{b,0}$ is the mean matter density in the universe, whose numerical value is around $\rho_{b,0} \simeq 2.6 \cdot 10^{-24} {\rm g}/{\rm m^3}$. The second and third lines are estimation of the ratio $\left(k/k_M\right)^2$ for two different values of $k$, namely $k_1 = 0.1 \, h \, {\rm Mpc}^{-1}$ and $k_2 = 0.15 \, h \, {\rm Mpc}^{-1}$. We compare these values with the expansion parameter of the loops, $\epsdl\sim \left(k/k_{\rm NL} \right)^{3+n}$, where $k_{\rm NL} \approx 4.6 \, h \, {\rm Mpc}^{-1}$ and $n \approx -1.7$. We have $\left( k_1/k_{\rm NL} \right)^{3+n} \approx 7 \cdot 10^{-3}$ and $\left( k_2/k_{\rm NL} \right)^{3+n} \approx 1 \cdot 10^{-2}$.} \centering \setlength{\tabcolsep}{8pt} \renewcommand{\arraystretch}{1.0} \begin{tabular}{c|cccccc} \hline\hline & Bin0 & Bin1 & Bin2 & Bin3 \\ [0.5ex] \hline $k_M [h \, \rm{Mpc}^{-1}]$ & $3.3-4.8$ & $2.3-3.3$ & $1.6-2.3$ & $1.1-1.6$ \\ $(k_1/k_M)^2$ & $(4.3-9.2) \cdot 10^{-4}$ & $(0.9-1.9) \cdot 10^{-3}$ & $(1.9-3.9) \cdot 10^{-3}$ & $(3.9-8.3) \cdot 10^{-3}$\\ $(k_2/k_M)^2$ & $(1.0-2.1) \cdot 10^{-3}$ & $(2.1-4.3) \cdot 10^{-3}$ & $(4.3-8.8) \cdot 10^{-3}$ & $(0.9-1.9) \cdot 10^{-2}$\\ \hline \end{tabular} \label{tb:kmvalue} \end{table*} In performing our study, we will find two additional ways to improve the findings of~\cite{Angulo:2015eqa}. First, we will find a factor of two of mistake in a contribution to the prediction for the halo-halo-halo bispectra in~\cite{Angulo:2015eqa}~\footnote{The mistake was in the Mathematica notebook, not in the text. We apologize.}. After correcting for this factor of two, we find that the predictions of the EFTofLSS, even before adding the additional higher derivative biases, match much better the measurements in simulations. This is interesting because it offers yet another verification of the correctness of the EFTofLSS and of its predicting power. In the EFTofLSS there are free parameters, but there are also contributions that do not depend on these parameters, which are called calculable terms. The fact that if we make a mistake in the calculable terms we cannot match the data as well as when we compute these terms correctly, is proof that the functional freedom induced by the free parameters of the EFTofLSS is not strong enough to erase the contribution from the calculable terms. This result is therefore a statement of the correctness and of the predicting power of the EFTofLSS, notwithstanding the presence of free parameters. A last improvement with respect to~\cite{Angulo:2015eqa} concerns the way the predictions of the EFTofLSS are compared to simulation data. This procedure is delicate for two different reasons. First, the predictions of the EFTofLSS depend on parameters that need to be measured from the same set of data that are used to asses the accuracy of the EFT predictions. Since simulation data have smaller sampling variance at higher wavenumbers, we would like to measure them at high wavenumber. But, as it is evident from (\ref{eq:dark_galaxy_galaxy_expansion}), the inaccuracy of the EFT predictions grows as we move to higher wavenumber, which pushes us to measure these parameters at low wavenumber. We address this counteractive trends by implementing a fitting procedure very similar to the one developed in~\cite{Foreman:2015lca} that ensures that, as we move our fitting to higher and higher wavenumbers, we do not degrade the fit at lower wavenumbers (where our prediction is more accurate). In Sec.~\ref{sec:equations} we construct the predictions for the two-point and three-point functions of highly massive tracers, and in Sec.~\ref{sec:results} we perform the comparison with simulations to determine the bias parameters and the accuracy of the predictions. We find that indeed higher mass bins match the data to a comparable level as the low mass bins, after the addition of the higher derivative terms. %=================================================================% | \label{sec:conclusion} %=================================================================% We have argued that The Effective Field Theory of Cosmological Large Scale Structures (EFTofLSS) when applied to biased tracers predicts the following. If we compute a correlation function for biased tracers at a given order in the dark matter non-linearities, the theoretical error is larger for tracers with larger biases. This theoretical error is mainly controlled by the size of the higher derivative terms, and by a subleading correction due to the size of the bias coefficients. Therefore, a prediction of the EFTofLSS is that if all tracers are treated as equal, the predictions for highly biased tracers underperform with respect to the ones for less biased ones. However, by adding just higher derivative operators, it is predicted that the theoretical results for all traces should work comparably well. We have implemented this construction by adding the contribution from higher derivative biases just for highly biased tracers, and have found that indeed all tracers perform comparably well. At the order at which we have computed, we are able to predict all two-point and three-point functions up to $k\sim 0.17\hinvMpc$ which is a remarkable improvement with respect to former techniques. Of course, our findings are affected by the precision of our numerical data, and by the relatively low order of the calculations, that do not allow us to use data at very high wavenumbers. It will therefore be very interesting to perform a similar comparison by performing higher-order calculations, by computing higher-$N$ point functions, as well as by using more precise numerical data and potentially more accurate fitting procedures, so that our findings can be better verified. We plan to do this in future work. %=================================================================% | 16 | 9 | 1609.00717 |
|
1609 | 1609.02481_arXiv.txt | This is the second in a series of papers associated with cataclysmic variables (CVs) and related objects, formed in a suite of simulations for globular cluster evolution performed with the MOCCA Monte Carlo code. We study the properties of our simulated CV populations throughout the entire cluster evolution. We find that dynamics extends the range of binary CV progenitor properties, causing CV formation from binary progenitors that would otherwise not become CVs. The CV formation rate in our simulations can be separated into two regimes: an initial burst ($\lesssim$ 1 Gyr) connected with the formation of the most massive white dwarfs, followed by a nearly constant formation rate. This result holds for all models regardless of the adopted initial conditions, even when most CVs form dynamically. Given the cluster age-dependence of CV properties, we argue that direct comparisons to observed Galactic field CVs could be misleading, since cluster CVs can be up to 4 times older than their field counterparts. Our results also illustrate that, due mainly to unstable mass transfer, some CVs that form in our simulations are destroyed before the present-day. Finally, some field CVs might have originated from globular clusters, as found in our simulations, although the fraction of such escapers should be small relative to the entire Galactic field CV population. | Cataclysmic variables (CVs) are interacting binaries composed of a white dwarf (WD) undergoing stable mass transfer from a main sequence (MS) star or a brown dwarf (BD) \citep[e.g.][]{Warner_1995_OK,Knigge_2011_OK}. They are expected to exist in non-negligible numbers in globular clusters (GCs), that are natural laboratories for testing theories of stellar dynamics and evolution. CVs in GCs have been studied by many authors, both theoretically and observationally \citep[e.g.][and references therein]{Knigge_2012MMSAI}. GCs are thought to play a crucial role in CV formation, since their densities are sufficiently high that dynamical encounters involving binaries should be common. Thus, in dense GCs, it is natural to expect that many CV progenitors will have been affected by dynamics in some way prior to CV formation \citep[e.g.][]{Ivanova_2006,Belloni_2016a}. \subsection{Formation and Destruction Channels} \label{formation_channel} The primary channels associated with CV formation in GCs, based on the results of numerical simulations, can be summarized as \citep[][]{Ivanova_2006} following: (i) only $\sim$ 27 per cent of CVs form from binaries that have never experienced a dynamical interaction; (ii) $\sim$ 60 per cent of CVs did not evolve via a common-envelope phase (CEP); (iii) tidal capture does not play a significant role in CV formation; and (iv) dynamical encounters tend to exchange more massive WDs into the binary progenitors of CVs. Some of these formation channels have been independently discussed by \citet{Shara_2006}. The authors analyzed two cluster $N$-body models, simulated using the NBODY4 code with GRAPE-6 processors. In their simulations, they found 4 (out of 15) CVs had no field-like counterpart, i.e. four CVs were dynamically formed, either by exchange or successive dynamical encounters. In both \citet{Ivanova_2006} and \citet{Shara_2006}, the authors also discussed destruction channels for any CVs that do not survive to the present-day in their simulations. \citet{Ivanova_2006} found that most CVs cease mass transfer for (internal) evolutionary reasons; very few CVs are destroyed by dynamical encounters. \citet{Shara_2006} found similar results in this regard, however fewer CVs managed to escape from their simulated clusters relative to what was found by \citet{Ivanova_2006}, and the mechanism of escape was always weak encounters or two-body relaxation. In spite of the agreement between these two modeling efforts, we emphasize that \citet{Shara_2006} analyzed only two models (100k and 200k) and had very few CVs form (< 20), whereas \citet{Ivanova_2006} analyzed several Monte Carlo models with many CVs, but lacked any cluster evolution, i.e. their clusters had fixed spatial structure. We aim to complement these pioneering works with the MOCCA Monte Carlo simulations presented here, which offer both statistical significance and a realistic dynamical environment for the host clusters. \subsection{Dynamical Influence on CV formation and evolution} \label{dynamical_cv_evolution} One interesting feature described by \citet{Shara_2006} is a dynamically-induced acceleration in the onset and rate of accretion when CVs are formed. For example, the authors discuss a particular CV formed in their simulations that began the CV phase before its field-like counterpart, due to a prior dynamical interaction. Another CV had its evolution accelerated by a dynamical perturbation just after initiating the CV phase. We argue that the first of these two scenarios is more likely, since CV progenitors tend to be more massive than the mean stellar and even binary mass in the cluster, which reduces the time-scale for dynamical encounters prior to the onset of the CV phase. If these interactions decrease the binary progenitor orbital period (or increase its eccentricity), then the CE phase will begin earlier than for its field counterpart. This scenario would not necessarily rely on a single strong interaction, but could rather arise due to repeated weak interactions. The second scenario, on the other hand, seems much less likely, since this requires (very few) strong dynamical interactions and hence small impact parameters. CVs tend to have short orbital periods, which reduces the probability for direct encounters with sufficient force to significantly change their orbital parameters \citep{Leigh_2016}. However, if the CV is formed close to or in the cluster core, then the probability of a strong interaction is at its highest. This was the case for the specific CV that suffered accelerated mass transfer due to a dynamical perturbation in the simulations of \citet{Shara_2006}, since this binary was very close to the core at its formation. We further caution the reader that these conclusions taken from \citet{Shara_2006} rely on small number CV statistics, albeit accompanied by rich details for their formation and subsequent time evolution. Hence, we emphasize that these results need to be confirmed, by supplanting the small number statistics with a more robust coverage of the relevant parameter space for GC evolution and CV formation, using a much larger suite of realistic simulations. \subsection{CV age} \label{cv_age} We emphasize that observing CVs in GCs relies on much more than just dynamical interactions. Of comparable or even greater importance are the observational selection effects, as well as the ages of cluster CVs compared to Galactic field CVs. For instance, \citet{Belloni_2016a} quantified the observational selection effects that plague the search for CVs in GCs, and concluded that their detection rates could be dramatically increased if detectable during quiescence. \citet{Ak_2015} inferred the ages of a sample of field CVs from kinematic data, and concluded that 94 per cent of CVs in the solar neighbourhood belong to the thin-disc component of the Galaxy. The corresponding mean kinematical ages are 3.40 $\pm$ 1.03 Gyr and 3.90 $\pm$ 1.28 Gyr for the non-magnetic thin-disc CVs below and above the period gap, respectively. In GCs, on the other hand, some CVs can be up to 4 times older than this. Thus, it is critical to properly account for such age-related effects when comparing cluster and field CV populations, in an attempt to quantify the impact of the cluster dynamics on CV formation and evolution. \subsection{Structure of the paper} \label{paper_structure} For clarity, we have separated the results of our initial investigation into CV formation in GCs into two different papers. In the first paper in this series \citep[][]{Belloni_2016a}, we concentrated on the present-day population (PDP) of CVs and the observational selection effects that contribute to "hiding" most of the CV populations in GCs from observations. In this paper, the second of the series, we focus on the primary formation channels for CVs, as simulated by the MOCCA code (Section \ref{mocca}), and quantify the influence of the cluster dynamics in shaping the observed CV properties. We further address the age-dependence of CV properties, CVs destroyed before the present-day (i.e., after 12 Gyr of cluster evolution) and CVs formed from binary progenitors that previously escaped their host cluster. In Section \ref{model}, we describe the MOCCA and CATUABA codes and present the suite of models analyzed in this paper. In Section \ref{results}, the main results of this investigation are presented and discussed. We conclude and summarize our main results in Section \ref{conclusion}. | \label{conclusion} In the first paper of this series \citep{Belloni_2016a}, we discussed six specific MOCCA models with a focus on the properties of their present-day CV populations. In this paper, we concentrate instead on a discussion of the properties of the progenitor and formation-age populations. Our results show good overall agreement with previous investigations, both with respect to the most common CV formation channels \citep{Ivanova_2006} and the acceleration/retardation of CV evolution prior to CV formation, by (indirectly) affecting the CV progenitor binary \citep{Shara_2006} . The main results of this paper can be summarized as follows: \begin{description} \item[(i)] Dynamics can extend the parameter space applicable to CV progenitors (with respect to CVs formed without influence of dynamics), and allow binaries that would not become CVs to evolve into CVs. \item[(ii)] Sparse clusters have more CVs formed through a CEP, relative to denser clusters with more dynamically formed CVs. The number of dynamically formed CVs decreases with decreasing cluster density, as expected. \item[(iii)] The WD-MS binary formation rate is characterized by an initial burst, followed by a smoothly decreasing rate. The CV formation rate shows the same initial burst, although it is followed by a nearly constant formation rate. This is caused by the time-delay between the time of WD-MS binary formation and CV formation. This is, in general, in good agreement with the findings of \citet{Ivanova_2006}, who claimed that the relative number of CVs that appear is roughly constant throughout the cluster evolution. \item[(iv)] The CV formation rate can either be accelerated or retarded due to dynamical interactions, which is in good agreement with the results of \citet{Shara_2006}. Additionally, the CV is unlikely to change after CV formation, i.e. after CV formation, it is improbable that the CV will be affected by dynamical interactions, because the CVs are dynamically hard binaries with small interaction cross-sections. \item[(v)] The CVs are mainly formed as short-period systems, which indicates that they will be very faint objects by the present-day. \item[(vi)] Dynamically formed CVs tend to have massive WDs, in general, due to exchanges. This was pointed out by \citet{Ivanova_2006}. \item[(vii)] The properties of CV populations change with time, which can lead to confusion upon comparing predicted cluster CVs (older) to observed Galactic field CVs (younger). \item[(viii)] Before the present-day, CVs can be `destroyed' either via unstable mass transfer (most of them), dynamical interactions, or cluster escape, in good agreement with \citet{Shara_2006} and \citet{Ivanova_2006}. \item[(ix)] Very few field CVs could have their origins in GCs. \end{description} This concludes the first part of our investigation into CV formation in GCs using the MOCCA, split between two first papers of which this is the second. Thus far, our results have shown good overall agreement with previous observational and theoretical works. Future investigations will concentrate on the effects of the % empirical consequential angular momentum loss prescription \citep{Schreiber_2016} (which is associated with the mass loss from the system), and on the CEP parameters, in deciding the predicted CV properties. Special attention will be given to the absence of field-like CVs in the Kroupa models. Equally interesting are the CV siblings (AM CVn and symbiotic stars), especially upon considering that the first AM CVn in a GC might have just been discovered in NGC 1851 \citep{Zurek_2016}. We plan to extend the CATUABA code in order to include these interesting systems in order to extend our analysis to include the entire population of accreting white dwarf binary systems in GCs. After CATUABA is complete and automated, we will begin our analysis of the models of the MOCCA-SURVEY \citep{Askar_2016b}. | 16 | 9 | 1609.02481 |
1609 | 1609.00021_arXiv.txt | Polarization is a powerful diagnostic tool to constrain the site of the high-energy pulsed emission and particle acceleration in gamma-ray pulsars. Recent particle-in-cell simulations of pulsar magnetosphere suggest that high-energy emission results from particles accelerated in the equatorial current sheet emitting synchrotron radiation. In this study, we re-examine the simulation data to compute the phase-resolved polarization properties. We find that the emission is mildly polarized and that there is an anticorrelation between the flux and the degree of linear polarization (on-pulse: $\sim 15\%$, off-pulse: $\sim 30\%$). The decrease of polarization during pulses is mainly attributed to the formation of caustics in the current sheet. Each pulse of light is systematically accompanied by a rapid swing of the polarization angle due to the change of the magnetic polarity when the line of sight passes through the current sheet. The optical polarization pattern observed in the Crab can be well-reproduced for a pulsar inclination angle $\sim 60^{\rm o}$ and an observer viewing angle $\sim 130^{\rm o}$. The predicted high-energy polarization is a robust feature of the current sheet emitting scenario which can be tested by future X-ray and gamma-ray polarimetry instruments. | Gamma-ray observations show that pulsars are efficient particle accelerators \citep{2010ApJS..187..460A, 2013ApJS..208...17A}. In principle, the exact location of the accelerating regions can be constrained from the spectral and temporal properties of the gamma-ray emission. The detection of high-energy gamma rays $>$GeV in most pulsars pushes the emitting zone away from the polar caps of the star where they would be otherwise absorbed by the magnetic field. The careful analysis of lightcurve morphologies provides another independent constraint which also favors the outer parts of the magnetosphere as the main emitting regions (e.g., \citealt{2010ApJ...715.1270B, 2010ApJ...715.1282B, 2010ApJ...714..810R, 2015A&A...575A...3P}). However, due to our poor knowledge of the pulsar inclination and viewing angles, it turns out to be rather difficult to disentangle between models. In contrast, the expected polarization signature differs significantly from one model to another \citep{2004ApJ...606.1125D, 2005ApJ...627L..37P, 2007ApJ...670..677T, 2007ApJ...656.1044T, 2013MNRAS.434.2636P} because it is very sensitive to the electromagnetic geometry, and hence to the location of the emitting zones. While the polarization properties in radio (coherent emission) is well-documented (e.g., \citealt{2016JPlPh..82b6301P}), polarization measurements at higher energies (incoherent emission) exist for a few pulsars only (see \citealt{2009MNRAS.397..103S} for a review). The Crab pulsar presents the best multiwavelength coverage, from optical to soft gamma rays \citep{1988MNRAS.233..305S, 2009MNRAS.397..103S, 1996MNRAS.282.1354G, 1978ApJ...220L.117W, 2008Sci...321.1183D, 2008ApJ...688L..29F}. Phase-resolved optical and UV observations report a moderate degree of polarization (PD $\sim 10\%$--$30\%$) with significant swings of the polarization angle for each pulse, which suggests a rapid change in the field geometry. The equatorial current sheet forming beyond the light cylinder is a natural place for both particle acceleration via magnetic reconnection and sharp changes of the fields because this region separates the two magnetic polarities \citep{1990ApJ...349..538C, 2001ApJ...547..437L, 2005ApJ...627L..37P}. This scenario is supported by global particle-in-cell (PIC) simulations of plasma-filled magnetospheres \citep{2014ApJ...785L..33P, 2015ApJ...801L..19P, 2015ApJ...815L..19P, 2014ApJ...795L..22C, 2015MNRAS.448..606C, 2016MNRAS.457.2401C, 2015MNRAS.449.2759B}. These studies show that $\sim 10$--$20\%$ of the Poynting flux is efficiently dissipated in the current sheet within $1$--$2$ light-cylinder radii and channelled into non-thermal particles acceleration and synchrotron radiation. Pulses of high-energy radiation naturally result from the passage of the current sheet across the observer's line of sight \citep{2016MNRAS.457.2401C}. In this study, we model the high-energy phase-resolved polarization signal expected in gamma-ray pulsars. In the next section, we present the method to compute the Stokes parameters directly from the PIC simulations. We show a few representative cases as well as a Crab-like configuration in Section~\ref{sect_results}. We briefly discuss our results in Section~\ref{sect_discussion}. | \label{sect_discussion} We report on the self-consistent modelling of phase-resolved polarization of the incoherent pulsed emission in gamma-ray pulsar. The expected synchrotron radiation emitted by the equatorial current sheet is mildly polarized at a $\sim 15\%$ level on-pulse and $\sim 30\%$ off-pulse depending on the pulsar viewing angle and magnetic inclination. In most cases, there is a clear anticorrelation between the total observed flux and the degree of polarization, as also noted previously by \citet{2004ApJ...606.1125D} but in the context of the two-pole caustic model. Although the emitting regions are different in their model, the origin of the depolarization is similar here: it is due to the formation of caustics in the observed emission pattern. The lightcurve peaks are formed of photons emitted in different parts of the current sheet, and hence with different magnetic geometries, arriving in phase towards the observer \citep{2016MNRAS.457.2401C}. The resulting signal is depolarized by the superposition of the different components. This effect is particularly severe here because most of the emission occurs within $1$--$2 R_{\rm LC}$ where the orientation of the field changes rapidly (from a poloidal- to toroidal-dominated structure). The small scale turbulence in the current sheet generated by kinetic instabilities (tearing and kink modes, \citealt{2015ApJ...801L..19P, 2016MNRAS.457.2401C}) may also contribute to depolarize the emission. The other robust feature emerging from this study is the sudden swing of the polarization angle (by almost $180^{\rm o}$, i.e., visible as a loop in the vector diagram) coincident with each pulse of light. The swings can be interpreted as the change of magnetic polarity when the observer's line of sight crosses the current sheet \citep{2005ApJ...627L..37P}. The calculated polarization signatures are qualitatively in agreement with the phase-resolved optical data of the Crab pulsar \citep{2009MNRAS.397..103S}, for a pulsar inclination angle $\chi\sim 60^{\rm o}$ and viewing angle $\alpha\sim 130^{\rm o}$ consistent with the usual estimates inferred from the X-ray morphology of the nebula (e.g., \citealt{2012ApJ...746...41W}). This is the only solution which presents both the correct lightcurve morphology and the correct polarization pattern. However, there are differences in the phase-resolved PD and PA curves between the model and observations that we attribute to a background polarized component that is difficult to subtract \citep{2009MNRAS.397..103S}. We can recover a qualitative agreement by adding a constant polarized emission at a few percent level. The striking resemblance between the optical and gamma-ray lightcurves as well as the spectral continuity between these two bands in the Crab suggest a similar origin of the incoherent radiation. The optical emission may be radiated by low-energy pairs produced in the current sheet \citep{1996A&A...311..172L}. In addition, the close similarity between the optical and UV polarization data from the Crab implies that the polarization properties is not strongly frequency-dependent \citep{1996MNRAS.282.1354G}. Hence, one might expect a similar polarized emission at even higher energies as suggested by our results. If our predictions are correct, $10$--$20\%$ of gamma-ray polarization with the {\em Fermi}-LAT may be detectable for the brightest pulsars like Vela (R. Buehler, private communication). Future X-ray and gamma-ray missions dedicated to polarimetry will provide valuable constraints and tests of the current sheet emitting scenario. \begin{figure} \centering \includegraphics[width=8.75cm]{fig3.pdf} \caption{On-pulse and off-pulse degree of polarization averaged over the pulsar phase and viewing angle as a function of the pulsar obliquity. On-pulse regions are defined where $I>0.1I_{\rm max}$ for each lightcurve.} \label{fig_onoff} \end{figure} | 16 | 9 | 1609.00021 |
1609 | 1609.09100_arXiv.txt | Infrared variability is common among young stellar objects, with surveys finding daily to weekly fluctuations of a few tenths of a magnitude. Space-based observations can produce highly sampled infrared light curves, but are often limited to total baselines of about a month due to the orientation of the spacecraft. Here we present observations of the Chameleon I cluster whose low declination makes it observable by the {\it Spitzer} space telescope over a 200 day period. We observe 30 young stellar objects with a daily cadence to better sample variability on timescales of months. We find such variability is common, occurring in $\sim$80\% of the detected cluster members. The change in [3.6]-[4.5] color over 200 days for many of the sources falls between that expected for extinction and fluctuations in disk emission. With our high cadence and long baseline we can derive power spectral density curves covering two orders of magnitude in frequency and find significant power at low frequencies, up to the boundaries of our 200 day survey. Such long timescales are difficult to explain with variations driven by the interaction between the disk and stellar magnetic field, which has a dynamical timescale of days to weeks. The most likely explanation is either structural or temperature fluctuations spread throughout the inner $\sim$0.5 au of the disk, suggesting that the intrinsic dust structure is highly dynamic. | In young stellar objects the inner disk ($\lesssim$1 au) stands at the intersection between gas, dust, and the star itself. The gas disk is truncated by its interaction with the stellar magnetic field ($\sim$0.05 au), while the dust disk inner edge occurs where the grains are heated to a high enough temperature to sublimate (0.1-1 au). The exact structure can be difficult to study given the small size of these regions, making resolved observations challenging, although not impossible \citep[e.g.][]{men15,mil16}. Unresolved observations have been successful in revealing the general structure of this region. Spectral line profiles trace the free-fall of gas onto the stellar surface along magnetic field lines after it is lifted away from the disk \citep[e.g.][]{lim10} as well as outflows \citep{edw13,cau15}. Infrared observations find strong emission from T$\sim$1500 K dust \citep[e.g.][]{mcc13a}, consistent with a curved inner wall \citep{ise05,flo16}. Recent studies have found evidence for multiple populations of dust grains with different inner radii \citep{mcc13b}, consistent with the expectation that small dust grains reach the sublimation temperature farther from the star because they more efficiently absorb the stellar irradiation. While here we focus on the dust, much has been learned about the gas structure within this region \citep[see reviews by ][]{bou07,dul10}. Variability serves as an additional tool for studying the inner disk. Recent surveys have found that the vast majority of young stellar objects are variable in the mid-infrared on timescales of days to weeks \citep{cod14,reb14}, expanding on earlier ground-based near-infrared studies \citep[e.g.][]{car01}. These surveys have also revealed additional clues as to the structure of the inner disk. \citet{men16} use reverberation mapping to derive the location of the dust inner wall. \citet{esp11} demonstrate that the wavelength dependence of the variability in pre-transition disks, systems with an optically thick inner disk followed by an optically thin gap and an optically thick outer disk, can be explained by varying the height of the inner disk, indicating that this region is not static. \citet{mcg15} find, based on quasi-periodic occultations of the stellar surface, that the height of the inner wall can vary by $\sim$10\% over short timescales even in full disks. \citet{bou03} find that the variability of AA Tau is consistent with periodic occultations by a warped inner disk. Such non-axisymmetric structure is difficult to study with spatially un-resolved observations, which often rely on fits to axisymmetric models. Most previous {\it Spitzer} time domain studies of YSOs were restricted to baselines of 1-2 months due to the duration of a single visibility window for most star forming regions, while ground-based near-infrared studies have found variability extending out to year long timescales \citep{wol13,par14}, although with a sparser cadence than is possible with space-based observatories. Long timescales push towards larger radii in the disk; if the timescale of the variability is proportional to the local Keplerian period then year-long fluctuations imply variability at $\sim$1 au from the central star. A detailed characterization of long-timescale variability can improve our understanding of this important planet-forming region of the disk. Here we probe variability over weeks to months using {\it Spitzer} Space Telescope observations of the Chamaeleon I (Cha I) star-forming region \citep{luh08b}. Due to its low declination, Cha I can be observed by {\it Spitzer} over a 200 day window, much longer than the $\sim$40 day windows of other star forming regions. With photometry (Section~\ref{data}) taken roughly once-per-day for 200 days we produce well sampled light curves and select out a sample of stars with significant variability (Section~\ref{find_var}). We analyze the change in color (Section~\ref{color}) and the timescale of the variability (Section~\ref{timescale}) and relate this information to potential sources of the variability (Section~\ref{discussion}). We find that months-long variability is common and likely due to intrinsic instabilities in disk structure as far out as 0.5 au. | Based on {\it Spitzer} observations of the Cha I cluster taken roughly once per day over 200 days, we find that large (0.05-0.3) infrared fluctuations are common, occurring in $\sim$80\% of the observed young stellar objects. We find that the behavior seen in previous {\it Spitzer} surveys, which focused on well-sampled observations over $\sim$40 day observing windows, continues to much longer timescales. In examining the properties of the variability, we find that changes in color ($\Delta$[4.5]/$\Delta$[3.6]=0.75-1.61) occur in some of the young stellar objects, and that these fluctuations fall between the behavior expected of extinction and fluctuations in disk emission ($\Delta$[4.5]/$\Delta$[3.6]=0.84,1.25 respectively). We find a small handful of the cluster members to be periodic (5/30), including three with periods of 30-40 days, longer than the typical rotational periods of young stellar objects. With the combination of high cadence and long observing window, we are able to simultaneously sample both daily and months-long fluctuations. With these data, we find a smooth increase in power across two orders of magnitude in timescale in almost every young stellar object, with this behavior seen in the [3.6] and [4.5] fluxes as well as the [3.6]-[4.5] color. The shape of the power spectrum indicates that the infrared variability is largest on the longest timescales, with fluctuations $\sim$2 times larger over 200 days than over the typical 40 day windows sampled by previous {\it Spitzer} variability surveys. A comparison of our observations with prior {\it Spitzer} photometry of Cha I suggests that this trend extends out to decades-long timescales. Based on the size of the fluctuations we can rule out the direct contribution of star spots, while perturbations from a companion are possible for the three sources with long ($\sim$30 day) periods. Interactions at the disk/magnetosphere boundary can explain some of the days to week long fluctuations, while longer months to year long variability is likely a result of structural perturbations to the disk out as far as $\sim$0.5 au. These processes are not mutually exclusive, and can operate simultaneously within an individual system. Whichever process appears more prominent in the light curves depends on the timescales being probed, as well as the intrinsic properties of the system (e.g. accretion rate, stellar magnetic field strength, stellar luminosity). More detailed measurements of accretion rate, stellar rotation period and inclination could further guide our understanding of which processes are strongest within a given system. | 16 | 9 | 1609.09100 |
1609 | 1609.05604_arXiv.txt | We are pursuing a project to build a database of phase calibration sources suitable for Giant Metrewave Radio Telescope (GMRT). Here we present the first release of 45 low frequency calibration sources at 235 MHz and 610 MHz. These calibration sources are broadly divided into quasars, radio galaxies and unidentified sources. We provide their flux densities, models for calibration sources, ($u,v$) plots, final deconvolved restored maps and \textsc{clean}-component lists/files for use in the Astronomical Image Processing System (\textsc{aips}) and the Common Astronomy Software Applications (\textsc{casa}). We also assign a quality factor to each of the calibration sources. These data products are made available online through the GMRT observatory website. In addition we find that (i) these 45 low frequency calibration sources are uniformly distributed in the sky and future efforts to increase the size of the database should populate the sky further, (ii) spectra of these calibration sources are about equally divided between straight, curved and complex shapes, (iii) quasars tend to exhibit flatter radio spectra as compared to the radio galaxies or the unidentified sources, (iv) quasars are also known to be radio variable and hence possibly show complex spectra more frequently, and (v) radio galaxies tend to have steeper spectra, which are possibly due to the large redshifts of distant galaxies causing the shift of spectrum to lower frequencies. | The Giant Metrewave Radio telescope \citep[GMRT,][]{Swarupetal} is the most sensitive radio telescope in the world that is capable of operating at low radio frequencies from 150 MHz to 1450 MHz. In order to obtain reliable information about target astronomical sources, radio sources whose structure and flux density are known {\it a~priori} are routinely observed to determine antenna based calibration solutions. Any errors in the models used for these calibration sources reflect in errors in the antenna based calibration solutions, especially in the phase, and limit the quality of the radio images obtained. GMRT users have traditionally been using phase calibration sources from the Very Large Array (VLA) \citet{vla-cal-manual}, which is biased towards observations optimized for higher frequencies. In this paper we present a new database which is intended to facilitate science operations at the GMRT. The database presenting all products, i.e., their flux densities, models, ($u,v$) plots, final deconvolved restored maps and \textsc{clean}-component lists/files \citep{Cornwelletal,hogbom1974}, is available at the `Observing Help' web-page of the GMRT observatory. In this paper, our motivations for such a database are discussed in Sect.~\ref{motiv}. The sample is presented in Sect.~\ref{sample} and its archival data and data reduction are detailed in Sect.~\ref{obs-data} and Sect.~\ref{data-red}, respectively. The results from the database, i.e., their quality standards, sky distribution, comparison of images made using image model from the database and made in a routine manner and radio properties are discussed in Sect.~\ref{qual-fac}, Sect.~\ref{sky_dist}, Sect.~\ref{comparison} and Sect.~\ref{int-rad-spec}, respectively. Finally, we provide a summary in Sect.~\ref{summary}. | \label{summary} It is well known that the technique of phase referencing permits the coherence time of the target source data to be extended across the entire observation (many hours). This means that the sensitivity of the observations continue to scale as the square-root of the integration-time. Here, we have introduced and made available a database of phase calibration sources for the GMRT. We provide their flux densities, models, ($u,v$) plots, final deconvolved restored maps and \textsc{clean}-component lists/files covering fields-of-view of $\sim$4 deg$^2$ and $\sim$0.5 deg$^2$ at 235 MHz and 610 MHz, respectively, for use in the \textsc{aips} and the \textsc{casa} for all phase calibration sources in the database. We also assign a quality factor for each of the calibration sources. The data products are available through the GMRT observatory website. A screen-shot of the GMRT calibrator manual from the online web-page is shown in Fig.~\ref{screenshot-file}. Additional findings from this study are: \begin{itemize} \item The distribution of these 45 phase calibration sources in the sky is uniform with no visible large gaps or voids in the sky. We used the gap statistics and the two-point correlation function to demonstrate that the distribution of phase calibration sources are random and the right ascension and sin($\pi/2 - {\rm declination}$) plane is uniformly distributed. Our ongoing efforts to increase the size of this database would often provide a suitable choice of a phase calibration source that is within 20~deg to a given target source. \item Radio spectra have a variety of shapes, straight, curved and complex. We find that the relative frequencies of different shapes are nearly equal between straight, curved and complex shapes. \item Quasars tend to exhibit flatter radio spectra as compared to the radio galaxies or the unidentified sources. \item Quasars are also known to be radio variable and hence possibly tend to show complex spectra more frequently. \item Radio galaxies tend to have steeper spectra than either the quasars or the unidentified sources. The steeper spectra are possibly either due to the spectral ageing of synchrotron-emitting radio lobes or due to the large redshift of distant galaxies causing the shift of the spectrum to lower frequencies. \end{itemize} \begin{figure*} \begin{center} \begin{tabular}{c} \includegraphics[width=17.0cm]{fig5.ps} \end{tabular} \caption{A screen-shot of the GMRT calibrator manual from the online web-page at the GMRT observatory. Top-left panel and top-right are the images of a calibration source at 235 MHz and 610 MHz. All the data products for a calibration source are also listed, including % coordinates ($\alpha$, $\delta$), observing frequency, flux density, ($u,v$) plot (or visplot), quick-look image of the field-of-view, \textsc{clean} restored model map and \textsc{clean}-component model.} \label{screenshot-file} \end{center} \end{figure*} GMRT study of science target sources using calibration sources suitably chosen from the database is an effective way to determine the phase calibration for the secondary phase calibration sources and exploit fully the technique of phase-referencing. We believe this is a valuable database % (available at \url{http://gmrt.ncra.tifr.res.in}) in planning a GMRT observation, be it spectral-line or continuum or pulsar. Our ongoing and future efforts will increase the size of this database, thereby allowing the user to have a larger number of calibration sources. The database at these two frequencies along with MSSS \citep{Healdetal} and GLEAM-survey \citep{Waythetal} also help to interpolate the information at 325 MHz. 325 MHz band is another GMRT frequency band with very little information with regard to appropriate choices of suitable phase calibration sources. This database would also be useful at the new low-frequency bands of the upgraded GMRT\footnote{GMRT upgrade: A major upgrade of several sub-systems of the GMRT has been initiated, which will result in significant changes in almost all aspects of the GMRT with the aim of significantly improving its capability and sensitivity. Key features of the upgrade are near seamless frequency coverage from 125 MHz to 1450 MHz and instantaneous bandwidth of 400 MHz along with several matching improvements in computing, receivers, servo and mechanical systems, electrical, and civil structures. The upgrade is nearing completion and the first phase of the upgraded system has already been released to the astronomical community.} \citep{Gupta}. | 16 | 9 | 1609.05604 |
1609 | 1609.08726_arXiv.txt | Star formation in the Galactic disc is primarily controlled by gravity, turbulence, and magnetic fields. It is not clear that this also applies to star formation near the Galactic Centre. Here we determine the turbulence and star formation in the CMZ cloud G0.253+0.016. Using maps of $3\,$mm dust emission and HNCO intensity-weighted velocity obtained with ALMA, we measure the volume-density variance $\sigma_{\rho/\rho_0}=1.3\pm0.5$ and turbulent Mach number $\mathcal{M}=11\pm3$. Combining these with turbulence simulations to constrain the plasma $\beta=0.34\pm0.35$, we reconstruct the turbulence driving parameter $b=0.22\pm0.12$ in G0.253+0.016. This low value of $b$ indicates solenoidal (divergence-free) driving of the turbulence in G0.253+0.016. By contrast, typical clouds in the Milky Way disc and spiral arms have a significant compressive (curl-free) driving component ($b>0.4$). We speculate that shear causes the solenoidal driving in G0.253+0.016 and show that this may reduce the star formation rate by a factor of $7$ compared to nearby clouds. | \citet{RathborneEtAl2014,RathborneEtAl2015} showed that {G0.253+0.016} is a dense turbulent cloud in the central molecular zone (CMZ). However, so far it has been unclear what drives this turbulence and whether that turbulence plays a role in controlling the low star formation rate (SFR) seen in {G0.253+0.016} and in the CMZ as a whole \citep{LongmoreEtAl2013a,KruijssenEtAl2014,JohnstonEtAl2014}. Using high-resolution ALMA $3\,$mm dust and HNCO molecular line data, we determine the driving mode of the turbulence in {G0.253+0.016} and link the turbulence driving to the SFR. \begin{figure*} \centerline{\includegraphics[width=1.0\linewidth]{fig01.eps}} \caption{Sketch of the turbulence-regulated paradigm of star formation. Turbulence is fed by stellar feedback and/or large-scale dynamics (such as galactic shear). Different turbulence driving mechanisms can excite more solenoidal (rotational) modes, others inject more compressive (potential) modes. The mix of turbulent modes has profound consequences for star formation.} \label{fig:turbsf} \end{figure*} The turbulence-regulated paradigm of star formation \citep{MacLowKlessen2004,ElmegreenScalo2004,McKeeOstriker2007,HennebelleFalgarone2012,FederrathKlessen2012,PadoanEtAl2014} provides us with the basic framework for our approach to determine the turbulence parameters of {G0.253+0.016} and allows us to make predictions for the star formation activity in {G0.253+0.016}. Figure~\ref{fig:turbsf} shows a sketch of the turbulence-regulated picture of star formation. In this model, turbulence shapes the density distribution of the clouds, thereby controlling the dense-gas fraction and thus, the formation of stars. Then, stellar feedback (such as supernova explosions or stellar winds) and/or large-scale dynamics (such as galactic shear or magneto-rotational instability) drive the turbulence. Understanding and determining the drivers of the turbulence is of fundamental importance in this model of star formation. Idealised numerical simulations have shown that compressible, supersonic turbulence decays quickly, in about a crossing time \citep{ScaloPumphrey1982,MacLowEtAl1998,StoneOstrikerGammie1998,MacLow1999}. Given that {G0.253+0.016} and other galactic clouds are in a dynamic state of supersonic turbulence means that the turbulence is driven by some physical stirring mechanism(s). Turbulence driving mechanisms can be broadly separated into two groups: 1) stellar feedback, and 2) gas dynamics caused by mechanisms other than feedback. Stellar feedback includes supernova explosions, stellar winds, and ionisation fronts \citep{McKee1989,KrumholzMatznerMcKee2006,BalsaraEtAl2004,AvillezBreitschwerdt2005,BreitschwerdtEtAl2009,GritschnederEtAl2009,PetersEtAl2010,PetersEtAl2011,ArceEtAl2011,GoldbaumEtAl2011,LeeMurrayRahman2012}, primarily caused by high-mass stars, as well as jets and outflows from young stars, including low- and intermediate-mass stars \citep{NormanSilk1980,MatznerMcKee2000,BanerjeeKlessenFendt2007,NakamuraLi2008,CunninghamEtAl2009,CarrollFrankBlackman2010,WangEtAl2010,CunninghamEtAl2011,PlunkettEtAl2013,PlunkettEtAl2015,OffnerArce2014,FederrathEtAl2014}. The 2nd category (which we refer to as ``Dynamics'' in Figure~\ref{fig:turbsf}) includes accretion (such as accretion onto a galaxy) and gravitational collapse \citep{Hoyle1953,VazquezCantoLizano1998,KlessenHennebelle2010,ElmegreenBurkert2010,VazquezSemadeniEtAl2010,FederrathSurSchleicherBanerjeeKlessen2011,RobertsonGoldreich2012,LeeChangMurray2015}, the magneto-rotational instability (MRI) \citep{BalbusHawley1991,PiontekOstriker2004,PiontekOstriker2007,TamburroEtAl2009}, spiral-arm compression \citep{DobbsBonnell2008,DobbsEtAl2008}, cloud-cloud collisions \citep{TaskerTan2009,BenincasaEtAl2013}, and shear. While different drivers can play a role in different environments, \citet{KruijssenEtAl2014} found that most of these drivers are not sufficient to explain the turbulent velocity dispersion in the CMZ, but some of them can. A critical consideration is that the majority of turbulence drivers (e.g., supernova explosions, high-mass stellar winds, and accretion) primarily drive compressible (curl-free) modes, so we refer to these as ``compressive drivers''. By contrast, solenoidal (divergence-free) modes can be generated directly by shear and the MRI (so we call them ``solenoidal drivers''). The key aspect here is that the density probability distribution function (PDF) depends critically on the driving. \citet{FederrathKlessenSchmidt2008,FederrathDuvalKlessenSchmidtMacLow2010,PriceFederrathBrunt2011,MolinaEtAl2012,KonstandinEtAl2012ApJ,NolanFederrathSutherland2015,FederrathBanerjee2015} showed that the variance (width) of the density PDF is given by \begin{equation} \label{eq:sigrho} \sigma_{\rho/\rho_0} = b\,\mathcal{M}\left(1+\beta^{-1}\right)^{-1/2}, \end{equation} with the turbulent Mach number $\mathcal{M}=\sigma_v/c_\mathrm{s}$ (the ratio of velocity dispersion and sound speed), plasma $\beta$ (the ratio of thermal and magnetic pressure), and the turbulence driving parameter $b$, which smoothly varies from $b=1/3$ for purely solenoidal driving to $b=1$ for purely compressive driving \citep{FederrathDuvalKlessenSchmidtMacLow2010}. The theoretical models and simulations in \citet{FederrathKlessen2012} demonstrated that the SFR depends on $b$, with compressive driving producing up to an order of magnitude higher SFRs than solenoidal driving. Thus, our goal is to determine whether the driving of turbulence in {G0.253+0.016} is primarily solenoidal or compressive. We do this by measuring $\sigma_{\rho/\rho_0}$, $\mathcal{M}$, and $\beta$, and inverting Equation~(\ref{eq:sigrho}) to solve for $b$. Finally, we use our measurement of $b$ to predict the SFR in {G0.253+0.016} and to contrast this to the SFR in Milky Way clouds located in the Galactic disc rather than the Galactic Centre. | 16 | 9 | 1609.08726 |
|
1609 | 1609.04022_arXiv.txt | In this paper we investigate how observational effects could possibly bias cosmological inferences from peculiar velocity measurements. Specifically, we look at how bulk flow measurements are compared with theoretical predictions. Usually bulk flow calculations try to approximate the flow that would occur in a sphere around the observer. Using the Horizon Run 2 simulation we show that the traditional methods for bulk flow estimation can overestimate the magnitude of the bulk flow for two reasons: when the survey geometry is not spherical (the data do not cover the whole sky), and when the observations undersample the velocity distributions. Our results may explain why several bulk flow measurements found bulk flow velocities that \textit{seem} larger than those expected in standard $\Lambda$CDM cosmologies. We recommend a different approach when comparing bulk flows to cosmological models, in which the theoretical prediction for each bulk flow measurement is calculated specifically for the geometry and sampling rate of that survey. This means that bulk flow values will not be comparable between surveys, but instead they are comparable with cosmological models, which is the more important measure. | The term bulk flow in the context of cosmology refers to the average motion of matter in a particular region of space relative to the dipole subtracted cosmic microwave background (CMB) rest frame. One reason why bulk flows are interesting to cosmologists is that by measuring them we can learn more about the composition of the universe, the laws of gravity, and whether our current cosmological model is a good representation of the actual underlying dynamics.\\ A bulk flow is induced by density fluctuations, and thus the bulk motion we observe should match what we expect from the density distribution. The density distribution is in turn determined by cosmological parameters such as the strength of clustering, through $\sigma_8$, and the matter density, $\Omega_{\rm M}$. The magnitude of bulk flows can be predicted from theory given a model and set of cosmological parameters (e.g. $\sigma_8$ and $\Omega_{\rm M}$), some initial conditions (such as a fluctuation amplitude at the end of inflation), and a law of gravity (such as general relativity). If the observed bulk flow was to deviate from that predicted by theory, that would indicate that one or more of the given inputs is incorrect.\\ Currently tension exists in measurements of the bulk flow, with some measurements in apparent agreement with that predicted by $\Lambda$CDM \citep{2011MNRAS.414..264C, 2011JCAP...04..015D, 2011ApJ...736...93N, 2011ApJ...737...98O, 2012MNRAS.420..447T, 2013MNRAS.430.1617L, 2013MNRAS.428.2017M, 2014JCAP...09..019F, 2014MNRAS.437.1996M, 2014A&A...561A..97P, 2014MNRAS.445..402H, 2015MNRAS.450..317C} while others are not \citep{2008ApJ...686L..49K, 2009MNRAS.392..743W, 2010MNRAS.407.2328F, 2012MNRAS.419.3482A, 2015MNRAS.447..132W}. Relieving this tension is important if we are to gain physical insight into the nature of dark energy and dark matter.\\ The field of using large scale bulk flows to constrain cosmology has historically been limited by systematics due to the limited quality and quantity of the data available. Modern datasets now include peculiar velocity measurements of thousands of galaxies with moderate precision and hundreds of type Ia supernovae (SNe) with excellent precision. These have inspired a new generation of bulk flow studies. As these new datasets become increasingly abundant and precise, it is prudent to investigate the observational effects that may bias a bulk flow measured from one of these datasets.\\ One such effect is undersampling of the surveyed volume. Undersampling is especially relevant for estimates utilising a small number of distance indicators, like many recent estimates of the bulk flow done with observations of type Ia SNe \citep{2007ApJ...661..650H, 2007ApJ...659..122J, 2011MNRAS.414..264C, 2011JCAP...04..015D, 2011ApJ...732...65W, 2012MNRAS.420..447T, 2013A&A...560A..90F}. Attempts at addressing sampling issues have been proposed, see e.g. \cite{2009MNRAS.392..743W}, \cite{2012ApJ...761..151L} or \cite{2011ApJ...732...65W}. Another such effect is the geometry of a survey -- namely whether the survey covers the whole sky or a narrow cone. Methods such as the minimum variance method proposed by \cite{2009MNRAS.392..743W} attempt to weight arbitrarily shaped survey geometries so that the bulk flow they calculate approximates what would have been measured if the distribution of data was spherical. Other effects, besides observational, might also play an important role. See e.g. \cite{2015JCAP...12..033H} where the effects of velocity correlations between supernova magnitudes are included in the data covariance matrix, and are found to have a significant impact on the constraints from a derived bulk flow estimate.\\ The bias that might arise from estimating the bulk flow magnitude with a small number of peculiar velocities, effectively undersampling the surveyed volume, and with a non-spherical distribution of measurements, is the focus of this paper. We utilise data from the Horizon Run 2 \citep[HR2;][]{2011JKAS...44..217K} simulation to investigate how strong a bias undersampling introduces for various survey volumes, from spherically symmetric surveys, to hemispherical and narrow cone surveys. We focus on the Maximum Likelihood (ML) estimator of the bulk flow, as it is computationally cheap to perform, easy to interpret and used widely in the literature. Additionally, for a limited test case, we investigate how successful the Minimum Variance (MV) \citep{2009MNRAS.392..743W} estimator is at alleviating the bias that comes from undersampling. The ML and MV estimators are described in Appendix~\ref{app:mlemv}, where we take the opportunity to clarify some typographic errors and undefined terms in the original papers that can lead to confusion. \\ In section \ref{sec:hori2} we introduce the HR2 simulation. Then in section \ref{sec:lintheory} we summarise the theoretical footing of large scale bulk flows, and provide an expansion beyond the usual spherical assumptions so that the theory is also valid for non-spherical geometries. The theoretical estimate is established as the benchmark against which we test the effects of undersampling. Then in section \ref{sec:samplingeffects} we analyse the effects of undersampling on the Maximum Likelihood estimator, for a spherical, hemispherical and narrow cone geometry. Finally in section \ref{sec:discussion} we discuss our findings and the implications for future work using large scale bulk flows in cosmology.\\ Throughout this paper when we refer to the theoretically most likely bulk flow magnitude it will be denoted the \emph{most probable} bulk flow magnitude, $V_p$, to avoid confusion with bulk flows from the Maximum Likelihood estimator. | \label{sec:discussion} After reviewing linear theory we showed how it can be expanded to be valid for non-spherical geometries, developing code that numerically calculates the theoretical bulk flow magnitude for any arbitrary survey geometry. To test the validity of the developed code, the derived theoretical bulk flow magnitude was compared to that of a variety of spherical cone geometries in the Horizon Run 2 (HR2) cosmological simulation and found to be within 5\% or better agreement for all tested geometries.\\ However, when simulating more realistic surveys and applying the Maximum Likelihood (ML) estimator we found that undersampling effects severely bias measurements of the bulk flow magnitude when a small number ($n \lesssim 500$) of peculiar velocities are used in the bulk flow estimate. On average, undersampling pushes the measured bulk flow to higher values, with the bias being amplified when narrower survey geometries are used.\\ For our fixed volume of 40$\cdot 10^6 (h^{-1}\mathrm{Mpc})^3$ using 500 SNe corresponds to a sampling density of $\sim13 \, \mathrm{SNe}/10^6 (h^{-1}\mathrm{Mpc})^3$. Hence we expect undersampling could affect many recent measurements of the of the bulk flow magnitude utilising type Ia SNe as a distance indicator (i.e, \citealt{2007ApJ...661..650H, 2007ApJ...659..122J, 2011MNRAS.414..264C, 2011JCAP...04..015D, 2011ApJ...732...65W, 2012MNRAS.420..447T, 2013A&A...560A..90F}) where the number of supernovae are well below 300 and the sampling density is also well below $13\; \mathrm{SNe}/10^6 (h^{-1}\mathrm{Mpc})^3$.\\ Without a detailed analysis of each of the previous bulk flow estimates, which is beyond the scope of this paper, it is hard to determine whether or not a particular result is affected by undersampling. However, some examples that might deserve attention include e.g. \cite{2013A&A...560A..90F} where the SNe are subdivided into four shells, and for the SNe in each shell a bulk flow is estimated. We would expect the bulk flow to converge to the CMB frame as we go to higher redshifts and larger volumes, and yet \cite{2013A&A...560A..90F} find that in shells of both increasing redshift and increasing volume there is no clear trend in the magnitude of the bulk flow. Instead, the trend they see could potentially be explained by undersampling. Their bins contain varying numbers of supernovae, namely $n=[128, 36, 38, 77]$, in which they find bulk flows of $V_{\rm p}=[243, 452, 650, 105]$\kms. So there is a trend by which the bins with fewer supernovae find larger bulk flows (e.g. compare the middle two bins with the outer two bins).\\ Similarly, \citet{2012MNRAS.420..447T} provide two measurements of the ML bulk flow: one with all 245 SNe from the First Amendment compilation, the other with a subset of 136 SNe that excludes the nearby ones (excludes $z<0.02$). Naive expectations would suggest that the sample focussing on higher redshift SNe should be closer to converging on the CMB and thus have a lower bulk flow, however they find the opposite. The higher-redshift-only sample has a higher bulk flow, but since it has fewer data points than the full sample that would be consistent with our finding that undersampling overestimates the bulk flow. \\ Both \cite{2013A&A...560A..90F} and \citet{2012MNRAS.420..447T} found bulk flows that exceeded the predicted flow based on known density distributions in the nearby universe, so whether the estimates are inflated by undersampling is potentially an interesting question (although neither claimed significant deviation from $\Lambda$CDM). While we have selected these two as the most significant examples that could be affected by the sampling biases we discuss in this paper, we note that this trend is pervasive, as no other samples show significant opposing trends. Some show slight reduction in bulk flow with smaller samples, but it is much less significant than the positively correlated examples above (and much smaller than the uncertainties), e.g. in \cite{2011MNRAS.414..264C} increasing the sample from 61 to 109 SNe increases the estimated bulk flow from 250 \kms to 260 \kms, an effect of less than 5\%.\\ For bulk flow estimates where the typical number of observed peculiar velocities in a survey is $n \gtrsim 3000$, i.e., most estimates using the Tully-Fisher or Fundamental Plane relation \citep{2011ApJ...736...93N,2014MNRAS.437.1996M, 2015MNRAS.447..132W, 2016MNRAS.455..386S}, we found no bias from undersampling. It is however important to note that the analysis of this paper assumes type Ia SNe are used as distance indicators, and therefore the uncertainties in each distance measurement are small (Appendix~\ref{app:pecveluncer}). The typically larger uncertainties derived from Tully-Fisher or Fundamental Plane estimates would increase the variance in the individual bulk flow components, which in turn could mean we require larger numbers of objects to avoid biases than is found here.\\ Effects from uneven sampling have previously been discussed in the literature. One example is Eq.~10 of \cite{2012ApJ...761..151L} where a method of dividing the measured peculiar velocities by their selection function is proposed. In \cite{1982ApJ...258...64A} and \cite{2007ApJ...661..650H} Monte Carlo simulations of observations are used to better understand systematic effects, including sampling effects. Other works \citep{2011ApJ...732...65W, 2009MNRAS.392..743W} develop new estimators such as the Weighted Least Squares (WLS), the Coefficient Unbiased (CU), or the Minimum Variance (MV) estimators, with the MV estimator being the most popular alternative to the ML estimator. The MV estimator is constructed in part to account for sampling bias (with the motivation to be able to compare measurements of bulk flow between surveys); in our work we found that the MV estimator suffered the same bias as the ML estimator, again with the bias increasing for narrower geometries.\\ A number of recent papers compare a measured bulk flow directly to a $\Lambda$CDM prediction based on linear theory and an assumption of spherical symmetry. For example \cite{2011MNRAS.414..264C}, \cite{2011JCAP...04..015D}, and \cite{2016MNRAS.455..386S} plot bulk flow measurements as a function of redshift compared to a generic $\Lambda$CDM prediction. Our analysis suggests that such a comparison between bulk flows derived from different surveys, and therefore different survey geometries and sampling rates, is potentially problematic.\\ In \cite{2012ApJ...759L...7P} the HR2 simulation was used to show that the size of the large scale structure known as the Sloan Great Wall (SGW) is in agreement with what we statistically expect from $\Lambda$CDM cosmology, something that had previously been disputed. Similarly, as early as \cite{1982ApJ...258...64A} simulations were being used to compare measured bulk flows to theoretical predictions. Analogous to their arguments, our study highlights the importance of considering the full distribution of bulk flow magnitudes from theory, including sampling effects, rather than focusing on only the most probable bulk flow magnitude. That is, we propose that bulk flows should not be compared to the prediction from linear theory, but with the bulk flow magnitude distribution derived from a cosmological simulation using the method described above, with the actual survey geometry given as input. | 16 | 9 | 1609.04022 |
1609 | 1609.08660_arXiv.txt | A key question in extragalactic studies is the determination of the relative roles of stars and AGN in powering dusty galaxies at $z$\,$\sim$\,1-3 where the bulk of star-formation and AGN activity took place. In Paper I, we present a sample of $336$ 24\,$\mu$m-selected (Ultra)Luminous Infrared Galaxies, (U)LIRGs, at $z \sim 0.3$-$2.8$, where we focus on determining the AGN contribution to the IR luminosity. Here, we use hydrodynamic simulations with dust radiative transfer of isolated and merging galaxies, to investigate how well the simulations reproduce our empirical IR AGN fraction estimates and determine how IR AGN fractions relate to the UV-mm AGN fraction. We find that: 1) IR AGN fraction estimates based on simulations are in qualitative agreement with the empirical values when host reprocessing of the AGN light is considered; 2) for star-forming galaxy-AGN composites our empirical methods may be underestimating the role of AGN, as our simulations imply $>$\,50\,\% AGN fractions, $\sim$\,3$\,\times$ higher than previous estimates; 3) 6\% of our empirically classified ``SFG" have AGN fractions $\gtrsim$ 50\%. While this is a small percentage of SFGs, if confirmed, would imply the true number density of AGN may be underestimated; 4) this comparison {\rcomtwo depends} on the adopted AGN template -- those that neglect the contribution of warm dust lower the empirical fractions by up to 2$\times$; and 5) the IR AGN fraction is only a good proxy for the intrinsic UV-mm AGN fraction when the extinction is high ($A_V\gtrsim 1$ or up to and including coalescence in a merger). | Understanding galaxies at $z \sim 1$-$3$ is of key importance to galaxy evolution studies because both the star formation rate density \citep[see][for a recent review]{MadauDickinson2014} and quasar number density \citep{Richards2006b} peak at this epoch. Along with the $M_{\rm{BH}}-\sigma$ relation \citep{Ferrarese2000}, these observations suggest that the accumulation of stellar mass and growth of super-massive black holes are closely tied \citep[see e.g.][]{Hopkins2006, Hopkins2008}. The increase in number density of luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs respectively) up to $z \sim 2$ makes them the dominant contributor to the SFR density peak \citep{Murphy2011,Magnelli2011,Casey2012}. However, understanding exactly how much star formation takes place in such systems requires accurate determinations of the fraction of their power output that is due to recent star formation rather than AGN. The high levels of obscuration in such galaxies make answering this question notoriously difficult. % Analysis of the infrared spectral energy distribution (IR SED), especially mid-IR spectra when available, has been our best tool to determine the level of AGN activity in such heavily dust obscured systems \citep[e.g.][]{Armus2007,Sajina2007,Yan2007,Pope2008,Veilleux2009,Kirkpatrick2012,Sajina2012}. The contribution of AGN to the IR luminosity\footnote{Throughout this paper, IR refers to the integrated 8-1000\um\ emission.} is typically referred to as the IR ``AGN fraction" or $f{\rm{(AGN)_{IR}}}$. Traditionally, determining $f{\rm{(AGN)_{IR}}}$ is based on assuming that the hot dust giving rise to the mid-IR continuum is exclusively due to an AGN torus, while the far-IR cold dust emission peak is entirely powered by stars \citep[e.g][]{Polletta2007,Sajina2007}. The warm dust ($\sim$\,80-100K) giving rise to the 20-40\um\ continuum is more uncertain as it can be due to star formation \citep[e.g.][]{Veilleux2009} {\rcom or to reprocessing in an NLR} \citep[e.g. see][for a review]{Netzer2015}. This can account for the typically greater warm dust component in empirical AGN templates \citep[e.g.][]{Richards2006a,Mullaney2011} relative to pure AGN torus models \citep[e.g.][]{Nenkova2008,Honig2010}. Aside from the uncertainty regarding the role of the NLR, this view ignores the fact that the AGN is embedded in its host galaxy, and the light from it is subject to further processing therein. The effects of this galaxy-scale dust processing of the AGN emission can be investigated by performing radiative transfer on hydrodynamical simulations of galaxies. The goal of this paper is to inform empirical IR AGN fraction estimates by comparing simulated and observed IR SEDs of a sample covering the redshift and luminosity regime most critical to the build-up of stars and black holes in the Universe. This paper is second in a series. Paper I \citep{Kirkpatrick2015} presents our sample of 343 24$\mu$m-selected $z\sim$0.3-2.8 (U)LIRGs with exceptional coverage from the optical to the far-IR/mm including \emph{Spitzer}/IRS mid-IR spectra. That paper includes a state-of-the-art spectro-photometric analysis of the observed IR SEDs yielding empirical \tir{}. In this paper (Paper II), we test whether simulated galaxies can reproduce the observed SEDs of our sample, which covers a wide range in IR AGN fractions; compare the empirical and simulation-based \tir{}; and investigate how such IR AGN fractions constrain the intrinsic AGN contribution to the power output of dusty galaxies. In Paper III (Roebuck et al., in prep.), we will present a more detailed comparison between the simulated and observed SEDs, including a discussion of the merger stage/morphology, gas fractions, star formation rates, and stellar masses of the galaxies. The structure of the paper is as follows. In Section~\ref{sec:sample} we describe the observed data. In Section~\ref{sec:simdata} we summarize the methodology underlying the \textsc{gadget}+\textsc{sunrise} simulations and present the details of our specific simulation library. In Section~\ref{sec:analysis} we use our suite of simulations to explore the dependence of IR AGN fraction estimates on the intrinsic AGN fraction, and on parameters such as merger stage, level of obscuration, initial gas fraction and viewing perspective. We then present a direct comparison between empirical SED-fitting based AGN fractions to those implied by the best fitting simulated SED to the observed SED. We include estimates of the systematic uncertainties in the derived AGN fractions. In Section~\ref{sec:discussion}, we discuss the caveats associated both with the simulation-based and empirical AGN fractions. We present the summary and conclusions in Section~\ref{sec:conclusions}. In the appendix, we investigate the potential dependence of our results on the assumed AGN SED template and the sub-resolution structure of the ISM of the simulated galaxies. \begin{figure}[h] \centering \includegraphics[width=\columnwidth]{f1.pdf} \caption{The luminosity-redshift distribution of our {\rcom observed} sample. The redshifts are based on optical, near-IR or mid-IR spectra. The luminosities are based on the IR SED fitting \citep{Kirkpatrick2015}. The three classes shown (SFG, Composite and AGN) are based on mid-IR spectral fitting as described in the text.} \label{fig:lumz} \end{figure} | \label{sec:conclusions} This paper presents an analysis of the accuracy of and systematic uncertainties inherent in determining the AGN contribution to $L_{\rm{IR}}$ based on fitting IR SEDs as well as the relation between this IR AGN fraction and the bolometric AGN fraction. We used a suite of hydrodynamic simulations on which radiative transfer calculations were performed to yield simulated galaxy SEDs. These simulations were used to investigate the relations between the IR and bolometric AGN fractions and key properties such as merger stage and level of obscuration. The simulated SEDs were then directly fit to the observed IR photometry of a sample of 336 $z$\,$\sim$\,0.3\,--\,2.8, $\log (L_{\rm{IR}}) = 10.4$-$13.7$ galaxies spanning the full range in empirically derived AGN fractions \citep[see][for details]{Kirkpatrick2015}. Our conclusions are the following: \begin{itemize} \item An AGN fraction measured solely in the infrared (here \host{}) is a good predictor of the intrinsic AGN to stellar strength (here \inp{}) but only up to and including coalescence, or conversely while the extinction is high ($A_V \gtrsim 1$). We provide relations to convert empirical IR AGN fraction estimates to bolometric AGN fractions as a function of $A_V$. \item Our simulation library well represents our observed sample, as indicated both by the overall goodness of fit (Section~\ref{sec:fitting}) and the examples presented in Figure~\ref{fig:sedmos}. A more extensive discussion will be presented in Paper III (Roebuck et al. in prep.) \item We provide the first estimate of the systematic uncertainties in deriving the AGN fractions of galaxies. {\rcom We estimate that these uncertainties are significant with typical 1\,$\sigma$ uncertainties of $\sigma_{f{\rm (AGN)_{IR}}} \sim $\,0.4 }. \item Within the above uncertainties, there is agreement between our empirically derived and simulation-based IR AGN fractions (i.e. \host{}). Specifically, both the per-class median \host{} values, and the formal fit between individual \host{} and \iremp{} values support our previous classification: i.e. empirically classified SFG have the least AGN contribution to their total power output; empirically classified AGN have the most. \item However, in detail there are key differences. For Composite sources, we find a significant shift in that their median empirical IR AGN fraction is $\sim$15\,\%, but we infer $>$\,50\,\% from our simulations. This suggests heavily obscured AGN whose strength is underestimated in empirical methods relying on the observed mid-IR spectra. {\rcom In addition, 6\% of our empirically classified SFGs have AGN fractions $>$ 50\%. Both imply the true number density of luminous AGN may be potentially underestimated.} Given the large systematic uncertainties on our estimates, this result requires independent confirmation. \item Our empirical AGN fraction estimates rely on an AGN template that is heavy in warm dust emitting at 20-40\um. More common `torus-only' AGN templates that have less emission in this regime, will lead to AGN fraction estimates that are 2$\times$ lower and therefore will lead to much greater disagreement with our simulated AGN fractions. \end{itemize} | 16 | 9 | 1609.08660 |
1609 | 1609.04352_arXiv.txt | We investigate segregation phenomena in galaxy groups in the range of $0.2<z<1$. We study a sample of groups selected from the 4th Data Release of the DEEP2 galaxy redshift survey. We used only groups with at least 8 members within a radius of 4$\;$Mpc. Outliers were removed with the shifting gapper techinque and, then, the virial properties were estimated for each group. The sample was divided into two stacked systems: low($z\leq 0.6$) and high ($z>0.6$) redshift groups. Assuming that the color index ${\rm (U-B)_0}$ can be used as a proxy for the galaxy type, we found that the fraction of blue (star-forming) objects is higher in the high-{\it z} sample, with blue objects being dominant at $M_{B} > -19.5$ for both samples, and red objects being dominant at $M_{B} < -19.5$ only for the low-{\it z} sample. Also, the radial variation of the red fraction indicates that there are more red objects with $R < R_{200}$ in the low-{\it z} sample than in the high-{\it z} sample. Our analysis indicates statistical evidence of kinematic segregation, at the 99\% c.l., for the low-{\it z} sample: redder and brighter galaxies present lower velocity dispersions than bluer and fainter ones. We also find a weaker evidence for spatial segregation between red and blue objects, at the 70\% c.l. The analysis of the high-{\it z} sample reveals a different result: red and blue galaxies have velocity dispersion distributions not statistically distinct, although redder objects are more concentrated than the bluer ones at the 95\% c.l. From the comparison of blue/red and bright/faint fractions, and considering the approximate lookback timescale between the two samples ($\sim$3 Gyr), our results are consistent with a scenario where bright red galaxies had time to reach energy equipartition, while faint blue/red galaxies in the outskirts infall to the inner parts of the groups, thus reducing spatial segregation from $z\sim 0.8$ to $z\sim 0.4$. | A central issue concerning galaxy formation and evolution refers to environmental factors. It is well-established that the average properties of galaxies such as their mass, colours, morphologies, and gas content depend upon the environment where they reside. Galaxies in clusters tend to be more massive and have lower star formation rates (SFRs) than isolated field galaxies which are, in general, actively star forming \citep{dr1,o1,bl,co,co1,ka,Ta, l2, l3, r2}. It is also well-known that galaxy properties depend strongly on galaxy mass \citep[e.g.][]{Pog}, and that galaxy mass and environment are correlated, since denser environments tend to be inhabited by more massive galaxies \citep[e.g.][]{HO,BG}. Several physical processes are thought to be relevant in regulating star formation in dense environments by driving cold gas away from galaxies and by heating it up. Some of these mechanisms are more effective in dense regions like rich clusters, whereas in groups of galaxies other mechanisms play the most important role. For example, galaxy interactions as mergers and harassment are favoured in group environment because of the low relative velocities between galaxies \citep{z1}, while in high density environments galaxies can be strongly affected by mechanisms such as ram pressure stripping and strangulation due to the high temperature and pressure of the intra-cluster medium \citep[e.g.][]{vdb,Pre}. Coupled with these processes, massive galaxies tend to reduce their velocities through the energy equipartition by dynamical friction with less massive galaxies \citep{ch,Cape}. A possible consequence of these environmental factors are the so-called segregation effects, that is, correlations between galaxy properties and/or radial trends of those properties as a function of the group/cluster centre. The presence of the segregation effect in galaxy clusters and groups has been studied by several authors. \citet{b2} studying luminosity and morphological segregation in an ensemble of 59 rich nearby clusters, observed in the ESO Nearby Cluster Survey, found that luminosity segregation is evident only for elliptical galaxies brighter than $M_R$ = -22.0$\pm$0.1, and not located in substructures. \citet{gi2} analysed morphology and luminosity segregation of galaxies in loose groups identified in the Nearby Optical Galaxy catalogue. They concluded that spatial segregation is stronger than kinematical segregation and that luminosity is independent of morphological segregation. They argued that segregation phenomena are mainly connected with the initial conditions at the time of galaxy formation and that the mechanisms which influence galaxy luminosity and morphology should act in a similar way in groups and in clusters. \citet{la} examined a sample selected from the 2dF Galaxy Redshift Survey to analyse the segregation effect in galaxy groups. They found that passively star forming galaxies show a statistically narrower velocity distribution than that of galaxies with a substantial star forming activity. They also found that the sample of red galaxies, with colour index B$-$R $>$ 1, have a larger fraction of small velocities ($v/\sigma<$1) compared with the blue galaxies. \citet{go1} selected a sample of 335 clusters from the Sloan Digital Sky Survey (SDSS) and found that bright cluster galaxies ($M_z < -23$) have significantly smaller velocity dispersion than fainter galaxies. They also pointed out that the results remain the same when the sample is splitted in star forming late type and passive late type galaxies, with the former having a larger velocity dispersion in comparison with the last. \citet{r1}, using a sample of 57 groups selected from the 2df Percolation-Inferred Galaxy Group catalogue, found that galaxies brighter than $M_R$ = -21.5 show a decrease in normalized velocity dispersion, $\sigma_u$, while for the fainter ones the velocity dispersion is approximately constant. Interestingly, the result remains for groups considered dynamically non-evolved, but with a steeper correlation between $\sigma_u$ and $M_R$. \citet{vdb}, using the SDSS group catalogue of \citet{yan}, suggest that satellite galaxies become redder and more concentrated than central galaxies once they fall into a bigger halo. However, they do not find indication that the magnitude of the transformation depends on environment. Also using SDSS clusters, \citet{Von} find no evidence for mass segregation in four redshift bins at $z< 0.1$. A similar result is found by \citet{Vulc} using mass-limited samples at $0.3 \leq z \leq 0.8$ from the IMACS Cluster Building Survey and the ESO Distant Cluster Survey. Recently, \citet{Rob} show that failure to find mass segregation is due to a mass completeness cut at intermediate to high stellar mass, or to take only high-mass haloes. \citet{Rob} also show that mass segregation is enhanced with the inclusion of low-mass galaxies, and decreases with increasing halo mass. Currently, few studies are available regarding segregation phenomena at intermediate and high redshifts. For instance, \citet{Pre} find evidence for mass segregation in zCOSMOS groups at both $0.2 \leq z \leq 0.45$ and $0.45 < z \leq 0.8$. By splitting up their sample into poor and rich groups at $0.2 \leq z \leq 0.45$, they find evidence for mass segregation in rich groups but not in poor groups. Also, \citet{Bal} find evidence for mass segregation in the Group Environment Evolution Collaboration 2 (GEEC2) for groups at $0.8 < z < 1$, using a stellar mass-limited sample with $M_{star}>10^{10.3}~{\rm M}_\odot$. In a recent paper, \citet{Bst} find evidence for velocity segregation in a collection of 41 galaxy clusters at $0.4 \leq z \leq 1.5$. In the present work, we probe velocity and spatial segregation in low-mass galaxy groups, that is, the possibility of more luminous and redder galaxies being more central and move more slowly than fainter and bluer ones. Our aim is to compare these segregation phenomena for well selected samples defined in two redshift intervals, at $z\sim 0.4$ and $z\sim 0.8$. The paper is organized as follows: in Section 2 we present a description of the data used, i.e, the DEEP2 survey and group catalogue, and the method used to define the group virial properties; in Section 3 we present the main results of velocity segregation in luminosity and morphological type; in Section 4 we discuss some possible systematics; and finally in Section 5 we discuss our results. Throughout this work we assume a $\Lambda$CDM cosmology with the cosmological parameters $\Omega_M=0.3$, $\Omega_\Lambda=0.7$ and $h=0.7$. \section[]{data and methodology } \subsection{DEEP2 Sample} The DEEP2 Galaxy Redshift Survey \citep{n1} is considered the largest spectroscopic survey of homogeneously selected galaxies at $z \sim$ 1. The survey covers a total area of 2.8 deg$^2$ distributed across four fields observed up to limiting magnitude R$_{AB}$ = 24.1. Each field was chosen to lie in zones of low Galactic extinction based on the dust maps of \citet{s1}. The DEEP2 fields probe a volume of 5$\times$ 10$^6h^{-1}$Mpc$^3$ over the primary DEEP2 redshift range 0.75 $< z <$ 1.4. The photometric catalogue for DEEP2 is derived from Canada-France-Hawaii Telescope (CFHT) images taken with the 12k$\times$8k mosaic camera \citep{c1} in B, R and I bands. DEEP2 spectroscopic observations were carried out using the 1200-line diffraction grating on DEIMOS multi-object spectrograph \citep{f1} on Keck II telescope. The spectral resolution of R $\sim$ 6000 yielded a velocity accuracy of $\sim$ 30~km~s$^{-1}$. The typical exposure time is 1 hr per mask. The total number of spectra obtained is 52,989, and the total number of objects with secure redshift is 38,348 (DEEP2 redshift quality flag 3 or 4 which correspond to 95\% and 99\% confidence in the redshift identification, respectively). Objects are pre-selected in DEEP2 fields 2-4 using broad-band CFHT 12k BRI photometry to remove foreground galaxies below $z \sim$ 0.7. In the DEEP2 field 1 or Extended Groth Strip \citep[EGS,][]{d1}, however, there is no rejected low-{\it z} galaxies, both to test the selection methods and to take advantage of the wide multiwavelength coverage data in that field. K-corrections, absolute M$_{B}$ magnitudes, and rest-frame (U-B) colours have been derived as described in \citet{wi}. Absolute magnitudes presented in this paper are in the AB system and are $M_B$ - 5log {\it h} with $h = 0.7$. \begin{figure*} \includegraphics[width = 180mm]{groups.pdf} \caption{Phase-space diagrams of 3 massive galaxy groups shown as examples. The velocity and radial offset are with respect to the group centre. We apply a shifting gapper procedure for the selection of group members (filled black squares) and exclusion of interlopers (open circles).} \label{fig1} \end{figure*} \subsection{DEEP2 Group Catalogue and Virial Analysis} This section gives a brief description of the DEEP2 group sample and for more details the reader is referred to \citet{g1}. Groups were identified using the Voronoi-Delaunay Method \citep{m1}. The algorithm yielded 1165 groups with two or more members with accurate redshifts in the EGS over the range 0 $< z <$ 1.5 and 1295 groups at $z > $ 0.6 in the rest of DEEP2. In additional to the coordinates and central redshift, the group catalogue provides estimates of the total number of galaxies in the group and its velocity dispersion. However, we only consider the positional and redshift information, re-deriving the member list and group properties (velocity dispersion, radius and mass). \begin{figure*} \includegraphics[width = 130mm]{comp_mag1_new2a.pdf} \caption{Rest-frame colour-magnitude diagram for DEEP2 si\-mi\-lar to obtained by \citet{g2} but considering only galaxy groups with at least eight member galaxies. Each panel correspond to bins of width $\delta$z = 0.05. The red crosses and blue diamonds represent groups and field galaxies, respectively. The dashed lines show the selection cut as illustrated in equation \ref{eq1} while the dotted lines indicate the separation between red and blue galaxy population as given in equation \ref{eq2}.} \label{fig2} \end{figure*} To select group members and exclude interlopers we adopted the ``shifting gapper'' technique \citep{f96, a1, l1}, using all galaxies with redshift quality 3 or 4 of the DEEP2 Data Release 4 (DR4). Around each DEEP2 group we initially considered galaxies within a maximum radius of 4 Mpc and velocity offset $|cz - cz_{group}|$~$\le$~4000~km~s$^{-1}$, where c is the speed of light, {\it z} and $z_{group}$ are galaxy and group redshifts, respectively. This large maximum radius is important to probe the effect of secondary infall on to groups. The ``shifting gapper'' technique applies the gap technique \citep{k1, l07} in radial bins from the cluster centre. The advantage of this method is that it makes no assumption about the dynamical state of the group. For more details on the procedure we adopted see \citet{l1}. After removing interlopers, we kept the 221 groups with at least 8 member galaxies selected. Such low multiplicity allow us to explore galaxy groups in the low mass regime. Figure \ref{fig1} illustrates the procedure for three groups of our sample. In each panel, the filled black squares represent the group members and the open circles represent the rejected interlopers. Next, we estimate the line-of-sight velocity dispersion, $\sigma_p$, for all group members. Then, we obtain an estimate of the projected virial radius (R$_{PV}$) and a first estimate of the virial mass is derived from equation 5 of \citet{gi1}. A first estimate of R$_{200}$, and a Navarro, Frenk \& White (1997; NFW) profile are assumed when applying the surface pressure correction. After that we obtain a refined estimate of R$_{200}$ considering the virial mass density. We assume again a NFW profile to obtain estimates of M$_{500}$ and M$_{200}$, and then R$_{500}$, R$_{200}$. This procedure is analogous to \citet{bv} and \citet{l1}. The results of the virial analysis for the ten richest groups are listed, as an example, in Table \ref{tab1}. The columns represent: group name; coordinates (Right Ascension and Declination); mean redshift; velocity dispersion ($\sigma_p$); number of galaxies used to compute the velocity dispersion (N$_{\sigma}$); characteristic radii and masses (R$_{500}$, M$_{500}$, R$_{200}$, M$_{200}$). In general our groups represent low masses systems with estimates between 5 $\times 10^{12}M_\odot \leq M_{200} \leq$ 1.63 $\times 10^{14}M_\odot$. \begin{table*} \centering \begin{minipage}{140mm} \caption{Velocity dispersion, characteristic radii and masses of 10 of the 221 DEEP2 groups. The full table is available in eletronic form.} \label{tab1} \begin{tabular}{c c c c c c c c c c} \hline ID & RA & DEC & z & $\sigma_p$ & $N_{\sigma}$ & $R_{500}$ & $M_{500}$ & $R_{200}$ & $M_{200}$ \\ &(J2000) & (J2000) & & kms$^{-1}$ & & (Mpc) & ${\rm (10^{14})M_\odot}$ & (Mpc) & ${\rm (10^{14})M_\odot}$ \\ \hline\hline \vspace{0.1cm} 1 & 215.0325 & 53.1012 & 0.2009 & 300.87{\tiny$_{-19.26}^{+27.64}$} & 104 & 0.69{\tiny$_{-0.03}^{+0.04}$} & 1.16{\tiny$_{-0.15}^{+0.21}$} & 0.95{\tiny$_{-0.04}^{+0.06}$} & 1.18{\tiny$_{-0.15}^{+0.22}$}\\ \vspace{0.1cm} 2 & 215.3142 & 53.1008 & 0.2014 & 278.44{\tiny$_{-15.24}^{+22.52}$} & 100 & 0.66{\tiny$_{-0.02}^{+0.03}$} & 1.00{\tiny$_{-0.11}^{+0.16}$} & 0.90{\tiny$_{-0.03}^{+0.05}$} & 1.03{\tiny$_{-0.11}^{+0.17}$}\\ \vspace{0.1cm} 5 & 215.1649 & 53.1322 & 0.2010 & 237.76{\tiny$_{-17.01}^{+22.77}$} & 89 & 0.58{\tiny$_{-0.03}^{+0.04}$} & 0.69{\tiny$_{-0.10}^{+0.13}$} & 0.80{\tiny$_{-0.04}^{+0.05}$} & 0.70{\tiny$_{-0.10}^{+0.13}$}\\\vspace{0.1cm} 7 & 215.2346 & 53.1516 & 0.2017 & 204.24{\tiny$_{-16.25}^{+22.31}$} & 74 & 0.52{\tiny$_{-0.03}^{+0.04}$} & 0.50{\tiny$_{-0.09}^{+0.11}$} & 0.72{\tiny$_{-0.04}^{+0.05}$} & 0.51{\tiny$_{-0.08}^{+0.11}$}\\\vspace{0.1cm} 33 & 214.9645 & 53.0123 & 0.7444 & 292.30{\tiny$_{-20.57}^{+27.68}$} & 71 & 0.60{\tiny$_{-0.03}^{+0.04}$} & 1.44{\tiny$_{-0.20}^{+0.27}$} & 0.83{\tiny$_{-0.04}^{+0.05}$} & 1.47{\tiny$_{-0.21}^{+0.28}$}\\\vspace{0.1cm} 41 & 215.3367 & 53.0569 & 0.2008 & 222.21{\tiny$_{-15.87}^{+20.03}$} & 84 & 0.55{\tiny$_{-0.03}^{+0.03}$} & 0.59{\tiny$_{-0.08}^{+0.11}$} & 0.76{\tiny$_{-0.04}^{+0.04}$} & 0.60{\tiny$_{-0.09}^{+0.11}$}\\\vspace{0.1cm} 52 & 214.3444 & 52.5873 & 0.2367 & 258.41{\tiny$_{-21.36}^{+29.95}$} & 72 & 0.72{\tiny$_{-0.04}^{+0.05}$} & 1.36{\tiny$_{-0.23}^{+0.32}$} & 0.99{\tiny$_{-0.05}^{+0.08}$} & 1.40{\tiny$_{-0.23}^{+0.32}$}\\\vspace{0.1cm} 62 & 215.1013 & 53.0645 & 0.2000 & 292.23{\tiny$_{-20.33}^{+28.64}$} & 102 & 0.67{\tiny$_{-0.03}^{+0.04}$} & 1.06{\tiny$_{-0.15}^{+0.21}$} & 0.92{\tiny$_{-0.04}^{+0.06}$} & 1.09{\tiny$_{-0.15}^{+0.21}$}\\\vspace{0.1cm} 78 & 215.1344 & 53.0142 & 0.2025 & 267.70{\tiny$_{-18.94}^{+26.69}$} & 89 & 0.65{\tiny$_{-0.03}^{+0.04}$} & 0.96{\tiny$_{-0.14}^{+0.19}$} & 0.89{\tiny$_{-0.04}^{+0.06}$} & 0.99{\tiny$_{-0.14}^{+0.20}$}\\\vspace{0.1cm} 210 & 215.0737 & 52.9612 & 0.7452 & 236.67{\tiny$_{-17.75}^{+25.39}$} & 65 & 0.53{\tiny$_{-0.03}^{+0.04}$} & 1.00{\tiny$_{-0.15}^{+0.22}$} & 0.73{\tiny$_{-0.04}^{+0.05}$} & 1.02{\tiny$_{-0.15}^{+0.22}$}\\ \hline \end{tabular} \end{minipage} \end{table*} \subsection{Galaxy Sample selection} To define an uniform sample of galaxies in the DEEP2 redshift interval, we follow the procedure described in \citet{g2}. According to this work, in galaxy evolution studies it is possible to produce volume-limited catalogues with a colour-dependent, absolute magnitude cut by defining a region of rest-frame colour-magnitude space that is uniformly sampled by the survey at all redshifts of interest. Such a selection cut is illustrated in Fig. \ref{fig2} and is given by the equation $$ M_{cut} - 5\log h = Q(z - z_{lim})~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $$ \begin{equation} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + \min\{[a(U-B)~+~b], [c(U-B)~+~d]\}, ~~~~~~~ \label{eq1} \end{equation} \noindent where $z_{lim}$ is the limiting redshift beyond which the selected sample becomes incomplete; a, b, c and d are constants that depend on $z_{lim}$ and are determined by inspection of the colour-magnitude diagram; and Q is a constant that allows for linear redshift evolution of the characteristic galaxy absolute magnitude $M_B^*$. For the parameter Q, we adopt the \citet{f2} value of Q~=~-1.37, determined from a study of the B-band galaxy luminosity function in the COMBO-17 \citep{w1}. Adopting this approach and using $z_{lim}$ = 1 and consequently (a, b, c, d) = (-1.34, -18.55, -2.08, -17.77), we constructed a volume-limited sample for each color containing 835 galaxies in the range of $0.2 \le z \le 1$ and distributed over 105 galaxy groups. The result of the selection cut is illustrated in Fig. \ref{fig2} which shows rest-frame colour-magnitude diagrams for DEEP2 galaxies split into redshift bins of $\Delta z$ = 0.05. The red crosses and blue diamonds represent group galaxies and field galaxies, respectively. The dashed lines show the selection cut as illustrated in equation \ref{eq1} while the dotted lines indicate the separation between red and blue galaxy populations described mathematically by \begin{equation} (U-B)_0 = -0.032(M_B + 21.62) + 1.035 \label{eq2} \end{equation} \noindent This equation was derived from the \citet{v1} colour-magnitude relation for red galaxies in distant clusters and converted to the cosmological model used in this work. From now on all analyses will be made considering only galaxies whose absolute magnitude is below the completeness cut, i.e. M$_B \le M_{cut}$. It is noteworthy that, since the DEEP2 groups contain only a few members, the group properties such as velocity dispersion, characteristic radius and mass were obtained considering the full member galaxies defined after interloper removal. We choose to do this, to achieve the best statistical reliability in determining the group properties. \begin{figure} \includegraphics[width = 80mm]{bicol.pdf} \caption{Histograms of $(U-B)_0$ for low-redshift (violet) and high-redshift sample (green). The vertical dotted lines indicate the separation between blue and red objects. These limits are $(U-B)_0=1.0$ and $(U-B)_0=1.1$ for low and high redshift sample, respectively.} \label{fig3} \end{figure} | In this work, we searched for segregation phenomena in galaxy groups in the range of $0.2<z<1$, using a sample of groups selected from the 4th Data Release of the DEEP2 galaxy redshift survey. The sample was divided into two stacked systems: low($z\leq 0.6$) and high ($z>0.6$) redshift groups, with members being classified in red and blue objects. Assuming that the color ${\rm U-B}$ can be used as a useful proxy for the galaxy type, we found that the fraction of blue objects is higher in the high-{\it z} sample, with blue objects being dominant at $M_{B} > -19.5$ for both samples, and red objects being dominant at $M_{B} < -19.5$ only for the low-{\it z} sample. Also, the radial variation of the red fraction indicates that there are more red objects with $R < R_{200}$ in the low-{\it z} sample than in the high-{\it z} sample. Our analysis also indicates statistical evidence of kinematic segregation for the low-{\it z} sample: redder and brighter galaxies present lower mean velocity dispersions than bluer and fainter ones. Red and blue objects, however, present less separated mean groupcentric distance distributions, with the pairwise test indicating that the red population is more concentrade only at the 70\% c.l. Interestingly, the analysis of the high-{\it z} sample reveals an opposite result: while red and blue galaxies have velocity dispersion distributions not statistically distinct, redder objects are significantly more concentrated than the bluer ones at the 95\% c.l. From the mean difference in redshifts of the two samples, we estimate that the minimum timescale for the appearance of these inverted segregation effects is approximately 3.0$\pm$0.3 Gyr. The challenge, then, is envisioning how these results can emerge in the context of galaxy evolution. Our main result is presented in Fig.~\ref{fig4}. To understand the difference at the bright end observed in this figure we should consider that in the low-{\it z} sample the first bins are dominated by red objects, while blue galaxies dominate all the magnitude range in the high-{\it z} sample (see Fig.~\ref{fig5}). The red galaxies in the low-{\it z} sample show lower velocity dispersions (see Fig.~\ref{fig6}), in agreement with the works of e.g. \citet{a2}, \citet{go1} and \citet{AG} for different samples of low redshifts cluster galaxies ($z< 0.1$). This suggests that brighter and redder objects are former inhabitants of the system, having experienced more environmental effects along time, and that have achieved the energy-equipartition status through dynamical interactions on a timescale of $\sim$3 Gyr since $z\sim 0.8$. The lower fraction of red/bright/low velocity objects in the high-{\it z} sample explains the difference observed at the bright end in Fig.~\ref{fig4}. Still looking at this figure, we see a velocity upturn only observed in the last bins of the low-{\it z} sample. This effect may indicate a fraction of faint blue galaxies which entered into $2R/R_{200}$ before a significant quenching has happened. Their higher velocity offsets would have acquired as they approach the group core, falling into the gravitational potential \citep[e.g.][]{Fal,Jaf}. The absence of similar objects in the high-{\it z} sample suggests that infalling faint blue galaxies have not yet travelled a long journey across the group at $z\sim 0.8$. Other important result we reported in Section 3.3 is the reversing behaviour of red and blue galaxies with respect to velocity and groupcentric distances segregation, with redshift. Regarding velocity segregation, the preceding paragraph provides a qualitative scenario. Now, to explain the spatial segregation, we shoud notice that our analyses in Sections 3.2 and 3.3 take account galaxies within $2R/R_{200}$. One can reasonably assume that such objects at lower redshifts correspond to a mixture of descendants of galaxies at higher redshifts in the same radii and of infalling objects from outer radii. Thus, both survival and replenishment of galaxies should be expected over the time, and two important factors come into play: (i) the accretion rate of galaxies; and (ii) the orbital dependence of galaxy properties \citep[e.g.][]{Bi4,ID}. Indeed, regarding velocity segregation, it has also been interpreted as red and blue galaxies having different kinds of orbits, with the orbits of blue galaxies being more anisotropic than the red ones \citep[e.g.][]{Bi4}. Recently, \citet{Bi5} verified that the anisotropy profile of $z\sim 1$ clusters is nearly isotropic near the cluster center, and increasingly elongated with radius. This result is consistent with a halo evolution through an initial phase of fast collapse and a subsequent slow phase of inside-out growth by accrection of field material \citep[e.g.][]{Lapi}. Since the accretion rate of galaxies from the field is higher at higher redshifts \citep[e.g.][]{Mc09}, our sample at $z\sim 0.8$ is expected to be more affected by recent infalls, which had less time to go deeper into the group potential. This could explain the development of a more marked difference between the mean groupcentric distance of red and blue galaxies (see Fig.~\ref{fig12}). After $\sim$3 Gyr, part of these infalling galaxies may reach the $R < 2R_{200}$ region, at $z\sim 0.4$, mixing with virialized and backsplash objects, and thus presenting a less pronounced radial segregation between red and blue galaxies. | 16 | 9 | 1609.04352 |
1609 | 1609.03572_arXiv.txt | Although there has been much progress in understanding how galaxies evolve, we still do not understand how and when they stop forming stars and become quiescent. We address this by applying our galaxy spectral energy distribution models, which incorporate physically motivated star formation histories (SFHs) from cosmological simulations, to a sample of quiescent galaxies at $0.2<z<2.1$. A total of 845 quiescent galaxies with multi-band photometry spanning rest-frame ultraviolet through near-infrared wavelengths are selected from the CANDELS dataset. We compute median SFHs of these galaxies in bins of stellar mass and redshift. At all redshifts and stellar masses, the median SFHs rise, reach a peak, and then decline to reach quiescence. At high redshift, we find that the rise and decline are fast, as expected because the Universe is young. At low redshift, the duration of these phases depends strongly on stellar mass. Low-mass galaxies ($\log(M_{\ast}/M_{\odot})\sim9.5$) grow on average slowly, take a long time to reach their peak of star formation ($\gtrsim 4$ Gyr), and the declining phase is fast ($\lesssim 2$ Gyr). Conversely, high-mass galaxies ($\log(M_{\ast}/M_{\odot})\sim11$) grow on average fast ($\lesssim 2$ Gyr), and, after reaching their peak, decrease the star formation slowly ($\gtrsim 3$ Gyr). These findings are consistent with galaxy stellar mass being a driving factor in determining how evolved galaxies are, with high-mass galaxies being the most evolved at any time (i.e., downsizing). The different durations we observe in the declining phases also suggest that low- and high-mass galaxies experience different quenching mechanisms that operate on different timescales. | \label{sec:intro} Over the past decade, multi-wavelength observational surveys and cosmological simulations of galaxies have greatly improved our understanding of the formation and evolution of galaxies. Observations of colors, morphology, spectral type, and star formation of galaxies show a clear bimodality in the population, where \textit{blue} star-forming galaxies are separated from \textit{red} quiescent galaxies. One key unknown is how and when galaxies stop forming stars and become ``red and dead''. The classical picture for red, early-type galaxies is that they form in a single-burst very early in the Universe (\citealt{baade1963}). This theory was successfully challenged. By looking at spectral indices of galaxies, \citet{worthey1992}, \citet{faber1995}, and \citet{trager2000} found that early-type galaxies span a large range of ages and thus showed that blue galaxies can become red via different mechanisms occurring at different times and masses. Since then, other parameters have been studied to explain the variety of histories observed. \citet{graves2009a} (see also \citealt{graves2009b,graves2010a,graves2010b}) explored the ages and metallicities of red galaxies and found correlations with not only stellar mass, but also radius, velocity dispersion, and surface brightness. Furthermore, \citet{cheung2012}, \citet{fang2013}, and \citet{barro2015} observed that the path to quiescence is strongly correlated with central surface density. How and when star-forming galaxies move to the red sequence is however still a matter of debate. A combination of different physical processes can explain the evolution of luminosity functions and color-magnitude diagrams (\citealt{willmer2006}, \citealt{bell2006}, \citealt{faber2007}, \citealt{skelton2012}). Passive evolution of the $z\sim 1$ quiescent population has been disfavored to explain the age-mass and metallicity-mass relations of local galaxies by \citet{harker2006}, \citet{schiavon2006}, \citet{ruhland2009}, and \citet{gallazzi2014}. However, \citet{choi2014} and \citet{shetty2015} find negligible evolution in the metal content of massive galaxies at $0.1<z<0.7$ and ages consistent with passive evolution (see also \citealt{mendel2015}). Hydrodynamical simulations and semi-analytic models of galaxy formation and evolution are a powerful tool (see \citealt{somerville2015} for a review). In these models, galaxies are fed by cold flows of gas, stars, and dark matter which generate episodes of star formation (\citealt{keres2005}, \citealt{dekel2006}). When galaxies (or their dark matter haloes) reach a certain critical mass, a virial shock is created, slowing down the cooling rate and the galaxy star formation rate decreases. This is commonly referred to as ``mass quenching'' (\citealt{birnboim2007}) because the mechanism responsible for the decrease in star formation happens at a certain critical mass. Other physical processes invoked to quench galaxies are feedback events (e.g., AGN and stellar feedback; \citealt{croton2006}, \citealt{somerville2008}, \citealt{hopkins2014}), environmental effects (e.g., \citealt{peng2010}, \citealt{woo2013}), and morphological transformations (e.g., \citealt{gavazzi2015}, \citealt{zolotov2015}, \citealt{tacchella2016}). By connecting observations of galaxies with predictions from simulations, we can attempt to understand the mechanisms that lead galaxies to quiescence. For example, \citet{porter2014} managed to reproduce the observed correlations between the stellar population parameters, age and metallicity, and the structural parameters, size and velocity dispersion, of early-type galaxies using a semi-analytic model based on the Bolshoi cosmological simulation. Other methods to compare simulations and observations are based on identifying the progenitors of galaxies and infer the processes involved in the transformation from one population to the other (\citealt{vandokkum2013}, \citealt{patel2013}, \citealt{papovich2015}). The strength of this technique is the ability to assess the evolution of galaxies in a model independent way. \citet{torrey2015} and \citet{terrazas2016} show, however, that the large variety of stellar and dark matter assembly histories in cosmological simulations cannot be captured by constant number density analyses. Another method is to infer galaxy star formation histories from the fossil record of their past stellar populations (e.g., \citealt{panter2003}, \citealt{thomas2005}, \citealt{panter2007}, \citealt{gonzalez2014}, \citealt{mcdermid2015}, \citealt{citro2016}, \citealt{fumagalli2016}), sampling wide ranges of stellar masses and redshifts. For example, \cite{mcdermid2015} and \cite{citro2016} measure the SFHs of massive early-type galaxies and find that these systems are very old, forming the bulk of their mass in the first 1--2 Gyr. For our work, we choose this strategy, and we therefore need a large dataset that samples the variety of galaxies in the Universe and accurate models of their spectral energy distributions. We already used a similar approach in \citet{pacifici2016} where we assessed the SFHs of local ($z\sim0.07$) galaxies. The Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS; \citealt{grogin2011}, \citealt{koekemoer2011}) provides us with deep photometric data from the \textit{Hubble Space Telescope} (\textit{HST}) optical and near-infrared cameras (ACS and WFC3). These photometric data are carefully matched with ground-based observations from the $U$ to the $K$ band and with \textit{Spitzer}/IRAC photometry up to 8$\mu m$. Such a catalog is the optimal dataset to sample a large range in galaxy properties with sufficient statistics. To interpret large, multi-wavelength datasets like CANDELS, we have developed a comprehensive spectral energy distribution (SED) fitting tool (\citealt{pacifici2012}) that relies on physically motivated models of galaxy formation and evolution. Instead of relying on simple parametric forms for galaxy star formation histories (SFHs) and assuming galaxies do not evolve in metallicity, as is generally done, our model is based on a combination of star-formation and chemical enrichment histories from hierarchical simulations of galaxy formation. Even though our model SEDs are based on such histories, our results are not biased by the particular model adopted. Such SFHs provide a large variety of possible galaxy evolutionary paths and thus the parameter space sampled by the models is much larger than traditional approaches. This is particularly evident when comparing model and observed colors of galaxies (\citealt{pacifici2015}). Furthermore, the assumption of an evolving metallicity is crucial to overcome the degeneracy between age and metallicity when interpreting the colors of galaxies. In addition to adopting complex SFHs, our models incorporate nebular emission and state-of-the-art models of the spectral evolution of stars, gas, and dust, spanning a very wide range in the space of star formation rates (SFRs), metallicities, and dust and gas properties. They thus have the power to constrain the SFHs of different populations of galaxies at different redshifts. For example, assuming simple functional forms for the SFHs where the metallicity is fixed and the SFR can only decline with time does not allow one to sample properly the colors of all galaxies, especially the youngest ones, and thus correctly interpret their SEDs. Key to distinguishing quiescent galaxies from dusty, star-forming ones is the treatment of dust attenuation in SED models. It has been shown that the attenuation by dust is more complex than the single attenuation law that is typically assumed (see for example \citealt{witt2000}, \citealt{chevallard2013}, and \citealt{salmon2015} for studies on different dust attenuation curves). Thus, building on the work by \citet{chevallard2013}, in our SED modeling, we implement a two-component dust model that spans a variety of attenuation laws. Combining the CANDELS dataset and our new approach, we focus on red, quiescent galaxies and measure average SFHs as a function of stellar mass and redshift. We can thus answer questions such as: What are the average shapes of the SFHs of quiescent galaxies? Do these shapes change with redshift and stellar mass? Does the formation time of quiescent galaxies vary with stellar mass? At what time and at what stellar mass do galaxies stop forming stars? With these questions answered, we can then place important constraints on the main mechanisms involved in the formation and evolution of quiescent galaxies. This paper is organised as follows. In Section~\ref{sec:data} we present the details of the observational dataset. The SED modelling approach, fitting procedure, and selection of quiescent galaxies are described in Section~\ref{sec:model}. In Section~\ref{sec:assembling} we show how we create median SFHs of galaxy populations as a function of stellar mass and redshift. In Section~\ref{sec:results}, we show that stellar mass and redshift regulate the quenching of star formation. In Section~\ref{sec:discussion}, we place the constraints on the mechanisms involved in the evolution of quiescent galaxies. We summarize our results in Section~\ref{sec:concl}. Throughout the Paper, we adopt a Chabrier initial mass function (IMF, \citealt{chabrier2003}) and a standard $\Lambda$CDM cosmology with $\Omega_{\mathrm{M}}=0.3$, $\Omega_{\Lambda}=0.7$, $h=0.7$. Magnitudes are given in the AB system. | \label{sec:concl} Although there has been much progress in understanding how galaxies evolve to the present day, we still do not understand how and when galaxies stop forming stars and become quiescent. Using the CANDELS dataset, we measure the SFHs of 845 quiescent galaxies at $0.2<z<2.1$. Our galaxy SED models allow us to extract full SFHs of galaxies from the fossil record embedded in their photometric measurements. Specifically, our model library of SEDs adopts complex SFHs and metal enrichment histories from the semi-analytic post-processing of a large cosmological simulation. These histories are consistent with the observed evolution in the mass-metallicity relation. Moreover, adoption of such histories acts as an important prior, limiting the effects of degeneracies in age and metallicity. Using the individual SFHs we measure from the observations, we compute median SFHs of quiescent galaxies in bins of stellar mass and redshift. They are quasi bell-shaped: SFR rises, reaches a peak, and then declines towards quiescence. We find that on average galaxies take as much time as they can to quench. At high redshift, when the Universe is young, the median SFHs can only be narrow and the quenching phase fast. Given that the dynamical time of galaxies evolve with redshift, timescales of about 1 Gyr at $z\sim2$ are consistent with an evolving halo quenching mass and do not necessarily require catastrophic events such as strong feedback and violent environmental effects. Low-redshift, low-mass galaxies, on average, reach their peak of star formation later in their lifetimes compared with high-mass galaxies. This is downsizing. Given this and the fact that we are selecting quiescent galaxies, low-mass galaxies, on average, shut off their star formation fast. A catastrophic event (such as strong feedback) might be required to reproduce a fast declining phase at low redshift. Such low-mass galaxies might also be satellites in big halos subject to gas stripping. Low-redshift, high-mass galaxies show on average long declining phases. Galaxies could reach a critical mass which prevents new cold gas to inflow. Such long declining phases would then be explained by slow consumption of residual gas after the inflow of new gas stops. The residual gas is consumed slowly and the star formation decreases gradually. This is consistent with the turn over of the star-formation main sequence at the high-mass end, as observed in previous works. In this work, we have uncovered the dependences of the SFHs on stellar mass and redshift. We will explore the characteristics of individual SFHs in relation to environment and morphology, in a future work. The possible correlations between SFH shape and environment is of particular interest, although larger fields would be required. Also, we will examine the constraints on the SFHs of both star-forming and quiescent galaxies. By studying the entire population, we will be able to derive the probability that a galaxy shuts off its star formation and moves to the quiescent population as a function of stellar mass and redshift. The comparison of our constraints with detailed simulations of galaxy formation and evolution will be crucial to find the realistic scenarios that best resembles the observations, and thus quantify the importance of the different evolutionary mechanisms. | 16 | 9 | 1609.03572 |
1609 | 1609.09499_arXiv.txt | We present results from the ``Ponos'' simulation suite on the early evolution of a massive, $M_{\rm vir}(z=0)=1.2\times 10^{13}$~M$_{\sun}$ galaxy. At $z\gtrsim6$, before feedback from a central supermassive black hole becomes dominant, the main galaxy has a stellar mass $\sim 2\times 10^{9}$~M$_{\sun}$ and a star formation rate $\sim 20$~M$_{\sun}$~yr$^{-1}$. The galaxy sits near the expected main sequence of star-forming galaxies at those redshifts, and resembles moderately star-forming systems observed at $z>5$. The high specific star formation rate results in vigorous heating and stirring of the gas by supernovae feedback, and the galaxy develops a thick and turbulent disc, with gas velocity dispersion $\sim 40$~km~s$^{-1}$, rotation to dispersion ratio $\sim 2$, and with a significant amount of gas at $\sim 10^5$~K. The Toomre parameter always exceeds the critical value for gravito-turbulence, $Q\sim 1.5-2$, mainly due to the contribution of warm/hot gas inside the disc. Without feedback, a nearly gravito-turbulent regime establishes with similar gas velocity dispersion and lower $Q$. We propose that the ``hot and turbulent'' disc regime seen in our simulations, unlike the ``cold and turbulent'' gravito-turbulent regime of massive clumpy disc galaxies at $z\sim 1-2$, is a fundamental characterisation of main sequence galaxies at $z\gtrsim 6$, as they can sustain star formation rates comparable to those of low-mass starbursts at $z=0$. This results in no sustained coherent gas inflows through the disc, and in fluctuating and anisotropic mass transport, possibly postponing the assembly of the bulge and causing the initial feeding of the central black hole to be highly intermittent. | Since the early 90's, the growing number of galaxy surveys exploring different wavelengths and cosmological volumes have provided an immense body of data to reconstruct the formation and evolution of galaxies (e.g. \citealt{york+00,steidel+03,lefevre+05,lilly+07,walter+08,baldry+10,grogin+11,koekemoer+11,kochanek+12}). At the same time, the $\Lambda$CDM cosmological paradigm of structure formation has produced detailed predictions on the statistical matter distribution in the Universe (e.g. \citealt{percival+01,springel+05,reed+07,viel+09,percival+10,reid+10,klypin+11}), but the theory of galaxy formation within this framework is still developing, through analytical work (e.g. \citealt{white+78,blumenthal+84,mo+98}) and semi-analytic models (e.g. \citealt{kauffmann+93, cole+94,somerville+99,springel+05,bower+06,croton+06,guo+11,henriques+13}), as well as cosmological numerical simulations (e.g. \citealt{diemand+08,crain+09,schaye+10,agertz+11,guedes+11,dubois+14,hopkins+14,vogelsberger+14,schaye+15}; and references therein). Most of the theoretical successes have been achieved at low to moderate redshifts ($z\sim 0 - 1.5$), where the majority and the highest quality data are available. The latter have been fundamental to gauge the characteristics and the parameters of phenomenological, sub-resolution recipes introduced in numerical simulations (as well as in semi-analytic models) in order to model physical processes on scales that are currently inaccessible directly, such as gas radiative cooling, gas chemistry evolution, star formation, stellar feedback, black hole accretion and feedback (e.g. \citealt{stinson+06,dallavecchia+08,gnedin+09,wiersma+09,vogelsberger+13,keller+14}). Large-box cosmological simulations, despite suffering from relatively low resolution, have been able to statistically reproduce the main properties of different galaxy populations, from small, star-forming irregular galaxies to massive quiescent ellipticals \citep{vogelsberger+14,schaye+15}. On the other hand, high-resolution zoom-in simulations focussing on the formation and growth of a limited number of systems have also satisfactory modelled the formation and growth of dwarf galaxies \citep[e.g.][]{governato+10}, Milky-Way-like hosts \citep[e.g.][]{agertz+11,guedes+11}, as well as massive ellipticals at the centre of galaxy groups \citep[e.g.][]{feldmann+10,feldmann+15,fiacconi+15}. At higher redshifts $z \sim 2$, recent observational campaigns have boosted the interest in the population of massive star forming galaxies that show peculiar properties when compared to local counterparts of similar size. Such systems are often characterised by massive discs with baryonic mass $\sim 10^{11}$~M$_{\sun}$ and star formation rates as high as $\sim 100$~M$_{\odot}$~yr$^{-1}$, with a turbulent interstellar medium that accounts for $\gtrsim 30 \%$ of the baryonic mass (e.g. \citealt{genzel+06,foster-schreiber+09,daddi+10,tacconi+10,wisnioski+15}). The new observations have triggered lively discussions in the theoretical community, also requiring the development of new theoretical ideas to explain the observations and to make new predictions (e.g. violent disc instability; \citealt{mandelker+14,inoue+16}). Pushing it forward, the very high redshifts ($z \gtrsim 4$) still remain a partially unexplored territory, clearly because of the larger technical difficulties involved in new, cutting-edge observations. Nonetheless, galaxies at $z > 4$ have been detected in a few different ways. Optical and near infra-red observations have targeted star-forming galaxies by identifying them through the flux dropout in adjacent bands around the Lyman break (e.g. \citealt{madau+96,steidel+99,bouwens+03,oesch+10}). Those have permitted to constrain the evolution of the cosmic star formation rate density as well as of the ultraviolet (UV) luminosity function of star forming galaxies out to $z \gtrsim 8-10$, showing that the latter has a steep low luminosity tail, when compared to local samples (e.g. \citealt{bouwens+07,bouwens+11,oesch+12,oesch+14,bouwens+15}). Moreover, other wavelengths have been effective in providing information about the early galaxy population. Sub-millimetre galaxies are an example of massive (stellar mass $\sim 10^{11}$~M$_{\sun}$), highly star-forming (star formation rates $\gtrsim 500$~M$_{\sun}$~yr$^{-1}$), dusty galaxies that have been detected mostly at $z > 2.5-3$ (e.g. \citealt{chapman+05,younger+09,casey+14}). While those studies have been important to understand the global properties of the first galaxies in the Universe, they have mostly revealed the luminous tail of the galaxy population and they are still not able to characterise their structure (but see \citealt{oesch+10b,debreuck+14}). Nonetheless, both available facilities, such as the Hubble Space Telescope (HST) or the Very Large Telescope (VLT), as well as new observatories that recently came online, such as the Atacama Large Millimeter Array (ALMA), are starting to discover smaller and possibly more typical galaxies at $z \geq 6$. For example, \citet{bradley+12} have used HST imaging to identify a few Lyman break galaxy candidates at $z \approx 7$, lensed by the foreground galaxy cluster A1703. The most luminous likely has a stellar mass $\sim 10^{9}$~M$_{\sun}$ and a star formation rate $\sim 8$~M$_{\sun}$~yr$^{-1}$. Similarly, \citet{watson+15} have combined HST, VLT, and ALMA observations to constrain the stellar mass, star formation and gas content of another highly magnified Lyman break galaxy beyond the Bullet cluster. They also find a stellar mass $\sim 2 \times 10^{9}$~M$_{\sun}$, a star formation rate $\sim 10$~M$_{\sun}$~yr$^{-1}$, and a gas fraction $\sim 40-50\%$, all confined within a physical surface $\sim 1.5$~kpc$^2$. All these objects typically have specific star formation rates $\sim5$-10~Gyr$^{-1}$ (see also e.g. \citealt{tasca+15}). These recent observations, combined with those from the next generation of both space-based (James Webb Space Telescope; JWST) and earth-based (e.g. European Extremely Large Telescope; E-ELT) telescopes, require new interpretations and predictions on the theoretical side, where less has been done compared to low/medium redshifts, except regarding the most massive population of galaxies at $z > 6-8$ (e.g. \citealt{choi+12,oshea+15,paardekooper+15,ocvirk+16,waters+16}). Motivated by this, we investigate the early phases of the formation and the evolution of a galaxy that becomes a massive elliptical at $z=0$. We focus on the first burst of star formation, prior to the assembly of the central supermassive black hole and before active galactic nuclei (AGN) feedback becomes dominant. We use a new high-resolution hydrodynamic run that is part of the recent Ponos program of zoom-in cosmological simulations of massive galaxies \citep{fiacconi+16}. Our new simulation reproduces the main features of recently observed star forming galaxies at $z \sim 7$, and allows us to study in details the properties of the early interstellar medium that drive the star formation and may determine the early feeding habits of the central black hole. The paper is organised as follows. In Section \ref{sec_2}, we describe our numerical techniques and the features of the PonosHydro simulation. We describe our main results in Section \ref{sec_3}, focussing on the properties of the interstellar medium and the early star formation history of the simulated system at $z\sim 6$. We present our conclusions in Section \ref{sec_4}, cautioning the reader about the limitations of our results and discussing the possible implications of our findings. In the following, when not explicitly specified, all lengths and densities are given in physical units. | \label{sec_4} In this paper we present the results from PonosHydro, a high-resolution, zoom-in cosmological simulation meant to model the early evolution of a present-day massive galaxy down to $z \sim 6$, whose global properties appear to be consistent with the available data for galaxies of similar stellar masses at those redshifts \citep{iye+06,bradley+12,watson+15}. Specifically, we study the assembly of the galaxy during its first starburst phase, before the supermassive black hole can exert significant feedback and quench star formation. We focus on the properties of the interstellar medium and the transport of mass across the galactic disc and study the conditions that determine the early evolution of the central regions of present day massive galaxies. \begin{figure} \begin{center} \includegraphics[width=\columnwidth]{./PHASE_DIAGRAM.pdf} \caption{Comparison of the phase diagram of run PH at $z=7.1$ (upper panel) and ErisMC at $z=3$ (lower panel). The colour bar shows the logarithm of the mass fraction per bin in the density-temperature plane. The red dotted line in the upper panel marks the density and star formation thresholds adopted in run PH. } \label{fig_phase_diagram} \end{center} \end{figure} Before we discuss the potential implications of our findings, we briefly comment on the possible shortcomings of our calculations. Our results may be subject to the feedback model that we have used and this could in principle quantitatively affect our conclusions, at least to some extent. Various feedback schemes differently change the temperature of the gas locally after supernovae explosions. The delayed-cooling blast wave feedback produces gas at $\sim 10^5$~K and at densities $\sim 10-100$~H~cm$^{-3}$ by injecting energy in the surrounding of the star-forming regions and preventing them from cooling. Before this gas expands adiabatically and gets blown away, it significantly contributes to the global stability of the galaxy against the onset of gravito-turbulence and fragmentation. While the contribution of this phase might be artificially enhanced by the feedback scheme, we argue that the physical conditions of run PH (in particular, the high specific star formation rate and the relatively small mass) are more prone to form a warm and dense gas phase than in local disc galaxies. Figure \ref{fig_phase_diagram} shows the density-temperature diagram of the gas within 3 and 10 physical kpc around the main galaxy in run PH at $z=7.1$ and ErisMC\footnote{ErisMC is a simulation of a Milky Way-like galaxy that adopts a sub-grid model very similar to ours and therefore it allows to compare the thermodynamics of the gas in different physical conditions, though with the same feedback scheme. For further details about ErisMC, see \citet{shen+12}. Unfortunately, a snapshot at redshift lower than 3, which might have strengthened our considerations providing a more quiescent galaxy, is not available.} at $z=3$, respectively. Despite that both simulations show some amount of gas around $10-100$~H~cm$^{-3}$ and $\sim 10^5$~K, this accounts for an order of magnitude less mass fraction in the more quiescent ErisMC, that has almost ten times smaller specific star formation rate \citep{shen+12}. Similar results have been obtained with different feedback models (see e.g. Fig. 11 of \citealt{hopkins+12b}, where the warm phase is more sub-dominant compared to the cold phase at $\sim 100$~H~cm$^{-3}$ in a Milky Way-like galaxy than in a high-$z$-like galaxy). Moreover, the latest generation of stronger feedback models, designed to capture well the run between stellar mass and halo mass across cosmic scales and epochs, tend to produce lower density, thicker discs by driving more powerful and hot ($T \gtrsim 10^7$~K) gas outflow \citep{hopkins+14,keller+14}. Such galactic discs would likely be less gravitationally unstable and yet turbulent in the gas component (e.g. \citealt{hopkins+12b,hopkins+12,mayer+16}). Therefore, we conclude that a different and stronger feedback model would likely lead to qualitatively similar conclusions, namely that the gaseous discs of typical star-forming $z \sim 6$ galaxies would be maintained turbulent and stable against gravitational fragmentation by feedback, albeit future tests with different feedback schemes could better assess potential differences. Two main processes have been often advocated in the literature to shape the global dynamics of the interstellar medium: gravitational instability and supernova feedback. In Section \ref{sec_3} we discussed the features of the gaseous disc of run PH in terms of star formation, outflows, turbulence, mass transport, and gravitational stability, arguing that feedback likely plays a dominant role in the early evolution of a typical $z \sim 6-7$ galaxy. This seams to be somewhat different from what is usually expected both at low ($z \sim 0$) and intermediate ($z \sim 2$) redshift. Recently, \citet{goldbaum+15,goldbaum+16} have thoroughly explored the relative role of gravity and stellar feedback with controlled simulations of present day Milky Way-like galaxies. Consistently with previous results (e.g. \citealt{agertz+09,bournaud+10,agertz+15}), they find that stellar feedback is important to locally regulate star formation and to create a multi-phase interstellar medium, but the galaxy nonetheless settles to a gravito-turbulent state with a Toomre parameter $Q \sim 1$ that mostly controls the velocity dispersion and the mass transport through the disc. Those results match the observations of nearby spiral galaxies with low star formation rates (e.g. \citealt{tamburro+09,bagetakos+11}). They are conceptually similar to what has been often argued for massive $\sim 10^{11}$~M$_{\sun}$, gas-rich galaxies at $z \approx 2$, i.e. star forming galaxies that have not been quenched yet and are likely the progenitors of the most massive quiescent galaxies at $z = 0$, undergoing so called violent disc instability, i.e. gravitational instability that leads to the formation of massive star-forming clumps (e.g. \citealt{dekel+09,ceverino+10,mandelker+14,inoue+16}; but see also \citealt{hopkins+12,tamburello+15}). In this respect, massive discs at $z \approx 2$ would be the most extreme manifestation of the ``cold and turbulent'' regime that eventually leads to gravitational instability and fragmentation in the gas, since they are already as massive as the most massive discs in the local Universe but proportionally more gas rich, perhaps because they appear near the peak of the cosmic star formation history \citep{madau+14}. Motivated by this analogy, \citet{goldbaum+16} have proposed that gravitational instability is the dominant process setting mass transport and fuelling star formation over cosmic time. However, our results suggest that this might not be the case for typical $z \sim 6-7$ galaxies with stellar and gas mass $\gtrsim 10^{9}$~M$_{\sun}$, where the disc dynamics and mass transport seems to be significantly influenced by stellar feedback. Indeed, even in the favourable conditions of massive gaseous discs at $z \approx 2$, a phase of violent disc instability with its associated gravito-turbulent can or cannot occur depending on how effective is the feedback model at heating the gas and generating mass-loaded outflows. Recent work has shown that modern strong feedback models tend to suppress gravitational instability and fragmentation, and at the same time that blast wave feedback cannot suppress disc instability when conditions are favourable for its emergence \citep{mayer+16}, corroborating at least the qualitative distinction between the two cases. Interestingly, \citet{ceverino+16} recently reach analogous conclusions on the role of stellar feedback by looking at a galaxy with stellar mass $M_{\star} \sim 10^9$~M$_{\sun}$ comparable to ours but at $z \sim 1$. They find a qualitatively similar evolution over time of the Toomre parameter and the $V_{\phi}/\sigma_{\rm g}$ ratio despite they use a different approach to model stellar feedback, i.e. through non-thermal radiation pressure in addition to thermal dump without shut-off cooling. We thus argue that the dominant role of stellar feedback in the early evolutionary phase of massive galaxy progenitors is likely controlled by the combination of the high specific star formation rate ($\gtrsim 5$~Gyr$^{-1}$) and of the relatively low mass at $z > 5$ ($\sim 10^{9}$~M$_{\sun}$). The first favours the impact of stellar feedback on the interstellar medium, while the latter proportionally weakens the dynamical role of gravity to lead to instabilities and eventually fragmentation. Those specific star formation rates are expected for galaxies on the main star forming sequence at $z > 5$ (Figure \ref{fig_SFH}; \citealt{schreiber+15,tasca+15}); as our galaxy is consistent with the main sequence, this suggests that the ``hot and turbulent'' regime that we characterise here could be typical of star forming galaxies at $z > 5$ with baryonic/stellar masses comparable to ours. These should be fairly typical galaxies, as recent surveys begin to find \citep{bradley+12,capak+15,watson+15}. In particular, recent ALMA observations by \citet{maiolino+15} tend to qualitatively support the idea that stellar feedback has a dominant role in the early assembly of normal star-forming galaxies at $z\sim 6- 7$. This has immediate observational implications, as we would predict a significant amount of warm/hot gas with temperature $5\times 10^{4} \lesssim T/{\rm K} \lesssim 5 \times 10^{5}$ inside and around the disc, possibly $\sim 0.1$ of the gas mass. Note that these are temperatures more akin to the circumgalactic medium distributed in the virial volume around galaxies at low redshift \citep{werk+13}, but in our case it would be inside or surrounding the galactic disc. Possible analogues in the local Universe may serve as preliminary test bed for our predictions. Those might be low-mass starburst galaxies, such as the prototypical M82, that has stellar mass and star formation rate rather similar to the main galaxy of run PH (with a factor 3-4 lower specific star formation rate due to the higher stellar mass; e.g. \citealt{forster+03,greco+12}). While gas densities are expected to be lower at $z=0$, M82 might also host a significant fraction of warm/hot, turbulent gas in its disc, at least in the central kpc where the starburst is ongoing. This seems to be confirmed by observations (e.g. \citealt{griffiths+00}) and at least in qualitative agreement with our results since gas temperature and phases found in our simulations would be somewhat dependent on the specific feedback model. Detailed characterisation of the warm/hot interstellar medium in low mass starburst galaxies could thus provide useful constraints to test our scenario. In this ``hot and turbulent'' regime, the mass transport is influenced by intense and clustered stellar feedback episodes. As a result, the gas flow through the disc is fluctuating and anisotropic, with no sustained coherent gas inflow within the disc. A coherent circumnuclear disc, which can be a way to funnel accretion towards the ultimate stage of the accretion disc, is not clearly seen to form at $\sim 100$~pc scales (though this would be barely resolved at our resolution). This might have some implications for the feeding of a central massive black hole \citep{gabor+13,dubois+15}. On one hand, mean inflow rates could be small; however, episodic accretion events at high rates could occur through the infall of massive gas clouds, as we observe inflow rates that can occasionally peak at $\gtrsim 5$~M$_{\sun}$~yr$^{-1}$. Nonetheless, if super-Eddington accretion is assumed, recent models show that even episodic accretion is enough for the rapid growth of central black holes (e.g. \citealt{lupi+16,pezzulli+16}). Accretion may also occur in an anisotropic way, with large fluctuations in the angular momentum of the accreting matter, which would have implications for the nature of the accretion disc itself, if any, and for the evolution of the spin of the central black hole. However, we defer additional speculations on the evolution of a massive black hole in such environments to a forthcoming investigation. As steady central gas inflows are not sustained, bulge/spheroid formation from dynamical and/or secular disc instabilities are unlikely to take place (e.g. \citealt{guedes+13}). Indeed, the disc of PonosHydro remains nearly bulgeless for the whole simulation (see Figure \ref{fig_rot_curve}). However, we know from lower resolution runs going to $z=0$ that the galaxy will develop a dominant spheroid at lower redshifts as it grows to become a massive early-type galaxy (Fiacconi et al., in preparation). Since it has several mergers occurring at later times ($2 < z< 4 $; \citealt{fiacconi+16}), it is likely that such mergers will be the dominant driver of spheroid growth \citep{fiacconi+15}. However, if the ``hot and turbulent'' regimes characterises main sequence galaxies at $z > 5$, this would imply that bulge formation may occur after the first billion year of evolution, possibly post-dating the growth of the massive black hole at the centre (see also \citealt{dubois+15} and \citealt{habouzit+16}). Therefore, we predict that gas-rich star forming discs at $z > 5$ should not host a significant bulge. The exploration described in this paper leads to interesting predictions about the early assembly of massive galaxies. However, our interpretations remain rather speculative, both from the theoretical and the observational point of view. On one hand, future simulations including different subgrid models are necessary to quantitatively assess the different nature of galaxies at low and high redshifts, also comparing the results from codes with intrinsically different treatments of hydrodynamics (e.g. \citealt{kim+16}). On the other hand, more detailed characterisation of high redshift galaxies are starting to be available from current observational facilities (e.g. ALMA). However, it is going to be in the next future that forthcoming observatories (e.g. JWST, E-ELT) will provide deep enough data to definitely test our predictions and at the same time to better guide the theoretical study of galaxies at the cosmic dawn. | 16 | 9 | 1609.09499 |
1609 | 1609.07484_arXiv.txt | We have investigated a group of unassociated radio sources included in the 3CR catalogue to increase the multi-frequency information on them and possibly obtain an identification. We have carried out an observational campaign with the \sw satellite to observe with the UVOT and the XRT telescopes the field of view of 21 bright NVSS sources within the positional uncertainty region of the 3CR sources. Furthermore, we have searched in the recent AllWISE Source Catalogue for infrared sources matching the position of these NVSS sources. We have detected significant emission in the soft X-ray band for nine of the investigated NVSS sources. To all of them, and in four cases with no soft X-ray association, we have associated a \wse infrared counterpart. Eight of these infrared candidates have not been proposed earlier in the literature. In the five remaining cases our candidate matches one among a few optical candidates suggested for the same 3CR source in previous studies. No source has been detected in the UVOT filters at the position of the NVSS objects, confirming the scenario that all of them are heavily obscured. With this in mind, a spectroscopic campaign, preferably in the infrared band, will be necessary to establish the nature of the sources that we have finally identified. | \let\thefootnote\relax\footnote{$\dagger$~Dan Harris passed away on December~6th, 2015. His career spanned much of the history of radio and X-ray astronomy. His passion, insight, and contributions will always be remembered.} The extragalactic subset of the revised Third Cambridge Catalogue (3CR) of radio sources \citep[see, \eg,][]{1962MmRAS..68..163B,1985PASP...97..932S} has a long history as one of the fundamental samples used to understand the nature and evolution of powerful radio galaxies and quasars, as well as their relationship to their host galaxies and environments on parsec through megaparsec scales. Extensive imaging and spectroscopic observations have long been available from the radio through the infrared (IR) and optical bands, with data from {\it Spitzer} \citep{2012ApJ...759...86W}, the {\it Hubble Space Telescope} \citep[\eg,][]{2000A&A...355..873C,2009ApJS..183..278T} and ground-based telescopes \citep[see, \eg, the description of observations performed with the Telescopio Nazionale Galileo reported in][]{2009A&A...495.1033B}. \begin{table*} \centering \scriptsize \caption{The list of unidentified 3CR sources, with the corresponding NVSS source, when present. 1) The 3C designation; 2-3) Right Ascension (J2000) with its rms uncertainty; 4-5) Declination (J2000) with its rms uncertainty; 6-7) Galactic Longitude and Latitude (J2000); 8) flux density at 178~MHz, corrected following Laing et~al.~(1983); 9-10) corresponding NVSS source, with its flux density at 1.4~GHz; 11) radio spectral index $\alpha$ computed in the range 178~MHz-1.4~GHz.} \label{tab:3cr} \begin{tabular}{lcccccccccc} \hline ~\\ 3C & R.A. & Error & Dec. & Error & l & b & $S_{178}$ & NVSS & $S_{1.4}$ & $\alpha$ \\ & (hh mm ss) & (s) & (dd mm ss) & (arcmin) & (deg) & (deg) & (Jy) & & (Jy) & \\ ~\\ \hline ~\\ 11.1 & 00 29 56.43 & 18.0 & $+$63 40 34.2 & 45.0 & 120.55 & $+$0.90 & 13.5 & J002945$+$635841 & 2.99 & 0.73 \\ % 14.1 & 00 36 27.13 & 18.0 & $+$59 46 30.3 & 45.0 & 121.04 & $-$3.04 & 17.5 & - & - & - \\ % 21.1 & 00 45 35.25 & 18.0 & $+$68 04 23.5 & 45.0 & 122.38 & $+$5.21 & 9.8 & - & - & - \\ % 33.2 & 01 10 19.72 & 18.0 & $+$69 21 57.4 & 60.0 & 124.61 & $+$6.56 & 6.0 & - & - & - \\ % 86 & 03 27 20.10 & 2.0 & $+$55 18 49.7 & 1.0 & 143.91 & $-$1.08 & 31.6 & J032719$+$552029 & 6.94 & 0.73 \\ % 91 & 03 37 42.67 & 2.5 & $+$50 45 45.1 & 3.0 & 147.81 & $-$3.90 & 15.4 & J033743$+$504552 & 3.34 & 0.74 \\ % 125 & 04 46 16.16 & 5.0 & $+$39 42 23.9 & 7.0 & 164.14 & $-$3.69 & 15.4 & J044617$+$394503 & 2.02 & 0.98 \\ % 131 & 04 53 22.56 & 3.0 & $+$31 27 47.9 & 3.0 & 171.46 & $-$7.82 & 15.9 & J045323$+$312924 & 2.87 & 0.83 \\ % 134 & 05 04 42.19 & 1.0 & $+$38 06 12.7 & 1.0 & 167.64 & $-$1.90 & 81.1 & J050443$+$380539 & 2.14 & 1.05 \\ % 137 & 05 19 32.65 & 3.0 & $+$50 55 40.3 & 3.0 & 158.78 & $+$7.76 & 13.6 & J051932$+$505432 & 2.07 & 0.91 \\ % 139.2 & 05 24 28.20 & 3.0 & $+$28 13 41.5 & 3.0 & 178.06 & $-$4.29 & 13.0 & J052427$+$281255 & 0.29 & 0.94 \\ % 141 & 05 26 42.60 & 1.5 & $+$32 49 32.1 & 2.5 & 174.54 & $-$1.32 & 16.2 & J052642$+$324958 & 2.17 & 0.97 \\ % 152 & 06 04 29.42 & 3.0 & $+$20 21 10.9 & 3.0 & 189.57 & $-$0.64 & 13.5 & J060428$+$202122 & 1.86 & 0.96 \\ % 158 & 06 21 40.95 & 5.0 & $+$14 29 31.5 & 8.0 & 196.68 & $+$0.15 & 19.7 & J062141$+$143211 & 2.24 & 1.05 \\ % 250 & 11 08 52.12 & 3.0 & $+$25 00 54.2 & 3.0 & 212.37 & $+$66.91 & 9.6 & J110851$+$250052 & 1.09 & 1.05 \\ % 389 & 18 46 18.63 & 7.0 & $-$03 19 44.5 & 12.0 & 29.38 & $-$0.38 & 22.9 & - & - & - \\ % 390 & 18 45 34.41 & 3.0 & $+$09 52 12.9 & 4.0 & 41.08 & $+$5.77 & 22.9 & J184537$+$095344 & 4.51 & 0.79 \\ % 394 & 18 59 20.89 & 6.0 & $+$13 00 11.8 & 7.0 & 45.42 & $+$4.17 & 16.5 & J185923$+$125912 & 2.88 & 0.85 \\ % 399.1 & 19 15 56.83 & 3.0 & $+$30 20 02.1 & 3.0 & 62.73 & $+$8.53 & 14.7 & J191556$+$301952 & 2.97 & 0.78 \\ % 409 & 20 14 27.74 & 1.0 & $+$23 34 58.4 & 2.0 & 63.40 & $-$6.12 & 83.5 & J201427$+$233452 & 13.68 & 0.88 \\ % 415.2 & 20 32 50.51 & 3.0 & $+$53 45 46.1 & 3.0 & 90.27 & $+$8.19 & 9.6 & J203246$+$534553 & 1.01 & 1.09 \\ % 428 & 21 08 25.59 & 3.0 & $+$49 34 05.7 & 3.0 & 90.50 & $+$1.28 & 18.1 & J210822$+$493637 & 2.41 & 0.98 \\ % 431 & 21 18 55.56 & 3.0 & $+$49 34 18.2 & 3.0 & 91.68 & $+$0.05 & 26.4 & J211852$+$493658 & 3.39 & 1.00 \\ % 454.2 & 22 52 15.62 & 18.0 & $+$65 03 57.3 & 45.0 & 110.79 & $+$5.04 & 9.6 & J225205$+$644010 & 2.29 & 0.69 \\ % 468.1 & 23 50 54.76 & 18.0 & $+$64 40 19.0 & 45.0 & 116.51 & $+$2.56 & 32.7 & J235054$+$644018 & 4.95 & 0.92 \\ % ~\\ \hline % \end{tabular} \end{table*} Since a large fraction of 3CR sources were already present in both the {\it Chandra} \cite[see, \eg,][for a recent review]{2015ApJS..220....5M} and \xmm archives of pointed observations \cite[\eg][and references therein]{2006ApJ...642...96E}, in 2008 a {\it Chandra} snapshot survey started to complete the X-ray coverage of the entire 3CR extragalactic catalogue (\citealt{2010ApJ...714..589M,2012ApJS..203...31M,2013ApJS..206....7M}). This Chandra survey has enabled investigations of peculiar sources (see, \eg, \citealp{2009ApJ...696..980M} for 3C~17 and \citealp{2012MNRAS.419.2338O} for 3C~105), samples of radio-loud objects \citep{2013ApJ...773...15W,2013ApJ...770..136I}, and was the genesis of, e.g., follow-up X-ray observations for 3C~89 (Dasadia et al. 2015), 3C~171 \citep{2010MNRAS.401.2697H}, and 3C~305 \citep{2009ApJ...692L.123M,2012MNRAS.424.1774H}. The total number of 3CR extragalactic sources now present in the Chandra archive is 248 out of the 298 included in the update of the 3CR catalogue performed by \cite{1985PASP...97..932S}. An additional 16 sources (out of 50) that remain unobserved by {\it Chandra} have recently been approved for observation in Cycle 17 (see Massaro et~al.~2016). Those observations began as of December 2015. Amid our investigation of recent {\it Chandra} observations, we realised that 25 out of the 298 3CR radio sources are not only unobserved in X rays, but are in fact completely {\it unidentified}, lacking an assigned optical or infrared counterpart. In the latest revised release of 3CR extragalactic catalogue \citep{1985PASP...97..932S}, each of these 25 unidentified sources (excluding 3C~86 and 3C~415.2) are marked as {\it obscured} active galaxies. This classification has remained unchanged for the past three decades, save for a few tentative associations requiring follow-up observations for confirmation \cite[see, \eg,][]{1987MNRAS.224..847P,1998AJ....115.1348M}. It therefore became necessary, in nearing completion of the 3CR {\it Chandra} snapshot survey, to enact an ancillary optical-to-X-ray campaign with the \sw observatory in order to better characterise the properties of these unidentified sources. Our \sw campaign was augmented by a search for infrared counterparts in the latest AllWISE Source Catalogue \footnote{\underline{http://wise2.ipac.caltech.edu/docs/release/allsky/}} from the Wide-field Infrared Survey Explorer (WISE, \citealt{2010AJ....140.1868W}) mission. \begin{table*} \centering \scriptsize \caption{The list of \sw-XRT detected sources matching one of the NVSS sources listed in Table~\ref{tab:3cr}. 1) The 3C designation; 2-3) Equatorial coordinates of the X-ray source; 4) error radius; 5) XRT exposure time; 6) XRT count rate with its error; 7) significance of the X-ray detection; 8) corresponding NVSS source; 9) angular separation between the X-ray and the radio source.} \label{tab:X} \begin{tabular}{lcccccccc} \hline ~\\ 3C & R.A.(J2000) & Dec. (J2000) & Error & Exposure & Count Rate & S/N & NVSS & Angular Separation \\ & & & (arcsec) & (s) & (ct/s) & ($\sigma$) & & (arcsec) \\ ~\\ \hline ~\\ 86 & 03 27 19.5 & $+$55 20 26.0 & 4.5 & 5170 & (1.43+/-0.19) $\cdot$ 10$^{-2}$ & 7.6 & J032719$+$552029 & 3.7 \\ 91 & 03 37 43.0 & $+$50 45 46.2 & 4.0 & 4809 & (4.39+/-0.39) $\cdot$ 10$^{-2}$ & 11.3 & J033743$+$504552 & 7.4 \\ 131 & 04 53 23.2 & $+$31 29 33.4 & 6.3 & 5255 & (1.96+/-0.74) $\cdot$ 10$^{-3}$ & 2.6 & J045323$+$312924 & 9.4 \\ 137 & 05 19 32.6 & $+$50 54 31.4 & 4.7 & 5092 & (9.98+/-1.60) $\cdot$ 10$^{-3}$ & 6.1 & J051932$+$505432 & 1.9 \\ 158 & 06 21 41.2 & $+$14 32 11.5 & 6.4 & 4974 & (2.04+/-0.78) $\cdot$ 10$^{-3}$ & 2.6 & J062141$+$143211 & 1.6 \\ 390 & 18 45 37.6 & $+$09 53 48.7 & 4.4 & 4348 & (2.60+/-0.30) $\cdot$ 10$^{-2}$ & 8.6 & J184537$+$095344 & 4.4 \\ 409 & 20 14 27.5 & $+$23 34 54.5 & 4.0 & 5366 & (3.27+/-0.28) $\cdot$ 10$^{-2}$ & 11.6 & J201427$+$233452 & 1.9 \\ 428 & 21 08 22.1 & $+$49 36 42.1 & 4.6 & 7913 & (7.79+/-1.10) $\cdot$ 10$^{-3}$ & 6.9 & J210822$+$493637 & 5.6 \\ 454.2 & 22 52 05.2 & $+$64 40 13.1 & 4.6 & 5571 & (7.76+/-1.40) $\cdot$ 10$^{-3}$ & 5.6 & J225205$+$644010 & 4.6 \\ ~\\ \hline % ~\\ \end{tabular} \end{table*} Here we present the results of this new observational effort. Our \sw observing strategy is described in \S~\ref{sec:nvss}, the reduction and analysis of \sw X-ray data is discussed in \S~\ref{sec:obs}, and the search for infrared and optical counterparts is described in \S~\ref{sec:lower}. Our results, including detections of both infrared and soft X-ray counterparts, are given in \S~\ref{sec:details} and summarised in \S~\ref{sec:summary}. Throughout this paper we use CGS units, unless stated otherwise. The spectral index $\alpha$ is defined in terms of the flux density S$_{\nu}$, where S$_{\nu}\propto\nu^{-\alpha}$ and $\nu$ is the frequency. | \label{sec:summary} After conducting \sw observations of 21 bright NVSS sources corresponding to 3CR sources classified as unassociated in the third update of the 3CR catalogue, we have obtained new X-ray detections for nine of them. Moreover, cross-matching the NVSS with the recent AllWISE Catalogue, we have found a \wse counterpart to all these nine X-ray sources, as well as to four cases with no X-ray detection. We have provided candidate counterparts emitting in the infrared band for 3C~125, 3C~137, 3C~139.2, 3C~152, 3C~158, 3C~390, 3C~409, and 3C~454.2. Furthermore, we have confirmed an unambiguous association for 3C~86, 3C~91, 3C~131, 3C~428, and 3C~468.1 where multiple candidates had been suggested in previous analysis. Four of these infrared sources are listed in the recent all-sky catalogue of $\gamma$-ray blazar candidates \citep{2014ApJS..215...14D}: the infrared colours of these objects are similar to those of quasars \citep{2011ApJ...740L..48M,2012ApJ...748...68D}, and only a spectroscopic campaign will reveal the real nature of these as well as of the remaining identified \wse counterparts. It is worth mentioning that no optical/UV counterpart has been detected in the UVOT filters at the position of the 21 NVSS sources: this is in agreement with the notes reported in the 3CR catalogue \citep{1985PASP...97..932S} in which the large fraction of these 3CR unidentified radio sources were classified as {\it obscured} active galaxies. Therefore, our analysis suggests that a spectroscopic analysis in the infrared range will be more helpful to identify their nature as well as potentially obtain a redshift measurement. | 16 | 9 | 1609.07484 |
1609 | 1609.02097_arXiv.txt | Data dimensionality reduction in radio interferometry can provide {\revised savings} of computational resources for image reconstruction {\revised through reduced memory footprints and lighter computations per iteration}, which is {\revised important} for the scalability of imaging methods to the big data setting of the next-generation telescopes. This article sheds new light on dimensionality reduction from the perspective of the compressed sensing theory and studies its interplay with imaging algorithms designed in the context of convex optimization. We propose a post-gridding linear data embedding to the space spanned by the left singular vectors of the measurement operator, providing a dimensionality reduction below image size. This embedding preserves the null space of the measurement operator and hence its sampling properties are also preserved in light of the compressed sensing theory. We show that this can be approximated by first computing the dirty image and then applying a weighted subsampled discrete Fourier transform to obtain the final reduced data vector. This Fourier dimensionality reduction model ensures a fast implementation of the full measurement operator, essential for any iterative image reconstruction method. The proposed reduction also preserves the i.i.d. Gaussian properties of the original measurement noise. For convex optimization-based imaging algorithms, this is key to justify the use of the standard $\ell_2$-norm as the data fidelity term. Our simulations confirm that this dimensionality reduction approach can be leveraged by convex optimization algorithms with no loss in imaging quality relative to reconstructing the image from the complete visibility data set. {\revised Reconstruction results in simulation settings with no direction dependent effects or calibration errors show promising performance of the proposed dimensionality reduction. Further tests on real data are planned as an extension of the current work.} \textsc{matlab} code implementing the proposed reduction method is available on GitHub. | Image reconstruction in radio interferometry is intrinsically an ill-posed inverse problem due to the fact that the visibilities essentially identify an incomplete Fourier coverage of the image of interest. The theory of compressed sensing demonstrates that a signal admitting a sparse representation in some adequate basis can be recovered from incomplete sampling~\citep{donoho_compressed_2006, candes_robust_2006, candes_stable_2006}. As a consequence, the development of compressed sensing-based imaging methods in radio interferometry is an active research area, and novel work applying compressed sensing theory was reported soon after its establishment~\citep{wiaux_compressed_2009, wiaux_spread_2009}. More involved work to handle specific problems has also been performed, primarily on wide field-of-view observations~\citep{mcewen_compressed_2011} and non-coplanar effects~\citep{wolz_revisiting_2013}. Approaches implementing sparse reconstruction for radio interferometry continue to be investigated, and report consistently increasing reconstruction performance, as recent work described in~\citet{li_application_2011, carrillo_sparsity_2012, carrillo_purify:_2014, garsden_lofar_2015, dabbech_moresane:_2015, ferrari_multi-frequency_2015} demonstrates. Large radio telescopes -- like the Low Frequency Array (LOFAR), the upgraded Karl G. Jansky Very Large Array (VLA) and the future Square Kilometre Array (SKA) -- are expected to produce data at an extremely high rate. For instance, estimates for data rates in the first phase of SKA operation are around five terabits per second~\citep{broekema_square_2015}. The resulting images are designed to be in the gigapixels range, and with a high dynamic range of six/seven orders of magnitude~\citep{cornwell_wide_2012, wijnholds_signal_2014}. This high data rate requirement presents a great signal processing challenge and has led to new research in the design and development of scalable image recovery and data-handling methods in radio interferometry. Due to the very demanding requirements for image reconstruction algorithms, big data methods need to be studied and employed; in particular, High Performance Computing (HPC)-ready solutions are needed to scale with the memory and CPU requirements of these decidedly compute-intensive processing tasks. From a data acquisition standpoint, radio-interferometric imaging is strictly a compressed sensing problem only when the amount of continuous visibilities measurements is lower than the image size. In the big data regime of next-generation telescopes, the data volumes would actually be much larger than the image size, to reach high dynamic ranges. However, this does not change the ill-posed nature of the problem due to the intrinsic incomplete Fourier coverage. Therefore, from a reconstruction standpoint, the properties that the measurement operator needs to satisfy to enable accurate recovery from sparsity promoting convex optimization algorithms are those prescribed by the compressed sensing theory. The question raised is thus: ``Can image reconstruction methods scale to the big data regime?'' One approach to this problem is to study parallelized and distributed optimization algorithms that can split the data as needed~\citep{ferrari_distributed_2014, carrillo_scalable_2015, onose_scalable_2016}. In this article we contemplate the idea of linearly embedding the data in a lower-dimensional space before feeding them to the image reconstruction algorithms. This linear data dimensionality reduction approach has recently been considered in the numerical linear algebra literature under the name of `sketching', which, in general terms, addresses the question of solving a high-dimensional optimization problem by embedding it into a lower-dimensional space~\citep{mahoney_randomized_2011, woodruff_sketching_2014}. Sketching and similar random projection methods for dimensionality reduction of manifold-modelled data~\citep{baraniuk_random_2007, hegde_random_2007} were introduced and studied at the same time as the emergence of compressed sensing theory. Recent work drawing parallels between dimensionality reduction and compressed sensing~\citep{baraniuk_simple_2008, krahmer_new_2010} can be traced back to the seminal work on the Johnson-Lindenstrauss lemma~\citep{johnson_extensions_1984}. Assuming an original linear measurement operator $\PPhi$ from the radio interferometry measurement equation, our task is to design a sketching/dimensionality reduction operator $\R$ leading to a full measurement operator $\PPhi'=\R\PPhi$ with the same properties as $\PPhi$ as dictated by the compressed sensing theory. In the context of sketching, dimensionality reduction is performed by random projections. We do not follow that approach here, but instead leverage the singular value decomposition of the original measurement operator. This article is organized as follows. Section~\ref{sec:csimaging} gives a brief overview of the ill-posed inverse problem of radio-interferometric imaging, and discusses convex optimization-based imaging methods. Additionally, we highlight key properties and guarantees that the compressed sensing theory requires and provides, respectively, for signal reconstruction. In Section~\ref{sec:dimreduction} we study dimensionality reduction techniques in the particular setting of using compressed sensing-based reconstruction algorithms. We present preliminary studies undertaken in this context, and derive the theoretically optimal dimensionality reduction operator from a singular value decomposition perspective of the measurement operator. We then introduce a novel post-gridding dimensionality reduction consisting of first mapping gridded visibilities back to image space, i.e., computing the dirty image, and then performing a weighted subsampled discrete Fourier transform to obtain the final reduced data vector with dimension below image size. We advocate that this procedure is optimal in reducing the dimension of the data vector, while preserving the compressed sensing properties and fast implementation of the final measurement operator $\PPhi'$. It also ensures that the independent and identically distributed (i.i.d.) Gaussian properties of the measurement noise are preserved, thus setting the image reconstruction problem appropriately for convex optimization-based reconstruction. We highlight alternative dimensionality reduction methods that lead to gridded visibilities of dimension above image size, and dirty images of dimension equal to image size, and make a comparative study on the reconstruction quality using these methods. We show that the image reconstruction quality with visibilities `reduced' using the proposed method is comparable to that using the complete visibilities set and that with gridded visibilities. The performance associated with the use of the dirty image as reduced data vector is suboptimal. These results are reported in Section~\ref{sec:plots} through simulations with data sets containing up to 26 million continuous visibilities using SKA-like simulated $uv$ coverages. We present our conclusions on this proposed dimensionality reduction method in Section~\ref{sec:conclusions}, and outline possible directions to extend this work and combine it with other concurrent approaches in scalable image recovery in radio interferometry. \textsc{matlab} code containing this work is available on GitHub\footnote{\url{http://basp-group.github.io/fourierdimredn}} and is expected to be integrated into \textsc{`purify'}\footnote{\url{http://basp-group.github.io/purify}}, a radio-interferometric imaging software proposed and described in \citet{carrillo_purify:_2014}. | \label{sec:conclusions} Data dimensionality reduction in radio interferometry is a key challenge for the scalability of imaging methods to the big data setting of the next-generation telescopes. We revisited the concept of dimensionality reduction of radio-interferometric data from a compressed sensing perspective. The proposed post-gridding linear data embedding approach consists of projecting the data, assumed to be of size much larger than the image size $M\gg N$, to the space spanned by the $\Nz$ left singular vectors of the measurement operator, thus preserving its null space. In the {\revised absence of DDEs and calibration errors}, we showed that this dimensionality reduction approach consists of first mapping gridded visibilities back to image space, i.e., computing the dirty image, and then performing a weighted subsampled {\revised discrete Fourier transform} to obtain the final reduced data vector with dimension below image size. The Fourier approximation model for the right singular vectors ensures a fast implementation of the full measurement operator after dimensionality reduction. This dimensionality reduction also preserves the i.i.d. Gaussian properties of the original measurement noise thus making it directly suitable for use with convex optimization algorithms with an $\ell_2$-norm data fidelity term. The number of significant singular vectors can be conservatively evaluated by retaining all non-zero singular values, or for further dimensionality reduction to $\Nz \ll N$, by retaining only singular values above a noise-based threshold, effectively introducing a low-rank approximation of the original measurement operator. This is in contrast with current gridding-based imaging in radio interferometry, which reduces data on the oversampled discrete Fourier grid of size $\nn$ or to the dirty image of size $N$. We show with realistic data simulated using SKA-like $uv$ coverages and using the SARA convex optimization method, that reconstruction quality is at least as good as with using the complete visibility data set of size $M$, while {\revised being computationally less expensive, both by having a smaller memory footprint thanks to a reduced data size, and through lower running time per iteration of the imaging algorithm.} It is also similar in reconstruction quality to results obtained with gridded visibilities or from the dirty image, but again enabling significantly more reduction below image size. Another contribution from this work is that dimensionality reduction below $\nn$ can also be achieved from gridded visibilities by discarding those visibilities below a noise-dependent threshold. This reduction by thresholding is however significantly less optimal when applied on gridded visibilities, than on the singular value decomposition. Our proposed dimensionality reduction method is available as \textsc{matlab} code on GitHub at \url{http://basp-group.github.io/fourierdimredn}. Further work integrating this method in the \textsc{purify} software is foreseen as part of the research towards scalable HPC-ready algorithms for radio-interferometric imaging. {\revised As the current proposed method assumes correctly calibrated data with negligible issues arising from imperfections in data acquisition, future work will also include extended testing with real data, including testing the robustness of the proposed method to w-term effects and calibration errors in particular.} | 16 | 9 | 1609.02097 |
1609 | 1609.02742_arXiv.txt | We pursue the investigation of a model for sub-Chandrasekhar supernovae Ia explosions (SNIa) in which the energy stored in the Pauli tower is released to trigger a nuclear deflagration. The simplest physical model for such a degeneracy breakdown is a phase transition to an exactly supersymmetric state in which the scalar partners of protons, neutrons, and leptons become degenerate with the familiar fermions of our world as in the supersymmetric standard model with susy breaking parameters relaxed to zero. We focus on the ability of the susy phase transition model to fit the total SNIa rate as well as the delay time distribution of SNIa after the birth of a progenitor white dwarf. We also study the ejected mass distribution and its correlation with delay time. Finally, we discuss the expected SNIa remnant in the form of a black hole of Jupiter mass or lower and the prospects for detecting such remnants. | }} In the 1930's S. Chandrasekhar \cite{Chandra} famously showed that electron degeneracy pressure would make certain stars now known as white dwarfs classically stable up to about 1.4 solar masses. Slightly below this mass spontaneous nuclear fusion would erupt to destabilize the star. In 1973 it was proposed \cite{Whelan-Iben},\cite{Webbink} that mass accretion onto white dwarfs from a binary partner could cause this Chandrasekhar mass to be approached from below at which point nuclear fusion would take over leading to an explosion which could be identified as a type Ia supernova. The clear evidence of fusion by-products expected from a Carbon or Oxygen White Dwarf progenitor supports the Whelan-Iben idea. In addition, the prediction that supernovae occur at the Chandrasekhar mass suggests a possible explanation for the crucial uniformity of the events. Now, more than four decades later, a quantitative understanding of the explosion and the supernova properties has been elusive in this now standard model. In addition, there is now strong evidence for a sub-Chandrasekhar component. Within the standard model for SNIa there is a distinction between the single degenerate (SD) scenario in which there is a main sequence star donating matter to the degenerate white dwarf and the double degenerate (DD) scenario in which a second degenerate white dwarf donates to a primary, more massive white dwarf progenitor. If both mechanisms are operative the supernovae uniformity is more difficult to understand. Both mechanisms are subject to a host of problems as discussed in a number of old and recent reviews for example \cite{Hillebrandt}, \cite{Maoz-Mannucci}. In particular both mechanisms when faced with observational constraints greatly underestimate the SNIa rate. Historically, when a phenomenon resists explanation in a standard model for multiple decades, the resolution of the puzzle often requires some radical new physics input. Up until some five years ago the DD scenario was strongly disfavored and the obstacles to a satisfying theory based on this scenario were summarized as follows in the still cogent 2000 Review by Hillebrandt and Niemeyer \cite{Hillebrandt}: ``Besides the lack of convincing direct observational evidence for sufficiently many appropriate binary systems, the homogeneity of `typical' SNe Ia may be an argument against this class of progenitors. It is not easy to see how the merging of two white dwarfs of (likely) different mass, composition, and angular momentum with different impact parameters, etc, will always lead to the same burning conditions and, therefore, the production of a nearly equal amount of $^{56} Ni.$'' On the other hand, the SD scenario, although conceptually easier to envision, comes with its own set of puzzles. For instance there is no evidence of a binary partner remnant and no evidence of significant absorbtion by the partner nor of significant asymmetry in the explosion as might be expected from a planar binary system. The dilemma was heightened in 2010 with the observation that accretion in the SD scenario would necessarily be accompanied by significant X-ray emission and observed X-ray activity was far below what would be required if the entire SNIa rate was to be understood as accretion onto white dwarfs several tenths of a solar mass below the Chandrasekhar mass. Quantitatively, whereas an average accretion rate of $100\, M_\odot/Gyr$ would be required to bring $1.2\, M_\odot$ dwarfs to the Chandrasekhar mass at a sufficient rate, no more than one to two percent of this rate is consistent with observations \cite{Bogdan-Gilfanov}\,\cite{DiStefano}. Recently, an analogous constraint on the the DD scenario has been proposed based on the absence of expected polarization in supernova light \cite{Bulla}. The purpose of this article is to refine the analysis of the susy phase transition model for SNIa \cite{Biermann-Clavelli}. In this model every white dwarf, whether in a binary system or not, has a characteristic mass-dependent lifetime. Most white dwarfs have a lifetime longer than the current age of the universe but those in a certain sub-Chandrasekhar mass range can have lifetimes in the tenths of a Gigayear range. Unless made explicit, masses in this article are defined relative to the solar mass, $M_\odot$. The primary parameters of this model were a critical matter density, $\rho_c$, and a minimum lifetime, $\tau_0$. We generalize the model via a third free parameter, $b_0$, to allow the possibility of a phase transition suppression at high pressure analogous to that observed in a superheated liquid. Finally, we assume, as a fourth parameter, an average white dwarf accretion rate parametrized by some $c_0$ which causes white dwarfs to increase in mass up to that at which a significant fraction of the white dwarfs undergo the supernova phase transition. This parameter is required to be consistent with the above-mentioned limits on the accretion in binary systems of a white dwarf with a main sequence partner. The number of these parameters is comparable to the minimum number in the standard model (mean and width of of the double mass distributions and mean and width of the accretion rate distribution or initial separation distribution). Clearly no prediction of the supernova rate and delay time distributions can be made without knowing or assuming initial state distributions and then they can be tested against present or future observations. At present no known binary systems are clearly supernova candidates. In the phase transition model, the supernova rates and delay time distribution are proportional to known white dwarf mass distributions. In recent years, relatively precise analyses have been made of the delay time distribution of SNIa. It is found that most of these events occur within a few tenths of a Gigayear after the birth of the progenitor white dwarf with only about $1\%$ occuring after Gigayear (Gyr) delay times. This seems surprising in view of common multi-Gyr stable orbits of binary objects. Prediction of the delay time distribution in the standard accretion models would seem to depend sensitively on unknown binary mass distributions, unknown orbital parameter distributions, and unknown accretion rates. Unless the corresponding distributions are surprisingly narrow, the supernovae uniformity is again puzzling. In the framework of the phase transition model we are able to quantitatively fit the total SNIa rate and the rates in three recently observed delay time bins, The ejected mass distribution is also predicted and shows a sharp peaking. The most recent high statistics data release from the Sloan Digital Sky Survey (SDSS) contains a clean sub-sample in which the mass of the white dwarfs and their age from birth as a white dwarf are reasonably well determined \cite{Bergeron}. This sample shown in fig.\ref{CoolWDs} contains 95 DA type white dwarfs which have a thin hydrogen atmosphere (about $10^{-5}$ of the total mass) and 55 DB type white dwarfs which have a similarly thin helium atmosphere. A clear dip in the distribution near a mass of about $0.45$ Solar was noted. In addition, fig.\ref{CoolWDs} suggests a dip in the DB distribution at a higher mass as well as an extension to higher masses compared to the DA white dwarfs. This could suggest that the DB dwarfs have arisen from an earlier DA phase due to an enhanced accretion leading to hydrogen to helium fusion on the surface. In this paper, however, we restrict our attention to the DA white dwarfs. \begin{figure}[ht] \centering \includegraphics[scale=0.65]{massagen.eps} \caption{The age in Gyr versus mass in a clean sample of old white dwarfs.} \label{CoolWDs} \end{figure} The organization of this paper is as follows. In Section \,\ref{WDdists}, we start with the mass distribution of hot white dwarfs which should approximate the distribution at birth. We then compare the mass distribution of the old white dwarfs with known ages \cite{Bergeron}. This allows us to estimate the average accretion rate. In Section \,\ref{phasetrans} we briefly review the theory of the phase transition to exact susy from \cite{Biermann-Clavelli} and discuss the possibility of extending the model to include a transition-suppressing pressure term in the action. The analog would be the suppression of the boiling transition in a liquid under high pressure. Conservation of degrees of freedom in this model requires the existence of a broken susy in our world although the masses in this phase can be quite high consistent both with their non-observation in current accelerator searches and with susy grand unification theory. In Section \,\ref{Carlo} we describe a four parameter monte carlo and discuss how the parameters are constrained by $1 \sigma$ fits to the observed delay time distribution. In Section \,\ref{massdists} we discuss the ejected mass distribution and its correlation with delay times. In Section \,\ref{remnants} we discuss the predicted supernova remnants and their eluding of current searches as well as some consequences for future searches. Section \,\ref{summary} is reserved for a summary and discussion of results. | } The phase transition model has a number of advantages relative to the standard model explosion at the Chandrasekhar mass. The delay time distribution although not linear in a log-log plot can easily fit the data. The ejected mass distribution naturally peaks below the Chandrasekhar mass. The total supernova rate is related to known single white dwarf mass distributions unlike the situation in the standard model which depends on unknown binary distributions and which, with plausible assumptions, greatly underestimates the total rate. The absence of observed remnants which is puzzling in the standard model is easily understood in the phase transition model which also makes an interesting prediction of remnant effects. The sphericity of supernova events and the absence of shadowing by a binary partner are predicted in the phase transition model with low accretion rates but remain puzzling in the standard model. In the DD scenario one must wonder why there are no observations of binary white dwarf systems with near Chandrasekhar combined mass and how the homogeneity of normal SNIa which is crucial to dark energy measurements is maintained. In the DD scenario one would expect that the peak of the white dwarf distribution at $0.6$ would lead to a secondary peak at $1.2$ due to a coalescence of binary white dwarfs. Indeed in fig.\,\ref{hotDAdwarfs} there seems to be such a secondary peak but it is known \cite{Madej04} that this is purely an artifact of the treatment of the high mass tail. Significant discussions with Peter Biermann, Ken Olum, and Akos Bogdan contributing to the work of this paper are gratefully acknowledged. | 16 | 9 | 1609.02742 |
1609 | 1609.00437_arXiv.txt | {} {We investigate the evolution of protoplanetary discs (PPDs hereafter) with magnetically driven disc winds and viscous heating.} { We considered an initially massive disc with $\sim 0.1 M_{\odot}$ to track the evolution from the early stage of PPDs. We solved the time evolution of surface density and temperature by taking into account viscous heating and the loss of mass and angular momentum by the disc winds within the framework of a standard $\alpha$ model for accretion discs. Our model parameters, turbulent viscosity, disc wind mass-loss, and disc wind torque, which were adopted from local magnetohydrodynamical simulations and constrained by the global energetics of the gravitational accretion, largely depends on the physical condition of PPDs, particularly on the evolution of the vertical magnetic flux in weakly ionized PPDs.} {% Although there are still uncertainties concerning the evolution of the vertical magnetic flux that remains, the surface densities show a large variety, depending on the combination of these three parameters, some of which are very different from the surface density expected from the standard accretion. When a PPD is in a wind-driven accretion state with the preserved vertical magnetic field, the radial dependence of the surface density can be positive in the inner region $<1-10$ au. The mass accretion rates are consistent with observations, even in the very low level of magnetohydrodynamical turbulence. % Such a positive radial slope of the surface density strongly affects % planet formation because it inhibits the inward drift or even causes % the outward drift of pebble- to boulder-sized solid bodies, and it also slows down or even reversed the inward type-I migration of protoplanets. } {The variety of our calculated PPDs should yield a wide variety of exoplanet systems.} | The evolution of protoplanetary disks (PPDs) is one of the keys to understand planet formation. There are still several unsolved problems, one of which is the dispersal of PPDs \citep[][]{hai01,her08,tak14,tak15}. The evolution and dispersal of PPDs have been extensively studied in the framework of viscously accreting discs that undergo % photoevaporation by the irradiation from the central star \citep[e.g,][]{shu93,hol00,alx06,kim16}. In addition to the viscous accretion and the photoevaporation, the role of magnetically driven disc winds has recently been received new attention. \citet{si09} and \citet{suz10} proposed that vertical outflows driven by magnetohydrodynamical (MHD; hereafter) turbulence might be a viable mechanism that disperses the gas component of PPDs; turbulence is triggered by magnetorotational instability \citep[MRI hereafter; ][]{vel59,cha61,bh91}, and the Poynting flux associated with the MHD turbulence drives vertical outflows. The idea of MHD turbulence-driven outflow has also been % extended by considering various effects, such as % a stronger magnetic field \citep{bs13a}, a large-scale magnetic field \citep{les13}, and the dynamics of dust grains \citep{miy16}, whereas its mass flux is still quantitatively uncertain \citep{fro13}. Although \citet{suz10} considered mass loss to be the sole role of the disc wind, the disc wind in reality also carries off the angular momentum \citep{bp82,pp92,fer06,sal11}. In particular, a dead zone, which is an MRI-inactive region because of the insufficient ionization, is supposed to form in a PPD \citep{gam96,san00}. In a dead zone the level of the excited turbulence is low, and it is not sufficient to sustain the observed mass accretion onto the central star. In these circumstances, the extraction of the angular momentum by the disc wind possibly plays a primary role in driving mass accretion \citep{bs13b,sim13}. \citet{bai16a} and \citet{bai16b} investigated the global evolution of PPDs in such a wind-driven accretion state, by also taking the effect of external heating into account, and reported that a large portion of the mass is removed by the disc wind in comparison to the accreting mass. A critical open question concerning the disc wind from PPDs is that the mass-loss rate. At the later stage of the evolution, a wind footpoint that is determined by the irradiation from a central star is expected to primarily control the mass-loss rate \citep{bai16a,bai16b}. On the other hand, at the earlier stage when the surface density is high, viscous heating plays an essential role in determining the thermal properties of PPDs \citep[e.g.,][]{rl86,nn94,ht11,oka11,bit15}. To investigate the time evolution from the early epoch, we here take the effect of viscous heating in the global evolution of PPDs into account in addition to the loss of mass and angular momentum by the disc wind. We focus in particular on the conditions that create a density structure that is very different from the structure of classic viscously accreting discs, which may help solving long-standing problems such as the radial migration of pebbles, boulders, and protoplanets. For this goal, we evaluate the mass-loss rate from the global energetics of PPDs; the kinetic energy of the vertical outflow is mainly supplied from the gravitational accretion energy. This strategy is different from the method adopted by \citet{bai16b}, in which the mass-loss rate was estimated based on the local profile of magnetically driven wind with external heating. A comparison between the two models is provided in Sect. \ref{sec:comp}. | \subsection{Uncertainties} \label{sec:unc} Our model has the three free parameters, $\overline{\alpha_{r\phi}}$, $C_{\rm w,0}$, and $\overline{\alpha_{\phi z}}$. Since these parameters are not yet tightly constrained by observations or theoretical calculations, we calculated the evolution of PPDs in the wide ranges of the parameters to test various possibilities (Sect. \ref{sec:res}). Uncertainties of the three parameters is largely attributed to the uncertainty of the initial distribution and to the evolution of the poloidal magnetic flux because these three parameters % depend on the vertical magnetic field strength \citep{suz10,oh11,bs13b}. The evolution of poloidal magnetic flux in accretion discs has been studied by a number of groups \citep{lub94,rl08,go12,si14} and has recently been specifically applied to PPDs \citep{oku14,go14,to14}. Accreting gas drags the vertical magnetic field inward, while the vertical field also possibly diffuses outward by magnetic diffusivity, which consists of both effective turbulent resistivity and non-ideal MHD effects (Sect. \ref{sec:prm}). The radial motion of the vertical magnetic flux is determined by the balance between these inward dragging and outward diffusion. % The direction of the magnetic flux itself is still uncertain, which depends on the initial configuration of the poloidal magnetic field, in addition to the combination of accretion and magnetic diffusion. One future possibility is that we finally obtain a universal tendency for the time evolution of vertical magnetic fields. In this case, we can constrain our free parameters, and evolutions of surface densities will not show a variety but converge to a unified trend. On the other hand, if the evolution of the poloidal magnetic flux is different in different PPDs, depending on physical circumstances, such as initial magnetic flux and disc mass, and stellar irradiation, which controls the non-ideal MHD effects through the ionization, then the evolutions of surface densities are also different in different PPDs as shown so far, which should lead to a wide variety of the subsequent planet formation processes and final exoplanet systems. At present, the unified picture of the evolution of the poloidal magnetic field is not well understood at all, and therefore it is worth pursuing various possibilities. Our calculations took the effect of the evolution of the vertical magnetic field in the wind torque into account; the two cases of constant $\overline{\alpha_{\phi z}}$ and $\Sigma$-dependent $\overline{\alpha_{\phi z}}$ correspond to the case in which the magnetic energy decreases in the same manner as the decrease of the surface density and the case with the preserved magnetic flux, respectively. The $\Sigma$-dependent torque cases show a runaway behavior of the gas dispersal in an inside-out manner; once the gas is dispersed, $\overline{\alpha_{\phi z}}$ increases, which further accelerates the dispersal of the gas. This is the main reason why the positive slope of $\Sigma$ is produced. Although we did not consider this effect, $\overline{\alpha_{r\phi}}$ and $C_{\rm w,0}$ depend similarly on $\Sigma$, which causes an additional runaway dispersal of the gas \citep[][see also Subsection \ref{sec:MRIinactive}]{suz10}. The case with constant $\overline{\alpha_{\phi z}}$ even gives the moderately positive slope (Fig. \ref{fig:profile85}). Within the two cases we tested, the positive slope of $\Sigma$ on $r$ is not peculiar, but a common feature. However, we should note that our calculations do not cover all the possible distributions and evolutions of the vertical magnetic field. Therefore, it would be % premature to conclude that the positive slope of $\Sigma$ is a natural outcome of the accretion induced by the magnetically driven disc wind. For example, when the outward diffusion of vertical magnetic field is effective and the magnetic flux is dispersed more rapidly than the gas, the effect of the wind torque is suppressed with time. In this case, the $\Sigma$ profile would maintain a normal negative slope. We now discuss other ambiguities of the mass flux of the disc winds, in addition to the uncertainty of the vertical magnetic field. At the moment, the mass flux, $C_{\rm w,0}$, is available only from local MHD simulations \citep[e.g.][]{si09,fro13,bs13a}. As discussed % in Sect. \ref{sec:prm}, these local simulations may overestimate the mass flux. Although we adopted the conservative $C_{\rm w,0}$ by reducing the simulation results by half (see Sect. \ref{sec:prm}), it might be even lower \citep{fro13}. We here briefly discuss how the results are affected and particularly focus on the slope of the surface density when $C_{\rm w,0}$ is smaller. As shown in Figs. \ref{fig:Cw83} and \ref{fig:Cw85}$, C_{\rm w}$ is already constrained by the energetics. In most cases except for the MRI-inactive cases with $\Sigma$-dependent torque, the energetics constraint already suppresses $C_{\rm w}$ in the inner region. Therefore, adopting a smaller $C_{\rm w,0}$ does not affect $C_{\rm w}$ in the inner region but reduces $C_{\rm w}$ in the outer region, which suppresses the gas dispersal there. Hence, the slope of $\Sigma$ would be more positive in these cases. On the other hand, in the MRI-inactive cases with $\Sigma$-dependent torque, the energetics constraint suppresses $C_{\rm w}$ at the relatively outer location, $r\sim 10$ au. In these cases, a smaller $C_{\rm w,0}$ reduces $C_{\rm w}$ in the inner region. As a result, the obtained large positive $\Sigma$ slopes in these cases (Fig. \ref{fig:Cw85}) would be reduced to moderately positive ones. When we determined the mass flux of the disc winds, we applied the energetics constraint from the gravitational accretion without external heating or momentum inputs (Sect. \ref{sec:Cw}; Eq. \ref{eq:Cwe,0}). This treatment is expected to give a reasonable constraint at the early phase when viscous heating dominates the radiative heating or other effects from the central star. However, at the later time this is not the case because the surface density decreases and the viscous heating becomes relatively unimportant. Effects of external heating or momentum inputs need to be considered. They weaken the energetics constraint to give a larger $C_{\rm w}$ in the region with $C_{\rm w,e} < C_{\rm w,0}$ (see Sect. \ref{sec:swpe}). \subsection{Radial drift of pebbles and boulders} \label{sec:drift} \begin{figure} % \begin{center} \includegraphics[width=0.45\textwidth]{./glbdsk_pgrf_a85_3.eps} \end{center} \caption{Comparison of normalized pressure gradient force, $-\left(\frac{1}{\rho_{\rm mid}}\frac{\partial p_{\rm mid}}{\partial r}\right) /(2r\Omega^2)$, of MRI-inactive PPDs at $t=0$ (dotted), $10^5$ (solid), and $10^6$ years (dashed). % The MRI-inactive cases with $\Sigma$-dependent torque in Table \ref{tab:MRIina}, blue lines for weak DW and red lines for strong DW, which corresponds to the red and blue lines in Fig. \ref{fig:profile85}, are compared to the MRI-inactive no DW case with $C_{\rm w,0}=0$ and $\overline{\alpha_{r\phi}} =8\times 10^{-5}$ (black lines). \label{fig:pgrf} } \end{figure} Although calculations still include uncertainties that mainly stem from the ambiguity of the evolution of poloidal magnetic fields, the positive slopes of the surface densities obtained in Sect. \ref{sec:res} are % a possible consequence of the evolution of PPDs with disc winds, as discussed in Sect. \ref{sec:unc}. These positive slopes % raise various interesting implications for planet formation. In this and the next subsections, we demonstrate how the obtained $\Sigma$ profiles affect the solid component of PPDs by studying cases that show large positive slopes of $\Sigma$. The first example is the radial drift of solid bodies through gas drag. In general the rotation velocity of the gas in PPDs is slightly slower than the local Keplerian velocity because of the radial pressure gradient force. On the other hand, solid particles rotate with Keplerian velocity without the support from the gas pressure. As a result, the solid particles feel a head wind from the gas, which causes them to drift inward. Considering the momentum balance, solid particles with nondimensional stopping time $\approx 1$, % which corresponds to a meter-sized spherical boulder at 1 au of the MMSN, % experience the radial drift most severely \citep{wei77,nak86}, and their drift timescale in the midplane is given by \begin{equation} \tau_{\rm dr,max} \approx \frac{1}{\eta \Omega_{\rm K}}, \end{equation} where $\eta$ is pressure gradient force normalized by the twice of centrifugal force, \begin{equation} \eta = -\frac{1}{\rho_{\rm mid}}\frac{\partial p_{\rm mid}}{\partial r} \frac{1}{2r\Omega_{\rm K}^2}. \end{equation} In the usual condition, $\eta\sim 10^{-3}-10^{-2}>0$, which causes solid particles to drift inward. Smaller $\eta$ leads to slower inward drift; if $\eta < 0$, the direction of the drift is opposite and solid particles move outward. Figure \ref{fig:pgrf} shows $\eta$ of the two MRI-inactive ($\overline{\alpha_{r\phi}}=8\times 10^{-5}$) cases with $\Sigma$-dependent torque of Table \ref{tab:MRIina} (red and blue lines; the same as in Figs. \ref{fig:profile85} -- \ref{fig:t-Mdot85}) in comparison to the no disc wind (no DW) case with the same $\overline{\alpha_{r\phi}}=8\times 10^{-5}$ (black lines). We here derive $p_{\rm mid}$ from $\Sigma$ by \begin{equation} p_{\rm mid} = \rho_{\rm mid} c_{\rm s}^2 = \frac{\Sigma\Omega c_{\rm s}}{\sqrt{2\pi}} \end{equation} The no DW case shows $\eta$ remains within $10^{-3}-10^{-2}$, which implies fast inward drift. In contrast, $\eta$'s are considerably reduced in the $\Sigma$-dependent torque cases. % In particular, the red lines (strong DW case) show negative $\eta$ in part (red lines are truncated between 0.04-0.4 au at $t=10^5$ years and 1-2 au at $t=10^6$ years), which indicates that solid particles move outward in this region. As a result, the solid component will accumulate around the outer edge of the negative $\eta$ region, which offers suitable conditions for planet formation \citep{kob12}. Furthermore, this location moves outward with time; the suitable site for the planet formation also moves outward. \subsection{Type I migration} \label{sec:TypeImig} \begin{figure} % \begin{center} \includegraphics[width=0.45\textwidth]{./mig2.eps} \end{center} \caption{Migration efficiency for Earth-mass planets for MRI-inactive cases with $\Sigma$-dependent torque (red for strong DW and blue for weak DW of Table \ref{tab:MRIina}) at $t=10^6$ yr (corresponding to the solid red and blue lines in Fig. \ref{fig:profile85}) in comparison to the MRI-inactive no DW case (black). $C_{\rm I} > 0$ means outward migration. \label{fig:TypeImig} } \end{figure} Another interesting implication of the positive $\Sigma$ slopes is that an inward migration of low-mass planets (type I migration) can be slowed down or even reversed. The torque for type I migration can be expressed by the sum of Lindblad and corotation torques. The corotation torque is more sensitive to the slope of the gas surface density and can be positive for positive slopes. Here we estimate the migration rate of Earth-mass planets embedded in MRI-inactive PPDs with the surface densities shown in Fig.~\ref{fig:profile85}. We used the formulae of \citet{paa11} to calculate the migration timescale, $t_a$ (see Eqs.~(8)-(16) in \citet{ogi15a} for details of the formulae). We introduced a parameter of the efficiency of inward type I migration, $C_{\rm I} \equiv -t_{a,{\rm TTW}}/t_a$, where $t_{a,{\rm TTW}}$ is the migration time in a locally isothermal disc derived by a linear analysis by \citet{tan02}. The migration timescale is defined as $t_a \equiv a/(-\dot{a})$; positive migration time means inward migration. Figure \ref{fig:TypeImig} shows the migration efficiency for the $\Sigma$-dependent torque case (the red and blue curves in Fig.~\ref{fig:profile85}) at $t = 10^6$yr in comparison to the no DW case (black line). The migration rate depends on the planetary mass and the orbital eccentricity; Earth-mass planets with zero eccentricity were considered here. The blue curve shows that the type I migration is slowed down inside a few au by several factors from $t_{a,{\rm TTW}}$. The migration is even reversed (outward migration) between 0.1-0.5 au in the red curve (strong DW case). Thus the disc wind would also play important roles in the late stage of planet formation. \subsection{Comparison to previous work} \label{sec:comp} Recently, \citet{bai16b} also presented a global evolution model for PPDs with magnetically driven disc winds. However, none of the cases in his model calculations resulted in a surface density with a drastic positive slope relative to $r$ as some of our cases have shown. The two main differences between his setup and ours is the mass-loss rate by the disc wind and the evolution of the vertical magnetic field. Our calculations, which started from a relatively massive initial disc ($M_{\rm disc,int}=0.11M_{\odot}$) to study the evolution from the early stage, neglected the heating by the irradiation from a central star but considered viscous heating, and the mass-loss rate was constrained by the global energetics of the viscous accretion. In contrast, the initial disc mass adopted by \citet{bai16b} is lower, $=0.035M_{\odot}$, to focus on the later stage of the evolution, and the location of the wind base in the inner region $r\lesssim 10-30$ au is determined from heating by far-ultraviolet (FUV hereafter) irradiation from a central star. Here, the penetration depth of the FUV was assumed to be spatially constant. Since the surface density decreases with $r$, the penetration depth normalized by the scale height is deeper for larger $r$. Therefore, the mass loss by the disc wind affects the depletion of the gas at outer locations more severely than in our model setting, and consequently a positive slope of $\Sigma$ was not obtained in the results of \citet{bai16b}. As for the evolution of the vertical magnetic field, \citet{bai16b} considered two cases: in the first case the total magnetic flux is preserved with time, and in the second case it decreases in the same manner as the total mass. % In both cases, the plasma $\beta = (B_z^2/8\pi(\rho c_{\rm s}^2)_{\rm mid})^{-1}$ at the midplane was assumed to be spatially uniform. Even in the first case, the vertical magnetic field was redistributed to follow the density profile \citep{arm13}. This spatially uniform $\beta$ was also adopted in our constant torque setting. In contrast, our $\Sigma$-dependent torque assumed the preserved vertical magnetic field at each location, which led to a runaway inside-out dispersal and produced a large positive slope of $\Sigma$ (Sect. \ref{sec:res}), compared to the above-mentioned cases with the spatially uniform $\beta$. \subsection{Stellar wind and photoevaporation} \label{sec:swpe} We did not take the effects of a central star into account except to determine the radiative equilibrium temperature, $T_{\rm req}$ (Eq. \ref{eq:treq}). However, the stellar wind and irradiation affect the evolution of PPDs. In our calculations, the mass flux of the disc wind is $C_{\rm w,e}$ constrained by the energetics of accretion, and % it can be smaller than $C_{\rm w,0}$ determined by the mass loading expected from the local MHD simulations. When this is the case, gaseous clouds are lifted up by vertical upflows but cannot stream out to large $z$; they float in the disc atmosphere or return to the disc because they are bound by the gravity of the central star. The stellar wind from the central star would change this situation. The mass flux of the stellar wind from pre-main sequence stars is much higher, by an order of 4 -- 6, than that of the current solar wind partly because of the energy supply from accretion \citep{hir97,mp05,cra09}. Even after the accretion terminates, the mass flux of the stellar wind is expected to be still high because of the high magnetic activity \citep{wood05,cs11,suz13}. The strong stellar wind would blow away the clouds that are lifted up by the disc winds \citep[see][for the energetics]{suz10}. In the framework of our model, the contribution from the stellar wind would increase $C_{\rm w,e}$ in Eqs. (\ref{eq:Cwcn1}) and (\ref{eq:Cwcn2}), in the small $r$ region. The increase of $C_{\rm w}$ in the inner region reduces $\Sigma$ there, which also produces a larger positive slope of $\Sigma$. In this discussion, we neglected the roles of global magnetic fields that are rooted in the central star and in the PPD. When the field strength is strong enough, the stellar wind region and the disc wind region are separated by a boundary layer formed by magnetospheric ejections \citep{zf13}. In this case the stellar winds will not contribute to driving the disc winds. It depends on the relative strength of the magnetic energy to the sum of the dynamic pressure and the gas pressure whether the interaction between the stellar winds and the disc winds is efficient. % When the magnetic energy is weaker, the interaction is stronger, and vice versa. Photoevaporation by irradiation from the central star or neighbouring stars has been extensively studied as a viable source for dispersing PPDs \citep[e.g.,][]{shu93,hol00,adm04}. The mass-loss rate by the photoevaporation, which depends on the flux in different spectral ranges, FUV, extreme UV, and X-rays, yields a wide variety of $\sim 10^{-10}-10^{-8}M_{\odot}$yr$^{-1}$ \citep{alx06,erc08,gor09,owe10,tan13}. After the mass accretion rate or the mass-loss rate by the disc wind decreases below this level, the photoevaporation would quickly disperse PPDs \citep[e.g.][]{arm11}; our results would be affected at the late stage of the evolution. However, we expect that the evolution of the $\Sigma$ profile of a photoevaporating PPD is qualitatively different from our results with the magnetically driven disc wind because the photoevaporation mostly affects the disc dispersal in the outer region where the sound speed of the heated gas exceeds the local escape velocity from the central star. Although the photoevaporation could create an inner hole by the combination with the viscous accretion, the local slope of $\Sigma$ remains negative except at the inner edge of the hole \citep[e.g.][]{alx06,owe11}. This is in clear contrast to the evolution with the magnetically driven disc wind. | 16 | 9 | 1609.00437 |
1609 | 1609.09516_arXiv.txt | We present a concept of surface decomposition extended from double Fourier series to nonnegative sinusoidal wave surfaces, on the basis of which linear ion sources apply to the ultra-precision fabrication of complex surfaces and diffractive optics. It is the first time that we have a surface descriptor for building a relationship between the fabrication process of optical surfaces and the surface characterization based on PSD analysis, which akin to Zernike polynomials used for mapping the relationship between surface errors and Seidel aberrations. Also, we demonstrate that the one-dimensional scanning of linear ion source is applicable to the removal of surface errors caused by small-tool polishing in raster scan mode as well as the fabrication of beam sampling grating of high diffractive uniformity without a post-processing procedure. The simulation results show that, in theory, optical fabrication with linear ion source is feasible and even of higher output efficiency compared with the conventional approach. | The optics community has taken a lot of effort into the development of surface modeling methods for optical design~\cite{forbes2007shape,jester2011b,jester2012wavelet,forbes2013fitting,ferreira2016orthogonal}. Unfortunately, none of those methods are developed to improve manufacturability~\cite{forbes2011manufacturability} or to reduce the difficulty of fabrication of optical surfaces. For example, Zernike polynomials are widely applied to describe surface errors and express wavefront data in the field of optical fabrication and testing. Because there is a theoretical relationship between Zernike coefficients and Seidel aberrations often observed in optical tests~\cite{tyson1982conversion}. However, basically, the standard 36-term Zernike polynomial set does not aim to or help to optimize the process of optical fabrication or polishing. When it comes to ultra-precision fabrication of optical surfaces, ion beam technologies play a key role in improving surface precision to extreme. As one of the most precise methods, ion beam figuring (IBF)~\cite{xie2015ion} is employed for finishing lithography optics and telescope mirrors. IBF is realized with a dwell time algorithm akin to that used in computer controlled optical surfacing (CCOS). Longer time the ion beam dwelling at a point results in more material removal around the point, thus it allows correction of surface figures through controlled variations of scanning velocity. In particular, one-dimensional IBF~\cite{zhou2016one}, or sometimes called ion beam profiling~\cite{peverini2010ion}, applies to the fabrication of elongated synchrotron optics such as aspherical X-ray mirrors. Compared with the conventional IBF, one-dimensional IBF is generally implemented by a simpler algorithm meanwhile the long-rectangular-shaped ion beam adopted in one-dimensional case leads to higher output efficiency under the condition for ensuring similar finishing precision. Inspired by Zernike polynomials bridging the relationship between surface errors and optical aberrations, we propose a surface modeling method on the basis of double Fourier series~\cite{moricz1989convergence} to narrow the gap between optical fabrication and surface characterization. The Fourier series decomposition of an optical surface produces a set of wave surfaces with a sinusoidal profile, which by and large are of different periods, amplitudes, and propagation directions. Conceptually, we can sequentially fabricate the decomposed wave surfaces by linear scanning with a linear ion source and the superposition of those fabricated wave surfaces finally build up a surface that approximates to the desired optical surface. Moreover, the power spectral density (PSD) analysis is the statistical analysis of the spatial-distributed wave surfaces described as components of double Fourier series. As to the characterization of optical surfaces, the PSD function is typically utilized~\cite{youngworth2005overview}, especially for evaluating errors in the mid-spatial frequency (MSF) range. So, we realized, a surface descriptor based on Fourier series can build a relationship between the technique of optical fabrication with linear ion source and the PSD-based surface characterization method. This paper introduces the basic theory of surface modeling and decomposition, then illustrates the principle of optical fabrication with linear ion source, and finally demonstrates two applications, i.e., fabrication of large-aperture beam sampling gratings (BSGs) and removal of errors in the MSF range. | We propose a surface modeling method based on double Fourier series and the concept of surface decomposition makes it feasible to fabricate an ultraprecise optical surface with linear ion source. Also, we demonstrate two applications. The first application shows that optical fabrication with linear ion source can be applied to direct fabricating a BSG of high diffractive uniformity without post-processing (for example, chemical mechanical polishing) for correcting the spatial distribution of diffraction efficiency. The second application presents a new approach to remove surface errors in MSF range and we think the basic concept can be realized with other advanced polishing tools. Moreover, optical fabrication with linear ion source will significantly improve the working efficiency compared with the conventional IBF, though small round beam has a higher reachability in the fabrication of complex surfaces. | 16 | 9 | 1609.09516 |
1609 | 1609.02604_arXiv.txt | Using an effective one body approach we describe in detail gravitational waves from classical three body problem on a non-rotating straight line and derive their basic physical characteristics. Special attention is paid to the irregular motions of such systems and to the significance of double and triple collisions. The conclusive role of the collinear solutions is also discussed in short. It is shown that the residuals may contain information about irregular motion of the source of gravitational waves. \pacs{} | Owing to LIGO discoveries \cite{LIGO,LOGOOPEN} we already live in the epoch of the gravitational waves astronomy. It becomes of critical importance to have a full list of the significant sources of Gravitational Waves (GW) in the Nature. A description of many of them can be found in \cite{Thorne87,Maggiore,Buonanno15,Miller16b}. The commonly recognized astrophysical sources of GW are the inspiraling and merging binary compact objects \cite{LIGO,LOGOOPEN}. \begin{figure}[!ht] \centering \begin{minipage}{8.cm} \vskip .truecm \hskip .truecm \includegraphics[width=.8\textwidth,natwidth=200,natheight=200]{Fig1a.png} \vskip .truecm \hskip .truecm \includegraphics[width=.7\textwidth,natwidth=200,natheight=200]{Fig1b.png} \vskip .truecm \hskip .truecm \includegraphics[width=.9\textwidth,natwidth=200,natheight=200]{Fig1c.png} \vskip .truecm \hskip .truecm \includegraphics[width=.65\textwidth,natwidth=200,natheight=200]{Fig1d.png} \end{minipage} \vskip -.8truecm \caption{\small The Gabor transform of GW150914 data from \cite{LIGO,LOGOOPEN}. One sees clear indications of an irregular motion of the source. (In all figures $f=\text{frequency}$, $a=\text{amplitude}$, $t=\text{time}$.)} \label{Fig1} \end{figure} \begin{figure}[!ht] \centering \begin{minipage}{8.cm} \vskip .truecm \hskip .truecm \includegraphics[width=\textwidth,natwidth=200,natheight=200]{Fig2a.png} \vskip .truecm \hskip .truecm \includegraphics[width=\textwidth,natwidth=200,natheight=200]{Fig2b.png} \end{minipage} \vskip .truecm \caption{\small The Gabor transform of NR-template used in \cite{LIGO,LOGOOPEN}. Here we have no low hills, interpreted entirely as random noise in \cite{LIGO}.} \label{Fig2} \end{figure} A basic condition for a significant radiation of GW by a system of bodies is the large acceleration of at least one of them. The initial studies of regular periodic solutions of classical Three Body Systems (3BS) showed that these are not perspective sources of GW for LIGO-type of GW-detectors \cite{Chiba07,Torigoe09,Asada09} just because large accelerations do not exist, even for quite complicated 3BS motions \cite{Zeigel71,Arnold06}. The Letter [12] looks for 3BS periodic sources of GW and emphasizes the role of the two-body-collisions (2BC) for emission of intense quadrupolar GW. An irregular motion (deterministic chaos) is impossible in a binary system, see Fig.\ref{Fig2}. Irregular motions with large accelerations are possible only in N-Body System (NBS) if $N>2$ and only when some singular point is approached. The experience from the study of binary systems is not much helpful for $N>2$. For example, in point particle idealization of NBS the energy conservation is not an obstacle for a resonant transfer of an unbounded amount of energy to one of the particles using the "infinite" Newton reservoir of potential energy of some pair of other particles. To obtain intense GW, one must consider trajectories which approach singular points and transform a significant amount of potential energy into kinetic energy. In the simplest case of an irregular motion $N=3$. Then only two types of singular points exist: 2BC and Three-Body-Collisions (3BC). In the 18-dimensional set of all 3BS-orbits the set of orbits with 2BC has 16 dimensions and consists of three analytic manifolds \cite{Zeigel71,Arnold06}. In the general case, the set of orbits with 3BC has an unknown structure and analytical properties. The 3BC in the collinear 3BS was described in \cite{McGehee74}. The situation may be very complicated. According to the Poincar\'e hypothesis, in an arbitrary small vicinity of each point of the phase space of 3BS there may exist all 7 types of qualitatively different solutions of 3BS-dynamics described by the Chazy classification \cite{Zeigel71,Arnold06}. However, dimensional arguments show that 2BC are more probable than 3BC. Indeed, 2BC can happen for any value of the total angular momentum $\mathbf{K}$ of 3BS. In contrast, 3BC are possible only if $\mathbf{K}\equiv 0$, i.e. the corresponding orbits form some unknown nontrivial subset of this 16-dimensional analytic manifold. When $\mathbf{K}\equiv 0$, 3BS approaches 3BC via central configurations of two types: a) equilateral triangle configuration; b) collinear configuration. We do not consider here the case a) in which 2BC are impossible around 3BC. Thus, our main topic becomes the 3BS on a non-rotating straight line. It describes the basic state of 3BS and introduces the new special functions needed to solve the general three body problem \cite{Fiziev87a}. It is important to stress that this case is produced just by a special choice of the initial conditions for the general 3-dimensional 3BS. From a physical point of view we have to know the intensity of GW emitted not just from the exact solutions with 2BC and 3BC. Actually, we need to study part of the phase flow which is able to follow closely these solutions for a long enough time. It is likely that the needed part of the phase flow has a positive measure in the 18-dimensional manifold of 3BS solutions. Special analytical and numerical methods must be developed for its study. Hence, one can consider the collinear solutions of 3BS with 2BC and 3BC as the simplest physical idealization of the real problem. In this Letter we make the first step to study the collinear 3BS in the context of GW emission. | 16 | 9 | 1609.02604 |
|
1609 | 1609.00601_arXiv.txt | We revisit the photometric variability of stars in the M\,67 field using {\it Kepler/K2-Campaign-5} light curves. In our previous work, we limited the search area around M\,67 to that of a recent ground-based study. In the present work, we expand the search area and apply a more rigorous period-finding algorithm to determine the rotation periods of 98 main sequence cluster members from the same data. In addition, we derive periods of 40 stars from the K2SC detrended light curves. We determine the mean period of single sun-like main sequence cluster members to be $29.6 \pm 0.6$ d. Assuming the periods correspond to stellar rotation, the corresponding mean gyro-age is $5.4 \pm 0.2$ Gyr. | In \citet{gg16}, hereafter Paper I, we presented analyses of the light curves of 639 stars in the field of M\,67 using data from {\it Kepler/K2-Campaign-5}. We derived a gyro-age of $3.7 \pm 0.3$ Gyr from the rotation periods of 28 sun-like single cluster members. Shortly thereafter, \citet{barnes16}, hereafter B16, published independent analyses of the rotation periods of 20 M\,67 cluster members also using {\it K2} data; they derived a mean gyro-age of $4.2 \pm 0.2$ Gyr. There are several reasons to conduct another analysis of the rotation periods of stars in M\,67 using {\it K2} data. First, while these two age estimates are consistent with each other, we would like to track down the source of the 0.5 Gyr age difference and try to arrive at an improved estimate. Second, both studies only examined a subset of the M\,67 member stars observed during {\it Kepler/K2-Campaign-5}. B16 limited their full gyro-age analysis only to 20 cluster members, all within 25 arc minutes of the cluster center and outside the inner 10 arc minutes. In Paper I we restricted the sample to the same region of M\,67 observed by \citet{nard16} in their extensive ground-based study. Third, for nearly half the stars in common between Paper I and B16, the derived rotation periods are very different. Unlike studies conducted on photometry collected during the original {\it Kepler} four year mission, analyses of stellar rotation based on {\it K2} photometry are limited to a mere 80 days or so. This is enough to sample only two to three full rotations for a typical solar age main sequence star. As we showed in Paper I with simulations of rotation period extraction from solar irradiance data, such a short timespan limits the accuracy of the derived period for a sun-like star. Depending on where a particular star is on its activity cycle, it might not even be possible to derive a period for it. Therefore, it becomes necessary to employ as large a sample as possible to arrive at a reliable average period for stars of a given spectral type. The purpose of the present work is to revisit the photometric variability of M\,67 member stars using the {\it Kepler/K2 Campaign-5} data. Our primary goal is to derive a more accurate mean gyro-age for the cluster. We describe and prepare the data for analysis in Section 2. In Section 3 we discuss the results. We present our conclusions in Section 4. | Using {\it Kepler/K2-Campaign-5} light curves, we have performed an improved period analysis of M\,67 member stars compared to our earlier similar study (Paper I). We found that some of the period estimates in Paper I were not true rotation periods. Our new analysis includes stars observed by {\it Kepler} over a wider area than we explored in Paper I, but, because of our more restrictive criteria in the present work, actually yields fewer rotation period determinations from the same data. In addition, we derived periods from a second {\it K2} database containing detrended light curves. The new rotation periods are in excellent agreement with those of B16, where our samples overlap. We determine the mean period for sun-like stars in M\,67 to be $29.6 \pm 0.6$ d, which implies a gyro-age of $5.4 \pm 0.2$ Gyr. These results are similar to those B16 for their smaller sample of sun-like stars in the cluster. However, we obtain different gyro-ages for the cluster depending on which region of the main sequence we consider. Progress in the study of rotation periods can be made by increasing the time baseline of {\it K2} observations of M\,67, which would be possible if it is retargeted. Ground-based observations can also be employed for those stars with larger amplitude variations. | 16 | 9 | 1609.00601 |
1609 | 1609.07241_arXiv.txt | Red quasars are candidate young objects in an early transition stage of massive galaxy evolution. Our team recently discovered a population of extremely red quasars (ERQs) in the Baryon Oscillation Spectroscopic Survey (BOSS) that has a suite of peculiar emission-line properties including large rest equivalent widths (REWs), unusual ``wingless'' line profiles, large \nv /\lya , \nv /\civ , \siiv /\civ\ and other flux ratios, and very broad and blueshifted [\oiii ] \lam 5007. Here we present a new catalog of \civ\ and \nv\ emission-line data for 216,188 BOSS quasars to characterize the ERQ line properties further. We show that they depend sharply on UV-to-mid-IR color, secondarily on REW(\civ ), and not at all on luminosity or the Baldwin Effect. We identify a ``core'' sample of 97 ERQs with nearly uniform peculiar properties selected via \imw\ $\ge 4.6$ (AB) and REW(\civ ) $\ge$ 100 \AA\ at redshifts 2.0--3.4. A broader search finds 235 more red quasars with similar unusual characteristics. The core ERQs have median luminosity $\left<\log L ({\rm ergs/s})\right> \sim 47.1$, sky density 0.010 deg$^{-2}$, surprisingly flat/blue UV spectra given their red UV-to-mid-IR colors, and common outflow signatures including BALs or BAL-like features and large \civ\ emission-line blueshifts. Their SEDs and line properties are inconsistent with normal quasars behind a dust reddening screen. We argue that the core ERQs are a unique obscured quasar population with extreme physical conditions related to powerful outflows across the line-forming regions. Patchy obscuration by small dusty clouds could produce the observed UV extinctions without substantial UV reddening. | Quasars are signposts of rapid accretion onto supermassive black holes (SMBHs) in the centers of galaxies. The observed present-day correlation between the masses of SMBHs and their surrounding galactic spheroids suggests that SMBH accretion/growth is intimately connected to star formation and mass assembly in the host galaxies \citep{Gebhardt00, Tremaine02, Haring04, Gultekin09, Shankar09, Kormendy13}. The similar redshift peaks in the space density of quasars and the cosmic star formation rate at $z\sim 2$--3 indicate that these phenomena occurred together, perhaps in a physically-related way, at early cosmic times \citep{Boyle98,Merloni04, Marconi04, Wall05, Silverman05, Richards06, Rudnick06}. Popular models of galaxy evolution describe major episodes of SMBHs growth occurring in obscurity, deep inside dusty starbursts that appear observationally as sub-mm galaxies (SMGs) or ultra-luminous infrared galaxies \citep[ULIRGs, e.g.,][]{Sanders88,Hopkins05, Hopkins08,Veilleux09b,Simpson14}. Visibly luminous quasars are thought to appear near the end of this evolution when the SMBHs are massive enough to power quasars and a major blowout of gas and dust unveils the bright central source. ``Feedback" from quasar outflows during this evolution stage might play a role in driving the blowouts and regulating star formation in the host galaxies \citep[see also][]{DiMatteo05, Hopkins05, Hopkins10,Rupke11, Rupke13, Liu13, Wagner13}. Quasars that are obscured and reddened by dust can provide important tests of this evolution scheme if they appear preferentially during the brief transition phase from dusty starburst to normal blue quasar \citep[e.g.,][]{Hopkins05, Urrutia08, Glikman12, Glikman15,Wu14,Banerji15, Assef15}. However, other explanations for quasar reddening and obscuration are also possible. The Unified Model of AGN attributes the observed differences between Type 1 (broad line) and Type 2 (narrow line) AGN to orientation effects associated with an axisymmetric dusty torus that resides near the central engine of all AGN \citep{Antonucci93, Urry95,Netzer15}. In this scenario, Type 1 AGN offer direct views of the central engine and broad emission line regions while in Type 2s these regions are heavily obscured due to our nearly edge-on view of the torus/accretion disk geometry. Intermediate orientations might produce intermediate amounts of obscuration such that we observe Type 1 quasars with red colors and perhaps a wavelength-dependent mix of Type 1 and Type 2 properties \citep{Greene14}. In this context, red quasars provide valuable tests of the geometry and physical structure of quasar environments. Searches for red and obscured quasars have been propelled recently by wide-field surveys such as the Sloan Digital Sky Survey \citep[SDSS,][]{Zakamska03, Reyes08, Alexandroff13}, the Two Micron All Sky Survey \citep[2MASS,][]{Gregg02,Glikman07,Glikman12}, the United Kingdom Infrared Deep Sky Survey \citep[UKIDSS,][]{Glikman13}, Spitzer Space Telescope \citep{Lacy04, Lacy13, Stern05, Stern07,Hickox07,Donley12}, and the Wide-field Infrared Survey Explorer \citep[WISE,][]{Mateos12,Stern12,Assef13,Yan13}. Most of these searches combine broad-band photometry with other data such as visible-wavelength spectra or radio or X-ray fluxes to identify regions of color space populated by obscured AGN \citep[see also][and refs. therein]{Hao13}. Obscured quasars also turn up serendipitously in galaxy searches. For example, ``HotDOG'' satisfy the color selection criteria of dust obscured galaxies \citep[DOGs,][]{Dey08} even though their luminosities and especially their mid-IR emissions are believed to be dominated by hot dust powered by luminous embedded AGN \citep[][and refs. therein]{Eisenhardt12,Wu12,Tsai15,Toba16,Fan16b}. In \cite{Ross15}, our team discovered a unusual population of extremely red quasars (ERQs) in Data Release 10 (DR10) of the Baryon Oscillation Sky Survey \citep[BOSS,][]{Dawson13,Ross12} in the Sloan Digital Sky Survey-III \citep[SDSS-III,][]{Eisenstein11}. Starting with spectroscopically confirmed quasars in the BOSS quasar catalogs \citep[][]{Paris14, Paris16}, we combined photometry from the SDSS and WISE to select the most extreme cases with red colors similar to DOGs, e.g., with $r-W4 > 14$ and $W4 < 8.0$ (in Vega magnitudes, where $W4$ measures observed-frame $\sim$22 \mum ). This search finds 65 quasars across a wide range of redshifts ($0.28 < z_e < 4.36$) with a variety of properties. It includes a mix of Type 1 and 2 quasars, some starburst-dominated quasars, and several with broad absorption lines (BALs) that are strong and broad enough to suppress the $r$ band flux and satisfy the $r-W4$ color criterion even though the emitted spectrum is not extremely red. However, there was also a remarkable discovery that many ERQs at $z_e\ga 2$ appear to be a unique population with an ensemble of peculiar emission-line characteristics including very large rest equivalent widths (REWs), line profiles that are lacking strong Lorentzian (or logarithmic) wings characteristic of other broad-line AGN, and unusual line flux ratios that can include \nv\ \lam 1240 $>$ \lya , strong \aliii\ \lam 1860, and large ratios of \nv /\civ\ \lam 1549 and \siiv\ \lam 1400/\civ\ (see Figure~15 in \citealt{Ross15} for examples). These properties were discussed earlier by \cite{Polletta08} for an individual red quasar that is clearly in the same class as ERQs. Followup near-IR observations of ERQs have revealed even more remarkable properties, notably [\oiii ] \lam 5007 emission lines with the largest FWHMs and highest blueshifted wing velocities ever reported, both reaching $\sim$5000 \kms\ \citep[][Hamann et al. 2016a, in prep.]{Zakamska16}. The [OIII] lines identify powerful quasar-driven outflows in relatively low-density environments that are inferred (from photoionization arguments) to reside at least $\sim$1~kpc from the quasars. The near-IR observations also reveal that these ERQs have extreme kinematics in their broad emission-line regions, including blueshifts that can exceed 2500 \kms\ in \civ\ and other high-ionization UV lines, e.g., compared to the \hi\ Balmer lines and low-ionization permitted lines in the UV (Hamann et al. 2016a, in prep., also \S5.8 below). This ensemble of exotic emission-line properties is central to the physical nature of ERQs and their possible relationship to an early transition stage of quasar-galaxy evolution. We present a detailed analysis of the emission lines and line-forming regions of ERQs in Hamann et al. (2016a, in prep.). In the present paper, we combine broad-band photometry from SDSS and WISE with new measurements of the \civ\ and \nv\ emission lines in the final BOSS data release (DR12) to 1) quantify the emission-line properties of ERQs compared to the overall BOSS quasar population, 2) examine the relationships of these properties to quasar colors and luminosities, and 3) revise the selection criteria to find many more ERQ with similar exotic properties. How rare are the emission-line properties of ERQs in BOSS quasars overall? Are they closely tied to reddening and obscuration? Do they correlate with outflow signatures such as blueshifted broad absorption lines (BALs)? Are ERQs with exotic properties a unique population or just outliers in trends that occur across the larger BOSS quasar population? Section 2 describes the quasar samples and photometric data used in this study. \S3 and Appendix A presents our new catalog of UV line and continuum measurements. \S4 examines the relationships of ERQ emission-line properties to the quasar colors and luminosities across the BOSS quasar population. \S5 describes the selection and important characteristics of a new large sample of ERQs with exotic properties. \S6 discusses some of the implications of our results and \S7 provides a summary. Appendix B tabulates a supplemental sample of ``ERQ-like'' quasars. Throughout this paper, we adopt a cosmology with $H_o = 71$ \kms\ Mpc$^{-1}$, $\Omega_M = 0.27$ and $\Omega_{\Lambda}=0.73$. We also use magnitudes in the AB system except as noted. | Our analysis in \S4 and \S5 shows that high-redshift ERQs defined by \imw\ $\ge$ 4.6 often have a suite of peculiar emission-line properties, a high incidence of broad outflow absorption lines, and unusual SEDs that are not consistent with simple reddening\citep[see also][]{Polletta08}. This ensemble of exotic properties identifies the ERQs as a unique new quasar population with unique physical characteristics. The additional requirement for REW(\civ ) $>$ 100 \AA\ in our core ERQ sample (\S5.1) helps to weed out interlopers that are just normal quasars reddened by dust to focus the sample more narrowly on quasars in this exotic new population. We present analyses of the physical conditions in the line-forming regions of the core ERQs in Hamann et al. (2016a, in prep.). Below we discuss possible causes for their red colors (\S6.1) and physical models that might explain the overall ERQ phenomenon (\S6.2). \subsection{On the Origins of Red \imw\ Colors} The median color of the core ERQs is almost 3 magnitudes redder than the median overall in the $W3$-detected quasar sample (\S5.1). This could be caused by UV obscuration, enhanced emission in the mid-IR, or a combination of these factors. Given the extreme and peculiar nature of ERQs, we consider a number of possibilities. \subsubsection{UV Suppression} Red \imw\ colors can be caused by dust obscuration in the rest-frame UV. This interpretation is not straightforward for the core ERQs because their relatively flat UV spectra are inconsistent with simple reddening (\S5.5, Figures~11 and 16). Most of the core ERQs have Type 1 emission lines, so we do appear to have direct views of the central engines in the UV. However, the flat UV spectral slopes resemble the high-redshift candidate Type 2 quasars described by \cite{Alexandroff13}. These authors attribute the Type 2 SEDs to moderate dust reddenings with typically $E(B-V) \sim 0.5$ plus scattered UV light or patchy obscuration that allows some direct UV/blue quasar emission to be viewed relatively unreddened \citep[see also][]{Greene14}. Patchy obscuration was also invoked by \cite{Veilleux13a, Veilleux16} to explain the spectrum of the low-redshift BAL quasar Mrk 231. This quasar's SED is very red across the visible but remarkably flat at rest wavelengths $\la$2400 \AA . Patchy obscuration is strongly favored over scattered light in Mrk 231 because the flat UV spectrum has negligible polarization \citep{Smith95}. Patchy obscuration could explain the unusual UV to mid-IR SEDs of the core ERQs, although scattered light contributions in the UV cannot be ruled out with existing data (see Alexandroff et al., in prep.). One important implication of patchy obscuration is that the dust patches/clouds cannot be much larger than the UV emission source in the accretion disk, which is only $\sim$0.01 pc across in luminous quasars \citep[e.g.,][and 2016c, in prep.]{Hamann11}. Patchy obscuration seems much more plausible than the explanations favored for HotDOG SEDs. In particular, \cite{Assef15} and \cite{Toba16} attribute HotDOG SEDs to very large dust extinctions in front of the quasars, typically with $E(B-V)\sim 7.8$ to explain the very red colors across the rest-frame visible to mid-IR, plus hot stars from high star formation rates that create the flat UV spectral slopes \citep[but cf.][]{Assef16}. This picture seems unlikely for the core ERQs because their UV spectra are quasar-dominated down to at least the wavelengths where we measure very strong and broad emission lines of \ovi\ \lam 1034 and \nv\ \lam 1240 \citep[Figures 8 and 12, also][]{Ross15}. It is not clear this picture can even apply generally to HotDOGs because many of them also have Type 1 quasar-dominated spectra in the rest-frame UV \citep[\S5.6][]{Wu12,Toba16}. Another way to suppress the UV flux might be viewing angle effects in a flattened accretion disk geometry. This could produce red \imw\ colors if the mid-IR emission is roughly isotropic while the observed UV flux is diminished by a $\sim$$\cos\theta$ factor that derives from the projected area of the UV-emitting disk \citep[with negligible limb darkening effects,][and $\theta$ measured from the disk axis]{Nemmen10}. The problem with this picture is that $\sim$3$^m$ of UV suppression in the core ERQs would require viewing angles very close to edge-on, with disk axis angles $\theta\sim 86^o$ from the line of sight. This seems highly implausible given that a dusty torus/wind must be present to intercept UV light and reprocess it into the observed strong mid-IR emission. The expected covering fractions of this dusty material ($\sim$50\%, see \S6.1.2 below) correspond to angular elevations $\sim$30$^o$ above and below the disk plane (ignoring clumpiness, which would lead to even higher elevations). Lines of sight that skim the edge of this torus/wind material, with $\theta\sim 60^o$, would produce only a factor of $\sim$2 UV flux suppression from projection effects, not the requisite $\sim$3$^m$. We do note however that, if the dusty torus/wind is clumpy, it might be possible to have some nearly-equatorial sight lines pass through the torus without being blocked by dusty clumps. A more exotic way to suppress the UV flux without UV reddening might be by electron scattering in a thick layer of highly-ionized gas above the UV-emitting accretion disk. Large amounts of this material are expected to develop in BAL winds due to the intense ionizating radiation from the inner accretion disk \citep{Murray95}. This gas fails to accelerate and can hover above the disk because it is too ionized and too transparent for radiative driving \citep[see also][and refs. therein]{Proga07, Sim10}. This highly-ionized failed wind material is believed to cause the X-ray weakness of BAL quasars and, in some cases, it might be Compton thick in front of the X-ray source even though the quasars are bright and visible to us in the UV \citep{Gallagher07}. The core ERQs might be extreme cases where a failed wind is spatially extended to cover larger portions of the UV-emitting disk. The amount of UV flux suppression and the resulting observed colors would depend on the geometry and optical depths of the obscuring material above different portions of the disk. However, a potential serious problem is that strong UV continuum fluxes are still needed to power the observed strong emission lines (Hamann et al. 2016a, in prep.). The failed wind material would need to be elevated above the disk enough to give the emission-line regions a clear view of the UV continuum source while our view is still substantially attenuated. Another exotic possibility is structural disruptions in the inner accretion disk. This should be a transient phenomenon with $\sim$3$^m$ drops in the UV emission followed by similar drops in the broad emission-line fluxes after time delays of $<$1 yr corresponding to the light travel time out to the broad emission-line regions \citep{Kaspi07}. This scenario appears to be ruled out by 12 ERQs in our sample with repeat spectroscopic observations in BOSS, SDSS-I/II or the VLT obtained $>$0.5 yrs apart in the rest frame (including 9 with spectra $>$1 year apart, Hamann et al. 2016a, in prep.). We do not find any instances of dramatic variability in the line shapes or the line strengths relative to the continuum. \subsubsection{Mid-IR Flux Enhancements} Red \imw\ colors might also be caused by enhanced mid-IR emission. Hot dust in the inner torus is believed to dominate the SEDs of luminous Type 1 quasars from $\sim$2 \mum\ to $>$10 \mum\ \citep{Efstathiou95, Netzer07a, Mor09, Mor11, Deo11}. It overwhelms contributions from starlight and possible PAH emission at these wavelengths. The amount of mid-IR flux relative to the UV depends on our viewing angle and the dust covering factor as seen from the central source. Hot dust covering fractions in quasars are believed to be in the range 30--70\% \citep{Gaskell07,Mor09,Netzer16} with a nominal value around 50\% \cite{Lawrence10}. Larger covering factors might occur in extreme cases if the dusty ``torus" is a dusty wind \citep{Konigl94,Gallagher15,Netzer15} extending farther than normal vertically above the accretion disk. This would allow the dust to reprocess more UV luminosity into mid-IR emission \citep[also][]{Wang11,Wang13}. Similarly, high-speed BAL winds might ablate dusty clumps off of a traditional torus to increase the dust covering fractions and enhance the mid-IR flux \citep{Wang13, Wagner13}. However, this scenario cannot explain the red colors of ERQs because, even with dust covering factors increased to unity (which is not realistic), the maximum mid-IR enhancement would be only $\sim$0.8$^m$ instead of the requisite $\sim$3$^m$. Dust heated by star formation is another unlikely contributor to the mid-IR flux because the radiation temperatures needed for emission in $W3$ (rest-frame $\sim$3.4 \mum ) are very high, nominally $\sim$850 K. This is a natural temperature for dust near quasars \citep{Rowan-Robinson95,Efstathiou95, Nenkova08, Mor09}, but in star forming galaxies the dust temperatures are observed to be $\la$60 K with the dust emissions peaking at wavelengths $\ga$50 \mum\ \citep{Kirkpatrick12, Magnelli12,Melbourne12,Chapman05}. If dusty starbursts were somehow important to the mid-IR fluxes of ERQs, they should produce very red colors across the mid-IR (e.g., in \wtmwf ), which are not observed (Figure~10). Another possibility for mid-IR enhancements is strong PAH emissions in the bands at 3.2, 6.2 and 7.7 \mum . However, this can also be ruled out because i) PAHs are nominally destroyed by the hard UV radiation in quasar environments, and ii) the 3.2 \mum\ feature is weak compared to 6.2 and especially 7.7 \mum\ such that a PAH-dominated spectrum would produce red \wtmwf\ colors at the ERQ redshifts, which are not observed \citep[Figure 10, see][and refs. therein]{Sales10,Draine11}. \subsection{Toward a Physical Model} We conclude from \S6.1 that the red \imw\ colors of the core ERQs are caused by dust obscuration, probably by a patchy medium that suppresses the observed UV fluxes without substantial UV reddening. A critical point for models of the core ERQs is that this obscuration is closely related to their peculiar line properties. Is this relationship defined by geometry and orientation effects or by unique physical conditions that are perhaps tied to a particular phase of quasar evolution? A good starting point is to ask where the obscuring dust is located. \cite{Banerji12,Banerji13} argue that the obscuration in highly reddened Type 1 quasars (HR1s) occurs on galactic scales. Recall that these quasars have SEDs consistent with a simple dust reddening screen (\S5.5, Figure~16). This is not the case for the core ERQs. If patchy obscuration is involved, then dust extinction on galactic scales might be ruled out by the requirement for dust patch/cloud sizes $\la$0.01 pc across (\S6.1.1), because clouds with these sizes are not expected in a galactic interstellar medium. Another problem is the close relationship between red \imw\ colors and the specific emission-line properties of ERQs. This seems to favor obscuration on small scales where it can be readily coupled to the orientation or physical conditions in quasar environments. It might be possible to couple the line properties of the core ERQs to obscuration on galactic scales if the quasars drive high-speed outflows that ablate and disperse dusty molecular clouds in the host galaxies. This is expected to occur when quasars provide ``feedback'' to their galactic environments \citep{Hopkins10, Faucher12, Wagner13}. It could, in principle, connect the physical conditions on small scales in quasar line-forming regions to the amounts of obscuration occurring on large scales in the host galaxies. Cloud shredding might also produce small dusty clumps capable of patchy obscuration far from the quasars. Alternatively, the obscuration might occur on small scales in a dusty torus/wind just outside the traditional BLR. Recent studies suggest that this material is clumpy \citep[e.g.,][]{Hoenig07, Nenkova08, Thompson09}, so it might also produce the purported patchy obscuration in the core ERQs. In clumpy torus models that posit self-gravitating clumps stable against tidal forces from the central black hole \citep{Hoenig07}, the predicted clump sizes satisfy a prerequisite for patchy obscuration in that they are smaller than the UV continuum source. For example, equation 5 in \cite{Hoenig07} predicts that dusty clumps 1 pc away from a black hole of mass $10^9$ M$_{\odot}$ should have maximum diameters of $\sim$0.001 pc. One consequence of small-scale obscuration by a dusty torus/wind could be strong orientation effects in an axisymmetric geometry. However, it seems very difficult to explain the unique emission-line properties of the core ERQs if there are only orientation effects, e.g., if the core ERQs are like other quasars except for a particular viewing perspective that intersects $\sim$3$^m$ of dusty torus/wind material, Most problematic for an orientation-only model is the very broad and blueshifted [\oiii ] \lam 5007 lines that identify powerful outflows on galactic ($\sim$1 kpc) scales in the four core ERQs tested so far \citep[][Hamann et al. 2016a, in prep.]{Zakamska16}. It does not seem feasible to hide these features by orientation effects in a majority of quasars while revealing them only for specific viewing angles in ERQs. Given that the core ERQs are only about 2\% of the similarly-luminous quasar population in our $W3$-detected sample (\S5.9), the range of viewing angles that produces core ERQ properties would have to be only $\sim$2\%. Other aspects of the core ERQ emission lines are also not readily explained by orientation effects, including the peculiar flux ratios such as large \nv /\civ . We conclude that while orientation might play an important role in the ERQ phenomenon, their unique line properties overall appear to require unique physical conditions. These physical conditions might be unusually powerful outflows that encompass large portions of line forming regions as well as the dusty ``torus.'' The [\oiii ] data mentioned above for a small subset of the core ERQs, along with high fractions of BALs and large \civ\ emission-line blueshifts (\S5.3 and \S5.8), indicate that outflows are pervasive in ERQs across a wide range of spatial scales. \civ\ blueshifts are often interpreted in terms of a two-component broad line region (BLR), with one component near the disk plane dominated by virial motions and another that is outflowing and vertically extended above the disk \citep[][and refs. therein]{Gaskell82, Collin88, Marziani96, Leighly04b, Leighly07b, Richards11}. Higher ionization lines like \civ\ and \nv\ are more likely to participate in the outflow while lower ions favor the denser and more radiatively shielded disk component. The outflow lines are blueshifted because the accretion disk bisects the flow and obscures receding material from our view. The ERQs might be extreme examples of outflow-dominated BLRs. The puzzle for ERQs in this BLR outflow picture is that they have dramatically larger REWs than other quasars with large \civ\ blueshifts (\S5.8). Well-studied quasars with large blueshifts \citep[e.g., PHL 1811 and its analogs,][]{Leighly04a,Leighly04b,Leighly07b,Wu11j,Wu12j,Luo15} are also X-ray weak. This is consistent with large-blueshift quasars having soft far-UV spectra favorable for radiative acceleration. The reasoning here is that soft far-UV spectra lead to moderate degrees of ionization in the outflow gas where ions like \civ\ and \ovi\ are then available for line driving in the near-UV \citep[see][and the Leighly et al. papers cited above]{Murray95}. Small \civ\ REWs are a natural consequence of this outflow picture because BLRs photoionized by a soft spectrum should produce less \civ\ emission relative to the near-UV continuum \citep[also][]{Korista97}. In contrast to this, all but one of the ERQs and ERQ-like quasars with blueshifts $>$2500 \kms\ have REW(\civ ) $\ge$ 87 \AA\ up to 281 \AA\ (in J101326+611219, Figure~18). ERQs might have unprecedented large REWs in this outflow picture if their BLRs are more vertically extended above the accretion disk than other quasars. This would lead to the line-forming regions intercepting more of the quasar continuum luminosity for reprocessing into line radiation (Hamann et al. 2016a, in prep.). Extended BLRs in an outflow might also blend smoothly with the high-speed low-density [\oiii ] gas much farther out. The idea of BLR outflows connecting to large-scale [OIII] outflows would be consistent with studies of less extreme lower-redshift quasars that show \civ\ blueshifts correlated with the blueshifts and outflow kinematics measured in [\oiii ] \citep{Zamanov02,Aoki05}. In the core ERQs, where the \civ\ and [\oiii ] lines can have similar widths, the distinction between ``broad'' and ``narrow'' line regions is particularly ambiguous \citep[\S5.4][Hamann et al. 2016a, in prep.]{Zakamska16}. Dusty winds \citep[e.g.,][]{Keating12,Gallagher15} in the ERQs might also be more vertically extended and participating in the same general outflow as the ionized gas. If the inner edge of the dusty wind is at the dust sublimation radius overlapping with the outer BLR \citep[as expected,][]{Gaskell09, Mor11, Goad12}, then portions of the BLR outflow would be dusty \citep[also][]{Wang13}. This outflow should be clumpy based on the evidence for a clumpy torus \citep{Nenkova08, Thompson09} and clumpy BLRs and BAL outflows \citep[e.g.,][]{deKool97, Arav97, Hamann13}. It could therefore produce patchy obscuration across the UV continuum source like we infer for the ERQs (\S6.1). Extended dusty outflows could also distribute small dusty clumps across larger fractions of sky as seen from the central quasar, thus avoiding the problem mentioned above that small-scale obscuration in a torus/wind would produce strong orientation effects. If the obscuration in the core ERQs does occur in dusty outflows, then all core ERQs should have considerable outflow gas accompanying the dust along our lines of sight and we might wonder why they do not all have strong outflow absorption lines in their spectra. The reason could be that the dusty clumps are opaque to UV radiation, so they suppress the observed UV flux without producing UV absorption lines \citep{Veilleux13a,Veilleux16}. BALs and BAL-like outflow features would form mainly on the periphery of these clumps, or in the spaces between them, where there is less dust and we do still see the UV continuum source. This could lead to a situation where BALs and BAL-like features are usually weak and sometimes absent from the observed spectra of ERQs even though powerful dusty outflows are present along our lines of sight. If outflows are the key ingredient to understanding the ERQ phenomenon, then we must explain why the outflows are more powerful or more spatially extended in ERQs compared to other quasars. Outflows driven by magneto-centrifugal forces \citep{Proga03b,Everett05,Fukumura10,Keating12} might be enhanced in ERQs if the quasars have unusually strong magnetic fields threaded vertically through their accretion disks. Flows driven by radiation pressure might be enhanced by higher accretion rates (relative to Eddington), higher metallicities (that can increase the opacities for radiative acceleration), or softer far-UV spectra (that favor line driving in the near-UV without over-ionization). There is some evidence for high metallicities in the ERQs based on the strong \nv\ \lam 1240 emission lines and large \siiv\ \lam 1400/\civ\ flux ratios \citep[][Hamann et al. 2016a, in prep.]{Polletta08}. Other studies have reported an observational link between large \civ\ blueshifts and high accretion rates \citep{Baskin05, Wang11, Wang13, Marziani12,Luo15}, which would be consistent with high accretion rates occurring in the ERQs. The last critical question is whether the core ERQs are tied to a particular stage of quasar-galaxy evolution (\S1). Observations of ERQ host galaxies and extended environments are needed to address this question. The outflow scenario that we favor above does not directly connect the quasars to galaxy evolution because it emphasizes small-scale phenomena controlled by accretion physics. However, that connection could be established by ERQ outflows shredding dusty clouds in the galaxies to create patchy obscuration on galactic scales (\S6.1.1). The relationship of ERQs to galaxy evolution might also be more holistic, e.g., powerful outflows and high accretion rates are expected to occur generally in obscured quasars during the aftermath of a triggering event that funnels matter toward the central black hole in young gas-and-dust-rich galaxies \citep{Sanders88,Hopkins05, Hopkins08,Veilleux09b,Rupke11, Rupke13, Liu13}. ERQs might be interpreted within this paradigm like other red quasar populations -- caught in the transition between the initial triggering event and a more quiescent phase of galaxies hosting normal blue (unobscured) quasars (see refs. in \S1). If we want to place ERQs in a simple monotonic evolution sequence like this with HotDOGs \citep[see][and refs. therein]{Wu12,Fan16}, then the lesser obscurations in ERQs (Figure~16) suggest that they are in a slightly more advanced stage than HotDOGs, farther in time from the triggering event and closer to the blue quasar phase. We could also infer from the numbers of core ERQs and ERQ-like quasars compared to luminous blue quasars (\S5.9) that the lifetime of the core ERQ/ERQ-like phase is a few percent of total quasar lifetimes. | 16 | 9 | 1609.07241 |
1609 | 1609.04845_arXiv.txt | After a long low-activity period, a $\gamma$-ray flare from the narrow-line Seyfert 1 PKS 1502$+$036 ($z=0.4089$) was detected by the Large Area Telescope (LAT) on board {\em Fermi} in 2015. On 2015 December 20 the source reached a daily peak flux, in the 0.1--300 GeV band, of (93 $\pm$ 19)$\times$10$^{-8}$ ph cm$^{-2}$ s$^{-1}$, attaining a flux of (237 $\pm$ 71)$\times$10$^{-8}$ ph cm$^{-2}$ s$^{-1}$ on 3-hr time-scales, which corresponds to an isotropic luminosity of (7.3 $\pm$ 2.1)$\times$10$^{47}$ erg s$^{-1}$. The $\gamma$-ray flare was not accompanied by significant spectral changes. We report on multi-wavelength radio-to-$\gamma$-ray observations of PKS 1502$+$036 during 2008 August--2016 March by {\em Fermi}-LAT, {\em Swift}, {\em XMM-Newton}, Catalina Real-Time Transient Survey, and the Owens Valley Radio Observatory (OVRO). An increase in activity was observed on 2015 December 22 by {\em Swift} in optical, UV, and X-rays. The OVRO 15 GHz light curve reached the highest flux density observed from this source on 2016 January 12, indicating a delay of about three weeks between the $\gamma$-ray and 15 GHz emission peaks. This suggests that the $\gamma$-ray emitting region is located beyond the broad line region. We compared the spectral energy distribution (SED) of an average activity state with that of the flaring state. The two SED, with the high-energy bump modelled as an external Compton component with seed photons from a dust torus, could be fitted by changing the electron distribution parameters as well as the magnetic field. The fit of the disc emission during the average state constrains the black hole mass to values lower than 10$^8$ M$_{\odot}$. The SED, high-energy emission mechanisms, and $\gamma$-ray properties of the source resemble those of a flat spectrum radio quasar. | Relativistic jets are mainly produced by radio-loud active galactic nuclei (AGN) such as blazars and radio galaxies hosted in giant elliptical galaxies \citep{blandford78}. The discovery by the Large Area Telescope (LAT) on-board the {\em Fermi Gamma-Ray Space Telescope} of variable $\gamma$-ray emission from narrow-line Seyfert 1 (NLSy1) galaxies revealed the presence of a new class of AGN with relativistic jets \citep[e.g.,][]{abdo09a,abdo09b,dammando12,dammando15a}. Considering that NLSy1 are usually hosted in spiral galaxies \citep[e.g.,][]{deo06}, the presence of a relativistic jet in these sources seems to be in contrast to the paradigm that the formation of relativistic jets could happen in elliptical galaxies only \citep{boett02,marscher10}. This finding poses intriguing questions about the nature of these objects and the formation of relativistic jets. In particular, one of the debated properties of NLSy1 is their relatively small black hole (BH) mass ($M_{BH}$ = 10$^{6-8}$ M$_{\odot}$) in comparison to blazars and radio galaxies. It was suggested that the BH masses of NLSy1 are underestimated due either to the effect of radiation pressure \citep{marconi08} or to projection effects \citep{baldi16}. Higher BH masses than those derived by the virial method \citep[e.g.,][]{yuan08} are in agreement with the values estimated by modelling the optical/UV data with a Shakura and Sunyaev disc spectrum \citep{calderone13}. PKS\,1502$+$036 has been classified as a NLSy1 on the basis of its optical spectrum: full width at half-maximum FWHM (H$\beta$) = (1082 $\pm$ 113) km s$^{-1}$, [OIII]/H$\beta$ $\sim$ 1.1, and a strong Fe II bump \citep{yuan08}. Among the radio-loud NLSy1, PKS 1502$+$036 has one of the highest radio-loudness values ($RL$ = 1549)\footnote{$RL$ being defined as the ratio between the 1.4\,GHz and 4400\,\AA\, rest-frame flux densities.}. The source exhibits a compact core-jet structure on pc-scales, with the radio emission dominated by the core component, while the jet-like feature accounts for only 4 per cent of the total flux density \citep{orienti12,dammando13a}. Simultaneous multi-frequency Very Large Array observations carried out at various epochs showed substantial spectral and flux density variability. \citet{lister16} analyzing the MOJAVE images of PKS 1502$+$036 collected during 2010--2013 found a jet component moving at sub-luminal speed (i.e., 1.1$\pm$0.4 $c$). Optical intra-day variability with a flux amplitude of about 10 per cent was reported for PKS 1502$+$036 by \citet{paliya13}. In infrared bands, a variation of 0.1--0.2 mag in 180 days was observed by the {\em Wide-field Infrared Survey Explorer} \citep{jiang12}. In the $\gamma$-ray energy band PKS 1502$+$036 was not detected in the 90's by the Energetic Gamma-Ray Experiment Telescope (EGRET) on board the {\em Compton Gamma Ray Observatory} at E $>$ 100 MeV \citep{hartman99}. On the other hand, the source has been included in the first, second, and third {\em Fermi}-LAT source catalogues \citep[1FGL, 2FGL, 3FGL;][]{abdo10,nolan12,acero15}. No significant increase of $\gamma$-ray flux was observed between 2008 August and 2012 November \citep{dammando13a}. In 2015 December, $\gamma$-ray flaring activity from PKS 1502$+$036 was detected on a daily time-scale by {\em Fermi}-LAT \citep{dammando15b}, confirmed at lower energies by {\em Swift} observations \citep{dammando15c}. In this paper, we discuss the flaring activity of PKS\,1502$+$036 observed in 2015 December--2016 January in comparison to the 2008--2015 data collected from radio to $\gamma$ rays. The paper is organized as follows. In Section 2, we report the LAT data analysis and results. In Section 3 we present the results of the {\em Swift} and {\em XMM-Newton} observations. Optical data collected by the Catalina Real-Time Transient Survey (CRTS) and radio data collected by the 40 m Owens Valley Radio Observatory (OVRO) single-dish telescope are reported in Section 4. In Section 5, we discuss the properties and the modelling of the spectral energy distribution (SED) of the source during an average activity state and the high activity state. Finally, we draw our conclusions in Section 6. Throughout the paper, a $\Lambda$ cold dark matter cosmology with $H_0$ = 71 km s$^{-1}$ Mpc$^{-1}$, $\Omega_{\Lambda} = 0.73$ and $\Omega_{\rm m} = 0.27$ \citep{komatsu11} is adopted. The corresponding luminosity distance at $z =0.4089$ \citep[i.e. the source redshift;][]{schneider10} is d$_L = 2220$\ Mpc. In the paper, the quoted uncertainties are given at the 1$\sigma$ level, unless otherwise stated, and the photon indices are parametrized as $dN/dE \propto E^{-\Gamma}$ with $\Gamma$ = $s$+1 ($s$ is the spectral index). | In this paper we reported on the observation by the {\em Fermi}-LAT of flaring $\gamma$-ray activity from the NLSy1 PKS 1502$+$036 in 2015 December. On 2015 December 20 the source reached an apparent isotropic luminosity in the 0.1--300 GeV energy range of (2.9 $\pm$ 0.6)$\times$10$^{47}$ erg s$^{-1}$, which is only a factor of 2--3 lower than those reached by the NLSy1 SBS 0846$+$513 and PMN J0948$+$0022 during a flare \citep{dammando13b,dammando15d}. On a 3-hr time-scale the source reached a peak flux of (237 $\pm$ 71)$\times$10$^{-8}$ ph cm$^{-2}$ s$^{-1}$, corresponding to an apparent isotropic luminosity of (7.3 $\pm$ 2.1)$\times$10$^{47}$ erg s$^{-1}$. The average photon index ($\Gamma_{\gamma}$ = 2.62 $\pm$ 0.04) and apparent isotropic luminosity (L$_{\gamma}$ = 1.3 $\pm$ 0.1)$\times$10$^{46}$ erg s$^{-1}$ estimated over 2008 August 5--2016 March 24 period are similar to the values observed for FSRQ \citep[e.g.,][]{ackermann15}. No significant change of the $\gamma$-ray spectrum was observed during the flare, with a photon index of $\Gamma_{\gamma}$ = 2.54 $\pm$ 0.04. In addition to the {\em Fermi}-LAT data, we presented multi-wavelength observations of PKS 1502$+$036 during the period 2008 August--2016 March including {\em Swift}, {\em XMM-Newton}, CRTS, and OVRO data. An increase of the activity was observed by {\em Swift} in X-rays, UV, and optical on 2015 December 22, just a couple of days after the $\gamma$-ray peak, suggesting a common mechanism for the multi-frequency variability during the flare. \noindent The source remained in a bright X-ray state during 2015 December--2016 January, with a photon index ranging between 1.0 and 1.8. These values are harder than those observed in 2012, when the source had no significant high-energy outbursts. This suggests a dominant contribution of the jet emission in the X-ray energy range during the high activity period. The X-ray spectrum collected by {\em XMM-Newton} in 2012 was quite well fit by a simple PL model, although some residuals are observed at low and high energies. These residuals hint at the presence of a soft X-ray excess and the Fe line, respectively. A better fit was obtained by using a broken power-law model, suggesting the presence of two emission components in X-rays, but the uncertainties related to the spectral parameters are quite large. Deeper {\em XMM-Newton} observations are required for investigating these features in detail. Flaring activity was also observed in the radio band. At 15 GHz the peak was detected on 2016 January 12, about three weeks after the $\gamma$-ray peak. This radio flare may be the delayed counterpart of the $\gamma$-ray one due to opacity effects and the propagation of the shock along the jet. This suggests that the $\gamma$-ray emitting region is placed at $\sim$0.3 pc from the radio 15 GHz radius, and therefore at a distance between 3.0 and 5.2 pc from the central BH, well beyond the BLR. We compared the broad-band SED of the 2016 flaring activity state with that from an average state of PKS 1502$+$036 observed in 2012. Both the SED show a Compton dominance $\sim$10. This high value indicates that the EC emission is the main mechanism for producing $\gamma$ rays, such as for FSRQ \citep[e.g.,][]{finke13}, confirming the similarities between $\gamma$-ray emitting NLSy1 and FSRQ. The two SED, with the high-energy bump modelled as an EC component of seed photons from a dust torus, could be modelled by changing both the electron distribution parameters and the magnetic field. An accretion disc is identified in the UV part of the spectrum for the average activity state, with a luminosity of L$_{\rm\,disc}$ = 6$\times$10$^{44}$ erg s$^{-1}$. This value is lower than the luminosity usually observed for FSRQ \citep[e.g.,][]{ghisellini14} as well as for the $\gamma$-ray NLSy1 PMN J0948$+$0022 \citep{dammando15d}. On the other hand, no evidence of thermal emission from the accretion disc has been observed for the $\gamma$-ray NLSy1 SBS 0846$+$513 and PKS 2004$-$447, with a luminosity of the accretion disc estimated to be very low \citep[10$^{42-43}$ erg s$^{-1}$;][]{dammando13b,orienti15}. No superluminal motion was observed in VLBI images during 2008--2012 \citep{dammando13a}, with only a sub-luminal component reported in \citet{lister16}. This is in contrast to the radio spectral variability, the one-sided structure, the observed $\gamma$-ray luminosity and the Doppler factor estimated by SED modelling. This result resembles the `Doppler factor crisis' observed in bright TeV BL Lacs. However, the SED of PKS 1502$+$036, in particular the high Compton dominance, does not resemble a TeV BL Lac, but an FSRQ. Future VLBA monitoring of this NLSy1 during flaring activity periods may help to investigate this behaviour. \noindent Assuming a BH mass of 4.5$\times$10$^7$ M$_{\odot}$, we obtain a $L_{\rm\,disc}/L_{\rm\,Edd}$ = 0.1. Within the assumed model, the fit of the disc emission of PKS 1502$+$036 during the average state constrains the black hole mass to values lower than 10$^8$ M$_{\odot}$, and therefore to $L_{\rm\,disc}/L_{\rm\,edd}$ $>$ 4$\times$10$^{-2}$, just above the threshold between a radiatively efficient disc, as expected for FSRQ, and an inefficient one, as expected for BL Lacs \citep{ghisellini14}. The constraint of 10$^8$ M$_{\odot}$ obtained by modelling the optical/UV part of the spectrum of the source confirms that the radio-loud NLSy1, or at least the $\gamma$-ray emitting ones, are blazar-like sources with a BH mass between a few 10$^{7}$ M$_{\odot}$ and a few 10$^{8}$ M$_{\odot}$, therefore at the low end of the blazar distribution. The most powerful jets are found in luminous elliptical galaxies with very massive central BH, where the formation of the relativistic jets is usually triggered by strong merger activity \citep[e.g.,][]{sikora07,chiaberge15}. In this context it is unlikely that the $\gamma$-ray NLSy1 are hosted in disc/spiral galaxies like the other NLSy1 \citep[e.g.,][]{leontavares14}, but further observations of their host galaxies are needed to unravel the mystery. | 16 | 9 | 1609.04845 |
1609 | 1609.01717_arXiv.txt | We investigate the accuracy of an approximate radiative transfer technique that was first proposed by Kylafis \& Bahcall (hereafter the KB approximation) and has been popular in modelling dusty late-type galaxies. We compare realistic galaxy models calculated with the KB approximation with those of a three-dimensional Monte Carlo radiative transfer code \textsc{skirt}. The \textsc{skirt} code fully takes into account of the contribution of multiple scattering whereas the KB approximation calculates only single scattered intensity and multiple scattering components are approximated. We find that the KB approximation gives fairly accurate results if optically thin, face-on galaxies are considered. However, for highly inclined ($i \gtrsim 85\degr$) and/or optically thick (central face-on optical depth $\gtrsim1$) galaxy models, the approximation can give rise to substantial errors, sometimes, up to $\gtrsim 40\%$. Moreover, it is also found that the KB approximation is not always physical, sometimes producing infinite intensities at lines of sight with high optical depth in edge-on galaxy models. There is no ``simple recipe'' to correct the errors of the KB approximation that is universally applicable to any galaxy models. Therefore, it is recommended that the full radiative transfer calculation be used, even though it's slower than the KB approximation. | The presence of interstellar dust in galaxies severely affects the way in which we observe galaxies. Interstellar dust grains efficiently scatter and absorb ultraviolet (UV), optical and near-infrared radiation, and reradiate the absorbed energy at infrared and submm wavelengths. Over the past decades, it has been demonstrated repeatedly that the effects of dust radiative transfer in galaxies are complex and often counter-intuitive \citep{1989MNRAS.239..939D, 1994ApJ...432..114B, 2001MNRAS.326..733B, 2004A&A...419..821T, 2010MNRAS.403.2053G}, and hence that full dust radiative transfer modelling is required in order to fully interpret the observed properties of galaxies. Dust radiative transfer modelling is complex, since the specific intensity (the quantity that needs to be solved) depends on space, propagation direction, wavelength and time. Moreover, the radiative transfer equation is a complex integro-differential equation that is both nonlinear and nonlocal. As a result, solving the radiative transfer problem in a general three-dimensional (3D) context is demanding and time-consuming. It is hence useful to investigate whether this complex problem can be simplified in some way. An interesting and original approach has been proposed by \citet{1987ApJ...317..637K}, hereafter referred to as the KB approximation. Inspired by early radiative transfer work by \citet{1937ApJ....85..107H} and \citet{1969Phy....41..151V}, \citet{1987ApJ...317..637K} wrote the specific intensity of the radiation field as a series of terms, in which each term represents the contribution to the radiation field of radiation that has been scattered exactly $n$ times. They argued that this series fairly quickly shows a geometrical behaviour. This allows estimating the higher-order terms, and hence the total intensity, based on the first-order terms only. \citet{1987ApJ...317..637K} first used this approach to model the dust distribution in the edge-on spiral galaxy NGC\,891, and the approach was extended and used later on to model several other edge-on spiral galaxies \citep{1997A&A...325..135X, 1999A&A...344..868X}. The KB approximation was used quite extensively in the following years in different radiative transfer problems, for example to quantify the attenuation signatures in disc galaxies \citep{1994ApJ...432..114B, 2004A&A...419..821T, 2013A&A...553A..80P}, to investigate the effects of spiral structure on dust lanes in edge-on spirals \citep{2000A&A...353..117M}, to derive correction factors for the change in the apparent disc scalelengths and central surface brightness due to the effect of dust in disc galaxies \citep{2006A&A...456..941M}, and to model the spectral energy distributions of dusty galaxies \citep{2000A&A...362..138P, 2011A&A...527A.109P, 2001A&A...372..775M}. In the past few years, the field of dust radiative transfer has changed drastically, thanks to a combination of increased computing power and the development of new algorithms and acceleration techniques. It is now possible to solve the full dust radiative transfer problem (i.e. including absorption, scattering and thermal emission) in an arbitrary 3D geometry. Several sophisticated codes have been developed for this goal \citep[e.g.,][]{2001ApJ...551..269G, 2006A&A...459..797P, 2006MNRAS.372....2J, 2008A&A...490..461B, 2011A&A...536A..79R, 2012A&A...544A..52L, 2014MNRAS.438.3137N, 2015A&C.....9...20C, 2016arXiv160602030S}. The vast majority of these codes are based on the Monte Carlo technique \citep[see][for an overview]{2011BASI...39..101W}. Thanks to these new developments, we can now critically assess the validity, strengths and limitations of the KB approximation. This is the goal of the present paper. Based on the Monte Carlo radiative transfer code \textsc{skirt}\footnote{http://www.skirt.ugent.be} \citep{2003MNRAS.343.1081B, 2011ApJS..196...22B, 2015A&C.....9...20C}, we will compute mock observed images for a simple but realistic dusty disc galaxy with and without the KB approximation, and compare the results as a function of various input parameters. In Section 2, we describe the methods with and without the approximation, and we present the galaxy models used in the modelling. The results of the calculations are presented in Section 3. In Section 4 we discuss the accuracy and the applicability of the approximate radiative transfer algorithm. A summary is given in Section 5. | We have critically assessed the strength, weaknesses and validity of the KB approximation by comparing it with the full radiative transfer without the approximation. We find that the KB approximation, which is cheaper and faster than the full radiative transfer, is very accurate in the case of an optically thin and face-on galaxy. However, results of our galaxy models show that the KB approximation can produce substantial errors as the optical depth and the inclination angle of the galaxy increase. In general, these errors of the approximate method may result in an overestimation of dust mass, which is relevant to the dust energy balance problem. We also find that the KB approximation for our galaxy models yields $I_{1} > I_{0}$ along some lines of sight and thus produces infinite intensities. The inapplicability and significant errors of the KB approximation are mainly found around the dust lane, where the optical depth is highest. This suggests that one should be careful especially in modelling an edge-on spiral galaxy with the KB approximation, because the parameters of the dust distribution are mainly determined from fitting the dust lane. More importantly, it is hard to predict a general trend to correct the error of the KB approximation for various types of galaxy models, due to its nonlinear character. Therefore, it is recommended to use full Monte Carlo radiative transfer without the KB approximation to avoid all the aforementioned errors for the radiative transfer study of spiral galaxies. | 16 | 9 | 1609.01717 |
1609 | 1609.08636_arXiv.txt | Many multiple planet systems have been found by the \emph{Kepler} transit survey and various Radial Velocity (RV) surveys. \emph{Kepler} planets show an asymmetric feature, namely there are small but significant deficits/excesses of planet pairs with orbital period spacing slightly narrow/wide of the exact resonance, particularly near the first order Mean Motion Resonance (MMR), such as 2:1 and 3:2 MMR. Similarly, if not exactly the same, an asymmetric feature (pileup wide of 2:1 MMR) is also seen in RV planets, but only for massive ones. We analytically and numerically study planets' orbital evolutions near/in MMR. We find that their orbital period ratios could be asymmetrically distributed around the MMR center regardless of dissipation. In the case of no dissipation, \emph{Kepler} planets' asymmetric orbital distribution could be partly reproduced for 3:2 MMR but not for 2:1 MMR, implying dissipation might be more important to the latter. The pileup of massive RV planets just wide of 2:1 MMR is found to be consistent with the scenario that planets formed separately then migrated toward MMR. The location of the pileup infers a $K$ value of 1-100 on order of magnitude for massive planets, where $K$ is the damping rate ratio between orbital eccentricity and semimajor axis during planet migration. | The \emph{Kepler} mission has discovered from its first 16 months data over $2300$ planetary candidates \citep{Bor11, Bat12}. Over one third ($>$800) of these candidates are in multiple transiting candidate planetary systems, and one remarkable feature of them, as shown by \citet{Lis11} and \citet{Fab12a}, is that the vast majority of candidate pairs are neither in nor near low-order mean motion resonance (MMR hereafter, see also in \citet{VF12}), however there are small but significant excesses/deficits of candidate pairs slightly wider/narrow of the exact resonance (or nominal resonance center), particularly near the first order MMR, such as 2:1 and 3:2 MMR. Such an intriguing asymmetric period ratio distribution has stimulated a number of theorists recently, who developed different models to understand and interpret it. \citet{LW12, BM12, Del12} consider that such an asymmetric period ratio distribution around MMR could be an outcome of resonant couples having underwent eccentricity damping during some dissipative evolutions, such as tidal dissipation (see also in \citet{TP07}). On the other side, \citet{Rei12} attempts to interpret it as a result of the combination of stochastic and smooth planet migrations. Beside and before the \emph{Kepler} transit survey, many near MMR planets had been found by various Radial Velocity (RV hereafter) surveys. As we will show below (section \ref{dis_rv}), similar, if not exactly the same, features of the period ratio distributions seen in \emph{Kepler} planets, have been also shown in RV planets. One question is how all these features/clues in both the \emph{Kepler} and RV samples could be understood systematically in a common context. This paper is such an attempt and it is organized as the following. We first analytically study the dynamics of planets near/in MMR in section \ref{sec_analytic}, and confirm the analytical results with numerical simulations in section \ref{sec_numerical}. We find that planets' orbital distribution could be asymmetric around the MMR center under certain conditions. We then discuss its implications to \emph{Kepler} and RV planets in section \ref{dis}. Finally, we summarize this paper in section \ref{sum}. Some analytical derivations are also given in the appendix A and B as supplementary. We note that \cite{Pet12} posted their paper to arxiv.org just a few days before submitting this paper, which, independently and in a different way, arrived at many of the results presented in this paper. | \label{dis} \subsection{Application to \emph{Kepler} Planets} \label{dis_kep} The period ratio distribution of \emph{Kepler} multiple planet candidate systems show an intriguing asymmetric feature near MMR, especially for 2:1 and 3:2 MMR, namely there are small deficits/excesses just a little bit narrow/wide of the nominal MMR center \citep{Lis11, Fab12a}. To interpret such an asymmetric feature, \citet{LW12, BM12} consider that it could be a result of planets undergoing some dissipative evolution, such as tidal dissipation. In such a case, as discussed in section \ref{dissipation1}, $\gamma_{a1}>\gamma_{a2}$, thus the planet period will always increase. To quantitively explain the observed asymmetric period ratio distribution, one needs to put a right amount of dissipation on them. In addition, as tidal effect is only efficient for short period planet, e.g., less 10 days, one needs to resort to other dissipations at larger orbital period where the observed asymmetry is still significant. \citet{Rei12} then considers if the observed period ratio is consistent with the scenario of planets migrating in disks. First, he considers smooth migration and finds that the excess or pileup of planet pairs is too large and too close to the MMR center. His result is expected from our analytical results in figure \ref{fig_mig} and equation \ref{deq}, which shows $\Delta_{\rm eq} \sim 10^{-4}$ (2 order of magnitude lower than the observed one) if assuming a typical \emph{Kepler} planet mass on order of 10 $M_{\oplus}$ and $K=10$. Nevertheless, he further shows that by including certain amount stochastic forces due to disk turbulence during migration, the large pileup at MMR center could be smeared out and a period ratio distribution similar to that of \emph{Kepler} planets could be reproduced. All the above attempts belong to the case with dissipation. As we have shown (section \ref{nod1} and \ref{nod2}), the period ratio distribution is intrinsically asymmetric near the MMR center even if there is no dissipation. In order to see whether and how the intrinsic asymmetry can reproduce \emph{Kepler} planets' period ratio distribution, we perform the following N-body simulations. Specifically, we draw 4000 planets pairs initially with a uniform period ratio distribution near MMR, Rayleigh eccentricity and inclination distributions, and uniformly random distribution for all the other angular orbital elements. We use the MERCURY integrator to simulate these 4000 systems individually on a timescale of $10^{5}$ days and intensively output their period ratio very 200 days. The final period ratio distribution is calculated with these output period ratios of all 4000 systems. As \emph{Kepler} multiple planet systems are believed to be highly coplanar within a few degree \citep{Fab12a}, we assume the mean inclination $<i>=2.5^{\circ}$. For simplicity, we only study equal mass pairs, i.e, $m_{1}=m_{2}$ because different mass ratios lead to similar results as long as their total masses are the same (Fig.\ref{fig_mas}). Figure \ref{fig_obs} compares the observed period ratio distribution to those from above simulations with different planetary masses from $10M_{\oplus}$ to $100 M_{\oplus}$ and mean eccentricities from $<e>=0.01$ to $<e>=0.1$. The simulated period ratio distributions have an asymmetric feature resembling the observation, i.e., a trough/pile up just a little bit narrow/wide of MMR center. As expected (Fig.\ref{fig_ecc} and \ref{fig_mas}), the asymmetric feature become weaker with increasing eccentricity and more extended with increasing mass. In order to reproduce the observed period ratio distribution, it requires a mean eccentricity less than a few percents and planetary mass about 10-20 $M_{\oplus}$ for 3:2 MMR and $\sim 100 M_{\oplus}$ for 2:1 MMR. The eccentricity requirement is consistent with recent eccentricity estimate with transit timing variation \citep{Fab12b, WL12}. As for the typical mass of \emph{Kepler} planets, it is expected to be 4-9 $M_{\oplus}$ given the typical radii of 2-3 $R_{\oplus}$ and a mass radio distribution either based on fitting of the solar system, $m=M_{\oplus}(r_{\rm}/R_{\oplus})^{2.06}$ \citep{Lis11}, or transit timing variation, $m=3M_{\oplus}(r_{\rm }/R_{\oplus})$ \citep{WL12}. Even considering a relatively large uncertain of mass measurements, say 100\%, such an expected mass is still too low to meet the requirement for 2:1 MMR, although it is comparable to the mass requirement for 3:2 MMR. Therefore, we conclude that the intrinsic MMR asymmetry (without any damping) could partially explain \emph{Kepler} planets' asymmetric period ratio distribution near 3:2 MMR but not 2:1 MMR. For the latter, other mechanisms, e.g., dissipation, should play a more important role. \subsection{Application to \emph{RV} Planets} \label{dis_rv} At the time of writing this paper, there are 409 exoplanets detected with radial velocity (RV) method (exoplanet.org) and about $30\%$ of them reside in multiple planet systems. These RV planets have a wide mass range featured with a bimodal distribution \citep{Pep11} as shown in the left panel of figure\ref{fig_rvobs}. The boundary is at about 0.2 $M_{\rm J}\sim64M_{\oplus}$, which separate the light RV planets (with a media mass of $\sim12M_{\oplus}$) and the massive ones (with a media mass of $\sim1.54M_{\rm J}$). This bimodal distribution may indicate planets undergo different formations and evolutions for the light and massive groups \citep{Mor09}. Interestingly, we find that these two groups may have different period ratio distributions. As shown in the right panels of figure \ref{fig_rvobs}, there is a strong pileup of planet pairs near 2:1 MMR in the massive planet group, which is not seen in the light group. Those massive planets piled up near 2:1 MMR seems unlikely formed in situ within a small annulus, but they are more likely formed with larger distance in a disk then brought into 2:1 MMR through convergent migration. Interestingly, we note that the pile up is just a few percent (in period ratio) wide of the 2:1 MMR center, which is expected from our analytical and numerical prediction with planetary migration (e.g., Fig.\ref{fig_mig}). Furthermore, from the location of the pileup (i.e., $\Delta_{\rm eq}$), we can infer the damping ratio between eccentricity and semi major axis during planetary migration (i.e., $K$) by using equation \ref{deq}. The result of such an exercise is shown in figure \ref{fig_k12}. Here we considered two migration scenarios. In scenario 1, only the outer planet undergoes migration, i.e., $\gamma_{e2}=K\gamma_{a2}$ and $\gamma_{e1}=\gamma_{a1}=0$. In scenario 2, the inner one migrates outward and the outer one migrates inward, i.e., $\gamma_{e2}=K\gamma_{a2}$, $\gamma_{e1}=-K\gamma_{a1}$ and $\gamma_{a1}=-\gamma_{a2}<0$. As can be seen from figure \ref{fig_k 12}, the $K$ value is constrained in a relative wide range about 1-100 on order of magnitude. We note this $K$ range is consistent with the hydrodynamical simulations by \citet{Kle04} which predicts a $K$ value of order of unity, and with dynamical modeling of the well-studied system GJ876 by \citet{LP02} which prefers $K=10-100$. | 16 | 9 | 1609.08636 |
1609 | 1609.07527_arXiv.txt | {% We briefly review how \xray\ observations of high-redshift active galactic nuclei (AGNs) at \hbox{$z=4$--7} have played a critical role in understanding their basic demographics as well as their physical processes; e.g., absorption by nuclear material and winds, accretion rates, and jet emission. We point out some key remaining areas of uncertainty, highlighting where further \chandra\ and \xmm\ observations/analyses, combined with new multiwavelength survey data, can advance understanding over the next decade.} | Over the past $\approx 17$~yr, the observational capabilities of \chandra\ and \xmm\ have allowed a large expansion, by more than an order of magnitude, in the number of \xray\ detected active galactic nuclei (AGNs) at \hbox{$z=4$--7}. This has come about via two primary routes. First, these missions have obtained follow-up observations in the \xray\ regime of high-redshift AGNs previously found in other multiwavelength surveys [e.g., the Sloan Digital Sky Survey (SDSS), the Palomar Sky Survey (PSS), and the Faint Images of the Radio Sky at Twenty-Centimeters (FIRST) survey]. Second, these missions have discovered new \xray\ selected high-redshift AGNs in their multiple \xray\ surveys. According to a regularly updated public list compiled by Brandt \& Vignali\footnote{http://www2.astro.psu.edu/users/niel/papers/highz-xray-detected.txt}, there are now 153 \xray\ detections of AGNs at \hbox{$z=4$--7}, allowing reliable basic \xray\ population studies into the reionization era. Most \xray\ detections at \hbox{$z=4$--7} have come from the first route described above. However, new \xray\ discoveries from the second route continue to advance rapidly, and these are extremely important because they mitigate many of the selection biases (e.g., due to obscuration and host-galaxy dilution) arising from optical/UV AGN selection. In this paper, we will briefly review some of the insights that \xray\ studies have provided about the first growing supermassive black holes (SMBHs) in the Universe. In \S2 we will discuss \xray\ surveys and AGN demographics, and then in \S3 we will cover \xray\ spectroscopy and AGN physics. For each of these topics, we will highlight areas of uncertainty and how these could be addressed in the next decade with \chandra\ and \xmm\ observations/analyses. Owing to space limitations, complex details will often need to be suppressed and citations cannot be complete but just representative. Please check the cited papers and relevant recent reviews (e.g., Brandt \& Alexander 2015; Reines \& Comastri 2016) for further references. | 16 | 9 | 1609.07527 |
|
1609 | 1609.00241_arXiv.txt | We investigate the consequences of fairly normal Type Ia supernovae being embedded in compact and dense envelopes of carbon and oxygen rich circumstellar material by means of detailed radiation hydrodynamic simulations. Our main focus rests on exploring the effects of the interaction between ejecta and circumstellar material on the ejecta evolution and the broad-band light curve. In our calculations, we find that a strong reverse shock efficiently decelerates and compresses the ejecta material. This leads to a significant broadening of the optical light curve, a longer rise to maximum and a slower decline in the tail phase. During the interaction, substantial radiative energy is generated, which mostly emerges in the extreme ultraviolet and X-ray regime. Only if reprocessing due to radiation--matter interactions is very efficient, a significant boost in the optical light curve is observed. We discuss these findings in particular in the context of the super-luminous event \sndc{}. As our calculations are able to reproduce a number of its peculiar properties, we conclude that the flavour of the interaction scenario investigated in this work constitutes a promising candidate to explain such `\sch{}' supernovae. | The presence of circumstellar material (CSM) is playing an ever more important role for the understanding of supernova (SN) evolution. For example, the interplay between CSM and the SN ejecta can be crucial for shaping some of the defining properties for particular SN classes. Prominent examples in this context are Type IIn supernovae (SNe IIn). Here, the eponymous narrow line features \citep{Schlegel1990} are ascribed to the presence of a dense CSM envelope, in which hydrogen recombines \citep[e.g.][]{Chugai2004}. The presence of substantial amounts of CSM is also often invoked as a possible explanation for the intense luminosity of some of the most powerful SN events \citep[e.g.][]{Ofek2007,Chevalier2011}, which are typically referred to as super-luminous SNe. In this scenario, the vast kinetic energy pool of the ejecta may be tapped through the shock heating processes in the ejecta--CSM interaction, converted partially to thermal and radiation energy and thus power the intense light output of such systems (see, for example, the ejecta--CSM interaction calculation for the super-luminous SN PTF12dam by \citealt{Baklanov2015}). Note, however, that in the context of super-luminous SNe, also other models, such as the pair-instability mechanism \citep[e.g.][]{Barkat1967,Gal-Yam2009} or the magnetar-powered scenario \citep[e.g.][]{Kasen2010a, Nicholl2013}, are heavily discussed. The increasing relevance of ejecta--CSM interaction is also owed to the success of modern survey programmes in catching SNe at ever earlier phases \citep[e.g.][]{Gal-Yam2014}. During these epochs, right after the explosion, the observables probe the immediate vicinity of the explosion site. Any interaction with CSM at these times imprints characteristic features onto spectra and the early light curves (see, for example, systematic exploration in the \snias{} context by \citealt{Piro2016}). Interpreting these, gives insights into the mass-loss history of the progenitor system and thus into the exploding object. In recent years, an increasing number of observations has revealed CSM interaction signatures in Type Ia supernovae (\snias{}) as well, which are associated with the complete thermonuclear incineration of a carbon-oxygen white dwarf (WD). A prominent examples was PTF11kx \citep{Dilday2012}, which exhibits multiple CSM shells in its immediate environment, but many more strongly interacting \snias{} have been identified \citep[see, for example, census by][]{Silverman2013}. In addition to the direct observational evidence, the presence of CSM is invoked as a potential explanation for a class of \snias{}, which often exhibit extraordinary luminosities. These events, commonly dubbed `\sch{}' explosions \citep{Howell2006}, of which \sndc{} \citep{Yamanaka2009,Silverman2011,Taubenberger2011} is the prototype, elude an explanation within the standard Chandrasekhar-mass explosion paradigm. In light of the relevance of the interplay between \snia{} ejecta and its circumstellar environment, we perform detailed radiation hydrodynamical calculations of interacting \snias{} in this work. Conceptually similar explorations have been performed by \citet{Khokhlov1993, Nomoto2005, Fryer2010, Blinnikov2010}. However, we focus here on a specific realisation of the interaction scenario, which draws inspiration from previous investigations of the ejecta--CSM interplay in the context of super-luminous \snias{} \citep{Taubenberger2013}. In particular, we consider fairly normal \snias{} occurring within a dense carbon and oxygen rich envelope and examine the consequences of the ensuing ejecta--CSM interaction for the overall evolution of the system and its energy output. Apart from determining the generic evolution of these interaction models, an important aspect of this work lies in exploring whether this scenario provides a plausible explanation for \sch{} \snias{}. We begin this study by briefly reviewing some key aspects of super-luminous \snias{} in Section \ref{sec:sn09dclikes}. This is followed by a detailed overview of the investigated models and the used numerical tool in Section \ref{sec:model_numerics}. The results of our simulations, which are presented and compared with observations of super-luminous \snias{} in Section \ref{sec:results}, will be discussed in detail in Section \ref{sec:discussion}. | In this work, we have investigated the consequences of \snias{} being surrounded by a thick carbon-oxygen rich CSM envelope. Our main interest rested on studying the effect of the ensuing ejecta--CSM interaction on the ejecta evolution and on the emergent light curve. Here, we focussed on a particular realisation of this scenario, which has previously \citep[c.f.][]{Taubenberger2013} been identified as a promising candidate for the explanation of \sch{} \snias{}, in particular for \sndc{}. We followed the evolution of the considered model using the radiation hydrodynamical code \stella \citep{Blinnikov1993,Blinnikov1998,Blinnikov2006}. At the ejecta--CSM interface, a strong forward and reverse shock form, sweeping up the CSM and compressing the ejecta material, respectively. Due to the shock heating processes, a substantial amount of energy is injected into the radiation field. However, this occurs mostly in the X-ray and UV regime and only part of it is shifted into the optical $UBVRI$ bands due to reprocessing in the CSM. As a consequence, no significant boost in the maximum $UBVRI$ luminosity is observed compared to a corresponding `bare' \snia{} explosion. However, we find that the ejecta--CSM interaction leads to a longer rise and a significant broadening of the light curve. Past maximum, a slower decline of the optical light curve is observed due to the increased $\gamma$-trapping induced by the compression of the ejecta material by the reverse shock. Apart from the density increase, the ejecta material has also been significantly decelerated, leading to an extended velocity plateau in mass space. Despite the missing luminosity boost in the fiducial model, we find that an increase in the light output in the optical regime may still be achieved if the reprocessing efficiency in the CSM is enhanced. Not observing this in the current calculations may simply be a consequence of simplifications adopted in the radiative transfer scheme implemented in the standard version of \stella. In particular, using a realistic near-complete line list significantly increases the opacity and the reprocessing efficiency. We performed simple test calculations with an enhanced CSM opacity and by carrying out calculations with an experimental \stella version, capable of treating millions of atomic line transitions, supporting these statements. During the light curve decline phase, the increased $\gamma$-trapping is a direct consequence of the compression due to the reverse shock. Thus, its strength regulates the optical luminosity during these phases and an additional boost may consequently be achieved here, if the ejecta is, for example, embedded into a more massive CSM envelope. In addition to these generic findings, the interaction scenario successfully reproduces a number of characteristic features of \sch{} \snias{}, despite the difficulty to produce a significant luminosity boost in the optical light curve. When comparing to the prototype of this class, \sndc{}, we find that the shape of the observed optical $UBVRI$ light curve is almost perfectly matched. In particular, the long rise time, the broad maximum and the delayed decline due to increased $\gamma$-trapping is well reproduced. Moreover, the deceleration of the ejecta material due to the reverse shock provides a natural explanation for the low line velocities observed in \sndc{}. The velocity distribution of the different elements found in the model is compatible with these observations. However, to establish a directly link, detailed spectral synthesis would have to be performed, a task which cannot be easily carried out with \stella. Despite these successes, the defining characteristic feature of \sndc{}, namely the high light output is not fully reproduced in the numerical calculations. However, as pointed out already above, limitations of the radiative transfer treatment in \stella may be partly responsible for that. Next to the compromises in the radiative transfer treatment, the restriction to spherically symmetric configurations is a shortcoming of the current study. In particular, if double degenerate scenarios are considered as the possible origin of the CSM material, deviations form spherical symmetry may play an important role. The exact consequences of these are difficult to predict, but line-of-sight effects seem plausible. To some extent, these could provide a natural explanation for some of the diversity seen in \sch{} objects. In summary, despite some shortcomings of our current study, the initial investigation of \snias{} interacting with a dense carbon-oxygen rich envelope shows that this scenario may provide a viable explanation for \sch{} objects. To further investigate this possibility and to better quantify the generic consequences of ejecta--CSM interaction, we aim to continue our study of this scenario in the future, specifically focussing on three points. Firstly, a better sampling of the possible parameter space, both in terms of the ejecta and the CSM properties, should be performed and thus different configurations of the interaction scenario investigated. In addition, we aim to map results from \stella simulations into dedicated radiative transfer approaches, such as \artis \citep{Kromer2009} and \tardis \citep{Kerzendorf2014}, once homology is approximately retained. This way, detailed colour light curves may be determined and the spectral appearance of the interacting models predicted. In parallel, it should be explored how alternative radiation hydrodynamical methods, such as \mcrh \citep{Noebauer2012,Noebauer2015}, may be applied to the interacting \snias{} problem, with the goal of eventually overcoming the current limitation to one-dimensional geometries. These steps will help establishing whether super-luminous \snias{} are interaction-powered and whether and to which extent ejecta--CSM interaction is relevant for other \snias{}. | 16 | 9 | 1609.00241 |
1609 | 1609.09360_arXiv.txt | Spectrum of radiation of a relativistic particle moving in a nonhomogeneous magnetic field is considered. The spectrum depends on the pitch-angle $\alpha$ between the velocity direction and a line tangent to the field line. In case of very small $\alpha$ the particle generates so-called curvature radiation, in an intermediate case undulator-kind radiation is produced. In this paper we present the calculations of radiation properties in a case when both curvature and undulator radiation is observed. | 16 | 9 | 1609.09360 |
||
1609 | 1609.04979_arXiv.txt | {We explore the effective degrees of freedom in the early Universe, from before the electroweak scale at a~few femtoseconds after the Big Bang until the last positrons disappeared a~few minutes later. We look at the established concepts of effective degrees of freedom for energy density, pressure, and entropy density, and introduce effective degrees of freedom for number density as well. We discuss what happens with particle species as their temperature cools down from relativistic to semi- and non-relativistic temperatures, and then annihilates completely. This will affect the pressure and the entropy per particle. We also look at the transition from a~quark-gluon plasma~to a~hadron gas. Using a~list a~known hadrons, we use a~``cross-over'' temperature of 214 MeV, where the effective degrees of freedom for a~quark-gluon plasma~equals that of a~hadron gas.} \keyword{viscous cosmology; shear viscosity; bulk viscosity; lepton era; relativistic kinetic theory} \begin{document} | \label{Sec:Introduction} The early Universe was filled with different particles. A~tiny fraction of a~second after the Big Bang, when the temperature was $10^{16}~\textrm{K} \approx 1~\textrm{TeV}$, all the particles in the Standard Model were present, and roughly in the same abundance. Moreover, the early Universe was in thermal equilibrium. At this time, essentially all the particles moved at velocities close to the speed of light. The average distance travelled and lifetime of these ultra-relativistic particles were very short. The frequent interactions led to the constant production and annihilation of particles, and as long as the creation rate equalled that of the annihilation rate for a~particle species, their abundance remained the same. The production of massive particles requires high energies, so when the Universe expanded and the temperature dropped, the~production rate of massive particles could not keep up with their annihilation rate. The heaviest particle we know about, the top quark and its antiparticle, started to disappear just one picosecond ($10^{-12}~\textrm{s}$) after the Big Bang. During the next minutes, essentially all the particle species except for photons and neutrinos vanished one by one. Only a~very tiny fraction of protons, neutrons, and electrons, what makes up all the matter in the Universe today, survived due to baryon asymmetry (the imbalance between matter and antimatter in the Universe). The fraction of matter compared to photons and neutrinos is less than one in a~billion, small enough to be disregarded in the grand scheme for the first stages of the Universe. We know that the early Universe was close to thermal equilibrium from studying the Cosmic Microwave Background (CMB) radiation. Since its discovery in 1964 \cite{Penzias:1965}, the CMB has been thoroughly measured, most recently by the Planck satellite \cite{Planck:2015XIII}. After compensating for foreground effects, the CMB almost perfectly fits that of a~black body spectrum, deviating by about one part in a hundred thousand~\cite{Trodden:2004}. It remained so until the neutrinos decoupled. For a~system in thermal equilibrium, we can use statistical mechanics to calculate quantities such as energy density, pressure, and entropy density. These quantities all depend on the number density of particles present at any given time. How~the different particles contribute to these quantities depends of their nature---most important being their mass and degeneracy. The complete contribution from all particles is a~result of the sum of all the particle species' effective degrees of freedom. We call these temperature-dependent functions $\g$, and~we have one for each quantity, such as $\gn$ related to number density, and $\ge$, $\gp$, and $\gs$, related~to energy density, pressure, and entropy density, respectively. In this paper, we will show how to calculate these four quantities ($\nn$, $\ee$, $\pp$, $\ss$), as well their associated effective degrees of freedom ($\gn$, $\ge$, $\gp$, $\gs$). These latter functions describe how the number of different particles evolve, and we have plotted these values in Figure~\ref{Fig:gStarNRPS}. Throughout this paper, we will look more closely at five topics. After first having a~quick look at the elementary particles of the Standard Model and their degeneracy (Section \ref{Sec:ParticleDegeneracy}), we address the standard approach when everything is in thermal equilibrium in Section \ref{Sec:Theory}. Next, we take a~closer look at the behavior during the QCD phase transition; i.e., the transition from a~quark-gluon plasma~(QGP) to a~hot hadron gas (HG) in Section \ref{Sec:Evolution}. We then look at the behavior during neutrino decoupling (Section \ref{Sec:Decoupling}). For the fifth topic, we study how the temperature decreases as function of time (Section \ref{Sec:Time}). In Appendix \ref{Sec:GTable}, we have also included a~table with the values for all four $\g$s, as well as time, from temperatures of 10 TeV to 10 keV. The table includes three different transition temperatures as we go from a~QGP to a~HG. This article was inspired by the lecture notes by Baumann \cite{Baumann:Cosmology} and Kurki-Suonio \cite{KurkiSuonio:Cosmology}. Other important books on the subject are written by Weinberg \cite{Weinberg:Cosmology, Weinberg:GravitationAndCosmology}, Kolb and Turner \cite{Kolb:EarlyUniverse}, Dodelson \cite{Dodelson:ModernCosmology}, Ryden \cite{Ryden:IntroductionToCosmology}, and Lesgourgues, Mangano, Miele, and Pastor \cite{Lesgourgues:NeutrinoCosmology}. \begin{figure}[H] \centering \includegraphics[width=0.75\textwidth]{Fig1-gStarNEPS.pdf} \caption{The evolution of the number density ($\gn$), energy density ($\ge$), pressure ($\gp$), and entropy density ($\gs$) as functions of temperature.} \label{Fig:gStarNRPS} \end{figure} | Our knowledge of the very first stages of Universe is limited. In order to know for sure what is happening at these extreme energies and temperatures, we want to recreate the conditions using particle accelerators. The Large Hadron Collider at CERN can collide protons together at energies of 13 TeV, and with their discovery of the Higgs boson, all the elementary particles predicted by the Standard Model of particle physics have been found. This is, however, most likely not the complete story. Dark~matter particles are the hottest candidates to be added to our list of particles, and there is almost sure to be more particles at even higher temperatures, such as at the Grand Unified Theory (GUT) scale of $T \sim 10^{16}$ GeV. We have here used the statistical physics approach to counting the effective degrees of freedom in the early Universe at temperatures below 10 TeV. Some simplifications have been used, such as setting the chemical potential equal to zero for all particles. The aim of this article was to give a~good qualitative introduction to the subject, as well as providing some quantitative data~in the form of plots and tables. The early Universe is often thought of as being pure radiation (just relativistic particles). However,~when the temperature drops to approximately that of the rest mass of some massive particles, we~get interesting results, where we have a~mix of relativistic particles and semi- and non-relativistic ones. This mix is most prominent during the electron--positron annihilations, and just after the phase transition from a~quark-gluon plasma~to a~hadron gas. Approaching this, using our ``no-chemical potential'' distribution functions shows us how the entropy per particle increases when the ratio of semi- and non-relativistic particles becomes significant. The number of effective degrees of freedom for hadrons changes very quickly around the QCD transition temperature. We found a~cross-over temperature of 214 MeV using the known baryons and mesons. As there could be many more possible hadronic states than we have accounted for, this cross-over temperature could be lower. This is not meant as a~claim of a~new QCD transition temperature, but rather as an interesting fact. Our first-order approach based purely on the distribution functions has inconsistencies at the cross-over temperature. We have listed the effective degrees of freedom for number density ($\gn$), energy density ($\ge$), pressure ($\gp$), entropy density ($\gs$), and time ($t$) as function of temperature ($T$) in Table \ref{Tab:Values} in Appendix~{\ref{Sec:GTable}. Table \ref{Tab:OneParticleContribution} in Appendix \ref{Sec:OneParticleContribution} lists the different effective contributions to a~single intrinsic degree of freedom, corresponding to our plot in Figure \ref{Fig:BosonFermionIntegrals}. \appendixtitles{yes} \appendixsections{multiple} \appendix | 16 | 9 | 1609.04979 |
1609 | 1609.01071_arXiv.txt | Equal-mass stars in young open clusters and loose associations exhibit a wide spread of rotation periods, which likely originates from differences in the initial rotation periods and in the primordial disc lifetimes. We want to explore if the gravitational effects by nearby companions may play an additional role in producing the observed rotation period spread, as well as, the role that magnetic activity may also play. We measure the photometric rotation periods of components of multiple stellar systems and look for correlations of the period differences among the components to their reciprocal distances. In this paper, we analysed the triple system AU Mic + AT Mic A\&B in the 25$\pm$3-Myr $\beta$ Pictoris Association. \rm We have retrieved from the literature the rotation period of AU Mic (P = 4.85\,d) and measured from photometric archival data the rotation periods of both components of AT Mic (P = 1.19\,d and P = 0.78\,d) \rm for the first time. Moreover, we detected a high rate of flare events from AT Mic. Whereas the distant component AU Mic has evolved rotationally as a single star, the A and B components of AT Mic, separated by $\sim$27\,AU, exhibit a rotation rate a factor 5 larger than AU Mic. Moreover, the A and B components, despite have about equal mass, show a significant difference ($\sim$40\%) between their rotation periods. A possible explanation is that the gravitational forces between the A and B components of AT Mic (that are a factor $\sim$7.3$\times10^6$ more intense than those between AU Mic and AT Mic) have enhanced the dispersal of the AT Mic primordial disc, shortening its lifetime and the disc-locking phase duration, \rm making the component A and B of AT Mic to rotate faster than the more distant AU Mic. We suspect that a different level of magnetic activity between the A and B components of AT Mic may be the additional parameter responsible for the difference between their rotation periods. | Low-mass stellar members (M $<$ 1.2\,M$_\odot$) of young open clusters and stellar association (age $<$ 0.5\,Gyr) exhibit a wide spread of their rotation periods. Within each cluster/association, we note that stars with similar masses have their rotation periods within a range of values. This range is minimum at early spectral types (from mid- to late-F) and, generally, it increases when we move towards lower mass stars (see, e.g., Mamajek \& Hillenbrand 2008). This spread of rotation periods at the same stellar mass arises likely from differences in the initial rotation periods and in the primordial disc lifetimes. The shorter the disc lifetime, the shorter the disc-locking time, and the earlier the star begins to spinning up, owing to radius contraction (see, e.g., Camenzind 1990; Ribas et al. 2014).\\ We are carrying out a study to investigate if gravitational effects can shorten the disc lifetime by comparing the rotation periods of close components of multiple systems with those of single stars. \rm This study is part of the RACE-OC project (Rotation and ACtivity Evolution in Open Clusters; Messina 2007). For this study, cluster or association stars that belong to triple or multiple systems are the best suited, especially if the components of these systems have similar masses. The origin of significantly different rotation periods among the components can reside in different initial rotation periods and/or in a different duration of the disc lifetimes, being similar all the other basic parameters (age, mass, metallicity). The architecture of the system, that is the reciprocal distance among the components, in these cases can play its own key role in differentiating the rotation periods. We have already analysed two such triple systems, BD$-$21\,1074 in the $\beta$ Pictoris Association (Messina et al. 2014), and TYC\,9300-0891-1AB/TYC\,9300-0525-1 in the Octans Association (Messina et al. 2016a). In both systems, there are two components on a wide orbit, and one having a nearby companion. In the first system (BD$-$21\,1074), we found that the nearby companion at 16\,AU significantly shortened the disc lifetime making one component to rotate significantly faster than the wide companion. In the second case (TYC\,9300-0891-1AB/TYC\,9300-0525-1), we found that the nearby companion at 160\,AU was sufficiently distant to have a negligible effect on the rotation, given that there was no period difference between the tight binary and the wide companion. \rm \\ Now, we present a third system, AT Mic AB + AU Mic in the 25$\pm$3-Myr $\beta$ Pictoris Association (Messina et al. 2016b). AT Mic and AU Mic are at very large distance ($\sim$46200 AU) from each other, whereas AT Mic A and B are separated by only $\sim$27\,AU. We measured the photometric rotation periods of both components A and B. As we will show, AU Mic has a rotation period comparable to those of other single stars and very wide components of binary systems, therefore we can assume that it has evolved as a single star with negligible external gravitational perturbation. On the contrary, the close components of AT Mic with their rotation periods a factor 5 shorter than AU Mic, have likely reciprocally shortened their disc lifetime and started to spin up earlier than the coeval AU Mic. \\ \rm We also find that the difference between the rotation periods of the A and B components of AT Mic is significant, and explore the role that the flaring activity on one or both components may have played to produce such period difference.\\ In Sect.\,2, we present the literature information on AU Mic and AT Mic. In Sect.\,3 and 4, we present the photometric data and their periodogram analyses to measure the rotation periods of the AT Mic components. In Sect.\,5, we present our novel analysis on the flares detected on AT Mic. A discussion of the rotational properties of the components of the triple system is given in Sect.\,6. Conclusions are presented in Sect.\,7. | We have analysed the rotational properties of the triple stellar system AU Mic + AT Mic A\&B in the young 25$\pm$3-Myr \rm $\beta$ Pictoris association. We have measured the photometric rotation periods P = 1.19\,d and P = 0.78\,d of the AT Mic components, although we could not establish to which components the periods refer. \rm We find that AU Mic is sufficiently distant ($\sim$ 46200\,AU) from AT Mic to have evolved rotationally as a single star with a primordial disc life time typical of a M1V star. Therefore, its rotation period P = 4.85\,d fits well into the distribution of rotation periods of single members of the $\beta$ Pictoris association. On the contrary, for the A and B components of AT Mic we propose a scenario according to which they \rm are sufficiently close ($\sim$27\,AU) to have gravitationally perturbed the respective primordial discs, enhancing their dispersion and, consequently, shortening both the disc life time and the star-disc locking duration. In this scenario, \rm AT Mic A and B started to spin up, owing to radius contraction, at earlier epochs with respect to AU Mic, reaching a rotation rate about a factor 5 faster than AU Mic.\\ Interestingly, we find that the A and B components of AT Mic, although substantially equal (same mass, age, metallicity), have a significant ($\sim$40\%) difference between their rotation periods. This difference may arise from different initial rotation periods. However, we also note that \rm this system has a high rate of flaring, and we have some hints that only one component may be the flare star. If this hypothesis would be correct, then the different flaring activity may be the additional parameter responsible for the different rotational evolution of the two components. In fact, a prominent flare activity can enhance the mass loss rate and, consequently, the angular momentum loss, as well, it can significantly modify the topology of the external magnetic fields making more or less efficient the stellar magnetic braking. Certainly, spatially resolved photometry can allow us to see if one or both components have flares and to address this possible additional cause of the rotation period spread observed among the M-type stars. \\ {\it Acknowledgements}. Research on stellar activity at INAF- Catania Astrophysical Observatory is supported by MIUR (Ministero dell'Istruzione, dell'Universit\`a e della Ricerca). This paper makes use of data from the first public release of the WASP data (Butters et al. 2010) as provided by the WASP consortium and services at the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This research has made use of the Simbad database, operated at CDS (Strasbourg, France). We thank the anonymous Referee for useful comments that allowed us to improve the paper quality. | 16 | 9 | 1609.01071 |
1609 | 1609.04462_arXiv.txt | {} {We analyze near-infrared UKIDSS observations of a sample of 8325 objects taken from a catalog of intrinsically red sources in the Galactic plane selected in the \emph{Spitzer}-GLIMPSE survey. Given the differences in angular resolution (factor $>2$ better in UKIDSS), our aim is to investigate whether there are multiple UKIDSS sources that might all contribute to the GLIMPSE flux, or there is only one dominant UKIDSS counterpart. We then study possible corrections to estimates of the star formation rate (SFR) based on counts of GLIMPSE young stellar objects (YSOs). This represents an exploratory work towards the construction of a hierarchical YSO catalog.} {After performing PSF fitting photometry in the UKIDSS data, we implemented a technique to automatically recognize the dominant UKIDSS sources by evaluating their match with the spectral energy distribution (SED) of the associated GLIMPSE red sources. This is a generic method which could be robustly applied for matching SEDs across gaps at other wavelengths.} {We found that most ($87.0 \pm 1.6 \%$) of the candidate YSOs from the GLIMPSE red source catalog have \emph{only one} dominant UKIDSS counterpart which matches the mid-infrared SED (fainter associated UKIDSS sources might still be present). Though at first sight this could seem surprising, given that YSOs are typically in clustered environments, we argue that within the mass range covered by the GLIMPSE YSO candidates (intermediate to high masses), clustering with objects with comparable mass is unlikely at the GLIMPSE resolution. Indeed, by performing simple clustering experiments based on a population synthesis model of Galactic YSOs, we found that although $\sim 60\%$ of the GLIMPSE YSO enclose at least two UKIDSS sources, in general only one dominates the flux.} {No significant corrections are needed for estimates of the SFR of the Milky Way based on the assumption that the GLIMPSE YSOs are individual objects. However, we found that unresolved binaries in GLIMPSE objects (a few of them could be resolved at the UKIDSS resolution) have a non-negligible effect, and would increase the SFR estimate by a factor $\sim 1.2$--1.3.} | \label{sec:introduction} The new generation of Galactic plane surveys carried out in the last decade, from near-infrared (NIR) to millimeter wavelengths, has started to revolutionize our knowledge of star formation in the Milky Way. In the past, we have been limited to inferring properties of the star formation process from observations of good template regions or a selected sample of individual objects, but these surveys now allow us to explore the whole variety of star-forming environments in the Galactic plane. They are unbiased in spatial coverage within a certain range of coordinates, though still subject to observational limitations such as sensitivity, angular resolution, and (for short wavelengths) interstellar extinction. Using the mid-infrared (MIR) data from the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE), \citet{Robitaille2008} compiled a sample of almost $19\,000$~intrinsically red sources in the inner Galactic plane, thought to be mostly high- and intermediate-mass young stellar objects (YSOs) and asymptotic giant branch (AGB) stars. This population of YSOs was modeled by \citet{RobitailleWhitney2010} to estimate the star formation rate (SFR) of the Milky Way, for the first time using directly individual YSO counts in conjunction with a population synthesis model. On the other hand, recent (sub)mm continuum surveys \citetext{\citealp[Bolocam Galactic Plane Survey,][]{Aguirre2011}; \citealp[ATLASGAL,][]{Schuller2009}} have revealed thousands of potential star-forming cold dust clumps throughout the Galactic plane. By matching the detected (sub)mm sources with samples of ongoing star-formation indicators, namely (massive) YSOs identified in the GLIMPSE or \emph{MSX} MIR surveys, 24~\micron\ point sources from the MIPSGAL survey, \ion{H}{ii} regions, and methanol masers, several studies have characterized the population of these cold clumps, proposing tentative evolutionary stages, identifying ``starless'' clump candidates, and investigating the physical properties that give rise to different modes of star formation in our Galaxy \citep[e.g.,][]{Dunham2011, Tackenberg2012, Urquhart2014}. More recently, the \emph{Herschel} Hi-GAL survey \citep{Molinari2010}, covering wavelengths from 70~\micron\ to 500~\micron, which is the range where the cold dust emission peaks, provides a rich dataset to study the properties of both the embedded YSOs (through the protostellar radiation reprocessed by the surrounding dust) and their envelopes, as well as younger pre-stellar cores \citep[e.g.,][]{Veneziani2013, Elia2013}. None of these previous studies, however, have considered the potential multiplicity of a single object at a given wavelength when observed at a shorter wavelength providing higher angular resolution. The standard approaches to deal with multi-wavelength data is a plain ``nearest source'' matching to associate sources across different wavelengths or, in the case of sub(mm) clumps, a simple classification of the source based on the type (or absence) of higher-resolution objects that fall within the covered area in the sky, but without explicitly taking into account the multiplicity of these objects. In order to make use of the full high-resolution information of multi-wavelength data, we are working on the development of a hierarchical YSO catalog that will associate multiple sources from a higher-resolution survey with the corresponding (typically fewer) sources in a lower resolution survey. As a long-term plan, our idea is to apply this formalism to the whole set of Galactic plane surveys, from the NIR to the millimeter. In this paper, we present an exploratory study which constitutes the first step towards the construction of the hierarchical YSO catalog. Instead of constructing a catalog from scratch and using all the Galactic surveys available, we make here two simplifications: first, we only use data from the GLIMPSE survey and the NIR higher-resolution United Kingdom Infrared Deep Sky Survey (UKIDSS); and second, we start from the GLIMPSE individual objects already selected by \citet{Robitaille2008} and check whether they split into multiple sources when seen in UKIDSS. In particular, we investigate for each GLIMPSE object whether there are multiple UKIDSS sources that might all contribute to the GLIMPSE flux, or there is only one dominant UKIDSS counterpart. Though this approach is more similar to the previous studies mentioned above in the sense that it is based on a sample of known objects selected from a given survey to investigate how they look at a higher-resolution survey, to our knowledge the present work is the first study which tries to associate single GLIMPSE objects with multiple UKIDSS sources -- instead of just associating the nearest source -- in a large fraction of the Galactic plane. We have chosen the \citet{Robitaille2008} census as our starting point not only for simplicity and good coverage of the Galactic plane, but also because this sample is highly reliable. As a direct scientific application of this work, we can study the validity of the physical properties derived when assuming that the GLIMPSE YSOs in the Galactic plane are single objects. In particular, in this paper we investigate how clustering and unresolved binaries could affect the \citet{Robitaille2008} sample, and therefore the SFR estimate of \citet{RobitailleWhitney2010}. In Section~\ref{sec:observations}, we briefly describe the GLIMPSE observations and the corresponding YSO catalog, as well as the data from the UKIDSS Galactic Plane Survey we used in this work. Section~\ref{sec:photometry} gives details about the PSF fitting photometry we performed on the UKIDSS data, and the quality control of this photometry. In Section~\ref{sec:results} we report the main results of this study, in particular the implementation of a method to automatically identify dominant UKIDSS sources in the spectral energy distribution, and the statistics for the GLIMPSE YSO sample regarding these UKIDSS sources; Appendices~\ref{sec:decision-rules} and \ref{sec:convex} describe more specific aspects of our method, while in Appendices~\ref{sec:statistics-details} and \ref{sec:extended-sample} we give, respectively, further technical details about our statistics and extended results for special cases. In Section~\ref{sec:discussion}, we discuss the nature of possibly multiple UKIDSS sources, the sensitivity of our method to flux changes, and the presence of variable sources; we also present simple simulated YSO populations models \citep[based on the work by][]{RobitailleWhitney2010} to assess the importance of clustering and unresolved binaries in the GLIMPSE YSO sample and compare with the properties of the UKIDSS observations analyzed here, as well as to discuss the implications for SFR estimates. Finally, Section~\ref{sec:conclusions} summarizes the main conclusions of this paper. | \label{sec:conclusions} We have analyzed near-infrared UKIDSS observations of a sample of 8325 objects taken from the catalog of intrinsically red sources in the Galactic plane by \citet{Robitaille2008}, which were selected using the mid-infrared GLIMPSE survey. Since UKIDSS has a better angular resolution than that of GLIMPSE by a factor $> 2$, our primary aim was to investigate whether there are multiple UKIDSS sources that might all contribute to the GLIMPSE flux, or there is only one dominant UKIDSS counterpart. We did not use the published UKIDSS point source catalog which is based on aperture photometry only, and we instead performed PSF fitting photometry at the position of every GLIMPSE red source, in order to detect and properly separate the emission of multiple overlapping sources. The main results and conclusions presented in this paper are summarized as follows: \begin{enumerate} \item We noticed that the dominant UKIDSS sources are typically characterized by a smooth transition between their NIR SED and the MIR SED of the corresponding \citetalias{Robitaille2008} objects. We implemented a technique to automatically recognize these UKIDSS sources, which basically consisted in a comparison between two different interpolation methods at the NIR-MIR transition of the SED. This technique is very generic and could be perfectly applied for matching SEDs across gaps at other wavelengths. \item Most of the analyzed objects from the \citetalias{Robitaille2008} sample present only one dominant UKIDSS counterpart which matches the MIR SED (what we call ``UKIDSS-single'' objects). In particular, the fraction of UKIDSS-single objects is $92.1 \pm 1.2 \%$ for candidate AGB stars, and $87.0 \pm 1.6 \%$ for candidate YSOs, using the YSO/AGB-star approximate separation of \citetalias{Robitaille2008}. While this was expected for AGB stars, it was not intuitive for YSOs given the typically clustered nature of their environment. \item Practically the totality of the dominant UKIDSS sources were also the nearest in angular projection to the corresponding \citetalias{Robitaille2008} objects; therefore, a simple ``nearest-source'' matching between UKIDSS and GLIMPSE would be a statistically good approximation for the overall \citetalias{Robitaille2008} sample, though it would be wrong for the few specific objects showing multiple dominant sources in UKIDSS, or for different samples of \emph{Spitzer}-selected YSOs with lower fractions of UKIDSS-single objects. \item For the few \citetalias{Robitaille2008} objects that are not dominated by one UKIDSS source, we found by visual inspection some cases of apparently true multiple UKIDSS counterparts, typically two sources, but in exceptional cases three sources or even small clusters. However, given that the SED matching method was designed to identify the dominant UKIDSS sources, these multiple sources have $K$-band fluxes within a factor $\sim 5$, while fainter counterparts are, in general, not identified by our technique. \item We found that the SED matching method is not very sensitive to flux changes of up to a factor $\sim$~7--9, and therefore the dominant UKIDSS sources can still be identified in the SED if they are variable (considering the difference in the epochs between the GLIMPSE and UKIDSS observations). \item By doing simple clustering experiments using the population synthesis model by \citet{RobitailleWhitney2010}, in which we randomly assign neighbors within the GLIMPSE resolution to the ``detected'' synthetic YSOs, we were able to reproduce the high fraction of GLIMPSE YSOs that are dominated by only one UKIDSS counterpart, with a $K$-flux brighter than that of their neighbors by a factor of at least $\sim 5$. We argued that within the mass range covered by \citetalias{Robitaille2008} YSO candidates ($\sim$~3--20~$M_\sun$), clustering with objects with comparable mass is unlikely at the GLIMPSE resolution. \item We also carried out similar experiments to study the effect of unresolved binaries in the GLIMPSE YSO sample, but this time we rearranged the full initial set of synthetic YSOs of \citet{RobitailleWhitney2010} in a certain fraction of binaries and investigated how the number of ``detected'' objects change with respect to the original single-stars model. We found that this number is reduced by a factor $\sim 0.75$--0.85. \item According to these results, we conclude that no significant corrections are needed to the SFR estimated by \citet{RobitailleWhitney2010} from the effect of YSO clustering within the GLIMPSE resolution. However, the correction derived from the presence of unresolved YSO binaries might not be negligible, and would increase the SFR estimate by a factor $\sim 1.2$--1.3. \end{enumerate} The SED matching method implemented in this paper turned out to be very useful to characterize the UKIDSS observations of the GLIMPSE YSO candidates, especially for the detection of the dominant counterparts. Nevertheless, as shown by the clustering experiments of synthetic YSOs, a significant fraction of the GLIMPSE YSO candidates might contain at least two physically associated UKIDSS sources within the GLIMPSE resolution, even though only one dominates the flux. The challenge for the near future is to design procedures to identify these fainter multiple sources, in order to really take advantage of the full high-resolution information of UKIDSS, and progress towards the construction of the hierarchical YSO catalog in the long term. | 16 | 9 | 1609.04462 |
1609 | 1609.01301_arXiv.txt | We examine the baryon content of low-mass $\Lambda$CDM halos ($10^8<M_{200}/{\rm M_\odot}<5\times 10^{9}$) using the {\small APOSTLE} cosmological hydrodynamical simulations. Most of these systems are free of stars and have a gaseous content set by the combined effects of cosmic reionization, which imposes a mass-dependent upper limit, and of ram pressure stripping, which reduces it further in high-density regions. Halos mainly affected by reionization ({\small RELHICs}; REionization-Limited \ion{H}{I} Clouds) inhabit preferentially low-density regions and make up a population where the gas is in hydrostatic equilibrium with the dark matter potential and in thermal equilibrium with the ionizing UV background. Their thermodynamic properties are well specified, and their gas density and temperature profiles may be predicted in detail. Gas in {\small RELHICs} is nearly fully ionized but with neutral cores that span a large range of \ion{H}{I} masses and column densities and have negligible non-thermal broadening. We present predictions for their characteristic sizes and central column densities: the massive tail of the distribution should be within reach of future blind \ion{H}{I} surveys. Local Group {\small RELHICs} (LGRs) have some properties consistent with observed Ultra Compact High Velocity Clouds (UCHVCs) but the sheer number of the latter suggests that most UCHVCs are not {\small RELHICs}. Our results suggest that LGRs (i) should typically be beyond $500$ kpc from the Milky Way or M31; (ii) have positive Galactocentric radial velocities; (iii) \ion{H}{I} sizes not exceeding $1$ kpc, and (iv) should be nearly round. The detection and characterization of {\small RELHICs} would offer a unique probe of the small-scale clustering of cold dark matter. | \label{SecIntro} A defining prediction of hierarchically clustering models is that the Universe must be teeming with low-mass systems left over from the collapse of the early stages of the hierarchy \citep{White1978}. The $\Lambda$ cold dark matter ($\Lambda$CDM) paradigm is no exception; indeed, the abundance of $\Lambda$CDM halos massive enough, in principle, to host a galaxy is so high that they outnumber faint galaxies by a large factor \citep[see, e.g.,][]{Klypin1999,Moore1999}. For example, more than $1,000$ halos with virial\footnote{We define virial quantities as those calculated within a radius where the mean inner density equals 200 times the critical density of the Universe, $\rho_{\rm crit}=3H^2/8\pi G$. Virial quantities are identified by a ``200'' subscript.} mass exceeding $10^8 \rm \ M_\odot$ are expected within $\sim 2 \rm \ Mpc$ from the barycentre of the Local Group (LG), a region that contains fewer than $100$ galaxies with baryonic masses exceeding $10^5 \rm \ M_\odot$ \citep[][and references therein]{Sawala2016}. This discrepancy is usually explained by assuming that galaxies fail to form in halos below a certain halo mass, leaving a large number of systems essentially ``dark'', or free of stars. The main culprit is cosmic reionization, which heats most baryons to $\sim 10^4 \rm \ K$ at relatively high redshift and prevents them from settling and condensing into galaxies in the shallow potential wells of low-mass halos\cite[e.g.,][]{Bullock2000} The existence of these ``dark'' minihalos\footnote{Throughout this paper we shall refer to halos in the mass range $10^8<M_{200}/{\rm M_\odot}<5\times 10^{9}$ as minihalos.} is a cornerstone prediction of $\Lambda$CDM and their search has attracted great interest. Their presence could be inferred from their gravitational effects on dynamically cold structures, such as galaxy disks \citep[see][and references therein]{Feldmann2015} or thin stellar streams \citep{Ibata2002,Johnston2002,Carlberg2009}, or else from the distortions they may induce in gravitationally lensed images of distant galaxies \citep{Mao1998,Dalal2002,Vegetti2010,Hezaveh2016}. High-energy physicists, on the other hand, seek them as potential sources of energetic gamma rays powered by dark matter particle annihilation \citep{Diemand2007,Springel2008,Charles2016}. A more prosaic alternative is to look for direct signatures of their baryonic content (which should be a nearly pristine H+He gaseous mix, given the lack of internal enrichment sources) in redshifted absorption against the light of luminous distant objects. Indeed, minihalos were once hypothesized as responsible for the forest of Lyman-$\alpha$ lines in the spectra of high redshift quasars \citep{Rees1986,Ikeuchi1986}, until it was realized that the large coherence length of absorption features was more naturally explained by the density ripples induced by CDM-driven fluctuations on larger scales \citep[see][for a review]{Rauch1998}. ``Dark'' minihalos might also be detectable in 21 cm emission and are actively sought in \ion{H}{I} surveys of the local Universe \citep[see, e.g.,][for a recent review]{Giovanelli2016}. Indeed, minihalos were proposed early on as hosts of the ``high velocity'' clouds (HVCs) of neutral hydrogen seen in 21 cm surveys of large areas of the sky \citep{Blitz1999,Braun1999}. The large sizes of HVCs, however, were shown to be incompatible with that interpretation: current models predict that gas in minihalos should be highly ionized by the cosmic UV background, except for a small central ``core'' of neutral hydrogen \citep{Sternberg2002}. The mass and size of the neutral core depend sensitively on the mass of the halo and on the pressure of the surrounding medium. \ion{H}{I} cores of $\sim$ kpc size and mass $10^5$-$10^6 \rm \ M_\odot$ are expected in halos with virial mass in the $10^9$-$10^{10} \rm \ M_\odot$ range. At a putative distance of $\sim 1$ Mpc, these clouds would be much smaller and fainter than the typical HVC but still within range of current surveys \citep{Giovanelli2010}. The most promising minihalo candidates are the Ultra Compact High Velocity Clouds (UCHVCs) detected in surveys such as ALFALFA \citep{Adams2013} and GALFA \citep{Saul2012}. Their sizes and fluxes are consistent with minihalos in the Local Group volume, a result that has prompted deep follow-up imaging of some of the most prominent UCHVCs without obvious luminous counterparts in existing galaxy catalogs \citep[see, e.g.,][]{Sand2015,Bellazzini2015b}. These searches have revealed new dwarf galaxies, as illustrated by the discovery of Leo P, a gas-rich star forming dwarf at the edge of the Local Group \citep{Giovanelli2013}. \begin{figure} \includegraphics[width=\columnwidth]{FigMasses} \caption{{\it Top:} Baryonic mass content of simulated halos at $z=0$ as a function of halo virial mass for the L1 simulations. The blue curve indicates the median stellar mass of simulated galaxies (measured within the galactic radius, $r_{\rm gal}$), whereas the green dashed curve shows the median total {\it bound} baryonic mass of the same galaxies, measured within the virial radius, $r_{200}$. The baryon mass of ``dark'' minihalos (i.e., star free) is shown with open circles; red for {\small RELHICs} and grey for {\small COSWEBs}. The magenta solid line indicates the predicted gas mass of {\small RELHICs} according to the model of Appendix~\ref{SecApp}. For comparison, we also show the stellar mass vs halo mass relation derived using the abundance-matching technique by~\citet{Moster2013} (dot-dashed line) and~\citet{Behroozi2013} (dotted line). Gas-free minihalos are indicated in the middle panel. {\it Bottom:} Fraction of ``dark'' minihalos (thick dashed line). The other curves show the fraction of {\small RELHICs} computed for the resolution levels L1 (red solid) and L2 (purple dot-dashed), as well as for EAGLE run Recal-L025N0752 (brown dotted). Note the excellent agreement of all these simulations at the high-mass end.} \label{FigMasses} \end{figure} Some UCHVCs are thus clearly associated with faint galaxies, and, therefore, with minihalos. The converse, however, seems less clear. The sheer number of UCHVCs preclude many, if not most, of them from being associated with minihalos \citep{Garrison-Kimmel2014}, but it is unclear what criteria might be used to discriminate true minihalo candidates from \ion{H}{I} ``debris'' in the Galactic halo. \begin{figure*} \includegraphics[width=\textwidth]{FigSpatialDistribution} \caption{Panels, from left to right, show the distribution of gas, dark matter, and stars in one of the simulated volumes (namely V01-L1). Top and bottom rows show different orthogonal projections of a $7$ Mpc cubic box centred at the barycentre of the two main galaxies. Projections are chosen respect to the "sheet" that cross the volume. Colours indicate projected density, on a logarithmic scale. The location of {\small RELHICs} and {\small COSWEBs} are indicated in the left and middle panels, respectively. Note that {\small RELHICs} shun the high-density regions of the volume near the main galaxies, where cosmic web stripping is important and the population of {\small COSWEBs} dominates. Arrows show the positions of the individual {\small COSWEB} and {\small RELHIC} shown in Fig.~\ref{FigC} and Fig.~\ref{FigR}, respectively.} \label{FigSpatialDistribution} \end{figure*} We examine these issues here using the cosmological hydrodynamical simulations of the {\small APOSTLE}/EAGLE projects. We focus, in particular, on the gas content of ``dark'' minihalos. Given their lack of stars, and therefore of any energetic ``feedback'', two main mechanisms play a role in setting the gaseous content of minihalos: (i) cosmic reionization, which should evaporate much, but not all, of the baryons from such shallow potential wells, and (ii) ram pressure stripping by the cosmic web, which may unbind the gaseous content from minihalos that travel through dense filaments or ``pancakes'' of gas. \citet{Benitez-Llambay2013} show that the latter effect may reduce substantially the baryonic content of low-mass halos, especially in high-density regions such as groups of galaxies. This paper is organized as follows. We begin in Section~\ref{SecSims} with a brief summary of the {\small APOSTLE}/EAGLE suite of simulations, followed in Section~\ref{SecRes} by a discussion of our main results. We analyse the baryon content of dark minihalos in Sec.~\ref{SecMgasM200}. We identify two populations of dark minihalos in Sec.~\ref{SecCR}; one where the properties of the gas component are mainly set by the ionizing background, and another where the gas has been nearly completely removed by cosmic web stripping. We discuss the properties of the former in Sec.~\ref{SecR}, where we also present a simple model that reproduces their main structural properties. We use this model to make predictions for their \ion{H}{I} content, column density profiles, and 21 cm line widths, and compare them with the properties of UCHVCs in Sec.~\ref{SecObs}. We conclude with a brief summary of our main conclusions in Sec.~\ref{SecConc}, and provide an appendix with an analytic model for the gas density and temperature profiles in minihalos. \begin{figure*} \includegraphics[width=\textwidth]{FigC} \caption{Evolution of a cosmic web stripped system from the V01-L1 simulations, with $ M_{200} \sim 10^{9.1} \rm M_{\odot}$ at redshift $z=0$. The left panels show the evolution of (from top to bottom) the dark mass and gas mass within $r_{200}$; the logarithm of the virial temperature, $T_{200} \sim 10^4 {\rm K} \left ( V_{200} / 17 {\rm km \ s^{-1} }\right )^2$, and (bottom panel) the gas mass fraction ($M_{\rm gas}/M_{200}$) in units of the universal value, $f_{\rm bar}=\Omega_b/(\Omega_0+\Omega_{\rm b})$. The four panels on the right show snapshots of the evolution, at the times indicated by the solid circles in the left panels. Note how reionization heats up the gas at early times, reducing the halo baryon content. In this particular example, the system loses essentially all of its bound mass after passing through a dense region of the cosmic web at $z\sim 0.6$. } \label{FigC} \end{figure*} | \label{SecConc} We have used the {\small APOSTLE} suite of cosmological hydrodynamical simulations of the Local Group to examine the gas content of $\Lambda$CDM minihalos. We focussed our analysis on systems that are free of stars in our highest-resolution runs, since in such systems the bound gas content at $z=0$ should only depend on the effects of the UV ionizing background and on the ram pressure stripping that affects minihalos as they travel through the cosmic web. ``Dark'' minihalos (or, more precisely, systems with stellar mass $M_{\rm str}<10^4 \rm \ M_\odot$, the mass resolution limit of our simulations) split into two well-defined groupings: one where the mass of bound gas is set by the ionizing background and correlates tightly with the minihalo virial mass ({\small RELHICs}, for REionization Limited \ion{H}{I} Clouds), and another where there is little or no bound gas left within the halo after stripping by the cosmic web ({\small COSWEBs}, for COSmic WEb Stripped systems). The differentiation is thus mainly environmental; gas-free {\small COSWEBs} populate the high-density regions near the luminous galaxies of the Local Group, where gas densities are high and cosmic web stripping is important, whereas the relatively gas-rich {\small RELHICs} inhabit the underdense outskirts. Few {\small RELHICs} are found within $500$ kpc of either the Milky Way or the M31 analogues in the simulations. In terms of halo virial mass, the transition between luminous galaxies and dark systems like {\small RELHICs} and {\small COSWEBs} happens relatively quickly. Dark minihalos have masses that do not exceed $M_{200} \sim 10^{10} \rm \ M_\odot$; their fraction increase rapidly with decreasing mass, and they make up essentially all halos below $10^9 \rm \ M_\odot$. {\small RELHICs} make up most of the more massive dark minihalos; their abundance peaks at roughly $50\%$ for $M_{200}\sim 2\times 10^9 \rm \ M_\odot$. The {\small RELHIC} bound gas mass fraction decreases with decreasing mass; from $20\%$ of the universal baryon fraction at $M_{200} \sim 5 \times 10^9 \rm \ M_\odot$ to $0.3\%$ ($10^5 \rm \ M_\odot$, or ten particles in our highest-resolution runs) in $\sim 3\times 10^8 \rm \ M_\odot$ minihalos. The gas component in {\small RELHICs} is in approximate hydrostatic equilibrium with the dark matter potential and in thermal equilibrium with the ionizing UV background. Their thermodynamic properties are therefore well understood, and their gas density and temperature profiles are in excellent agreement with a simple model where UV-heated gas is in thermal and hydrostatic equilibrium within NFW halos. Gas in {\small RELHICs} is nearly pristine in composition and nearly fully ionized, with small (sub-kpc) neutral hydrogen cores that span a large range of \ion{H}{I} masses and column densities. These cores have negligible Doppler broadening and nearly round morphologies. The most massive {\small RELHICs} have properties comparable to those of some Ultra Compact High Velocity Clouds (UCHVCs) but the bulk of the Local Group {\small RELHIC} population should have \ion{H}{I} fluxes just below $\sim 3$ Jy km/s, the limit of the ALFALFA UCHVC detection. Other differences between {\small RELHICs} and UCHVCs are the following: (i) the sheer number of UCHVCs implies that most UCHVCs are not {\small RELHICs} (we expect fewer than 10 Local Group {\small RELHICs} with $S_{21}>0.1$ Jy km/s over the whole sky); (ii) {\small RELHICs} should mostly reside beyond $\sim 500$ kpc from the Milky Way, leading to low \ion{H}{I} fluxes ($<3$ Jy km/s), very small angular sizes ($<3'$), and predominantly positive Galactocentric radial velocities; (iii) {\small RELHICs} should be nearly round on the sky ($b/a>0.8$ at $10^{18}$ cm$^{-2}$) and (iv) have a very narrow distribution of thermally broadened line widths ($W_{50}\sim 20$ km/s). The small overlap in properties between UCHVCs and {\small RELHICs} suggest that the former are not part of the abundant dark minihalo population expected in the $\Lambda$CDM models. UCHVCs are either \ion{H}{I} ``debris'' in the Galactic halo, or else the \ion{H}{I} component of more massive halos, most of whom are expected to host a luminous stellar component as well. Further work is underway that aims to clarify the overall abundance of {\small RELHICs} in cosmological volumes; their contribution to the low-mass end of the \ion{H}{I} mass function; their relation to ultra faint galaxies; and the best strategies to detect them. Although {\small RELHICs} seem too faint to be a dominant source of \ion{H}{I} detections in extant or planned surveys, they may be easier to detect and study in absorption against the light of luminous background objects at moderate redshifts. {\small RELHICs} are a robust prediction of the $\Lambda$CDM paradigm so their detection and characterization would offer a unique opportunity to shed light onto the ``dark'' side of a cold dark matter-dominated universe. | 16 | 9 | 1609.01301 |
1609 | 1609.08220_arXiv.txt | We investigate a brane model based on Randall-Sundrum scenarios with a generic dark energy component. The latter drives the accelerated expansion at late times of the Universe. In this scheme, extra terms are added into Einstein Field equations that are propagated to the Friedmann equations. To constrain the dark energy equation of state (EoS) and the brane tension we use observational data with different energy levels (Supernovae type Ia, $H(z)$, baryon acoustic oscillations, and cosmic microwave background radiation distance, and a joint analysis) in a background cosmology. Beside EoS being consistent with a cosmological constant at the $3\sigma$ confidence level for each dataset, the baryon acoustic oscillations probe favors an EoS consistent with a quintessence dark energy. Although we found different lower limit bounds on the brane tension for each data sets, being the most restricted for CMB, there is not enough evidence of modifications in the cosmological evolution of the Universe by the existence of an extra dimension within observational uncertainties. Nevertheless, these new bounds are complementary to those obtained by other probes like table-top experiments, Big Bang Nucleosynthesis, and stellar dynamics. Our results show that a further test of the braneworld model with appropriate correction terms or a profound analysis with perturbations, may be needed to improve the constraints provided by the current data. | \label{Int} Several cosmological observations of Supernovae of the Type Ia (SNIa) at high redshift, show evidence of an accelerated expansion of the Universe at late times \cite{Schmidt,Perlmutter,Riess}. This is also supported by the observations of anisotropies in CMB and baryon acoustic oscillations (BAO). In the standard cosmological scenario, the responsible for the Universe accelerated expansion is an entity which made up the $\sim70\%$ of its total content and it is dubbed as dark energy \cite{PlanckCollaboration2013}. Several models try to explain this late time cosmic trend \cite{Shi:2012ma,Magana:2014voa,Magana:2015wra}, but the most favored candidate by the cosmological data is still the cosmological constant \cite{PlanckCollaboration2013}. However, the latter shows conceptual and theoretical problems when assuming that its energy density arises from quantum vacuum fluctuations \cite{Weinberg,Zeldovich}. Under this supposition, the theoretical prediction of the CC energy density differs $\sim120$ orders of magnitude from the observational estimations \cite{Weinberg,Zeldovich}. The other well-known difficulty of the CC is the coincidence problem, i.e. why DE density is similar to that of the dark matter (DM) component today \cite{Weinberg}. In this vein, the CC problems have motivated the appearance of alternative candidates for DE, being some of the most popular: the quintessence, phantom field, Chaplygin gas, Holographic DE, among others (see \cite{Copeland:2006wr} for an excellent DE models review). An interesting paradigm is to consider extra dimensions of space-time which could be the source of the current accelerated expansion. For instance, the Dvali-Gabadadze-Porrati (DGP) model \cite{Dvali:2000hr,Deffayet:2001pu} generates a natural accelerated expansion with a geometrical threshold associated to a five-dimensional space-time. However, a DE component must be added to achieve a stable late cosmic acceleration. Another example are the models proposed by Randall and Sundrum (RSI or RSII) \cite{Randall-I,Randall-II} that have the added benefit of providing a solution for the hierarchy and the CC quantum vacuum fluctuations problems (see \cite{m2000,Martinez,GarciaAspeitia:2011xv} for more details). Nevertheless, RS models drive a late time acceleration only by adding a dark energy field. In a covariant approach of the RSII models, the Einstein's field equations are modified assuming a five dimensional bulk with Schwarzschild-Anti'dSitter (S-$\rm AdS_{5}$) geometry and a four dimensional manifold embedded in this bulk, called the \emph{brane}. Note that for cosmological purposes the brane is considered as a FLRW structure, but in general it can take any geometry. The main modifications to the Einstein field equations lie in three new tensors: the first one considers second order corrections to the energy-momentum tensor; the second one allows matter in the bulk and the last one takes into account non-local effects associated with the Weyl's tensor \cite{sms}. An important term in the theory is the brane tension, $\lambda$, which shows the threshold between the corrections that come from branes and those who belong to the traditional Einstein's equation. These brane correction terms could produce important changes in the Universe dynamics that can be tested using the latest astrophysical or cosmological observations. Our main goal is to investigate the effect of one extra dimension on the background cosmology, mainly the DE properties. Indeed, we focus our inquiry on what is the preferred equation of state (EoS) for DE in brane models? and what is the constraint for the brane tension provided by current cosmological observations? In the present model, DE is located in our brane, together with the other Universe components (baryons, radiation and dark matter), with the restriction that gravity is the only interaction that can overstep to the extra dimension. The condition for the dark energy EoS is that it must always fulfill a generalized inequality, shown in Ref. \cite{Maartens:2003tw}, to obtain an accelerated dynamic on the brane. As it happens in General Relativity (GR), DE is divided in Quintessence ($-1<\omega_{de}<-1/3$), CC ($\omega_{de}=-1$), and Phantom field ($\omega_{de}<-1$), but parametrized by the extra dimensions \cite{Copeland:2006wr}. As mentioned before, although the late cosmic acceleration does not emerge from the extra dimension, the brane dynamics can help us to understand the dark energy and cosmic acceleration in this kind of scenario \cite{m2000,Martinez,GarciaAspeitia:2011xv}. Recent results using RS frame have only assumed a geometrical point of view (i.e. no DE component, see \cite{Wang:2006ue,Alam:2016wpf} as interesting examples). However, a robust analysis of the DE dynamic in a simple brane scenario is needed. In this work, we test a RS-like model that has all the basic components of the Universe, including a DE with a generic EoS, to constrain its parameters using recent cosmological observations at different energy scales. This kind of test also allow us to confirm whether the model is consistent at high and low energies in the cosmological evolution (i.e. using observational probes at different redshifts). To estimate the dark energy EoS and the brane tension, we use SNIa, $H(z)$, BAO and CMB distance constraints. These new bounds are complementary to those obtained by other probes like table-top (TT) experiments, Big Bang Nucleosynthesis (BBN), and stellar dynamics \cite{Gergely:2006xr}. The paper is organized as follows: in Sec. \ref{EM} we show the modified Einstein's equation by the presence of branes in the RS scenario. We find the modified Friedman equation assuming matter, radiation and a generic DE as the Universe components; in addition, we get the deceleration parameter in terms of brane corrections. In Sec. \ref{data} we perform a statistical analysis to constrain the EoS of the dark energy and the brane tension using various observations as $H(z)$ measurements, SNIa, BAO, CMB distance and finally a joint analysis. In Sec. \ref{Res}, we present and discuss the results obtained with the analysis of the previous section and finally in Sec. \ref{CR} we give some conclusions and remarks. In what follows, we work in units with $c=\hbar=1$, unless explicitly written. | \label{CR} Brane theory is an interesting paradigm with the potential to solve many fundamental problems in Particle Physics and Cosmology, being an important candidate to extend GR. In this paper, we explored the consequences in the cosmic acceleration by considering a generic dark energy in a Randall-Sundrum braneworld scenario. The modified Friedmann equations governing the dynamics of the Universe were derived to investigate whether the current cosmological observations suggest such gravity corrections. We put constraints on the dark matter density parameter, dark energy EoS, and the brane tension using the latest observational data (H(z), SNIa, BAO, and CMB distance constraints from Planck data release 2015). In particular, we provide brane tension lower limits in the low-energy regime (low redshift), complementary to those obtained in the high-energy regime. We found that all data sets provide dark energy equation of state ($w_{de}$) compatible with the CC at the $3\sigma$ confidence level. Different bounds in the brane tension were estimated using the cosmological data. While the high-redshift data (BAO and CMB) prefer no gravity modifications, the low-redshift data available ($H(z)$ and SNIa) slightly suggest that there is an extra dimension. However, as the brane effect is more important at higher redshifts, the bounds obtained from low redshift probes are less significant than the ones obtained from those at high redshift. Furthermore, a joint analysis of the cosmological data provides a tight constraint for the brane tension but the huge discrepancy with complementary observations/experiments persists. It is worth to note that a self-consistent brane perturbation analysis for this model on high-redshift data is needed in order to asses its effect on our constraints. We reconstructed the deceleration parameter using the best fit for each dataset and found that the dark energy component drives to a late-time cosmic acceleration independently of gravity modifications by an extra dimension. Finally, an appropriate extension of the modified FLRW equations for braneworld models is needed. For instance, by considering the crossed terms which take into account coupling between the different Universe components or the consideration of a variable brane tension. However, this work is out of our present scope. | 16 | 9 | 1609.08220 |
1609 | 1609.03903_arXiv.txt | The dispersal of the circumstellar discs of dust and gas surrounding young low-mass stars has important implications for the formation of planetary systems. Photoevaporation from energetic radiation from the central object is thought to drive the dispersal in the majority of discs, by creating a gap which disconnects the outer from the inner regions of the disc and then disperses the outer disc from the inside-out, while the inner disc keeps draining viscously onto the star. In this Letter we show that the disc around TW Hya, the closest protoplanetary disc to Earth, may be the first object where a photoevaporative gap has been imaged around the time at which it is being created. Indeed the detected gap in the ALMA images is consistent with the expectations of X-ray photoevaporation models, thus not requiring the presence of a planet. The photoevaporation model is also consistent with a broad range of properties of the TW Hya system, e.g. accretion rate and the location of the gap at the onset of dispersal. We show that the central, unresolved $870\ \mu\mbox{m}$ continuum source might be produced by free free emission from the gas and/or residual dust inside the gap. | Planets form from the reservoir of dust and gas residing in the circumstellar discs which surround young stars. The physical and chemical characteristics of this material influence the process of planet formation and are in turn influenced by the energetic radiation from the young stellar object. Indeed, young stars are strong sources of X-ray radiation, with approximately one thousandth of their bolometric luminosity being emitted at energies higher than $100\ \mbox{eV}$. X-rays play an important role in the disc evolution, by providing ionisation over a large range of columns (e.g. Igea \& Glassgold 1999; Ercolano \& Glassgold 2013), which is important for the chemical evolution of the material as well as for angular momentum transport mechanisms. In particular, ionisation of the disc atmosphere by the ``soft X-rays'' ($100\ \mbox{eV}<\mbox{eV}<1\ \mbox{keV}$) heats the gas and launches a thermal wind (e.g. Owen et al. 2010), which is able to disperse the disc, via (a) the formation of a gap, followed by (b) a hole which quickly grows in radius, with the outer disc being eroded from the inside-out. The X-ray photoevaporation model (Ercolano et al. 2008, 2009; Owen et al. 2010, 2011, 2012) is successful in reproducing the observed two-timescale dispersal (e.g. Luhman et al. 2010; Koepferl et al. 2013), and it can reproduce the intensities and profiles of emission lines produced in the wind (Ercolano \& Owen, 2010, 2016). However, the direct observation of a disc undergoing gap formation via photoevaporation is still lacking. In this Letter we propose that the gap at $1\ \mbox{au}$ in the nearest protoplanetary disc, TW~Hya, observed in the $870\ \mu\mbox{m}$ continuum by Andrews et al. (2016), using the long-baseline Atacama Large Millimeter/submillimeter array (ALMA), may indeed be the first directly imaged photoevaporative gap in a solar-type star to date. Surprisingly, this possibility has not yet been properly explored in the recent literature. This Letter is organised as follows: In Section 2 we summarise the relevant characteristics and current evidence for photoevaporation in the TW~Hya system. In Section 3 we explore the possible origin of the unresolved $870\ \mu\mbox{m}$ emission from the inner $0.5\ \mbox{au}$ of the disc. In Section 4 we show dust and gas density distributions from a numerical model of a 1D viscously evolving disc, subject to X-ray photoevaporation. Our conclusions are summarised in Section 5. | In this Letter we presented argument in support of X-ray photoevaporation as the origin of the recently detected gap in the continuum emission of the TW Hya disc. In this scenario, TW Hya is an object on the edge of dispersal, where the mass-loss-rate due to X-ray photoevaporation ($\sim$2$\times$10$^{-8} M_{\odot}$, corresponding to the observed X-ray luminosity of TW Hya) is about ten times larger than the (measured) gas accretion rate, and hence in the process of opening a gap between $1$ and $2\ \mbox{au}$. It is not surprising to find an object in this phase, since current statistics show that one should expect of the order of 4 to 6 early phase clearing objects in each of the nearby star forming regions. We further show that the detection of $\sim$1mJy continuum emission at 870$\mu$m (Andrews et al., 2016) is not in contrast with this scenario. We consider possible sources for the emission, finding that both free-free emission and dust continuum emission, or a combination of the two, are able to explain the observed flux level. Our new photoionisation models, in agreement with previous estimates by Pascucci et al. (2012) and Owen, Scaife \& Ercolano (2013) indicate that free-free emission is produced in the ionised bound disc atmosphere in the draining inner ($< 0.5\ \mbox{au}$) disc. Sub-mm size dust grains may also contribute to the emission, as they linger in the inner disc thanks to long stopping times in the disc of TW Hya. Indeed we calculate that the stopping time for $870\ \mu\mbox{m}$ grains is about $2\ \mbox{Myr}$ at $0.5\ \mbox{au}$ at the time of gap opening . In conclusion, we have shown that the X-ray photoevaporation model is consistent with a wide variety of observtional characteristics of the TW Hya disk and, as such, it is the most likely explanation of the observed gap at $1\ \mbox{au}$, instead of the presence of a planet. Our study thus suggests that our closest protoplanetary disc is an object caught at the start of the dispersal phase, making it the best suited natural laboratory to study this phenomenon. \vspace{-0.4cm} | 16 | 9 | 1609.03903 |
1609 | 1609.08528_arXiv.txt | Sudden singularities occur in FRW spacetimes when the scale factor remains finite and different from zero while some of its derivatives diverge. After proper rescaling, the scale factor close to such a singularity at $t=0$ takes the form $a(t)=1+ c \vert t \vert^\eta$ (where $c$ and $\eta$ are parameters and $\eta\geq 0$). We investigate analytically and numerically the geodesics of free and gravitationally bound particles through such sudden singularities. We find that even though free particle geodesics go through sudden singularities for all $\eta\geq 0$, bound systems get dissociated (destroyed) for a wide range of the parameter $c$. For $\eta <1$ bound particles receive a diverging impulse at the singularity and get dissociated for all positive values of the parameter $c$. For $\eta > 1$ (Sudden Future Singularities (SFS)) bound systems get a finite impulse that depends on the value of $c$ and get dissociated for values of $c$ larger than a critical value $c_{cr}(\eta,\omega_0)>0$ that increases with the value of $\eta$ and the rescaled angular velocity $\omega_0$ of the bound system. We obtain an approximate equation for the analytical estimate of $c_{cr}(\eta,\omega_0)$. We also obtain its accurate form by numerical derivation of the bound system orbits through the singularities. Bound system orbits through Big Brake singularities ($c<0$, $1<\eta<2$) are also derived numerically and are found to get disrupted (deformed) at the singularity. However, they remain bound for all values of the parameter $c$ considered. | \label{sec:Introduction} The observed accelerating expansion \citep{Tsujikawa:2010sc-dark-energy-review,Caldwell:2009ix-dark-energy-review,Copeland:2006wr-review-dark-en} of the universe has opened new windows for possible exotic physics on cosmological scales. The simplest model, \lcdm \cite{Bull:2015stt-lcdm-review}, based on the existence of a cosmological constant remains consistent with most cosmological observations including the cosmic microwave background (CMB) \cite{Ade:2015xua-planck2015}, baryon acoustic oscillations \citep{Aubourg:2014yra-bao-data,Delubac:2014aqe-bao-data1} large scale velocity flows \cite{Watkins:2014zaa-velocity-flows} Type Ia supernovae \cite{Betoule:2014frx-jla-snia-data}, growth rate of perturbations data \cite{Huterer:2013xky-growth-data1,Nesseris:2015fqa-growth-data2,Basilakos:2012uu-growth-data2,Nesseris:2007pa-growth-data3}, gamma ray burst data \cite{Izzo:2015vya-grb-dark-energy,Wei:2013xx-grb-dark-energy1,Samushia:2009ib-grb-dark-energy1}, $H(z)$ data \cite{Ding:2015vpa-lcdm-tension-hofz-data}, strong and weak lensing data \cite{Baxter:2016ziy-weak-lensing}, HII galaxy data \cite{Chavez:2016epc-hii-galaxies}, fast radio burst data \cite{Yang:2016zbm-fast-radio-burst}, cluster gas mass fraction data \cite{Allen:2007ue-gas-mass-fraction,Morandi:2016cet-gas-mass-fraction2} etc. However, some inconsistencies of \lcdm parameter estimates from specific datasets are beginning to emerge including inconsistent estimates of the Hubble parameter \citep{Bernal:2016gxb-h0-tension2,Roukema:2016wny-h0-tension1,Abdalla:2014cla-bao-anomaly2,Meng:2015loa-h0-tension2,Qing-Guo:2016ykt-lcdm-h0-tension2,DiValentino:2016hlg} in the context of \lcdm from different datasets, estimates of the amplitude of the (linear) power spectrum on the scale of $8 h^{-1} Mpc$ ($\sigma_8$) \cite{Bull:2015stt-lcdm-review} and estimates of the matter density parameter $\Omega_{0m}$ \cite{Gao:2013pfa-om0-tension}. In addition to these preliminary observational inconsistencies, there are naturalness theoretical arguments that indicate that physics beyond the standard \lcdm model remain a viable possibility\citep{Tsujikawa:2010sc-dark-energy-review,Caldwell:2009ix-dark-energy-review,Copeland:2006wr-review-dark-en}. A variety of extensions of \lcdm predict the existence (mostly in the future) of a wide range of singularities\cite{Barrow:2004xh-sfs-first,FernandezJambrina:2006hj-clasify-singularities-Tipler-Krolak,Cattoen:2005dx-visser-classify-milestones-en-cond,Dabrowski:2014fha-sfs-review-classif-varyingconst}. These singularities can be either geodesically incomplete (eg \cite{Caldwell:2003vq-bigrip-defined,Nesseris:2004uj-fate-bound-systems-big-rip,Perivolaropoulos:2004yr-crunch1,Lykkas:2015kls-crunch2}) (geodesics do not continue beyond the singularity and the universe ends at the classical level) or geodesically complete\cite{Dabrowski:2014fha-sfs-review-classif-varyingconst} (geodesics continue beyond the singularity and the universe may remain in existence). Geodesically incomplete singularities include the Big Rip\cite{Caldwell:2003vq-bigrip-defined,Nesseris:2004uj-fate-bound-systems-big-rip} where the scale factor diverges at a finite future time due to infinite repunsive forces of phantom dark energy, the Little Rip \citep{Frampton:2011rh-little-rip-models} and the PseudoRip \citep{Frampton:2011aa-pseudo-rip-some-bound-dissociate} where the divergence occurs at the infinite future time. They also include the Big Crunch where the scale factor vanishes due to the strong attractive gravity of future evolved dark energy eg in quintessence models with negative potentials \citep{Felder:2002jk,Giambo:2015tja,Perivolaropoulos:2004yr-crunch1,Lykkas:2015kls-crunch2}. Modified gravity, quantum effects and cosmological models that violate the cosmological principle have been shown to weaken or eliminate both geodesically complete and geodesically incomplete singularities \cite{Bamba:2009uf-avoid-sfs-fR,Bamba:2012ky-sfs-non-local-gravity+R^2-avoided,Bamba:2012vg-sfs-infT-torsion-gravity-avoided-with-T^b-like-fR,Barrow:2011ub-quantum-part-prod-doesnot-avoid-sfs,Bouhmadi-Lopez:2014jfa-sfs-smoothed-in=Born-Infeld-cosmology-bound-systems-survive-sfs,BouhmadiLopez:2009jk-brane-bigrip-goesto-sfs,BouhmadiLopez:2009pu-sfs-quantum-avoid,Kamenshchik:2012ij-only-strong-sing-bigbangetc-avoided-byquantum-sfs-noquantumavoidance,Dabrowski:2006dd-quantum-cosmology-big-rip-bigbang--avoided,Dabrowski:2013sea-sfs-regularized-by-varying-constants,FernandezJambrina:2008dt-sfs-mod-grav-Fried-Tipler-Krolak,Kamenshchik:2007zj-sfs-avoided-by-quantumeffects-nobigbrake,Nojiri:2008fk-fR-can-avoid-sfs-evenmore-withquantum,Nojiri:2009pf-cure-bigrip-fsf-modgrav-dark-matter-coupling,Sami:2006wj-avoid-sing-loop-quant-cosm-tsujikawa,Singh:2010qa-curved-loop-quantum-cosmo-avoids-many-sing-big-rip-etc} Geodesically complete singularities involve a divergence of a derivative of the scale factor $a$ while the scale factor remains finite and different from zero. Such singularities may involve divergence of the Ricci scalar ($R=\frac{6}{a^2} \left( {\ddot a}a + {\dot a}^2+k\right)$ for FRW metric) and Riemann tensor components. Despite of this divergence the geodesics are well defined through the time of the singularity and the Tipler and Krolak integrals\citep{Tipler:1977zza,Krolac1986,FernandezJambrina:2006hj-clasify-singularities-Tipler-Krolak} of the Riemann tensor components along the geodesics remain finite in most cases. The Tipler\cite{Tipler:1977zza} integral is defined as \be \int_0^\tau d \tau^\prime \int_0^{\tau^\prime } d\tau'' \vert R^i_{0j0}(\tau'') \vert \label{tiplerint} \ee while the Krolak integral\cite{Krolac1986} is defined as \be \int_0^\tau d\tau' \vert R^i_{0j0}(\tau') \vert \label{krolacint} \ee where $\tau$ is the affine parameter along the geodesic. The components of the Riemann tensor are expressed in a frame that is parallel transported along the geodesics. These integrals express the time integrals of the tidal forces along geodesics. In a cosmological setup a diverging Tipler integral corresponds to a geodesically incomplete singularity (eg Big Rip) while this is not necessarily true for a diverging Krolak integral. A finite Krolak integral means that a cosmological comoving observer on a bound system will experience a finite impulse at the singularity and thus it is possible that the bound system will survive through the singularity. On the other hand a diverging Krolak integral implies an infinite impulse which will dissociate all bound systems at the time of the singularity. However, free particle geodesics may go through such singularity. Since the Riemann tensor components involve up to second order derivatives of the scale factor, both integrals (\ref{tiplerint}) and (\ref{krolacint}) are finite if the scale factor has finite first derivative at the singularity even if the second derivative diverges. If however, the first derivative of the scale factor diverges then only the Tippler integral is finite while the Krolak integral diverges at the geodesically complete singularity and bound systems are expected to dissociate due to the infinite impulse they receive at the singularity. Singularities where the above integrals diverge are strong singularities. By solving the Friedman equations with respect to the pressure and density we may translate the possible divergence of the derivatives of the scale factor at the geodesically complete singularities to divergence of the density and pressure as well as to possible violation of energy conditions. Thus using the equations \ba \rho(t)&=&\frac{3}{8\pi G} \left( \frac{\dot a^2}{a^2}+ \frac{k}{a^2}\right) \\ p(t)&=&\frac{1}{8\pi G} \left( 2\frac{\ddot a}{a} +\frac{\dot a^2}{a^2}+ \frac{k}{a^2}\right) \ea it becomes clear that when the first derivative of the scale factor is finite at the singularity but the second derivative diverges (Sudden Future Singularities (SFS) \cite{Barrow:2004xh-sfs-first}) the density is finite but the pressure diverges. Near a geodesically complete singularity occurring (with no loss of generality) at coordinate time $t=0$, the scale factor after proper rescaling may be expressed in the form\citep{Cattoen:2005dx-visser-classify-milestones-en-cond,FernandezJambrina:2007sx-sfs-proper-time-issues} \be a(t)=1+ c \vert t \vert^\eta \label{scfactans} \ee where $c$ and $\eta$ are parameters and for geodesic completeness we assume $\eta\geq 0$. For $0<\eta <1$ the first derivative (and higher) of the scale factor diverges at the singularity (finite scale factor singularity) while for $1<\eta <2$ the second derivative (and higher) diverge at the singularity (SFS). For $c<0$ and $1<\eta <2$ the SFS is known as Big Brake \cite{Kamenshchik:2012ij-only-strong-sing-bigbangetc-avoided-byquantum-sfs-noquantumavoidance,Kamenshchik:2007zj-sfs-avoided-by-quantumeffects-nobigbrake} due to the negative sign of the diverging second derivative (deceleration) of the scale factor. Comoving free particle geodesics in a FRW metric approaching a geodesically complete singularity are easily obtained by solving the geodesic equation for the radial coordinate which may be written as \be {\ddot r}=\frac{\ddot a}{a} r=\frac{c\;\eta(\eta-1)\;\vert t\vert^{\eta-2}}{(c\;\vert t\vert^{\eta}+1)}r \label{freegeod} \ee where we used eq. (\ref{scfactans}). Eq. (\ref{freegeod}) may also be trivially obtained by demanding that the $\ddot \rho =0$ where $\rho \equiv \frac{r}{a}$ is the comoving coordinate of a comoving observer (not to be confused with the density). As will be discussed in the next section, eq. (\ref{freegeod}) has finite well behaved solutions for all $\eta \geq 0$ (finite scale factor at the singularity $t=0$) even though the expansion `force' $\frac{\ddot a}{a} r$ and the first derivative of the scale factor may diverge at the singularity. Therefore all singularities involving a finite scale factor are geodesically complete \citep{FernandezJambrina:2004yy-geodesics-sfs-smooth}. Geodesically complete singularities where the scale factor behaves like eq. (\ref{scfactans}) are obtained in various physical models including quintessence pontentials of the form \cite{Barrow:2015sga-phys-model} \be V(\phi) = A \phi^n \label{physmod1} \ee with $0<n<1$ and $A$ a constant. In this class of models, it may be shown that when $\phi=0$ the first and second derivatives of the scale factor are finite while the third derivative diverges. This behaviour corresponds to $2<\eta<3$ in eq. (\ref{scfactans}). Other physical models with geodesically complete singularities include tachyonic models \cite{Keresztes:2010fi-tacyonic-bigbrake-tobogcrunch-obs-constr}, modified gravity \cite{Nojiri:2009pf-cure-bigrip-fsf-modgrav-dark-matter-coupling}, loop quantum gravity \cite{Singh:2010qa-curved-loop-quantum-cosmo-avoids-many-sing-big-rip-etc}, anti-Chaplygin gas \citep{Keresztes:2012zn-sfs-crossing-geodesics-with-delta-function-pressure}, brane models \cite{BouhmadiLopez:2009jk-brane-bigrip-goesto-sfs} etc. The presence of geodesically complete singularities in our past light-cone is in principle possible and consistent with current observational data. Constraints on such abrupt events have been obtained in Refs. \cite{Park:2015qya-dark-energy-spike,DeFelice:2012vd-rapid-transitions} using standard ruler and standard candle cosmological data constraining the form of the past expansion history of the universe. The possible existence of such events in the future light cone has also been investigated under specific assumptions of the functional form of the future Hubble expansion rate \cite{Lazkoz:2016hmh-sfs-obs-constr-occurs-soon,Yurov:2007tw-obs-constr-bigfreeze-adotinfty-chaplyginalone-insufficient,Jimenez:2016sgs-obs-cons-approach-sfs,Ghodsi:2011wu-sfs-obs-cons-cmb-probs,Denkiewicz:2012bz-sfs-obs-constr-may-occur-near-fut,Denkiewicz:2015nai-sfs-data-growth-test,Dabrowski:2007ci-obs-cons-sfs}. An important effect of geodesically complete singularities is the disruption or dissociation of bound systems. Geodesically complete singularities with diverging second time derivative but finite first derivative (SFS corresponding to $1<\eta<2$) of the scale factor induce a finite impulse on geodesics which disrupts and may even dissociate bound systems for large enough impulse (large values of $c$ in eq. (\ref{scfactans})). In cases where the first derivative is diverging the induced impulse is infinite and all bound systems dissociate. Signatures of bound system disruption due to SFS may be observable in galaxies or clusters leading to additional constraints on the possible existence of such abrupt events in our past light cone. The goal of the present study is to use geodesic equations in order to identify the type of distortion induced on bound systems by SFS. We will also identify the range of parameters for which the distortion of the bound systems is large enough to lead to dissociation. The structure of this paper is the following: In the next section we review the derivation of the gravitationally bound particle geodesics in an expanding background and in physical coordinates. The properties of these equations at the SFS is also reviewed and the special case of a free particle is identified. In section III, the free particle geodesics are obtained by solving the geodesic equation both analytically and numerically for specific initial conditions. The geodesics corresponding to a bound particle going through a SFS are obtained numerically in section IV as a function of the parameters $c$, $\eta$ and the angular velocity $\omega_0$ of the bound particle. The range of parameters that lead to dissociation of the bound systems is identified and the form of the geodesics for both dissociated and disrupted systems is obtained. Finally in section V we summarise and discuss possible extensions of the present analysis. | \label{sec:Section 4} We have derived analytically and numerically the form of free particle geodesics through SFS and demonstrated their existence when the scale factor is finite through the singularity. We have also demonstrated that bound systems can survive through SFS provided that the impulse they receive at the singularity is less than a critical value which corresponds to a critical value of the parameter determining the form of the scale factor through the SFS. This critical parameter $c_{cr}(\eta,\omega_0)$ depends both on the exponent $\eta$ of the scale factor and on the mass and scale of the bound system through the parameter $\omega_0$. Bound systems that have survived through a SFS suffer deformations that may be detectable through cosmological observations. For example spiral galaxies that have gone through a SFS would have elongated and deformed spiral arms. The present analysis focuses on geodesically complete singularities which assume finite scale factor as is the case for SFS. Geodesically incomplete singularities where the scale factor is not finite (eg Big Rip) always lead to dissociation of all bound systems and have been studied in detail previously \cite{Nesseris:2004uj-fate-bound-systems-big-rip}. The fate of bound systems and the precise form of their geodesics, in other types of geodesically incomplete singularities (eg a Big Crunch) would be an interesting extension of this project. The detailed form of the predicted deformation of many particle multi-orbit systems is an interesting extension of the present analysis. In the context of such an analysis and after comparison with the observed forms of bound systems like clusters and galaxies it may be possible to obtain bounds on the strength of possible SFS in our past light cone or to detect signatures of such events in the form of existing bound systems. Another extension of the present analysis could be the investigation of the effects of SFS on cosmic defects like cosmic strings and domain walls in both the Nambu-Goto action approximation\cite{Balcerzak:2006ac} and in the full field theoretical formulation. Similar issues may be addressed regarding strongly bound systems like black holes \cite{Babichev:2004yx} where the approximate weak field metric we used is not applicable. {\bf Numerical Analysis:} The Mathematica file that led to the production of the figures may be downloaded from \href{https://drive.google.com/open?id=0B7rg6X3QljQXYW1SVjgtejExNVU}{here}. | 16 | 9 | 1609.08528 |
1609 | 1609.08002_arXiv.txt | Narrow-line Seyfert 1 galaxies have been identified by the {\it Fermi Gamma-Ray Space Telescope} as a rare class of $\gamma$-ray emitting active galactic nuclei (AGN). The lowest-redshift candidate among them is the source 1H~0323$+$342. Here we present quasi-simultaneous {\it Gemini} near-infrared and {\it Keck} optical spectroscopy for it, from which we derive a black hole mass based on both the broad Balmer and Paschen emission lines. We supplement these observations with a {\it NuSTAR} X-ray spectrum taken about two years earlier, from which we constrain the black hole mass based on the short timescale spectral variability. Our multiwavelength observations suggest a black hole mass of $\sim$2$\times$10$^7$~$M_\odot$, which agrees well with previous estimates. We build the spectral energy distribution and show that it is dominated by the thermal and reprocessed emission from the accretion disc rather than the non-thermal jet component. A detailed spectral fitting with the energy-conserving accretion disc model of Done et al. constrains the Eddington ratio to $L/L_{\rm Edd} \sim 0.5$ for a (non-rotating) Schwarzschild black hole and to $L/L_{\rm Edd} \sim 1$ for a Kerr black hole with dimensionless spin of $a^{\star}= 0.8$. Higher spin values and so higher Eddington ratios are excluded, since they would strongly overpredict the observed soft X-ray flux. | The majority of $\gamma$-ray emitting active galactic nuclei (AGN) discovered by the {\it Fermi Gamma-Ray Space Telescope} and listed in its third Large Area Telescope (LAT) catalogue \citep{Fermi3} are blazars, evenly distributed between flat-spectrum radio quasars and BL Lacertae objects. However, a very small number of $\gamma$-ray emitting AGN are optically classified as narrow-line Seyfert 1s, i.e. they have much lower optical luminosities than quasars and their broad emission lines are relatively narrow with full widths at half maximum (FWHM)$\la 2000$~km~s$^{-1}$. They usually also have very strong emission lines from permitted \FeII~transitions in their optical spectra \citep{Bor92}. Since the first discovery of $\gamma$-ray emitting narrow-line Seyfert 1s \citep{Abdo09}, only eight sources are known to date \citep{Fosch16a}. All of these sources are radio-loud and their $\gamma$-ray emission is thought to be produced via the external Compton (EC) mechanism whereby the relativistic jet electrons upscatter a photon field external to the jet, e.g. from the accretion disc, broad emission line region (BLR) or dusty torus, to higher energies. This interpretation is also often used to explain the $\gamma$-ray emission detected from broad-line quasars. The discovery of narrow-line Seyfert 1s as a class of $\gamma$-ray emitting AGN is intriguing, since they generally reside in spiral galaxies rather than in bright ellipticals which are usually the hosts of radio-loud AGN with powerful relativistic jets. Furthermore, as a class, the narrow-line Seyfert 1s tend to have lower black hole masses and higher accretion rates relative to their Eddington limit compared with the typical Seyfert 1 AGN. This means that the thermal accretion disc spectrum and its Comptonised components are expected to dominate over the jet emission at optical/UV wavelengths and X-ray energies. This dominance is rarely seen over this entire frequency range in the other $\gamma$-ray emitting blazar classes and so these sources offer us the unique opportunity to study the connection between jet and accretion power. Among the $\gamma$-ray detected narrow-line Seyfert 1s, the source 1H~0323$+$342 is of particular interest, since it has the lowest redshift \citep[$z=0.0629$;][]{Zhou07}. This not only means that its host galaxy can be resolved by ground-based imaging \citep{Anton08, Leon14} and that due to its relatively high flux good signal-to-noise (S/N) ratio observations can be obtained in relatively short exposure times, but also that its black hole mass can be reliably estimated from single-epoch spectra using several broad emission lines. Its optical spectrum covers simultaneously the two strongest Balmer lines, H$\alpha$ and H$\beta$, both for which reliable black hole mass scaling relations exist \citep[e.g.][]{Greene05, Xiao11, Bentz09, Bentz13} and a cross-dispersed near-infrared (near-IR) spectrum with its large wavelength coverage gives simultaneous observations of the two strongest Paschen lines, Pa$\alpha$ and Pa$\beta$, for which a black hole mass scaling relation has recently been presented by \citet{L11b, L13}. The black hole mass is a key ingredient for modelling the accretion disc spectrum which in turn determines the accretion power relative to the Eddington limit and the bolometric luminosity. Here we present recent quasi-simultaneous optical and near-IR spectroscopy of high quality (high S/N and moderate spectral resolution), from which we derive a black hole mass based on both the broad Balmer and Paschen emission lines. We supplement these observations with a {\it NuSTAR} X-ray spectrum taken about two years earlier, from which we constrain the black hole mass based on the short timescale spectral variability. This paper is organised as follows. In Section 2, we describe the near-infrared, optical and X-ray observations based on which we estimate the black hole mass as detailed in Section 3. In Section 4, we construct the multiwavelength spectral energy distribution (SED), which we fit with the energy-conserving accretion disc model of \citet{Done12, Done13} in order to constrain the Eddington ratio. Finally, in Section 5, we summarise our main results and present our conclusions. Throughout this paper we have assumed cosmological parameters $H_0 = 70$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_{\rm M}=0.3$, and $\Omega_{\Lambda}=0.7$. Photon spectral indices have been defined as $N(E) \propto E^{-\Gamma}$. | We have presented here recent quasi-simultaneous optical and near-IR spectroscopy of high quality (high S/N and moderate spectral resolution) for the source 1H~0323$+$342, which is the lowest-redshift member of the rare class of $\gamma$-ray detected narrow-line Seyfert 1s. We have supplemented these observations with a {\it NuSTAR} X-ray spectrum taken about two years earlier and constrained the black hole mass based on several optical and near-IR broad emission lines as well as the short timescale X-ray variability. With a reliable black hole mass estimate in hand, we have derived the Eddington ratio based on a detailed spectral fitting of our multiwavelength SED with the accretion disc model of Done et al. Our main results can be summarised as follows. \vspace*{0.2cm} (i) Our three estimates of the black hole mass based on the ionising continuum luminosity and the width of the hydrogen broad emission lines H$\alpha$, H$\beta$ and Pa$\alpha$ give a very small range of values of $\sim 1.5 - 2.2 \times 10^7$~solar masses, with an average value of $\sim 2 \times 10^7$~solar masses. This amazing consistency between the three estimates is suprising, given that the relationships which they are based on have uncertainties of the order of $\sim 40-50\%$ at the $1\sigma$~level. (ii) We obtain a very good agreement between the black hole mass estimates from the broad emission lines and those from the short-term X-ray variability, which lie in the range of $\sim 1.0 - 1.7 \times 10^7$~solar masses. In addition, we have considered alternative methods to estimate the black hole mass, which are based on the dispersion instead of the FWHM of the broad emission line and the line and X-ray luminosity instead of the ionising continuum luminosity. We find in general a good agreement with our previous estimates, except when using the emission line luminosities. These give black hole masses in the range of $\sim 0.6-1.2 \times 10^7$~solar masses, which are a factor of $\sim 2$ smaller than our other estimates. (iii) The main aim of our SED fitting is to constrain the spin value, which in turn determines the Eddington ratio and so the bolometric luminosity. In agreement with previous studies, we find that, in the absence of far-UV data, the spin value can in principle be constrained if a soft X-ray excess is detected. We detect this component in our co-added {\it Swift} spectrum, but its frequency coverage does not reach low enough to differentiate between zero spin and a spin value up to $a^{\star}=0.8$. Therefore, we constrain the Eddington ratio only to a range of values of $L/L_{\rm Edd} \sim 0.5 - 1$. However, we can exclude spin values of $a^{\star}>0.8$ and so a super-Eddington nature of the source, since these solutions strongly overpredict the observed soft X-ray flux. | 16 | 9 | 1609.08002 |
1609 | 1609.01912_arXiv.txt | r-mode astroseismology provides a unique way to study the internal composition of compact stars. Due to their precise timing, recycled millisecond radio pulsars present a particularly promising class of sources. Although their thermal properties are still poorly constrained, X-ray data is very useful for astroseismology since r-modes could strongly heat a star. Using known and new upper bounds on the temperatures and luminosities of several non-accreting millisecond radio pulsars we derive bounds on the r-mode amplitude as low as $\alpha\lesssim10^{-8}$ and discuss the impact on scenarios for their internal composition. | Astroseismology is an ideal method to probe the otherwise inaccessible interiors of stars. In case of compact stars their oscillations generally cannot be detected directly via an electromagnetic signal and require the connection to other astrophysical observables. Such a connection is provided by r-modes \cite{Papaloizou:1978zz,Andersson:1997xt,Friedman:1997uh,Lindblom:1998wf,Andersson:1998ze,Andersson:2000mf} which are unstable due to the Friedman-Schutz mechanism \cite{Friedman:1978hf} and emit gravitational waves spinning the star down. An important property of r-modes is that due to their unstable nature, the saturation of their amplitude at a finite value also dissipates a significant amount of energy that heats the star. As discussed in \cite{Alford:2013pma} this could be particularly important in recycled millisecond radio or high-energy pulsars, since r-modes with amplitudes that would explain the known spin-down behavior would heat these otherwise rather cold sources to large surface temperatures $\gtrsim\!10^{6}\,{\rm K}$. Temperature measurements or bounds on these sources therefore allow us to constrain the r-mode amplitude and to distinguish different scenarios \cite{Alford:2013pma}. For recycled, non-accreting millisecond pulsars detailed X-ray measurements are still scarce due to their faintness \cite{Becker:1998yf,Prinz:2015jkd}. Moreover, the pulsar beaming mechanism, creating a hot spot on the surface and hard x-ray components from the magnetosphere, complicates the X-ray analysis. Because of this an actual surface temperature measurement is only available for the closest source J0437$-$4715 \cite{Durant:2011je,2015MNRAS.452.3357G}. Unfortunately this source spins with a frequency that is too low that r-modes could be present. Other spectral analyses \cite{Bogdanov:2006ap,Forestell:2014lza,Prinz:2015jkd} so far only resolve the hot spot and the hard power law component, but fail to clearly detect a thermal surface emission. However, even in the absence of an observed thermal surface component such fits strongly limit the size of the undetected uniform thermal emission and one can give upper bounds on the surface temperature that have to hold in order to be consistent with the present data. Moreover, even for sources for which only the total X-ray luminosity is available, the luminosity likewise limits the temperature of a potential thermal surface component. In addition to the compiled data in the literature we also add a more stringent bound for another source via a detailed X-ray analysis of the nearby pulsar PSR~J1231$-$1411. In compact stars the damping and the heating due to the saturation of unstable global oscillation modes depends strongly on the internal composition. The same holds for the cooling of the star since certain forms of matter can feature fast cooling mechanisms. In the absence of fast cooling photon emission from the surface dominates at the low temperatures present in millisecond pulsars. However, when fast neutrino cooling, e.g in exotic forms of matter, is present the bulk emission dominates, which introduces additional uncertainties related to the heat transport between the core and the surface. We analyze both standard and exotic compositions and set robust bounds on the r-mode amplitude in the considered sources by taking into account the various uncertainties in the micro- and macro-physics. | Using recent X-ray data we set stringent bounds $\alpha \lesssim 10^{-8}$ on the r-mode amplitude in millisecond radio and high energy pulsars. These bounds are considerably tighter than the spin-down limits obtained from the pulsar timing data and even lower than those obtained previously for accreting sources in LMXBs. Correspondingly they show that there must be significant damping in these sources. However, non of the standard damping mechanism that are known to be present in standard neutron stars can provide such strong damping. An example for such a standard saturation mechanism, that is present independent of the composition, is the coupling of different oscillations modes \cite{Arras:2002dw,Bondarescu:2013xwa}, which is insufficient since it can only saturate r-modes at $\alpha_{\rm sat} \sim 10^{-6}-10^{-5}$. The same holds for Ekman-layer damping, which cannot damp r-modes in fast sources \cite{Alford:2013pma}, as well as for magnetic effects due to differential rotation \cite{Rezzolla:1999he,Friedman:2015iqa}, which likewise have no significant impact taking into account the small magnetic fields present in millisecond pulsars \cite{Rezzolla:pc}. Therefore, the new bounds strongly increase the discrepancy between standard, well-constrained damping mechanisms and the astrophysical data, so that in absence of such trivial explanations astroseismology becomes an efficient tool to study the internal composition of compact stars. Structurally more complicated stars, involving for instance multi-component superfluids \cite{2009MNRAS.397.1464H,Haskell:2013hja}, could have the potential to explain the data, while even more exotic compositions like ungapped quark matter \cite{Madsen:1999ci,Alford:2013pma} or hybrid stars \cite{Alford:2014jha} have already been shown to be fully consistent with the present data. % Our analysis also sets limits as low as $\lesssim 10^{-4}$ on the spindown fraction due to r-modes that underline the generic feature, that even when r-modes are so small that they are irrelevant for the spindown of a source, they nevertheless can have a significant impact on its thermal evolution. The obtained bounds also impose analogous bounds on the gravitational wave strain in current interferometers, like advanced LIGO, which rule out the possibility to detect the continuous gravitational wave emission from these sources without further enhancements or third generation detectors. We also demonstrated a simple yet effective method to put an observational limit on the surface emission of these objects, using \pulsar~as an example case. In a future study we will expand this search by taking into account the measurement uncertainties in the distances, radii and the amount of interstellar extinction for a number of pulsars for which there is high quality data. We note that the NICER mission that will be launched to the International Space Station in early 2017 (see e.g. \cite{2014SPIE.9144E..20A}), may have a significant contribution to the search of surface emission of these objects thanks to its large effective area in the soft X-ray band. | 16 | 9 | 1609.01912 |
1609 | 1609.06703_arXiv.txt | We have monitored the transient neutron star low-mass X-ray binary 1RXS J180408.9$-$342058 in quiescence after its $\sim$4.5 month outburst in 2015. The source has been observed using {\it Swift} and {\it XMM-Newton}. Its X-ray spectra were dominated by a thermal component. The thermal evolution showed a gradual X-ray luminosity decay from $\sim$18$\times 10^{32}$ to $\sim$4$\times 10^{32}$ ($D$/5.8 kpc)$^{2}$ erg s$^{-1}$ between $\sim$8 to $\sim$379 days in quiescence and the inferred neutron star surface temperature (for an observer at infinity; using a neutron star atmosphere model) decreased from $\sim$100 to $\sim$71 eV. This can be interpreted as cooling of an accretion-heated neutron star crust. Modeling the observed temperature curve (using \texttt{NSC\textsc{ool}}) indicated that the source required $\sim$1.9 MeV per accreted nucleon of shallow heating in addition to the standard deep crustal heating to explain its thermal evolution. Alternatively, the decay could also be modelled without the presence of deep crustal heating, only having a shallow heat source (again $\sim$1.9 MeV per accreted nucleon was required). However, the {\it XMM-Newton} data statistically required an additional power-law component. This component contributed $\sim$30 per cent of the total unabsorbed flux in 0.5 -- 10 keV energy range. % The physical origin of this component is unknown. One possibility is that it arises from low-level accretion. The presence of this component in the spectrum complicates our cooling crust interpretation because it might indicate that the smooth luminosity and temperature decay curves we observed may not be due to crust cooling but due to some other process. | Transient low-mass X-ray binaries (LMXBs) harbouring neutron stars are excellent laboratories to probe the neutron star structure. The donors in LMXBs are typically $\lesssim 1\, M_{\odot}$ and mass transfer on to the primary is by Roche lobe overflow of the donor. Transient neutron star LMXBs experience periods of accretion outbursts ranging from weeks to years. These outbursts can reach X-ray luminosities of $L_X \sim$10$^{35 - 38}$ erg s$^{-1}$. % Between the outbursts are periods of quiescence, which can last for a period of months to decades and the systems then typically have luminosities of $L_X \sim$10$^{30 - 34}$ erg s$^{-1}$. During outbursts the accreted material compresses the neutron star crust and heats it up by electron capture, neutron emission, and density driven fusion reactions \citep[e.g.,][]{haensel1990non,haensel2008models,steiner2012deep} and the crust can be heated out of equilibrium with the core if enough heat is generated. In total about 1.5 -- 2 MeV per accreted nucleon is expected to be released deep in the crust (primarily at densities of 10$^{12 - 13}$ g cm$^{-3}$; \citeauthor{haensel2008models} \citeyear{haensel2008models}). When accretion ceases in quiescence the crust cools down mainly by conducting the heat to the core and the surface. The thermal evolution of the neutron star crust is determined by the structure and composition of the crust, the strength and depth of the heating processes, and the properties of the accretion outburst \citep[e.g.,][]{shternin2007neutron,brown2009mapping,page2013forecasting}. The outermost layers cool fastest and hence as time progresses we probe the cooling of deeper and deeper layers. So far eight transient neutron star LMXBs have been monitored in quiescence to study crust cooling \citep{wijnands2001chandra,wijnands2002xmm,wijnands2003chandra,wijnands2004monitoring, cackett2006cooling,cackett2008cooling,cackett2010continued,cackett2013change, degenaar2009chandra,degenaar2011evidence,degenaar2013continued,degenaar2014probing, degenaar2015neutron,degenaar2011soft,degenaar2011accretion, fridriksson2010rapid,fridriksson2011variable,trigo2011xmm,homan2014strongly,waterhouse2016constraining,merritt2016neutron}. Reconstructing the obtained results using various theoretical cooling models has provided us with new insights into the properties of neutron star crusts \citep{rutledge2002crustal,shternin2007neutron,brown2009mapping,page2013forecasting,medin2015time,horowitz2015disordered,turlione2015quiescent,deibel2015strong,ootes2016}. The rapid temperature decay that the cooling crust exhibits implies a very high thermal conductivity. The thermal conductivity is parametrized by the level of atomic impurities in the crust, $Q_\mathrm{imp}$ , where a lower level of impurities implies a higher thermal conductivity % In addition, the high crust temperature in some systems can only be compatible with the theoretical models if an extra source of heat at relatively shallow depths is present which is not predicted by the standard deep crustal heating model described above. Other systems do not require this shallow heating to explain their thermal evolution \citep{page2013forecasting,degenaar2015neutron}. For those that need shallow heating the magnitude of the heating is not the same for all. Several sources studied need $\sim$1 -- 2 MeV per accreted nucleon \citep{brown2009mapping,degenaar2011evidence,degenaar2014probing,waterhouse2016constraining}, however, MAXI J0556$-$332 requires an exceptionally high magnitude of shallow heating of $\sim$6 -- 10 MeV per accreted nucleon \citep{deibel2015strong}. The cause of the shallow heating is unknown; we refer to the in-depth discussions in \citet{degenaar2013direct} and \citet{deibel2015strong} for more information about the potential shallow heating processes and the uncertainties therein. \subsection{1RXS J180408.9$-$342058} 1RXS J180408.9$-$342058 (hereafter 1RXS J1804) was first detected by {\it ROSAT} in 1990 \citep{voges1999rosat}. It was detected again by {\it Integral} and {\it Swift} in 2012 April during a faint accretion outburst (the source was only detected at luminosities of $L_X \sim$10$^{34}$ erg s$^{-1}$; \citeauthor{chenevez2012integral} \citeyear{chenevez2012integral}). It was classified as a neutron star LMXB as it showed a thermonuclear type-I burst during the {\it Integral} observation, reported by \citet{chenevez2012integral}. They calculated an upper limit on its distance as determined from the brightness of the thermonuclear burst, of $D$ $\lesssim$ 5.8 kpc (assuming an Eddington luminosity limit for helium-rich material $L_\mathrm{Edd}$ = 3.8$\times$10$^{38}$ erg s$^{-1}$; \citeauthor{kuulkers2003photospheric} \citeyear{kuulkers2003photospheric}). It subsequently returned to quiescence as reported by \citet{kaur2012swift}. It went into outburst again on 2015 January 22 as determined using the {\it BAT} instrument on board {\it Swift} \citep{barthelmy2015swift,barthelmy2015trigger,krimm2015swift}. The new outburst was also confirmed using {\it MAXI}/GSC \citep{negoro2015maxi}. The source showed a peak luminosity of $\sim$0.12 $L_\mathrm{Edd}$. A state transition from hard to soft was observed $\sim$70 days into the outburst \citep{degenaar2015neutron,degenaar2016disk}. Based on spectral fits that include relativistic disk reflection models, high-resolution X-ray studies of the outburst properties indicated that the accretion disk likely extended close to the neutron star surface both during the hard and soft spectral states \citep{ludlam2016nustar,degenaar2016disk}. 1RXS J1804 was also observed in the radio \citep{deller2015radio,gusinskaia2016} suggesting the presence of a jet. \citet{baglio20161rxs} reported on the NIR/optical/UV observations of the source during outburst which also suggests the presence of an jet. The source transitioned back to quiescence in 2015 June after a $\sim$4.5 month outburst. In this work we present the quiescent X-ray observations from 1RXS J1804 after the end of its 2015 outburst. We report on possible crust heating and cooling of the neutron star in this source and model the cooling curve to obtain insight into the neutron star crust. \begin{figure} \centering \begin{tikzpicture} \node[anchor=south west,inner sep=0] at (0,0) {\includegraphics[scale=0.24]{1RXS_img_xmm}}; \draw[black,thick,dashed](4.12,4.12) circle (0.27cm); \draw (7.65,0.6) -- (7,0.6) ; \draw (7.65,0.7) -- (7.65,0.5); \draw (7,0.7) -- (7,0.5); \node at (7.35,0.35) {1 arcminute}; \end{tikzpicture} \caption{The image of the field near 1RXS J180408.9$-$342058 (indicated by the dashed circle of radius 25$"$) as obtained using the EPIC-PN camera on board {\it XMM-Newton}.} \label{imag_src_pn} \end{figure} \begin{figure} \centering \includegraphics[scale=0.435]{outburst_light_curve_1804_xsel_metobs46_transition} \caption{The {\it Swift}/XRT light curve of 1RXS J1804 during its 2015 outburst and subsequent quiescence. The count rates are for the 0.5 -- 10 keV energy range and are averaged over each observation ID. The red arrow indicates the time of the {\it XMM-Newton} observation and the red $\ast$ indicates the {\it XMM-Newton} count rate converted to the {\it Swift}/XRT count rate using \texttt{WebPIMMS} (https://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3pimms/w3pimms.pl). The source transitioned from the hard state to the soft state around 2015 April 3, as shown by the solid cyan line. The transition into quiescence was estimated to be 2015 June 6, indicated by the dashed blue line. The inset shows a zoom of the count rate variation soon after the transition to quiescence.}% \label{img_1rxs_lightcurve} \end{figure} | We monitored the neutron star LMXB 1RXS J1804 after its 2015 outburst with {\it Swift} and {\it XMM-Newton} to search for the cooling of an accretion-heated neutron star crust. The observations analysed covered $\sim$8 to $\sim$379 days after the estimated transition to quiescence. We also analysed the archived 2011 {\it Chandra} observation to check if this observation could be used to obtain an estimate of the quiescent base level of the source. \subsection{Crust Cooling} \label{sect_crust_cooling} Initial studies of cooling neutron star LMXB crusts focussed only on sources that had outburst times $\gtrsim$ 1 yr \citep[e.g.,][]{wijnands2002xmm,cackett2008cooling}. But more recent work shows that crust cooling can also be observed in relatively bright X-ray transients that have short outburst times of weeks to months (e.g., IGR J17480$-$2446, Swift J174805.3$-$244637, and Aql X$-$1; \citeauthor{degenaar2013continued} \citeyear{degenaar2013continued}, \citeyear{degenaar2015neutron}, \citeauthor{waterhouse2016constraining} \citeyear{waterhouse2016constraining}). Therefore, one might expect that crust cooling could also potentially be observed for the neutron star in 1RXS J1804 since it had a relatively bright and intermediately long outburst.% The inferred neutron star surface temperature of 1RXS J1804 indeed shows a gradual decay in quiescence from $\sim$100 to $\sim$71 eV over $\sim$370 days when we fitted the spectra with an \texttt{nsatmos} model. This is consistent with a cooling neutron star crust after the cessation of a $\sim$4.5 month accretion-heating episode. The $kT^{\infty}_\mathrm{eff}$ at the beginning of the possible cooling phase is quite similar to what has been observed for other cooling neutron star LMXB sources (see Figure 5 of \citeauthor{homan2014strongly} \citeyear{homan2014strongly} for details). % The inferred cooling ($e$-folding) timescale for 1RXS J1804, found by fitting the cooling curve with an exponential decay function plus a constant, is $\sim$76$^{+94}_{-47}$ days. Compared to other sources, as summarised by \citet{homan2014strongly}, 1RXS J1804 has a smaller $e$-folding time. However, \citet{homan2014strongly} report the $e$-folding time of quasi-persistent sources (with outburst durations $\gtrsim$1 yr) whereas 1RXS J1804 experienced a relatively shorter $\sim$4.5 month outburst, more akin to IGR J17480$-$2446, Swift J174805.3$-$244637, and Aql X$-$1. The $e$-folding time of IGR J17480$-$2446, of 157$\pm$62 days, is much larger than 1RXS J1804 (i.e., similar to that of some of the quasi-persistent sources) but that for Swift J174805.3$-$244637, having an $e$-folding time of 77.7$\pm$49.1 days, is much closer to 1RXS J1804 \citep{degenaar2013continued,degenaar2015neutron}. Therefore, no firm conclusions can be drawn from these $e$-folding times. The theoretical model fit using \texttt{NSC\textsc{ool}}, taking into account the variability of the mass accretion rate during outburst, reveals that the source needs $\sim$1.5 to $\sim$1.9 MeV of shallow heating per accreted nucleon to explain the observed cooling curve, the lowest value being allowed when permitting a low conductivity, i.e., a large $Q_\mathrm{imp}$ (a value of 30 was used; Table \ref{tab_fit_NSCool}), in the outer crust. As in the other sources where the shallow heating is needed, it is required to reproduce the observed high $kT^{\infty}_\mathrm{eff}$ during the early phase of the post-outburst cooling. This amount of shallow heating is consistent with typical values found for most of the other sources that require it to explain their observations (e.g., \citeauthor{brown2009mapping} \citeyear{brown2009mapping}; \citeauthor{degenaar2011evidence} \citeyear{degenaar2011evidence}; \citeauthor{page2013forecasting} \citeyear{page2013forecasting}; \citeauthor{waterhouse2016constraining} \citeyear{waterhouse2016constraining}; we note that for MAXI J0556$-$332 a much larger amount of shallow heating was necessary to model its crust cooling curve; \citeauthor{deibel2015strong} \citeyear{deibel2015strong}). Our fit model A indicates that the crust of 1RXS J1804 has a high thermal conductivity with a low impurity content ($Q_\mathrm{imp} =1$), which is similar to what has been found for most of the other sources \citep[e.g.,][]{shternin2007neutron,brown2009mapping,page2013forecasting,ootes2016} but a low conductivity in the outer crust is also a possibility as in our model B, in agreement with \citet{page2013forecasting}. Finally, our model C shows that the currently available cooling curve of 1RXS J1804 can be modelled with no, or only little, deep crustal heating occurring during outburst. This might for example be a possibility if the neutron star in this source would have a hybrid crust consisting partly of accreted material and partly original matter \citep[see][]{wijnands2013testing}. Since deep crustal heating releases most of its energy in the inner crust by pycnonuclear reactions its absence/presence is mostly felt in the late time cooling curve: unfortunately our last two {\it Swift} data points have too large errors to allow detection of such a small difference. However, if 1RXS J1804 is observed further in quiescence then the difference between a cold/warm inner crust due to the absence/presence of deep crustal heating may be observable. As can be seen from Figure \ref{img_cooling_1rxs}, the \texttt{NSC\textsc{ool}} models A and C suggest that the temperature at the end of our cooling curve might have levelled off (i.e., reach a base-level), indicating that the crust and core might soon be in equilibrium again. However, we note that such behaviour is typical for these kind of simulations and it has already been shown several times that sources continued to cool to temperatures below previously determined base-levels \citep[e.g.,][]{shternin2007neutron,brown2009mapping,fridriksson2010rapid,fridriksson2011variable,cackett2013change}. The current simulations were constructed with input parameters based on neutron star properties that have been inferred from other cooling studies and they can accurately represent the observations. Therefore, despite the above mentioned uncertainty in determining the base-level, it could still indicate that the source is close to having a crust that is in equilibrium with the core again. If so, observations (i.e., performed using {\it Chandra} or {\it XMM-Newton} to reach the required sensitivity) obtained within the next $\sim$1 -- 2 yr should not show much further temperature evolution. Unfortunately the 2011 observation using {\it Chandra} did not allow us to obtain an estimate of the the base quiescent level of 1RXS J1804. The flux from the 2011 {\it Chandra} observation is similar to the {\it Swift} observations considered in interval 1 (in Table \ref{obsID_grouping}). Similar to our {\it XMM-Newton} spectrum, the {\it Chandra} spectrum required a power-law component in addition to the thermal component to obtain a good fit indicating possible low-level accretion during the {\it Chandra} observation as well (see Section \ref{sect_low_level_accr} for the possibility of low-level accretion in 1RXS J1804). Therefore, the {\it Chandra} observation cannot be used to determine (even an upper limit on) the core temperature of the neutron star in 1RXS J1804. More {\it Swift}, {\it XMM-Newton}, and {\it Chandra} observations will be useful to further constrain the thermal evolution and our cooling model. {\it Swift} is useful to monitor the source frequently which would allow us to determine whether the source has levelled-off, if multiple pointings indicate the same flux level. This would indicate that the crust is in equilibrium with the core again. Using {\it Swift}/XRT observations, we would also get a broad indication of the temperature evolution although the errors on the temperature will be large. {\it XMM-Newton} and {\it Chandra} give better constraints on the inferred neutron star crust temperature. However, they can observe the source much more infrequently than {\it Swift}, thereby missing the long term source evolution. \subsection{Low-level accretion?} \label{sect_low_level_accr} The thermal evolution of 1RXS J1804 can be interpreted as cooling (see Section \ref{sect_crust_cooling}), and the fact that the {\it Swift} data could be well fitted with a single \texttt{nsatmos} model is consistent with that. However, the {\it XMM-Newton} data statistically required an additional power-law component to obtain a good model fit. This power-law component was statistically not required by the {\it Swift} data, however, its presence could not be ruled out either (see Section \ref{sect_res_swift}). If a similar power-law component was also present during the {\it Swift} observations it would have a systematic effect on the inferred neutron star surface temperature $kT^{\infty}_{\mathrm{eff}}$. It is difficult to determine the outcome of these systematic effects without extensive assumptions (e.g., about the photon indices as well as the actual strength of the possible power-law components), and a full study of this is beyond this scope of the paper. However, at the end of Section \ref{sect_analysis_powerlaw_res} we have shown that the outcome of the single component fit to the {\it Swift} data and multiple component fit to the {\it XMM-Newton} data can be compared meaningfully. It is possible that the physical process producing the power-law component was only active at the time of the {\it XMM-Newton} observation. However, we consider this quite unlikely. It is more probable that the power-law component is also present during the {\it Swift} observations but could not be detected. We note that a similar power-law component has been detected during some of the observations of other cooling studies \citep[e.g.,][]{fridriksson2010rapid,fridriksson2011variable,degenaar2011further,degenaar2015neutron,waterhouse2016constraining} so also those studies might be affected by the uncertainties in the nature of the power-law component. It is unclear what the origin of the power-law component is, but it has been suggested that the power-law component in some quiescent neutron star LMXBs is related to low-level accretion on to the neutron star surface \citep[e.g.,][]{campana1998neutron,rutledge2002variable,cackett2010quiescent,chakrabarty2014hard,d2015radiative,wijnands2015low}. Low-level accretion also contributes a soft component to the spectra \citep{zampieri1995x,campana1998neutron}. The archival 2011 {\it Chandra} observation indicated a higher luminosity than some of the quiescent {\it Swift} data. It showed a similar type of spectra as that from the {\it XMM-Newton} data, requiring a power-law in addition to the thermal component. However, due to the limiting quality of the data the contribution from the power-law component was unconstraining. The source also showed a sub-luminous outburst in 2012 during which its peak luminosity likely did not exceed a few times 10$^{34}$ erg s$^{-1}$ \citep{chenevez2012integral,kaur2012swift}. This low peak luminosity makes it unclear if this was a real outburst or that it was due to a period of an increased low-level accretion rate. This very-faint outburst combined with the higher flux detected during the {\it Chandra} observation compared to our lowest observed {\it Swift} fluxes, indicates that before the 2015 outburst the source exhibited significant variability in quiescence, possible due to variable low-level accretion. If the power-law component we see in 1RXS J1804 is due to low-level accretion then this would indicate that at least during the {\it XMM-Newton} observation low-level accretion might have been present. The presence of low-level accretion could significantly alter our interpretation of a cooling crust. In the following we explore different scenarios for the observed slow decay in quiescence assuming low-level accretion occurs.% {\it Dominant Low-level Accretion} : Assuming what we observe is low-level accretion and if low-level accretion dominates in quiescence then it is possible that this accretion is strong enough to significantly heat up the neutron star surface and drive the thermal evolution. However, low-level accretion is expected to be variable in a more stochastic way compared to the smooth decay curve we observe. Such (sometimes strong) random fluctuations have been observed for example for the neutron star LMXB Cen X-4 \citep[e.g.,][]{campana2004variable,cackett2010quiescent} and the black hole LMXB V404 Cyg \citep[e.g.,][]{hynes2004correlated,bradley2007spectrum,hynes2009quiescent} in their quiescent state \citep[although sometimes more structured variability, i.e., in the form of brief faint flares, have also been observed in some systems; e.g.,][]{cackett2010quiescent,cackett2011quiescent,fridriksson2011variable,wijnands2013low,bernardini2013daily,zelati2014year}. But this does not entirely rule out the presence of low-level accretion, as an explanation for what we observe for 1RXS J1804, since its physics is not very well understood and could possibly lead to a smooth decay as well (as indicated by the smooth decay that has been observed for the black hole system SWIFT J1756.9$-$2508 by \citeauthor{padilla2013multiwavelength} \citeyear{padilla2013multiwavelength}). If low-level accretion is dominant then our interpretation of the neutron star cooling in quiescence after an accretion outburst is not valid. {\it Dominant Thermal Component} : It may be that the smooth decay observed from the neutron star is dominated by the cooling and variable low-level accretion occurs but its contribution is always overshadowed by the neutron star cooling and therefore does not contribute significantly to the decay trend. Thus, the cooling neutron star drives the thermal evolution and the results presented in Section \ref{sect_crust_cooling} apply directly. {\it Both the thermal and power-law components contribute significantly} : There is also an intermediate scenario in which both the thermal and non-thermal components contribute significantly to the X-ray flux and spectrum (e.g., as has been observed in some systems; \citeauthor{cackett2010quiescent} \citeyear{cackett2010quiescent}; \citeauthor{bahramian2013discovery} \citeyear{bahramian2013discovery}; \citeauthor{campana2014return} \citeyear{campana2014return}; see \citeauthor{wijnands2015low} \citeyear{wijnands2015low} for an in-depth discussion). For our {\it XMM-Newton} quiescent data we observe a power-law contribution of $\sim$30 per cent (for a total luminosity of $L_X$ $\sim$0.9$\times 10^{33}$ ($D$/5.8 kpc)$^{2}$ erg s$^{-1}$) which is compatible with a dominant thermal component in quiescence with continued low-level accretion that also contributes to the thermal evolution \citep{wijnands2015low}. If true, it will remain difficult to disentangle both effects and to determine the exact heating and cooling of the crust in this system due to the accretion of matter during its 2015 outburst. The above discussion, assuming low-level accretion is present, has so far assumed that the physical process producing the power-law component takes place very close to the neutron star and interacts with its surface \citep[e.g., see the discussions in][]{chakrabarty2014hard,d2015radiative,wijnands2015low}. Alternatively, it is also possible that the power-law component is produced far away from the neutron star and so contributes to the total observed luminosity but does not influence the temperature evolution of the neutron star as it does not interact with the neutron star surface. Processes such as shock interactions in a propeller outflow or pulsar wind happen far away from the neutron star and could possibly produce a power-law component in the observed spectra \citep[e.g.,][]{campana1998neutron,zhang1998spectral}. In this case the gradual thermal decay can be correctly interpreted as cooling in spite of the presence of the power-law component. However the observed luminosity is not only that of the cooling, the power-law component also contributes to the observed luminosity and therefore the exact neutron star surface temperature (and with that the exact heating and cooling of the crust) remains difficult to correctly extract from the data. | 16 | 9 | 1609.06703 |
1609 | 1609.03583_arXiv.txt | Utilizing high-resolution cosmological hydrodynamic simulations we investigate various ultra-violet absorption lines in the circumgalactic medium of star forming galaxies at low redshift, in hopes of checking and alleviating the claimed observational conundrum of the ratio of NV to OVI absorbers, among others. We find a satisfactory agreement between simulations and extant observational data with respect to the ratios of the following four line pairs examined, NV/OVI, SiIV/OVI, NIII/OVI and NII/OVI. For the pairs involving nitrogen lines, we examine two cases of nitrogen abundance, one with constant N/O ratio and the other with varying N/O ratio, with the latter motivated by theoretical considerations of two different synthetic sources of nitrogen that is empirically verified independently. Along a separate vector, for all line pairs, we examine two cases of radiation field, one with the Haardt-Madau background radiation field and the other with an additional local radiation field sourced by hot gas in the host galaxy. In all cases, two-sample Kolmogorov-Smirnov tests indicate excellent agreements. We find that the apparent agreements between simulations and observations will be strongly tested, if the bulk of current upper limits of various line ratios are turned into actual detections. We show that an increase in observational sensitivity by $0.2$ dex will already start to significantly constrain the models. | The nature of halo gas (a.k.a. circumgalactic medium; CGM hereafter), on galactocentric distances of $10-500$ kpc, is a problem of significant ongoing interest in galaxy formation. Halo gas links galaxies from the intergalactic medium and is the conduit for exchange of matter energy density, momentum, angular momentum and metals between star formation and active galactic nucleus induced outflow and gravitational inflow of gas. Thus, understanding halo gas is imperative before a satisfactory theory of galaxy formation and evolution may be constructed. There has been recent rapid advances on the observational front to address this important issue, made possible primarily by HST observations \citep[e.g.,][]{2009Chen, 2011bProchaska, 2011bTumlinson, 2011Tripp, 2012Thom, 2013Werk, 2014Werk, 2014Peeples,2016Werk}. In \citet[][]{2013Cen} we investigate the overall gas composition with respect to the density, temperature and metallicity and find that, on average, for $>0.1L_*$ ({\color{red} red}, {\color{blue} blue}) galaxies cold ($T<10^5$K) gas is the primary component in the inner regions, with its mass comprising 50\% of all gas within $r=({\color{red}30},{\color{blue}150})$ kpc. At $r>({\color{red}30},{\color{blue}200})$ kpc for ({\color{red}red}, {\color{blue}blue}) galaxies, the hot ($T>10^7$K) component becomes the majority component. The warm ($T=10^{5-7}$K) component is, on average, a perpetual minority in both red and blue galaxies, with its contribution peaking at $\sim 30\%$ at $r=100-300$ kpc in blue galaxies and never exceeding 5\% in red galaxies. These findings are in agreement with recent observations in many aspects, in particular with respect to the amount of warm gas in star forming galaxies and the amount of cold gas in early type galaxies at low redshift, both of which are physically intriguing and at first instant less than intuitive. In light of a new observational development with respect to the NV to OVI absorption line ratio and in particular the apparent need of seemingly complicated, perhaps contrived, models to explain the data, we here perform a detailed analysis of our high resolution cosmological hydrodynamic simulations to assess whether {\it ab initio} cosmological simulations are capable of accounting for this particular observation, in the larger context of the success of the model able to match the overall composition of halo gas, % among others. It is particularly relevant to note that the good agreement between our simulations and observations with respect OVI $\lambda \lambda$1032, 1038 absorption lines, presented earlier in \citet[][]{2012bCen}, suggests that the statistical description of the properties of the warm component in the simulations - mass, spatial distribution, density, temperature, metallicity, and their environmental dependences - has now been firmly validated and provides a critical anchor point for our model. Consequently, this additional, independent analysis with respect to NV/OVI ratio and other ratios becomes very powerful to further strengthen or falsify our model or our simulations. Our findings here are both encouraging and intriguing. If one uses a fixed, solar N/O ratio regardless of the O/H ratio, our model is acceptable, with all 4 KS (Kolmogorov-Smirnov) test p-values greater than 0.28 for either Haardt-Madau \citep[][HM hereafter]{2012Haardt} or HM+local radiation field, where the local radiation field is due to hot gas in the host galaxy. If one allows for a dependence of the N/O ratio on the O/H ratio, both measured by independent observations and motivated by theoretical considerations of two different sources of N, then our model is able to account for the observations highly successfully, with all KS test p-values exceeding 0.9. We additionally examine the following absorption line column density ratios where comparisons to observations may be made in a reasonable statistical fashion, SiIV/OVI, NII/OVI and NIII/OVI, and find that the ratios from our simulations are fully consistent with observations. We also investigate the model where UV radiation from local shock heated gas in concerned galaxies are added to the HM background, which is found to also agree with observations with comparable p-values for all line ratios examined. However, these good agreements come about because observational data points are dominated by upper and lower limits instead of actual detections. We discuss how some moderate improvment in observational sensitivity may provide much stronger tests of models. | In light of a recent conclusion that the observed line ratios of UV absorbers in the CGM may pose a significant challenge for theoretical models \citep[][]{2016Werk}, we study five UV absorption lines, OVI $\lambda \lambda$1032, 1038, SiIV $\lambda \lambda$1394, 1402, NV $\lambda \lambda$1239, 1243, NIII $\lambda $990, NII $\lambda $1084, in the CGM of simulated galaxies, utilizing {\it ab initio} ultra-high resolution ({\color{red}\bf LAOZI}) hydrodynamical simulations. Our simulated galaxies are chosen to have stellar masses and star formation rates similar to their observed counterpart. We examine uncertainties related to the radiation background by computing separately for two cases of radiation field, one with the HM radiation background and the other with both HM and local radiation due to hot gas in the host galaxy. Separately and orthogonally, we examine two separate cases of nitrogen to oxygen ratio, in one case with constant N/O and in the other with varying N/O that is theoretically consistent with two different synthetic sources of nitrogen and observationally confirmed by independent observations. \citet[][]{2016Werk} find constant density photoionization models to be excluded by the data. They find collisional (both in and out of equilibrium) ionization to be only broadly consistent with the data. They suggest either collisionally-ionized gas cooling behind a fast shock or a highly structured gas photo-ionized by a local high energy source as plausible models to account of the observed OVI column density range and line ratios. In contrast, we do not find significant difficulty in accounting for the same observational data in our cosmological simulations that capture the complex multi-phase structure of the CGM, as reflected by the acceptable KS test p-values for column density ratios of four pairs of lines NV/OVI, SiIV/OVI, NIII/OVI and NII/OVI examined. Inter-comparisons between results from different models employing different radiation fields in our simulations and comparisons between properties of the absorbers and expectations of collisional ionization indicate that collisional ionization play a major role in producing all the lines studied in realistic CGM produced in cosmological simulations. Photoionization process plays a significant role as well, to a varying degree, depending on the ion in question, although it seems clear that for NV and OVI lines photoionization effect is relatively minor. The success of our largely collisional ionization model in all cases is, however, in a significant part, due to very accommodative observational line ratio data points that are dominated, in number, by upper limits rather than actual detections. We find the apparent satisfactory agreement between simulations and extant observational data can be strongly tested and different cases (different radiation fields and different N/O ratio assumptions) differentiated, if most of the current upper limits in the observational data become detections. To demonstrate the power, we show, as an example, that if the upper limits of NV/OVI become detections with values that are lower by a mere $\sim 0.20$ dex than their respective current upper limits, the KS p-value for the NV/OVI line ratio becomes $\sim 0.01$ for the constant N/O case and $\sim 0$ for the varying N/O case. If, on the other hand, the actual detection values turn out to be lower than current upper limits by $0.6-0.7$ dex, then the varying N/O case obtains a satisfactory p-value of $(0.5,0.8)$, whereas the constant N/O case is endowed with a p-value equal to zero. Thus, it is highly desirable to increase the observational sensitivity and/or enlarge observational data sample size, in order to have a definitive test. \vskip 1cm We are grateful to Jessica Werk for sharing observational data with us prior to publication and stimulating discussion. We thank J. Xavier Prochaska for useful discussion. We have used the very useful and versatile analysis software yt version 2.6 \citep{2011Turk} for some of our analysis. Computing resources were in part provided by the NASA High- End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. The research is supported in part by NASA grant NNX11AI23G. | 16 | 9 | 1609.03583 |
1609 | 1609.06190_arXiv.txt | Ideal MHD provides an accurate description of low-frequency Alfvén waves in fully ionized plasmas. However, higher frequency waves in many plasmas of the solar atmosphere cannot be correctly described by ideal MHD and a more accurate model is required. Here, we study the properties of small-amplitude incompressible perturbations in both the low and the high frequency ranges in plasmas composed of several ionized species. We use a multi-fluid approach and take into account the effects of collisions between ions and the inclusion of Hall's term in the induction equation. Through the analysis of the corresponding dispersion relations and numerical simulations we check that at high frequencies ions of different species are not as strongly coupled as in the low frequency limit. Hence, they cannot be treated as a single fluid. In addition, elastic collisions between the distinct ionized species are not negligible for high frequency waves since an appreciable damping is obtained. Furthermore, Coulomb collisions between ions remove the cyclotron resonances and the strict cut-off regions that are present when collisions are not taken into account. The implications of these results for the modelling of high-frequency waves in solar plasmas are discussed. | \label{sec:intro} The pioneering work of \citet{1942Natur.150..405A} set the starting point of magnetohydrodynamics (MHD), which has become a remarkably successful theory for understanding the general properties of the most abundant state of matter in the universe, i.e., plasma. For instance, one of its fundamental predictions, the existence of magnetohydrodynamic waves driven by magnetic tension, was experimentally confirmed in a laboratory by \citet{1949Natur.164..145L} and corroborated later by \citet{1954PhRv...94..815L} and \citet{1959Natur.183.1652J}. Subsequent investigations have demonstrated the presence of this class of oscillations, now known as Alfvén waves, in Earth's aurora \citep{1988PhyS...38..841C}, in planetary ionospheres \citep{1960JGR....65.2233B,1981JGR....86..717G}, the solar wind \citep{1966PhysRevLett.17.207,1971JGR....76.3534B} or the interstellar medium \citep{1975ApJ...196L..77A,1996ApJ...465..775B}. \citet{2007Sci...317.1192T} and \citet{2007Sci...318.1574D} reported the detection of Alfvén waves in the solar atmosphere, although there is a debate about whether those observations are best interpreted in terms of Alfvén or kink waves \citep{2008ApJ...676L..73V,2009Sci...323.1582J,2012ApJ...753..111G}. In addition, they have been invoked as a mechanism for heating the solar corona \citep[e.g.,][]{1974SoPh...39..129W,2011Natur.475..477M} and may have a strong influence in many astrophysical phenomena like, e.g., the propagation of cosmic rays \citep{1969ApJ...156..445K} or the winds of hot stars \citep{1983ApJ...268L.127U}. Nevertheless, Alfvén waves, that correspond to the low range of frequencies, are only a subset of all the types of waves that can be found in plasmas \citep{1992wapl.book.....S}. MHD has been used to investigate waves in a great variety of environments, like extragalactic jets \citep{1993A&A...279..351G}, protostellar winds \citep{1989MNRAS.236....1J}, molecular clouds \citep{1990ApJ...350..195P,2011MNRAS.415.1751M}, laboratory plasmas \citep{1952PhysRev.87.671,1999JGRA:JGRA14819} and fusion devices \citep{1971PlPh...13..258W,1974PhFl...17.1399C,2008PhPl...15e5501H}. However, the properties of high frequency waves, that in the solar atmosphere may be driven by small-scale magnetic activity in the chromospheric network and reconnection of field lines \citep{1992sws..coll....1A,1997SoPh..171..363T} or by cascading from low frequencies in the solar corona \citep{1983JGR....88.3923I,1987SoPh..109..149T}, are not accurately described by this theory and more general approaches are required. Among other simplifications, ideal MHD treats the plasma as if it were fully ionized, ignores the possible presence of neutral species, assumes that there is no resistivity, neglects Hall's term in the induction equation and considers all the ionized species together as a single fluid. Extensions to ideal MHD have addressed various of the ignored effects. For instance, the effect of partial ionization on waves in plasmas has been studied by, e.g., \citet{1956MNRAS.116..314P,2001ApJ...558..859D,2007A&A...461..731F,2010A&A...512A..28S} and \citet{2011A&A...534A..93Z}, although those authors did not consider each ionized species as a separate fluid. Investigations of fully ionized plasmas through the application of a multi-fluid description can be found in, e.g., \citet{1973Ap&SS..20..391W,1982JGR....87.5023I,2001paw..book.....C} and \citet{2002JGRA..107.1147H}, but in those works some issues have still been overlooked: in the former and the third, elastic collisions between the different ionized species are not taken into account, and the other two publications focus exclusively on the low frequency Alfvén waves. Still in the range of low frequencies, \citet{2007ApJ...661.1222L} and \citet{2008ApJ...682..667L} examined cases where the Wentzel–Kramers–Brillouin (WKB) approximation does not hold. The effect of collisions is included in the work of \citet{2010Rahbarnia}, although it studies the case of plasmas composed of only two distinct ionized species. In addition, waves and instabilities in anisotropic magnetized plasmas have been analyzed through 16-moment transport equations \citep{1979JPhD...12.1051D,1999JGR...104.9963O,2008A&A...489..769D}. Multi-fluid approaches to describe multicomponent plasmas have been commonly used in aeronomy and space physics \citep{1977RvGSP..15..429S,1982PlPh...24..389B}. For instance, such models have been extensively applied to the investigation of Earth's ionosphere \citep[see, e.g.,][]{1988AdSpR...8...69G,1989P&SS...37.1157K,1994JGR....99.2215D,1996RvGeo..34..311G} and the solar wind \citep{2004AdSpR..33..681O,2011SGeo...32....1E,2016SSRv..tmp...34A}. The study of the solar and stellar winds through the application of multi-fluid equations started with \citet{1966PhRvL..16..628S} and \citet{1968ApJ...151.1155H}, where separated heat equations for protons and electrons where considered. Later, \citet{1972SoPh...23..238L} included the proton temperature anisotropy and \citet{1973Ap&SS..20..401W} and \citet{2000A&A...359..983K} took into account the presence of several ions, but assuming isothermal ion flows, assumption that was then removed in \citet{2001A&A...369..222K}. These early models were one-dimensional (1D) and essentially hydrodynamic and did not explicitly involve Faraday's law. The inclusion of the induction equation is necessary in multi-dimensional models and it has been incorporated in works like \citet{2000JGR...10512675U,2001SoPh..199..371C,2003ApJ...598.1361V,2004JGRA..109.7102O,2004JGRA..109.7103L,2006JGRA..111.8106L,2014ApJ...782...81V} and \citep{2015MNRAS.454.3697M}. Moreover, taking into account Faraday's law allows the investigation of the angular momentum loss due to magnetized multi-ion stellar winds \citep{2006A&A...456..359L,2007ApJ...661..593L} and the effect of ion temperature anisotropy on that momentum loss \citep{2009A&A...494..361L}. When considering a multi-fluid plasma, the distinct species may interact with each other in two ways: through electro-magnetic fields, which only affect the charged particles, and by means of collisions. For low-frequency waves the friction due to collisions between the ionized species is usually ignored. The reason to do so is that the magnetic field produces a strong enough coupling between the different charged fluids so that they behave almost as a single fluid. Consequently, the friction force between ionized species can be neglected. This may not be true for high-frequency waves, at which each charged fluid may react to the perturbations of the electric and the magnetic fields in different time scales and the effects of the cyclotron motions should be taken into account. At the range of high frequencies the velocity drifts are not negligible and the frictional force may be of great relevance. This frictional dissipation of the energy carried by the waves may have an important role in the heating of the plasma. The present paper is the first of a series whose general goal is the investigation of waves in multi-component plasmas, with the ultimate objective of studying the heating that can arise from the complex interactions between the different species. To that aim we have developed a numerical code that implements a multi-fluid model that takes into account the elastic collisions between species and makes use of a generalized Ohm's law. Although the code is able to simulate the effects of partial ionization and nonlinearity, in this paper we focus on the simple case of fully ionized homogeneous plasmas and perturbations in the small-amplitude regime. Thus, here the heat transfer due to collisions, which has a strong dependence on the amplitudes of the velocity perturbations, is not expected to have a prominent role. Nevertheless, the momentum transfer between different ionized species may be of great influence in the properties of waves. The effects of partial ionization and nonlinearity are not addressed in the present initial article and will be explored in forthcoming papers of the series. The inclusion of several ionized species, together with the consideration of Hall's term, produces the appearance of circularly polarized waves. We are interested in studying under which circumstances Coulomb collisions should be taken into account to properly describe the propagation of waves. In addition, we compare the multi-fluid approach with ideal MHD. The purpose is to check the applicability of MHD and to determine the conditions for which the multi-fluid description is necessary. The equations that describe the multi-fluid model are presented in Section \ref{sec:equations}. In Section \ref{sec:dispersion} we derive the general dispersion relation that characterize the properties of incompressible waves in a homogeneous medium and analyze the particular cases of two-ion and three-ion plasmas, with a focus in three distinct regions of the solar atmosphere: the upper chromospheric region, the lower corona and the solar wind at 1 astronomical unit (AU). In Section \ref{sec:simulations}, we show the results of simulations of the temporal evolution of small-amplitude perturbations and compare them with the predictions from the dispersion relations. Finally, the summary is presented in Section \ref{sec:concl}. | \label{sec:concl} This paper is the first of a series devoted to the comprehensive study of multi-fluid effects on the behavior and properties of high-frequency waves in plasmas. In this initial work, the multi-fluid approach has been applied to the investigation of incompressible waves in a fully ionized plasma. The subject of multi-ion plasmas has already been studied by numerous authors but most of them have focused exclusively on low frequency Alfvén waves \citep[e.g.,][]{1982JGR....87.5023I}, have analyzed plasmas composed of only two different ionized species \citep[e.g.,][]{2010Rahbarnia} or have not included the effect of collisions between the ions \citep[e.g.,][]{1973Ap&SS..20..391W,2001paw..book.....C}. On the contrary, we have explored a wide range of frequencies that goes from the low frequency Alfvén waves to the high frequency ion cyclotron and whistler waves, and our model takes into consideration the collisional interactions between the distinct species. Hence, it is more general than the approaches commonly employed in previous works and it can be applicable to a great number of astrophysical and laboratory plasmas. However, we have directed our attention to plasmas in the solar atmosphere, e.g., the upper chromospheric region, the lower corona and the solar wind at 1 AU. We have presented the system of non-linear equations that governs the temporal evolution of each species in a multi-ion plasma. From them, we have derived the dispersion relations that characterize the propagation of small-amplitude incompressible perturbations along the direction of the background magnetic field in an homogeneous medium. Those dispersion relations have allowed us to analyze the properties of waves excited both by an impulsive driver and by a periodic driver. In addition, we have compared the results given by those formulas with the predictions provided by the single-fluid model of ideal MHD. The first difference between the two approaches is that ideal MHD predicts the existence of the same number of oscillation modes independently of the kind of driver chosen, and it is not necessary to study the two cases separately as they are equivalent. This symmetry is not conserved in the multi-fluid model. The number of modes in the case of the periodic driver is independent of how many species compose the plasma. But when the effects of an impulsive driver are investigated, the number of solutions given by the dispersion relations increases with each additional ionized species considered. Moreover, from ideal MHD we obtain waves that are linearly polarized, while the waves from the multi-fluid description are circularly polarized and they show a clearly different behavior depending on whether their polarization is left-handed or right-handed. Apart from the analysis of the various dispersion relations, we have also performed numerical simulations to compute the temporal evolution of the perturbations in the plasma. The MolMHD code, initially developed to solve the ideal MHD equations \citep{Bona20092266}, has been extended to account for multi-fluid effects. In the present work, we have tested the results from the numerical code against those from the analytic dispersion relations. We checked that the oscillation frequencies and the amplitude ratios of the waves appearing in the simulations are consistent with the solutions given by the dispersion relations. If exposed to perturbations with frequencies much lower than the cyclotron frequencies, the various ionized species react as if they were a single fluid since they are strongly coupled by means of the magnetic field: they oscillate at the Alfvén frequency, in phase and with the same velocity amplitude, which is given by Equation (\ref{eq:wave_amp}). At higher frequencies, the interaction through the magnetic field is not enough to keep all the fluids as tightly coupled as before and the amplitude and the phase of the oscillations are different for each species and for each mode. At this regime the effect of elastic collisions should not be neglected since the frictional force associated to the velocity drifts may lead to a intense damping of the waves. We have found that this damping is stronger for the modes with the left-hand polarization than for the right-hand modes. We have computed the friction coefficient between the ions in the three solar plasmas of interest for this work. Due to the small value of this parameter in the lower solar corona, we have found that the effect of collisions is relevant only for times longer than several periods of the Alfvén wave. The friction coefficient in the solar wind at 1 AU is even smaller, so this environment can be treated as a collisionless fluid since the damping times of the oscillations are on the order of $10^{6} \ \Rm{s}$ or larger. Nevertheless, the multi-fluid model is generally still required to illustrate the properties of waves in those plasmas, in view of the fact that only perturbations with wavelengths larger than the critical value given by Equation (\ref{eq:lambda_min}) are described with a reasonable accuracy by ideal MHD. On the contrary, the collision frequencies computed using the parameters corresponding to an upper chromospheric region are not negligible in comparison with the cyclotron frequencies and, consequently, friction has a strong impact in the properties of the oscillation modes. There is another reason to take into account the effect of elastic collisions: when a periodic driver is considered, the momentum transfer removes the resonances and the strict cut-offs that appear in the collisionless case. Due to the diffusive effect of collisions, left-hand waves generated by a driver with a frequency that coincides with any of the cyclotron frequencies or is in the range of the cut-offs can propagate, instead of having a null phase speed or being evanescent. However, they are still strongly damped in space. The model developed and employed in this work provides more accurate results than the ones used in previous investigations. But, since we have also resorted to some simplifications, it still can be improved along several lines. For instance, we have not taken into account some effects produced by other kinds of collisions, like resistivity, caused by the interaction between ions and electrons and that is expected to be of importance for even higher frequencies than the ones explored here, or viscosity, that is due to self-collisions. Furthermore, we have focused exclusively on small-amplitude perturbations on fully ionized plasmas, while partial ionization effects have been shown to be of great relevance even for low frequency waves \citep[see, e.g.,][]{1956MNRAS.116..314P,2009ApJ...699.1553S,2011A&A...534A..93Z,2013ApJS..209...16S,2013ApJ...767..171S} and the non-linear regime is also of great interest, specially in respect to the matter of the heating of the plasma. In forthcoming papers we will address those issues. We remind also that we have only studied the case of a homogeneous medium but that it would be possible to apply our code to inhomogeneous media. In the presence of inhomogeneities, that can be caused, for example, by gravitational stratification, effects like wave amplification (e.g., amplitude of waves propagating upwards in the solar corona is amplified due to the decrease in density with height), shock generation, refraction and reflection of waves or parametric decay may appear. Some of these effects have been investigated through a single-fluid MHD approach \citep{2005ApJ...632L..49S,2006JGRA..111.6101S} but it may be expected that inhomogeneities have a different impact on each ionized species of the plasma in the range of frequencies where the multi-fluid model is more appropriate than the single-fluid approximation. Take the solar wind as an example of inhomogeneous non-static medium: \citet{2007JGRA..112.8102H} performed a numerical study of the reflection of Alfvén waves and found that outward propagating waves become less dominant than sunward propagating waves for distances from the Sun beyond the Alfvén critical point (where the plasma flow velocity is equal to the Alfvén speed), in agreement with the observations; in addition, \citet{2007ApJ...661.1222L} investigated the effect of the differential ion flow using a two-fluid model and found that at large distances beyond the Alfvénic point low frequency waves tend to equalize the speeds of the ions. It would be of interest the application of the multi-fluid model to the investigation of the effects of reflection and differential ion flow on high frequency waves. | 16 | 9 | 1609.06190 |
1609 | 1609.01253_arXiv.txt | We recently showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit into an expanding NEC-satisfying phase without encountering any singularities or pathologies. A drawback of these examples is that singular behavior is encountered at some time either just before or just after the NEC-violating phase. In this Letter, we show that it is possible to circumvent this problem by extending our method to actions that include the next order ${\cal L}_4$ Galileon interaction. Using this approach, we construct non-singular classical bouncing cosmological solutions that are non-pathological for all times. | Cosmological scenarios that involve a phase of contraction followed by a bounce to a phase of expansion are of great interest since they can smooth and flatten the cosmological background \cite{Khoury:2001wf} and generate a nearly scale-invariant spectrum of super-horizon curvature modes \cite{Lehners:2007ac,Buchbinder:2007ad} while avoiding the multiverse and initial conditions problems of inflationary cosmology. In these theories, the smoothing contraction phase is fully described by Einstein gravity and the quantum generation of curvature modes is described by standard semi-classical perturbation theory. The challenge has been to find a non-pathological theoretical framework for describing the bounce, {\it i.e.}, the transition from contraction to expansion. One possibility is to realize the transition through a singular (`quantum') bounce in which the scale factor passes through or tunnels through zero, as was proposed in \cite{Gielen:2015uaa}; this idea is intriguing, though the approach relies on some as-yet unproven assumptions about the analyticity of quantum gravity \cite{Bars:2013vba}. Another approach is a `classical bounce,' in which the universe bounces after contracting to a small but finite size with energy density well below the Planck scale such that quantum gravity effects can be neglected. The transition occurs through violation of the null energy condition (NEC) over a finite period of time that includes the bounce. On a smooth and flat Friedmann-Robertson-Walker (FRW) cosmological background with $ds^2=-dt^2 + a^2(t)dx_idx^i$ (where $a(t)$ is the scale factor), NEC violation means that the Hubble parameter $H=\dot{a}/a$ increases with time, $\dot{H}>0$, where dot denotes differentiation with respect to time $t$. The classical bounce has the advantage of not requiring any knowledge of quantum gravity. However, it is a well-known problem that NEC violation is prone to ghost or gradient instabilities or leads to singular behavior. In \cite{Ijjas:2016tpn}, we showed that it is possible to construct classical solutions that enter a contracting NEC-violating phase, bounce, and exit in an expanding NEC-satisfying phase without introducing pathologies by realizing the NEC-violating stage through a scalar field described by the generalized cubic Galileon action. We presented an `inverse method' for constructing the solutions and used it to derive explicit examples. The examples show that the universe can undergo a cosmological bounce at finite values of the scale factor and low energies well below the Planck scale without encountering singular behavior or requiring superluminal sound speed of co-moving curvature modes during the NEC-violating phase. A feature of the examples based on the cubic Galileon action, though, is that singular behavior is always encountered at some time either shortly before or shortly after the NEC-violating phase. Hence, the remaining open issue is whether these pathologies are inevitable or if a stable NEC-violating bounce stage can be embedded into a cosmology that is stable and non-singular throughout cosmic evolution. In this Letter, we show explicitly that it is possible to construct a fully stable bouncing cosmology by naturally extending our inverse method to actions that include the next order ${\cal L}_4$ Galileon interaction. This Letter is organized as follows: First, we give a brief review of Galileon cosmology and derive the stability conditions for linear-order scalar and tensor perturbations. Next, we explain why the cubic Galileon action inevitably leads to divergences and/or other singular behavior either just before or just after the stable NEC-violating phase in Sec.~\ref{singular}. In Sec.~\ref{l4}, we show that, in principle, by extending the action to include the ${\cal L}_4$ Galileon interaction, the pathological behavior can be avoided for all times. In Sec.~\ref{examples}, we use our inverse method to construct explicit solutions. (Readers only interested in the existence of non-pathological bouncing solutions may wish to jump to the figures.) | In this Letter, we presented geodesically complete, stable non-singular bouncing cosmological solutions that are non-pathological over all time, confirming and extending our previous result in Ref.~\cite{Ijjas:2016tpn} where we demonstrated that it is possible to construct solutions that are non-pathological during the NEC-violating bounce stage. The key was to identify the source of the singular behavior in cubic Galileon cosmologies, {\it i.e.,} actions where the coefficients of ${\cal L}_4$ and ${\cal L}_5$ are set to zero. What we have shown is that the bad behavior in this case is not directly related to the NEC-violating bounce stage, but to the fact that the Hubble parameter $H(t)$ switches sign at some point during cosmic evolution. Before or after $H(t)$ changes sign, the dynamical quantity derived from the shift constraint, $\gamma(t)$, has to change sign as well, which is what causes the pathological behavior. In fact, the pathological behavior arises in cubic Galileon cosmologies that smoothly transit from expansion to contraction without any bounce or NEC violation. This observation explains why earlier authors were able to find non-pathological NEC-violating solutions in cubic Galileon genesis models where $H(t)$ does not change sign ({\it e.g.}, see \cite{Pirtskhalava:2014esa}), but failed to find fully stable solutions with a bounce. Notably, the pathology of the cubic Galileon action is resolved in a natural way, simply by extending the action to include the next-order ${\cal L}_4$ interaction. Using this extension, we showed that we can construct geodesically complete, stable, non-singular bounce solutions. Another natural extension is to include additional degrees of freedom corresponding to NEC-satisfying matter and radiation \cite{Ijjas1}. The resulting construction of a fully stable bouncing solution should give one pause. Together with Ref.~\cite{Ijjas:2016tpn}, it removes the last major roadblock that has been holding back interest in cosmologies that explain the origin of the large-scale structure of the universe in terms of a contracting phase connecting to the current expanding phase through a cosmological bounce. {\it Acknowledgements.} We thank Frans Pretorius and Vasileios Paschalidis for helpful discussions. This research was partially supported by the U.S. Department of Energy under grant number DEFG02-91ER40671. | 16 | 9 | 1609.01253 |
1609 | 1609.08691_arXiv.txt | This document is prepared using LaTeX2e\cite{Lamport94} and shows the desired format and appearance of a manuscript prepared for the Proceedings of the SPIE.\footnote{The basic format was developed in 1995 by Rick Hermann (SPIE) and Ken Hanson (Los Alamos National Lab.).} It contains general formatting instructions and hints about how to use LaTeX. The LaTeX source file that produced this document, {\ttfamily article.tex} (Version 3.4), provides a template, used in conjunction with {\ttfamily spie.cls} (Version 3.4). These files are available on the Internet at \url{https://www.overleaf.com}. The font used throughout is the LaTeX default font, Computer Modern Roman, which is equivalent to the Times Roman font available on many systems. | \label{sec:intro} % Begin the Introduction below the Keywords. The manuscript should not have headers, footers, or page numbers. It should be in a one-column format. References are often noted in the text and cited at the end of the paper. \begin{table}[ht] \caption{Fonts sizes to be used for various parts of the manuscript. Table captions should be centered above the table. When the caption is too long to fit on one line, it should be justified to the right and left margins of the body of the text.} \label{tab:fonts} \begin{center} \begin{tabular}{|l|l|} % \hline \rule[-1ex]{0pt}{3.5ex} Article title & 16 pt., bold, centered \\ \hline \rule[-1ex]{0pt}{3.5ex} Author names and affiliations & 12 pt., normal, centered \\ \hline \rule[-1ex]{0pt}{3.5ex} Keywords & 10 pt., normal, left justified \\ \hline \rule[-1ex]{0pt}{3.5ex} Abstract Title & 11 pt., bold, centered \\ \hline \rule[-1ex]{0pt}{3.5ex} Abstract body text & 10 pt., normal, justified \\ \hline \rule[-1ex]{0pt}{3.5ex} Section heading & 11 pt., bold, centered (all caps) \\ \hline \rule[-1ex]{0pt}{3.5ex} Subsection heading & 11 pt., bold, left justified \\ \hline \rule[-1ex]{0pt}{3.5ex} Sub-subsection heading & 10 pt., bold, left justified \\ \hline \rule[-1ex]{0pt}{3.5ex} Normal text & 10 pt., normal, justified \\ \hline \rule[-1ex]{0pt}{3.5ex} Figure and table captions & \, 9 pt., normal \\ \hline \rule[-1ex]{0pt}{3.5ex} Footnote & \, 9 pt., normal \\ \hline \rule[-1ex]{0pt}{3.5ex} Reference Heading & 11 pt., bold, centered \\ \hline \rule[-1ex]{0pt}{3.5ex} Reference Listing & 10 pt., normal, justified \\ \hline \end{tabular} \end{center} \end{table} \begin{table}[ht] \caption{Margins and print area specifications.} \label{tab:Paper Margins} \begin{center} \begin{tabular}{|l|l|l|} \hline \rule[-1ex]{0pt}{3.5ex} Margin & A4 & Letter \\ \hline \rule[-1ex]{0pt}{3.5ex} Top margin & 2.54 cm & 1.0 in. \\ \hline \rule[-1ex]{0pt}{3.5ex} Bottom margin & 4.94 cm & 1.25 in. \\ \hline \rule[-1ex]{0pt}{3.5ex} Left, right margin & 1.925 cm & .875 in. \\ \hline \rule[-1ex]{0pt}{3.5ex} Printable area & 17.15 x 22.23 cm & 6.75 x 8.75 in. \\ \hline \end{tabular} \end{center} \end{table} LaTeX margins are related to the document's paper size. The paper size is by default set to USA letter paper. To format a document for A4 paper, the first line of this LaTeX source file should be changed to \verb|\documentclass[a4paper]{spie}|. Authors are encouraged to follow the principles of sound technical writing, as described in Refs.~\citenum{Alred03} and \citenum{Perelman97}, for example. Many aspects of technical writing are addressed in the {\em AIP Style Manual}, published by the American Institute of Physics. It is available on line at \url{https://publishing.aip.org/authors}. A spelling checker is helpful for finding misspelled words. An author may use this LaTeX source file as a template by substituting his/her own text in each field. This document is not meant to be a complete guide on how to use LaTeX. For that, please see the list of references at \url{http://latex-project.org/guides/} and for an online introduction to LaTeX please see \citenum{Lees-Miller-LaTeX-course-1}. | 16 | 9 | 1609.08691 |
|
1609 | 1609.01779_arXiv.txt | We observed the supernova remnant (SNR) Puppis A in the 21 cm line with the Australia Telescope Compact Array with the aim of determining the systemic velocity and, hence, the corresponding kinematic distance. For the compact, background sources in the field, we obtain absorption spectra by applying two methods: (a) subtracting profiles on- and off-source towards continuum emission, and (b) filtering short spacial frequencies in the Fourier plane to remove large scale emission. One of the brightest features to the East of the shell of Puppis A was found to be a background source, probably extragalactic. Removing the contribution from this and the previously known unrelated sources, the systemic velocity of Puppis A turns out to be limited between 8 and 12 km s$^{-1}$, which places this source at a distance of 1.3 $\pm$ 0.3 kpc. From the combined images that include both single dish and interferometric data, we analyze the distribution of the interstellar hydrogen. We suggest that an ellipsoidal ring at $v \sim +8$ km s$^{-1}$ could be the relic of a bubble blown by the progenitor of Puppis A, provided the distance is $\lesssim 1.2$ kpc. The main consequences of the new systemic velocity and distance as compared with previous publications ($v = + 16$ km s$^{-1}$ and $d = 2.2$ kpc) are the absence of a dense interacting cloud to the East to explain the morphology, and the decrease of the shell size and the neutron star velocity, which are now in better agreement with statistical values. | \label{Int} H{\sc i} absorption studies towards the continuum background offered by supernova remnants (SNR) reveal the distribution of the insterstellar medium (ISM) gas along the line of sight and, combined with Galactic rotation models, can set limits on the remnants' distance. Reliable distance estimates are important to determine intrinsic properties of a SNR such as size, age, explosion energy or expansion velocity. In addition, H{\sc i} emission at velocities beyond a SNR's systemic velocity or away from the direction of the remnant also give information about the ISM distribution and Galactic structure. Therefore, H{\sc i} observations help to construct a three dimensional picture of the ambient medium where a SNR is evolving, as well as to identify foreground or background structures in the Galaxy. The southern Galactic SNR Puppis A is an extended, distorted shell, $\sim 50^\prime$ in diameter, estimated to be between 3,700 \citep{Wink+1988} and 5,200 \citep{Becker+2012} yrs old. It is one of the brightest SNRs in X-rays \citep[e.g.][]{hwang+08} and has recently been detected in $\gamma$-rays \citep{Fermi+12}. A pulsating X-ray compact central object (CCO) inside Puppis A confirms that the progenitor was a high-mass star \citep{PBW96,ZTP99}. \citet{wp2007} showed that the CCO is moving away from the explosion centre inferred from optical filaments \citep{Wink+1988}. \citet{EMR+03} found an elongated minimum in the H{\sc i} emission at +16 km s$^{-1}$ coincident with the path followed by the CCO. Several suggestions of interaction between Puppis A and nearby clouds have been reported, although the picture is not completely clear yet. \citet{gd+ma88} observed Puppis A in the 21 cm line and in the CO (J=1--0) 2.6 mm line and found a molecular cloud to the East of the SNR coincident with a flattening in the radio continuum shell. The authors interpret this coincidence as evidence of a molecular cloud-SNR interaction, and set the systemic velocity of the remnant to be around +16 km s$^{-1}$. A subsequent H{\sc i} study using VLA observations \citep{EMR+95} supports the same result based on morphological coincidences, and infers a distance of 2.2 kpc. However, indubitable tracers of interactions between SNR and external clouds, like molecular broadenings or OH masers at 1720 MHz, have never been observed. A high resolution CO study \citep{paron+08} failed to detect any gas concentration associated with an X-ray bright knot to the East of the shell, previously interpreted as coming from a shocked interstellar cloud \citep{BEK+05}. \citet{frail+96} reported single dish observations at 1720 MHz towards Puppis A performed with the Parkes and Greenbank telescopes, with negative detections. \citet{beate+00} observed several pointings towards Puppis A and in the immediate vicinity using the 26-m antenna at the Hartebeestoek Radio Observatory in South Africa in the four 18-cm lines of OH and concluded that the systemic velocity of the remnant is 7.6 km s$^{-1}$ rather than +14 km s$^{-1}$, as proposed based on H{\sc i} \citep{EMR+95} and CO \citep{gd+ma88} observations. The authors drew attention on the fact that they did detect the 1720 MHz line in emission, albeit at $\sim 3 $ km s$^{-1}$, where the other three lines appear in absorption. This emission may be hinting at the presence of an anomalous OH cloud like those reported by \citet{turner82}, which are associated with giant clouds and are tracers of the spiral arms. The neutral and molecular density distribution around Puppis A is necessary to model the $\gamma$-ray emission and explain its origin. Additionally, the hydrogen column density is a key parameter to interpret the X-ray emission. In all cases, it is essential to establish the SNR's systemic velocity. Although morphological arguments help to infer this velocity, the most reliable method is to analyze the H{\sc i} absorption. We note that high quality absorption studies towards Puppis A are lacking. The previous VLA H{\sc i} study \citep{EMR+95} has a poor velocity resolution (5.2 km s$^{-1}$) and several residual sidelobes make the identification of emission or absorption features rather unclear. The other absorption study conducted by \citet{beate+00} in OH lines has poor angular resolution ($\sim 20^\prime$) and sampling (only 11 pointings on and off the SNR). In this paper we analyze new high angular and spectral resolution data in the H{\sc i} 21-cm line in a mosaic centered at Puppis A in order to shed light on its kinematic distance and on the gas density distribution into which the shock front is expanding. | We have performed H{\sc i} observations using the ATCA and subsequently combined these data with single-dish observations, to produce an H{\sc i} mosaic around the SNR Puppis A. The resultant data has high sensitivity (2-9 mJy\,beam$^{-1}$), good spatial resolution ($118\farcs3 \times 88\farcs9$) and a spectral resolution of 0.82 km\,s$^{-1}$. We use these data to investigate the physical properties of Puppis A in two ways: \begin{enumerate} \item We focus on five unresolved continuum point sources from \citet{pap1} and investigate the H{\sc i} absorption against the background continuum of these sources. In sources 1, 3, and 5, we find H{\sc i} absorption at velocities up to $\gtrsim$100\,km\,s$^{-1}$, as well as negative spectral indices confirming their extragalactic origin. In addition to this, we also identify G260.72-3.16, which is found on the eastern edge of the SNR, as a background source, probably extragalactic, approximately 2 arcminutes long and oriented north-south. We have filtered out the contribution from these background sources and discuss that the best match for the velocity of the SNR is $+10.0\pm2.5$\,km\,s$^{-1}$, which is significantly smaller than found by previous work. \item We investigated the morphology of H{\sc i} emission over Puppis A and surrounding regions. We find a good match of continuum and H{\sc i} emission morphologies at velocities of +7.51, +9.98, and +12.46\,km\,s$^{-1}$. This provides further evidence that the systemic velocity of Puppis A is found within this range although a moderate match at higher velocities does not permit to fully rule out the previously accepted velocity of +16 km s$^{-1}$. We also see some evidence for a shell-like structure in the H{\sc i} emission in the velocity range of +6.69 to +9.98\,km\,s$^{-1}$. This shell structure appears to surround the SNR, seen in radio continuum emission. We interpret this shell as a bubble in the H{\sc i} emission that was created by the supernova explosion. \end{enumerate} Based on our alternative systemic velocity of Puppis A of $+10.0\pm2.5$\,km s$^{-1}$, we compare this velocity to Galactic rotation curves in order to determine a kinematic distance. We therefore revise the estimated distance of Puppis A to $1.3\pm0.3$\,kpc. This distance is confirmed by a comparison to the distance separately estimated based on a colour excess model. Given the revised distance, we calculate a proper motion velocity of $440 \pm 175$\,km\,s$^{-1}$ for the CCO, which is significantly smaller than previous estimates and does not require a hydrodynamic recoil mechanism to accelerate it to unusually high velocities. We estimate the radius of Puppis A to be $\sim$10\,pc, with an expansion velocity of $\sim$750\,km\,s$^{-1}$, compatible with a SNR older than 1000 years. | 16 | 9 | 1609.01779 |
1609 | 1609.06645_arXiv.txt | Given the potential of ensemble asteroseismology for understanding fundamental properties of large numbers of stars, it is critical to determine the accuracy of the scaling relations on which these measurements are based. From several powerful validation techniques, all indications so far show that stellar radius estimates from the asteroseismic scaling relations are accurate to within a few percent. Eclipsing binary systems hosting at least one star with detectable solar-like oscillations constitute the ideal test objects for validating asteroseismic radius and mass inferences. By combining radial-velocity measurements and photometric time series of eclipses, it is possible to determine the masses and radii of each component of a double-lined spectroscopic binary. We report the results of a four-year radial-velocity survey performed with the \'echelle spectrometer of the Astrophysical Research Consortium's 3.5-m telescope and the APOGEE spectrometer at Apache Point Observatory. We compare the masses and radii of 10 red giants obtained by combining radial velocities and eclipse photometry with the estimates from the asteroseismic scaling relations. We find that the asteroseismic scaling relations overestimate red-giant radii by about 5\,\% on average and masses by about 15\,\% for stars at various stages of red-giant evolution. Systematic overestimation of mass leads to underestimation of stellar age, which can have important implications for ensemble asteroseismology used for Galactic studies. As part of a second objective, where asteroseismology is used for understanding binary systems, we confirm that oscillations of red giants in close binaries can be suppressed enough to be undetectable, an hypothesis that was proposed in a previous work. | \label{sect_update} The simplest analysis of asteroseismic data is based on the overall properties of the oscillations, which are the frequency of their maximum amplitude $\nu\ind{max}$, and the mean frequency separation $\Delta\nu$ between consecutive modes of same degree. Thanks to the pair of asteroseismic scaling relations and a measurement of effective temperature $T\ind{eff}$, one gets an estimate of a star's surface gravity $\log g$ and mean density $\bar{\rho}$ by respectively comparing $\nu\ind{max}$ and $\Delta\nu$ with those of the Sun \citep[e.g.][]{Kjeldsen_Bedding_1995}: \begin{eqnarray} \frac{\bar{\rho}}{\bar{\rho}_\odot}\ &=&\ \left(\frac{\Delta\nu}{\Delta\nu_\odot}\right)^2 \\ \frac{g}{g_\odot}\ &=&\ \frac{\nu\ind{max}}{\nu\ind{max_\odot}}\ \left(\frac{T\ind{eff}}{T\ind{eff,\odot}}\right)^{\frac{1}{2}}. \end{eqnarray}\\ It is then straightforward to deduce a star's mass $M$ and radius $R$ relatively to the Sun: \begin{eqnarray} \frac{R}{R_\odot}\ &=&\ \left(\frac{\nu\ind{max}}{\nu\ind{max_\odot}}\right)\ \ \left(\frac{\Delta\nu_\odot}{\Delta\nu}\right)^2\ \left(\frac{T\ind{eff}}{T\ind{eff,\odot}}\right)^{\frac{1}{2}}\\ \frac{M}{M_\odot}\ &=&\ \left(\frac{\nu\ind{max}}{\nu\ind{max_\odot}}\right)^3\ \left(\frac{\Delta\nu_\odot}{\Delta\nu}\right)^4\ \left(\frac{T\ind{eff}}{T\ind{eff,\odot}}\right)^{\frac{3}{2}}. \end{eqnarray}\\ In practice, the measurement of the asteroseismic global parameters $\nu\ind{max}$ and $\Delta\nu$ has been largely used to estimate masses and radii of the stars displaying solar like oscillations from the CoRoT and \textit{Kepler} data \citep[see][for recent reviews]{Chaplin_Miglio_2013, Belkacem_2013}. Given the importance of asteroseismology and its scaling laws, much effort has been carried out to test their validity. We may distinguish two kinds of approaches: those based on validating the relation between $\Delta\nu$ and mean density $\bar{\rho}$ from models and simulated data \citep[e.g.][]{Stello_2009b,White_2011,Miglio_2013}, the others based on measuring $R$ of actual stars independently from asteroseismology \citep[e.g.][]{Huber_2011,Huber_2012,Silva_Aguirre_2012,Baines_2014}. All works indicated that radius estimates from asteroseismic scaling relations are accurate to a few percent. On the contrary, similar tests with independent mass determination of oscillating stars for individual stars have not been possible so far. Indeed, theoretical studies focused on the reliability of the $\Delta\nu$-$\bar\rho$ scaling relation and not on $\nu\ind{max}$. This is because $\nu\ind{max}$ has no secure theoretical basis, as it is not yet possible to make reliable predictions of the amplitude of stochastically excited modes and their dependence with frequency \citep{Belkacem_2011,Christensen-Dalsgaard_2012}. Observationally, there is some evidence to support the conclusion that the scaling relations do provide biased masses in some instances. Epstein et al. (2014, ApJ 785, 28) have found that the masses of metal-poor halo giants are significantly overestimated. White et al. (2013, MNRAS 433, 1262) found that combining the interferometric radii with the asteroseismic density implied a mass for the F star $\theta$ Cyg that was significantly lower than expected from its position in the Hertzsprung-Russell diagram. Eclipsing binaries systems (EBs) hosting at least one star with detectable solar-like oscillations constitute an ideal test case. Indeed, it is possible to determine the projected masses of each component ($M_1 \sin i$, $M_2 \sin i$) for double-line spectroscopic binaries (SB2), and the mass function $M_2^3/(M_1+M_2)^2 \sin^3 i$ for single-line spectroscopic binaries (SB1), where $i$ is the inclination of the orbital plane. For EBs, the inclination $i$ is easily retrieved from modeling the eclipses in the light curves. Absolute stellar radii $(R_1, R_2)$ are obtained from combining radial velocity and eclipse photometric measurements. So far, all published stars known to both display solar-like oscillations and belong to EBs are red giants (RGs), and all have been detected by the \textit{Kepler} mission. The first detection was the 408-day period system KIC 8410637 \citep{Hekker_2010, Frandsen_2013}. Since then, \citet{Gaulme_2013, Gaulme_2014} reported a list 18 RG eclipsing-binary (RG/EB) candidates, of which 14 displayed oscillations. \citet{Beck_2014,Beck_2015} reported the discovery of 17 stars with tidally-excited pulsations (``heartbeat''), where each system has a RG component with oscillations, and two are also EBs. Two RG/EB systems, KIC 8410637 and 9246715 have been completely characterized in terms of masses and radii by combining photometry and radial velocities \citep{Frandsen_2013, Helminiak_2015,Rawls_2016}. Both show a fairly good agreement between asteroseismic and dynamical estimates of surface gravities and mean densities, even though \citet{Huber_2014} and \citet{Brogaard_2016} contested the agreement regarding KIC 8410637. \citet{Gaulme_2014} observed that among the 19 RG/EBs identified at the time, four systems did not display oscillations. This is observed in the closest systems where rotational and orbital periods are almost synchronized and where strong surface activity is detected. They suggested that tidal forces, which tend to synchronize and circularize binary systems, spin up RGs, with this phenomenon becoming stronger as systems are closer. This would lead to the development of a dynamo mechanism, and thus the generation of magnetic fields in the RGs that become visible at the surface. The resulting spots likely absorb part of the pressure mode energy making oscillations impossible to detect in the closest systems. Alternatively, it is proposed that the presence of spots shows that the convective energy is diverted into activity signal and not into global oscillations. This would mean that properties of convection are considerably affected by binarity in the closest systems, and that oscillation excitation is reduced, or suppressed altogether. In this paper, we report the result of a four-year radial-velocity (RV) survey performed with the \'echelle spectrometer of the Astrophysical Research Consortium (ARC) 3.5-m telescope at Apache Point Observatory (APO). We benefited from complementary observations by the Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectrograh for one system. The targets are 17 EB systems of the 18 \citet{Gaulme_2013,Gaulme_2014}'s the RG/EB candidates, whose orbital periods range from 15 to 1058 days. Among those, solar-like oscillations are detected in 13, of which nine are SB2s and four SB1s. The remaining four are RG/EB candidates where no oscillations are detected. Our first objective is to test the nature of the 17 systems, where RVs allow us to determine whether the RGs belong to or are aligned with EBs. The second consists of measuring the masses and radii of the four RG candidates with no oscillations to determine if their expected $\nu\ind{max}$ fall in the observable range, i.e.\ not much larger than the Nyquist frequency. The third and main objective is the comparison of masses, radii, mean densities, and surface gravities with those obtained with the asteroseismic scaling relations. For the latter, we consider the nine SB2 with oscillations as well as KIC 8410637 for which we re-estimate its asteroseismic parameters and use \citet{Frandsen_2013}'s dynamical measurement of the mass and radius of each star. | We have identified and studied a key set of red giant stars in eclipsing binaries that allow for independent methods to obtain masses and radii. By choosing the masses and radii obtained from the binary modeling as the ground truth, we find that (all) seismic scaling relations overestimate both quantities. Our measurements will be of tremendous use in detailed modeling of these red giants that may yield insights into how the scaling laws break down away from the asymptotic limit. In any case, a sense of caution is needed when applying the scaling laws to large samples of giants if, for example, a high accuracy on ages is needed. Even though it may be likely that a simple empirical recalibration of the scaling laws for evolved stars can be applied, as many recent studies have attempted, a more satisfactory understanding is certainly desired. It is also critical to increase the sample size. We have recently found 16 more RG/EB candidates (Gaulme et al., in prep) which will be promising systems to verify the findings in this work. Among those 16, 10 display oscillations, of which six are SB2s. We have started monitoring their RVs in early 2016, both with the \'echelle spectrographs ARCES at APO and HERMES of the Mercator telescope at La Palma Observatory. \begin{deluxetable*}{l l l l l l l l l} \tabletypesize{\scriptsize} \tablecaption{Atmospheric parameters of the red giants from the ARC 3.5-m visible spectra. APOGEE estimates from the DR12 release are indicated in the last three columns when available. Systems are sorted by increasing KIC number.\label{tab_atm}} \tablewidth{0pt} \tablehead{ && \multicolumn{3}{c}{ARCES} &&\multicolumn{3}{c}{APOGEE} \\ \cline{3-5} \cline{7-9} \\ KIC & $m\ind{Kep}$& $T\ind{eff}$ & $\log g$ &$\left[Fe/H\right]$ && $T\ind{eff}$ & $\log g$&$\left[Fe/H\right]$ \\ & & [K] & [dex] & [dex] & & [K] & [dex] & [dex] } \startdata 3955867 & 13.55 & 4884(83) & 3.2(2) & -0.55(4) & & 4623(91) & 3.0(1) & -0.53(5) \\ 4569590 & 12.80 & 4706(152) & 2.5(4) & -0.34(9) & & \nodata & \nodata & \nodata \\ 4663623 & 12.83 & 4812(92) & 2.7(2) & -0.13(6) & & 4803(91) & 2.7(1) & 0.16(4) \\ 5179609 & 12.78 & 5003(54) & 3.7(2) & 0.22(7) & & 4887(91) & 3.3(1) & 0.45(4) \\ 5308778 & 11.78 & 4900(44) & 2.5(2) & -0.43(2) & & 5044(91) & 3.3(1) & -0.23(4) \\ 5786154 & 13.53 & 4747(100) & 2.6(2) & -0.06(6) & & \nodata & \nodata & \nodata \\ 7037405 & 11.88 & 4516(36) & 2.5(2) & -0.34(1) & & 4542(91) & 2.3(1) & -0.13(6) \\ 7377422 & 13.56 & 4938(110) & 3.1(2) & -0.33(6) & & \nodata & \nodata & \nodata \\ 8054233 & 11.78 & 4971(90) & 2.8(2) & -0.15(5) & & \nodata & \nodata & \nodata \\ 8410637 & 10.77 & \nodata & \nodata & \nodata & & 4699(91) & 2.7(1) & 0.16(3) \\ 8430105 & 10.42 & 5042(68) & 3.04(9) & -0.49(4) & & 4918(91) & 3.0(1) & -0.43(8) \\ 8702921 & 11.98 & 5058(86) & 3.3(2) & 0.15(5) & & 4958(91) & 3.3(1) & 0.44(6) \\ 9246715 & 9.27 & 5030(45) & 3.0(2) & 0.05(2) & & \nodata & \nodata & \nodata \\ 9291629 & 13.96 & 4713(151) & 3.4(3) & 0.04(6) & & \nodata & \nodata & \nodata \\ 9540226 & 11.67 & 4692(65) & 2.2(2) & -0.33(4) & & 4662(91) & 2.5(1) & -0.16(8) \\ 9970396 & 11.45 & 4916(68) & 3.1(1) & -0.23(3) & & 4789(91) & 2.7(1) & -0.18(7) \\ 10001167 & 10.05 & 4700(66) & 2.6(1) & -0.69(4) & & 4539(91) & 2.3(1) & -0.7(2) \\ \enddata \end{deluxetable*} \newpage \floattable \begin{deluxetable*}{l l l l l l l l l l l l l } \rotate \tabletypesize{\scriptsize} \tablecaption{Orbital parameters from dynamical modeling with JKTEBOP. Systems are sorted by decreasing orbital period $P\ind{orb}$. $T\ind{p}$ stands for the time of periastron in Kepler Julian date, $\omega$ the argument of periastron, $e$ the eccentricity, $i$ the orbital plane inclination, $(R_1, T_1, L_1)$ and $(R_2,T_2,L_2)$ the RG and companion's radii, effective temperatures and luminosities. The quantities $K_1, K_2$ are the RV semi-amplitudes and $\gamma$ is the RV offset. The least significant digit in brackets after the value indicates the uncertainty. \label{tab_orb}} \tablewidth{0pt} \tablehead{ KIC & $P\ind{orb}$ & $T\ind{p}^\dagger$ &$\omega$ &$e$& $i$ &$\displaystyle\frac{R_2}{R_1}$& $\displaystyle\frac{R_1+R_2}{a}$& $\displaystyle\left(\frac{T_2}{T_1}\right)^4$& $\displaystyle\frac{L_2}{L_1}$&$K_1$ &$K_2$ &$\gamma$ \\ & [days] & KJD & [$^\circ$] & &[$^\circ$] & [\%] & [\%] & & [\%] &[km s$^{-1}$]&[km s$^{-1}$]&[km s$^{-1}$] \\ } \startdata 8054233 & 1058.16(2) & -27.69(2) & 302.22(6) & 0.2718(4) & 89.45(1) & 10.83(6) & 1.924(7) & 2.65(4) & 3.453(5) & 12.3(2) & \nodata & -8.68(5)\\ 4663623 & 358.0900(3) & 129.73(2) & 270.25(2) & 0.43(1) & 88.562(6) & 18.7(3) & 3.91(5) & 4.0(1) & 14.400(7) & 23.0(7) & 23(1) & -8.3(4)\\ 9970396 & 235.2985(2) & 142.050(2) & 314(2) & 0.194(7) & 89.5(1) & 14.05(7) & 4.39(8) & 2.83(4) & 5.808(4) & 21.4(2) & 24.0(3) & -15.70(5)\\ 7037405 & 207.1083(7) & 87.194(9) & 310.9(10) & 0.238(4) & 88.65(9) & 12.73(6) & 8.08(8) & 3.79(4) & 6.663(5) & 23.6(2) & 26.0(3) & -39.21(9)\\ 5786154 & 197.9180(4) & 170.865(3) & 24.7(4) & 0.3764(9) & 88.74(3) & 13.93(6) & 7.14(3) & 3.57(2) & 7.560(4) & 24.7(4) & 25.7(7) & -6.3(4)\\ 9540226 & 175.4439(6) & 131.415(9) & 4.1(4) & 0.3880(2) & 90 & 7.72(6) & 7.89(2) & 3.46(3) & 2.110(4) & 23.2(3) & 31.4(5) & -12.51(9)\\ 10001167 & 120.3903(5) & 110.368(9) & 213(2) & 0.159(3) & 87.5(2) & 7.66(4) & 11.4(2) & 3.01(5) & 1.849(4) & 25.1(1) & 25.9(8) & -103.40(6)\\ 7377422 & 107.6213(4) & 165.185(7) & 356(1) & 0.4377(5) & 85.82(8) & 9.15(6) & 8.84(8) & 2.36(7) & 1.92(1) & 27.5(2) & 34(1) & -56.78(8)\\ 8430105 & 63.32713(3) & 152.7374(4) & 349.3(2) & 0.2564(2) & 89.01(10) & 10.06(2) & 9.78(3) & 1.716(8) & 1.720(3) & 27.5(2) & 43.7(3) & 16.29(7)\\ 5179609 & 43.931080(2) & 137.3016(3) & 124.1(1) & 0.150(1) & 86.47(5) & 10.57(2) & 6.92(1) & 2.0(4) & 2.4(1) & 25.0(4) & \nodata & -21.4(2)\\ 4569590 & 41.3710(1) & 164.286(5) & 261(4) & 0.004(1) & 88.6(6) & 6.85(4) & 21.7(1) & 3.54(7) & 1.615(6) & 34.1(5) & 51(1) & 24.6(1)\\ 5308778 & 40.5661(3) & 137.281(5) & 272(3) & 0.006(5) & 82.6(2) & 6.02(3) & 17.4(3) & 0.66(2) & 0.222(2) & 23.8(1) & \nodata & 17.406(9)\\ 3955867 & 33.65685(7) & 160.104(3) & 254(2) & 0.019(2) & 88.0(1) & 11.38(5) & 15.98(6) & 2.79(3) & 3.923(8) & 37.9(2) & 45(1) & 14.82(4)\\ 9291629 & 20.68643(4) & 154.288(1) & 265(2) & 0.007(2) & 84.10(3) & 23.23(4) & 23.65(5) & 2.70(1) & 15.10(2) & 50.2(2) & 51.2(5) & -30.97(5)\\ 8702921 & 19.38446(2) & 141.0929(7) & 173(3) & 0.0964(8) & 86.2(3) & 5.34(2) & 15.6(3) & 0.076(2) & 0.0227(6) & 14.0(3) & \nodata & -10.28(9)\\ 7943602 & 14.69199(4) & 142.542(3) & 103(5) & 0.001(3) & 81.55(7) & 12.63(6) & 24.40(9) & 2.54(3) & 3.48(2) & 46.0(8) & 58(3) & -185.0(1)\\ \enddata \tablecomments{$^\dagger$ Kepler Julian dates KJD are related to barycentric Julian dates BJD by: KJD = BJD - 2454833 days.} \tablecomments{$^\star$ As regards 9540226, we fixed the inclination at $90^\circ$ as JKTEBOP would not converge properly and as its inclination is almost $90^\circ$, as the almost vertical ingress and egress of the companion star indicates (Fig. \ref{fig_ph_rv_sb2}).} \end{deluxetable*} \newpage \floattable \begin{deluxetable}{l l l } \tabletypesize{\scriptsize} \tablecaption{Asteroseismic frequencies at maximum amplitude $\nu\ind{max}$ and observed mean large spacings $\Delta\nu\ind{obs}$ of the oscillating RG of our sample. Systems are sorted by increasing KIC number. All $\nu\ind{max}$ were obtained with DIAMONDS but for KIC 7377422, where the low signal-to-noise ratio of the oscillation spectrum prevented the routine from giving an accurate estimate. This specific $\nu\ind{max}$ was fine-tuned with the help of the \'echelle diagram.\label{tab_ast}} \tablewidth{0pt} \tablehead{ KIC & $\nu\ind{max}$& $\Delta\nu\ind{obs}$ \\ & [$\mu$Hz] & [$\mu$Hz] } \startdata 4663623 & 54.09 $\pm $ 0.24 & 5.212 $\pm $ 0.019 \\ 5179609 & 321.84 $\pm $ 1.00 & 22.210 $\pm $ 0.050 \\ 5308778 & 48.47 $\pm $ 1.10 & 5.050 $\pm $ 0.050 \\ 5786154 & 29.75 $\pm $ 0.16 & 3.523 $\pm $ 0.014 \\ 7037405 & 21.75 $\pm $ 0.14 & 2.792 $\pm $ 0.012 \\ 7377422 & 40.10 $\pm $ 2.10 & 4.643 $\pm $ 0.052 \\ 8054233 & 46.49 $\pm $ 0.33 & 4.810 $\pm $ 0.015 \\ 8410637 & 46.00 $\pm $ 0.19 & 4.641 $\pm $ 0.017 \\ 8430105 & 76.70 $\pm $ 0.57 & 7.138 $\pm $ 0.031 \\ 8702921 & 195.57 $\pm $ 0.47 & 14.070 $\pm $ 0.010 \\ 9246715 & 106.40 $\pm $ 0.80 & 8.310 $\pm $ 0.020 \\ 9540226 & 27.07 $\pm $ 0.15 & 3.216 $\pm $ 0.013 \\ 9970396 & 63.70 $\pm $ 0.16 & 6.320 $\pm $ 0.010 \\ 10001167 & 19.90 $\pm $ 0.09 & 2.762 $\pm $ 0.012 \\ \enddata \end{deluxetable} \newpage \floattable \begin{deluxetable*}{l l l l l l l l l l l l l l } \rotate \tabletypesize{\scriptsize} \tablecaption{Stellar physical parameters from dynamical modeling (subscripts ``rv'') and asteroseismic scaling relations (subscripts ``ast''). The parameters $M, R, \log g$, and $\bar{\rho}$ refer to stellar masses, radii, surface gravities and mean densities, and $T\ind{eff}$ effective temperatures. Systems are sorted by decreasing orbital period.\label{tab_MR}} \tablewidth{0pt} \tablehead{ & \multicolumn{9}{c}{Red Giant} &&\multicolumn{3}{c}{Companion} \\ \cline{2-10} \cline{12-14} \\ KIC & $M\ind{rv}$ & $M\ind{ast}$ &$R\ind{rv}$ & $R\ind{ast}$ & $\log g\ind{rv}$ & $\log g\ind{ast}$ & $\bar{\rho}\ind{rv}$ & $\bar{\rho}\ind{ast}$ & $T\ind{eff}$ & & $M$ & $R$ & $T\ind{eff}$ \\ & [$M_\odot$] & [$M_\odot$] & [$R_\odot$]& [$R_\odot$]& [dex] & [dex] & [$10^{-3}\bar{\rho}_\odot $] & [$10^{-3}\bar{\rho}_\odot $] &[K] & &[$M_\odot$]& [$R_\odot$]& [K] \\ } \startdata \multicolumn{14}{c}{Double-line Spectroscopic Binaries (SB2)}\\ \hline 8410637 & 1.56(3) & 1.70(7) & 10.7(1) & 11.2(2) & 2.57(1) & 2.569(5) & 1.26(6) & 1.205(9) & 4800(100) & & 1.32(2) & 1.57(3) & 6490(160) \\ 4663623 & 1.36(9) & 1.74(7) & 9.7(2) & 10.5(1) & 2.60(2) & 2.640(5) & 1.48(6) & 1.52(1) & 4812(92) & & 1.34(7) & 1.82(6) & 6808(140) \\ 9970396 & 1.14(3) & 1.36(4) & 8.0(2) & 8.47(7) & 2.69(2) & 2.716(3) & 2.2(1) & 2.234(7) & 4916(68) & & 1.02(2) & 1.12(2) & 6378(91) \\ 7037405 & 1.25(4) & 1.25(4) & 14.1(2) & 14.2(2) & 2.24(1) & 2.230(3) & 0.45(1) & 0.436(4) & 4516(36) & & 1.14(2) & 1.80(2) & 6303(53) \\ 5786154 & 1.06(6) & 1.36(6) & 11.4(2) & 12.5(2) & 2.35(2) & 2.377(5) & 0.71(2) & 0.694(6) & 4747(100) & & 1.02(4) & 1.59(3) & 6527(138) \\ 9540226 & 1.33(5) & 1.45(5) & 12.8(1) & 13.6(2) & 2.349(8) & 2.334(4) & 0.639(8) & 0.578(5) & 4692(65) & & 0.98(3) & 0.99(1) & 6399(90) \\ 9246715 & 2.149(7) & 2.19(6) & 8.30(4) & 8.28(8) & 2.932(4) & 2.943(4) & 3.76(5) & 3.86(2) & 5030(45) & & 2.171(7) & 8.37(5) & 4990(90) \\ 10001167 & 0.81(5) & 1.06(4) & 12.7(3) & 13.6(2) & 2.14(2) & 2.200(4) & 0.39(2) & 0.427(4) & 4700(66) & & 0.79(3) & 0.98(2) & 6191(91) \\ 7377422 & 1.05(8) & 1.2(2) & 9.5(2) & 9.9(6) & 2.50(2) & 2.52(2) & 1.21(4) & 1.21(3) & 4938(110) & & 0.85(3) & 0.87(2) & 6120(143) \\ 8430105 & 1.31(2) & 1.52(6) & 7.65(5) & 8.1(1) & 2.788(4) & 2.802(4) & 2.93(3) & 2.85(3) & 5042(68) & & 0.83(1) & 0.770(5) & 5771(78) \\ 4569590 & 1.56(10) & \nodata & 14.1(2) & \nodata & 2.33(1) & \nodata & 0.56(1) & \nodata & 4706(152) & & 1.05(4) & 0.96(2) & 6456(211) \\ 3955867 & 1.10(6) & \nodata & 7.9(1) & \nodata & 2.68(1) & \nodata & 2.19(4) & \nodata & 4884(83) & & 0.92(3) & 0.90(1) & 6312(108) \\ 9291629 & 1.14(3) & \nodata & 7.99(5) & \nodata & 2.691(5) & \nodata & 2.24(2) & \nodata & 4713(151) & & 1.12(2) & 1.86(1) & 6041(194) \\ 7943602 & 1.0(1) & \nodata & 6.6(2) & \nodata & 2.79(2) & \nodata & 3.40(9) & \nodata & 5096(100) & & 0.78(5) & 0.83(2) & 6431(128) \\ \hline \multicolumn{14}{c}{Single-line Spectroscopic Binaries (SB1)}\\ \hline 8054233 & \nodata & 1.60(6) & \nodata & 10.7(1) & \nodata & 2.581(5) & \nodata & 1.294(8) & 4971(90) & & 1.10(4) & 1.16(2) & 6344(117) \\ 5179609 & \nodata & 1.18(3) & \nodata & 3.50(3) & \nodata & 3.423(3) & \nodata & 27.6(1) & 5003(54) & & 0.60(1) & 0.370(3) & 5950(304) \\ 5308778 & \nodata & 1.5(1) & \nodata & 10.1(3) & \nodata & 2.60(1) & \nodata & 1.43(3) & 4900(44) & & 0.64(3) & 0.61(2) & 4416(52) \\ 8702921 & \nodata & 1.67(5) & \nodata & 5.32(5) & \nodata & 3.209(4) & \nodata & 11.07(2) & 5058(86) & & 0.274(9) & 0.284(3) & 2654(49) \\ \enddata \tablenotetext{a}{For SB1 systems, the parameters of the companion stars are deduced by combining asteroseismic masses and radii of the RG with the mass function obtained from light curve and radial velocity modeling. } \tablecomments{The dagger symbols $^\dagger$ indicate that the dynamical values of KICs 8410637 and 9246715 are taken from \citet{Frandsen_2013} and \citet{Rawls_2016} respectively.} \end{deluxetable*} \newpage \clearpage \appendix Complete set of radial velocities we present in this paper. \begin{deluxetable}{l l l } \tabletypesize{\scriptsize} \tablecaption{Radial velocities (part I). \label{tab_4}} \tablewidth{0pt} \tablehead{ Date & RV1 & RV2 \\ KJD & [km s$^{-1}$] & [km s$^{-1}$] \\ } \startdata \multicolumn{3}{c}{KIC 3955867} \\ \hline 1704.7441 & -16.20(5) & 51.9(5)\\ 1741.7754 & 1.85(5) & 22.7(2)\\ 1766.5527 & -19.15(5) & 55.8(3)\\ 1936.9669 & -22.96(5) & 61.4(3)\\ 1958.9400 & 37.85(6) & -8.9(5)\\ 1990.8794 & 45.86(5) & -19.9(6)\\ 2032.6426 & -5.46(5) & 40.5(7)\\ 2111.7190 & 0.43(5) & 31.4(4)\\ 2113.5592 & 14.49(5) & \nodata\\ 2121.6013 & 52.47(4) & -29.9(4)\\ 2125.7532 & 43.68(5) & -21.7(2)\\ 2126.7446 & 37.69(5) & -15.4(5)\\ 2286.9775 & 45.42(5) & -21.6(3)\\ 2315.8251 & 15.98(4) & \nodata\\ 2315.8500 & 16.67(4) & \nodata\\ \hline \multicolumn{3}{c}{KIC 4569590} \\ \hline 1741.7931 & 43.87(7) & -10(1)\\ 1936.9265 & -5.57(7) & 69.4(8)\\ 1958.8371 & 52.25(8) & -12(1)\\ 1967.9110 & 9.08(7) & 47(1)\\ 1980.8471 & 1.97(6) & 59.0(8)\\ 2032.7087 & 51.27(6) & -13.0(7)\\ 2069.6493 & 31.99(6) & \nodata\\ 2111.7513 & 33.93(7) & \nodata\\ 2113.7085 & 42.82(6) & -5(1)\\ 2121.6195 & 58.69(6) & -22.9(7)\\ 2125.6981 & 47.16(6) & -8.9(4)\\ 2126.6056 & 43.86(6) & -4.7(4)\\ 2129.5493 & 29.78(7) & \nodata\\ 2315.8739 & 20.64(7) & \nodata\\ 2315.8975 & 20.38(7) & \nodata\\ 2462.6855 & 18.50(7) & \nodata\\ \hline \multicolumn{3}{c}{KIC 4663623}\\ \hline 1737.7064 & -7.11(2) & \nodata\\ 1741.6719 & -8.52(2) & \nodata\\ 1958.8201 & 16.01(2) & -31.0(3)\\ 1980.8653 & 12.99(2) & -30.2(3)\\ 2032.6816 & 6.25(2) & -21(2)\\ 2069.6872 & -4.53(2) & -13(4)\\ 2113.6769 & -11.13(4) & -1(4)\\ 2121.7263 & -10.87(5) & -1(3)\\ 2126.6409 & -13.93(2) & 1(7)\\ 2462.6391 & -11.27(2) & \nodata\\ 2475.7933 & -12.71(2) & \nodata\\ 2487.5708 & -12.22(3) & 1(6)\\ 2639.9061 & -5.46(2) & \nodata\\ 2670.8693 & 13.17(2) & -32.2(3)\\ 2674.8132 & 13.00(2) & -31.8(3)\\ 2685.9605 & 14.79(2) & -30.9(3)\\ 2736.8396 & 6.57(2) & -21.5(3)\\ 2780.6121 & -2.25(3) & \nodata\\ 2780.6286 & -2.13(2) & \nodata\\ \hline \multicolumn{3}{c}{KIC 5179609}\\ \hline 1257.8837 & -30.77(3) & \nodata\\ 1272.7406 & -33.86(3) & \nodata\\ 1341.9043 & -25.34(3) & \nodata\\ 1569.8694 & -41.63(3) & \nodata\\ 1591.9183 & 7.53(3) & \nodata\\ 1611.8624 & -37.44(3) & \nodata\\ 1704.6737 & -43.11(3) & \nodata\\ 1711.7021 & -36.07(3) & \nodata\\ 1737.6376 & -25.79(4) & \nodata\\ 1765.5876 & 5.79(3) & \nodata\\ 1765.6280 & 5.01(3) & \nodata\\ 1939.9000 & 2.11(3) & \nodata\\ 1990.8967 & 1.88(3) & \nodata\\ 2069.7258 & -5.34(3) & \nodata\\ 2111.7697 & -17.07(3) & \nodata\\ 2113.7604 & -6.73(3) & \nodata\\ 2121.6748 & 3.89(3) & \nodata\\ 2125.6580 & -4.89(3) & \nodata\\ 2126.5887 & -7.13(3) & \nodata\\ 2286.9007 & -18.59(3) & \nodata\\ 2286.9223 & -17.95(3) & \nodata\\ 2462.5796 & -17.41(3) & \nodata\\ 2462.5988 & -18.06(3) & \nodata\\ 2506.5914 & -18.11(3) & \nodata\\ \hline \multicolumn{3}{c}{KIC 5308778}\\ \hline 1569.9394 & 38.33(4) & \nodata\\ 1591.9508 & -0.21(4) & \nodata\\ 1611.9306 & 36.32(4) & \nodata\\ 1623.8267 & -1.31(4) & \nodata\\ 1683.6971 & 34.83(4) & \nodata\\ 1737.5909 & 24.54(4) & \nodata\\ 1737.7662 & 22.29(4) & \nodata\\ 1741.6243 & 9.89(4) & \nodata\\ 1765.6147 & 36.30(4) & \nodata\\ 1939.9725 & 25.86(4) & \nodata\\ 1958.9553 & 5.30(4) & \nodata\\ 1990.9345 & -5.07(4) & \nodata\\ 2111.7005 & -4.58(4) & \nodata\\ 2113.6109 & -6.16(4) & \nodata\\ 2121.7445 & 5.25(4) & \nodata\\ 2125.5745 & 20.99(4) & \nodata\\ 2126.6561 & 23.74(4) & \nodata\\ 2286.9375 & 16.88(4) & \nodata\\ \hline \multicolumn{3}{c}{KIC 5786154}\\ \hline 1272.7870 & -17.16(2) & \nodata\\ 1340.8309 & 19.10(2) & \nodata\\ 1569.8874 & 6.49(2) & -17.1(4)\\ 1591.9356 & -15.03(2) & 2.05(5)\\ 1611.8805 & -21.27(2) & 8.5(5)\\ 1623.8985 & -22.68(2) & 11.7(3)\\ 1704.6241 & -4.94(2) & \nodata\\ 1711.6255 & 1.25(2) & -12.3(2)\\ 1741.5950 & 26.26(2) & -38.2(3)\\ 1765.6455 & 9.62(2) & \nodata\\ 1939.8774 & 25.15(2) & -40.6(3)\\ 1980.9316 & -9.30(2) & \nodata\\ 2032.7296 & -22.03(2) & 10.9(1)\\ 2069.7759 & -16.79(2) & \nodata\\ 2111.5711 & 4.26(2) & \nodata\\ 2113.5789 & 5.45(2) & -18.1(2)\\ 2121.7081 & 9.31(2) & -22.5(1)\\ 2125.6755 & 13.28(2) & -27.5(3)\\ 2126.7248 & 13.64(2) & -29.4(3)\\ 2129.5945 & 18.22(2) & -32.6(1)\\ 2487.7330 & -8.26(2) & \nodata\\ 2506.5403 & 3.05(3) & \nodata\\ \hline \multicolumn{3}{c}{KIC 7037405}\\ \hline 1623.9163 & -44.44(4) & -31.5(9)\\ 1724.7334 & -40.6(1) & \nodata\\ 1726.7233 & -38.4(1) & \nodata\\ 1727.7210 & -37.4(1) & \nodata\\ 1751.6322 & -14.3(1) & \nodata\\ 1752.6307 & -13.7(1) & \nodata\\ 1924.8930 & -46.4(1) & \nodata\\ 1925.9023 & -45.6(1) & \nodata\\ 1927.9058 & -43.9(1) & \nodata\\ 1928.8729 & -42.9(1) & \nodata\\ 1929.8687 & -42.1(1) & \nodata\\ 1930.8812 & -41.1(1) & \nodata\\ 1936.9120 & -35.26(3) & \nodata\\ 1950.8357 & -20.5(1) & \nodata\\ 1951.8220 & -19.7(1) & \nodata\\ 1952.8254 & -18.8(1) & \nodata\\ 1953.7985 & -18.0(1) & \nodata\\ 1954.8094 & -17.3(1) & \nodata\\ 1955.8431 & -16.5(1) & \nodata\\ 1958.7673 & -15.22(4) & -67.6(5)\\ 1967.9409 & -11.77(3) & -67.9(8)\\ 1979.7451 & -13.7(1) & \nodata\\ 1980.8136 & -14.84(3) & -65.0(8)\\ 1981.7555 & -14.6(1) & \nodata\\ 1982.7855 & -14.9(1) & \nodata\\ 1983.7663 & -15.5(1) & \nodata\\ 1984.7620 & -15.9(1) & \nodata\\ 1985.7646 & -16.3(1) & \nodata\\ 1986.7622 & -17.0(1) & \nodata\\ 1987.7560 & -17.4(1) & \nodata\\ 1990.8100 & -19.47(3) & -59.1(8)\\ 2032.6241 & -42.64(3) & \nodata\\ 2069.6345 & -55.72(3) & -21.1(9)\\ 2111.5547 & -56.78(3) & \nodata\\ 2113.5972 & -56.50(3) & -20.5(8)\\ 2121.5857 & -53.13(3) & -23.1(8)\\ 2125.6083 & -51.09(3) & -24.2(8)\\ 2126.6259 & -50.67(3) & -26.4(9)\\ 2129.5633 & -48.59(3) & -27.5(6)\\ 2286.9600 & -58.05(3) & -19.3(10)\\ 2315.9580 & -57.50(3) & -19.3(9)\\ 2462.5620 & -50.71(5) & \nodata\\ 2475.7807 & -53.66(3) & -23.3(7)\\ 2487.6314 & -55.83(3) & -19.4(8)\\ 2506.6085 & -59.54(3) & -18.8(8)\\ \hline \multicolumn{3}{c}{KIC 7377422}\\ \hline 1697.7442 & -61.74(4) & \nodata\\ 1711.7231 & -69.59(3) & -39.0(2)\\ 1741.7342 & -70.96(3) & -39.3(4)\\ 1936.8880 & -72.75(4) & -38.5(4)\\ 1958.9203 & -69.58(4) & -41.9(2)\\ 1990.8380 & -23.12(4) & -96.2(4)\\ 2032.7870 & -68.31(3) & -39.4(4)\\ 2069.7564 & -68.27(3) & -44.2(5)\\ 2111.6801 & -35.26(3) & -81.5(4)\\ 2113.7270 & -41.95(3) & -78.3(5)\\ 2121.6539 & -55.06(3) & \nodata\\ 2125.6373 & -59.11(3) & \nodata\\ 2126.6746 & -61.66(3) & \nodata\\ 2315.9421 & -18.81(3) & -102.2(8)\\ \hline \multicolumn{3}{c}{KIC 7943602}\\ \hline 1704.7023 & -218.7(1) & -143.2(3)\\ 1711.7633 & -145.8(1) & -231.7(6)\\ 1741.7134 & -154.1(1) & -222.2(4)\\ 1939.9178 & -217.7(1) & -144.9(3)\\ 1958.8983 & -143.3(2) & -241.8(4)\\ 1980.8297 & -223.3(1) & -138.2(5)\\ 1990.8576 & -146.5(1) & -234.3(4)\\ 2069.7047 & -228.5(1) & -132.5(6)\\ 2111.6127 & -201.9(1) & -155.0(7)\\ 2113.6475 & -228.4(1) & -131.8(4)\\ 2125.5576 & -188.7(1) & \nodata\\ 2126.7027 & -210.3(1) & -153.2(4)\\ 2462.6563 & -172.0(2) & -198.9(5)\\ \hline \multicolumn{3}{c}{KIC 8054233}\\ \hline 1737.6793 & -18.11(2) & \nodata\\ 1741.6890 & -18.58(2) & \nodata\\ 1936.8672 & -17.35(2) & \nodata\\ 1939.9853 & -16.26(2) & \nodata\\ 1958.8028 & -14.97(2) & \nodata\\ 1980.9473 & -13.20(2) & \nodata\\ 2032.7695 & -5.82(2) & \nodata\\ 2069.7403 & -1.89(2) & \nodata\\ 2113.7753 & 1.15(2) & \nodata\\ 2121.7568 & 2.09(2) & \nodata\\ 2125.7701 & 2.36(2) & \nodata\\ 2129.6116 & 4.72(2) & \nodata\\ 2462.6225 & -7.37(2) & \nodata\\ 2487.5853 & -6.28(2) & \nodata\\ \hline \multicolumn{3}{c}{KIC 8430105}\\ \hline 1257.8962 & -1.52(2) & 47.1(8)\\ 1272.7620 & 0.80(2) & 43.2(9)\\ 1332.7746 & -2.76(3) & \nodata\\ 1332.9388 & -5.14(2) & \nodata\\ 1333.8804 & -2.60(3) & \nodata\\ 1340.9038 & 8.43(5) & \nodata\\ 1569.8560 & 0.83(2) & 40(2)\\ 1591.8649 & 3.74(3) & 38(1)\\ 1611.9079 & 50.06(2) & -36(2)\\ 1623.9504 & 17.79(2) & \nodata\\ 1704.6859 & -3.85(3) & 49(1)\\ 1711.6113 & -3.19(2) & 47(1)\\ 1737.7522 & 49.07(2) & \nodata\\ 1765.6598 & -3.0(4) & 46(2)\\ 1936.9847 & 27.30(2) & -0.0(8)\\ 1990.9240 & 50.95(2) & -36.3(10)\\ 2111.6517 & 40.25(2) & -22.5(9)\\ 2113.5453 & 46.46(3) & -30(2)\\ 2121.5395 & 44.10(3) & -26(1)\\ 2125.6213 & 31.29(2) & -9(1)\\ 2126.6890 & 25.64(2) & -3.8(8)\\ 2129.5366 & 20.33(3) & \nodata\\ \hline \multicolumn{3}{c}{KIC 8702921}\\ \hline 1239.8587 & -1.48(7) & \nodata\\ 1239.9301 & -1.21(7) & \nodata\\ 1257.8566 & 1.54(8) & \nodata\\ 1272.7136 & -1.28(7) & \nodata\\ 1332.9188 & 1.07(8) & \nodata\\ 1333.9232 & 1.62(8) & \nodata\\ 1340.8599 & -19.91(8) & \nodata\\ 1569.9025 & -3.72(8) & \nodata\\ 1591.8791 & -15.99(8) & \nodata\\ 1611.9427 & -18.60(7) & \nodata\\ 1683.6718 & 1.95(8) & \nodata\\ 1737.6059 & -2.25(7) & \nodata\\ 1741.6564 & 2.21(8) & \nodata\\ 1939.9603 & -12.52(8) & \nodata\\ 1958.9676 & -10.18(8) & \nodata\\ 1980.9624 & -21.36(7) & \nodata\\ 1990.9465 & 0.95(8) & \nodata\\ 2111.7367 & -1.58(7) & \nodata\\ 2113.6943 & -8.52(7) & \nodata\\ 2121.6368 & -17.51(7) & \nodata\\ 2125.7331 & -1.82(8) & \nodata\\ 2126.7805 & -0.17(8) & \nodata\\ \hline \multicolumn{3}{c}{KIC 9291629}\\ \hline 1704.7220 & -50.05(9) & -9.5(1)\\ 1711.7861 & 20.76(9) & -79.9(1)\\ 1741.7565 & -80.69(9) & 18.0(1)\\ 1936.9442 & 12.37(8) & -73.4(1)\\ 1958.8578 & 17.26(8) & -77.7(1)\\ 1980.8990 & 18.53(8) & -80.1(1)\\ 2032.6612 & -79.81(8) & 19.0(2)\\ 2069.6667 & -53.60(9) & -6.5(1)\\ 2111.6369 & -61.39(8) & 1.1(2)\\ 2113.6266 & -78.82(8) & 18.1(1)\\ 2121.5667 & -3.73(9) & -56.1(1)\\ 2121.7727 & -4.00(9) & -62.32(9)\\ 2125.7167 & 17.79(8) & -80.76(10)\\ 2126.7643 & 9.88(9) & -77.36(9)\\ 2315.9212 & -26.15(8) & \nodata\\ \hline \multicolumn{3}{c}{KIC 9540226}\\ \hline 1257.9142 & -25.15(2) & 7.8(7)\\ 1272.7712 & -26.14(2) & 7.7(4)\\ 1332.8001 & -7.65(3) & \nodata\\ 1332.8900 & -6.28(2) & \nodata\\ 1333.9536 & -5.28(2) & \nodata\\ 1340.8854 & 1.48(2) & -32.8(8)\\ 1569.9639 & -15.21(2) & \nodata\\ 1591.9752 & -23.25(2) & 4(3)\\ 1623.8139 & -26.23(2) & 6.9(5)\\ 1704.6592 & 18.43(2) & -54.1(6)\\ 1711.6883 & 20.28(2) & -53.3(6)\\ 1737.7419 & -10.24(2) & \nodata\\ \hline \multicolumn{3}{c}{KIC 9970396}\\ \hline 1569.9516 & 6.63(2) & -43.9(4)\\ 1591.9628 & 4.21(2) & \nodata\\ 1611.9547 & -3.76(2) & -29.9(6)\\ 1623.8389 & -10.27(2) & -23.5(2)\\ 1697.7919 & -33.74(2) & 3.2(6)\\ 1711.6722 & -34.64(2) & 4.1(5)\\ 1737.5785 & -30.52(2) & 1.4(5)\\ 1741.5789 & -29.26(2) & 0.0(4)\\ 1939.8576 & -35.19(2) & 4.4(3)\\ 1958.7833 & -33.76(3) & 6.5(5)\\ 1980.8812 & -27.58(2) & -0.3(6)\\ 1990.9108 & -22.65(2) & \nodata\\ 2032.7486 & 6.01(2) & \nodata\\ 2069.7919 & 0.45(2) & -35.8(3)\\ 2111.5885 & -17.17(2) & \nodata\\ 2113.7456 & -20.41(2) & \nodata\\ 2121.6929 & -22.55(2) & -8.9(3)\\ 2125.5948 & -22.54(2) & -6.4(4)\\ 2125.7828 & -25.14(2) & -10.1(3)\\ 2126.5730 & -22.75(2) & -7.9(2)\\ 2129.5787 & -24.04(2) & -7.0(2)\\ 2475.7632 & -14.59(2) & \nodata\\ 2487.7494 & -5.29(2) & -32.7(6)\\ \hline \multicolumn{3}{c}{KIC 10001167}\\ \hline 1569.8111 & -107.32(2) & \nodata\\ 1591.8177 & -83.34(2) & -123.8(8)\\ 1611.8137 & -84.09(2) & -123.1(7)\\ 1623.8500 & -90.59(2) & -114(2)\\ 1648.8167 & -116.85(3) & -87.3(6)\\ 1697.7284 & -95.28(2) & -110.1(6)\\ 1711.6021 & -83.61(2) & -123.7(7)\\ 1737.5673 & -86.59(2) & -122.4(7)\\ 1741.6099 & -89.97(3) & -116.0(8)\\ 1765.5998 & -113.77(2) & \nodata\\ 1958.7502 & -82.01(3) & \nodata\\ 1967.9514 & -82.26(2) & -123.0(9)\\ 1980.9162 & -87.70(2) & -121(1)\\ 1990.8210 & -95.77(2) & -110.1(6)\\ 2032.6951 & -130.34(2) & -74.2(9)\\ 2111.6633 & -97.47(2) & -111.2(3)\\ 2113.6633 & -99.72(2) & \nodata\\ 2121.5500 & -106.60(2) & \nodata\\ 2125.5424 & -111.15(2) & -97.5(8)\\ 2129.6399 & -117.27(2) & \nodata\\ 2286.9958 & -113.77(2) & -92(1) \enddata \end{deluxetable} | 16 | 9 | 1609.06645 |
1609 | 1609.07369_arXiv.txt | We infer distances and their asymmetric uncertainties for two million stars using the parallaxes published in the \gaia{} DR1 (GDR1) catalogue. We do this with two distance priors: A minimalist, isotropic prior assuming an exponentially decreasing space density with increasing distance, and an anisotropic prior derived from the observability of stars in a Milky Way model. We validate our results by comparing our distance estimates for 105 Cepheids which have more precise, independently estimated distances. For this sample we find that the \mw{} prior performs better (the RMS of the scaled residuals is 0.40) than the \expp{} prior (RMS is 0.57), although for distances beyond 2\,kpc the \mw{} prior performs worse, with a bias in the scaled residuals of -0.36 (vs. -0.07 for the \expp{} prior). We do not attempt to include the photometric data in GDR1 due to the lack of reliable colour information. Our distance catalogue is available at \url{http://www.mpia.de/homes/calj/tgas\_distances/main.html} as well as at CDS. This should only be used to give individual distances. Combining data or testing models should be done with the original parallaxes, and attention paid to correlated and systematic uncertainties. | The ESA \gaia{} mission \citep{gaiamission} is obtaining highly accurate parallaxes and proper motions of over one billion sources brighter than $G\simeq 20.7$. The first data release (\gaia{} DR1), based on early mission data, was released to the community on 14 September 2016 (\citealt{gdr1paper}). The primary astrometric data set in this release lists the positions, parallaxes, and proper motions of 2\,057\,050 stars which are in the \tyc{}-2 \citep{hoeg00} catalogue (93\,635 of the these are \hip{} \citep{per97,van07} sources). This data set is called the \tyc{}-\gaia{} astrometric solution (TGAS; \citealt{mic15,gdr1astrometry}). The 5-parameter astrometric solutions for TGAS stars were obtained by combining \gaia{} observations with the positions and their uncertainties of the \tyc{}-2 stars (with an observation epoch of around J1991) as prior information \citep{gdr1astrometry}. This was necessary because the observation baseline in the early \gaia{} data was insufficient for a \gaia{}-only solution. The resulting solutions have median parallax uncertainties of $\sim$0.3\,mas, with an additional systematic uncertainty of about $\sim$0.3\,mas \citep{gdr1paper, gdr1astrometry}. Using the TGAS parallaxes $\varpi$ and uncertainties $\errVarpi{}$, we here infer the distances to all TGAS stars along with (asymmetric) distance uncertainties (as Bayesian credible intervals). The motivation and methods to estimate distances from parallaxes have been described in our earlier works (\citet{cbj15, ast16}, henceforth Paper~I and Paper~II respectively). We will not repeat the discussion here, except to remind readers that inverting parallaxes to estimate distances is only appropriate in the absence of noise. As parallax measurements have uncertainties---and for many TGAS stars very large uncertainties---distance estimation should always be treated as an inference problem. | We have inferred the distances of two million stars in the \gaia{} DR1 catalogue using Bayesian inference. The priors used are the \expp{} prior with scale length $L=1.35$\,kpc, and the \mw{} prior with the same parameters as in Paper~II. The median fractional distance uncertainties ($\fr=\sigma/r_{Mo}$) are 0.38 and 0.27 for the \expp{} and the \mw{} prior respectively. If we only consider stars with the estimated distances $\rmode<200$\,pc, the median value of $\fr$ improves at about $\sim$0.04 for both priors. This applies to about 193\,000 stars (the exact number is different for both priors) or about 9\% of TGAS. We validate our distance estimates using more precise distances for Cepheid stars in TGAS taken from \cite{gro13}. We found that for distances closer than 2000\,pc, the \mw{} prior performs better than the \expp{} prior. Beyond 2000\,pc, the \mw{} prior performs worse for this sample (which are intrinsically bright and distant stars) because it assumes that stars are more likely to be closer in the disc than further away. Our \expp{} prior has a longer scale length and thus performs better on this sample when faced with the same poor measurements. But overall the \mw{} prior performs better. Due to the lack of reliable colours, we do not use these in combination with the parallaxes to estimate distances. Rather than using the \tyc{} magnitudes, significant improvements can be achieved taking spectrophotometric information from other surveys. We choose here just to present astrometric distances. The distance estimates presented in this paper are useful for \textit{individual} stars. To obtain the mean distance to a group of stars, such as a cluster, one should do a combined inference using the original parallaxes and taking into account the correlated parallax uncertainties for stars observed in a small field. Note, however, that this combination will still not reduce the uncertainty in the mean below the limit presented by the TGAS systematic parallax error. Similarly, if one wishes to compare a model for distances to the TGAS data, this is normally best done by projecting the model-predicted distances into the parallax domain, rather than to use individual estimated distances. | 16 | 9 | 1609.07369 |
1609 | 1609.07705_arXiv.txt | The nature and origin of the {\it Fermi} bubbles detected in the inner Galaxy remain elusive. In this paper, we briefly discuss some recent theoretical and observational developments, with a focus on the AGN jet model. Analogous to radio lobes observed in massive galaxies, the {\it Fermi} bubbles could be naturally produced by a pair of opposing jets emanating nearly along the Galaxy's rotation axis from the Galactic center. Our two-fluid hydrodynamic simulations reproduce quite well the bubble location and shape, and interface instabilities at the bubble surface could be effectively suppressed by shear viscosity. We briefly comment on some potential issues related to our model, which may lead to future progress. | The {\it Fermi} bubbles are a large structure recently discovered in the inner Galaxy by the {\it Fermi Gamma-ray Space Telescope} (\citealt{su10}, \citealt{dobler10}, \citealt{ackermann14}). The two gamma-ray bubbles have a bilobular shape, extending to $\sim 50^{\circ}$ above and below the Galactic center (GC). Assuming the distance of the GC to be $d\sim 8.5$ kpc, the major axis of each bubble roughly aligns with the Galaxy's rotation axis, having a length of $\sim d {\rm tan}50^{\circ}\sim10$ kpc. The {\it Fermi} bubbles have a hard $\sim E^{-2}$ spectrum between $1$ GeV and $100$ GeV, and sharp edges. They have counterparts in microwave, previously observed by the {\it Wilkinson Microwave Anisotropy Probe} (WMAP) and referred as the WMAP haze \citep{finkbeiner04a}. The microwave emission from the {\it Fermi} bubbles is usually considered to arise from synchrotron emission of a hard population of cosmic ray (CR) electrons (\citealt{dobler08}, \citealt{dobler12}), while the origin of their gamma-ray emission remains debated. The leptonic scenario assumes that the gamma ray emission comes from inverse Compton scattering (ICS) of the ambient interstellar radiation field (ISRF) by the same population of hard electrons (\citealt{dobler10}, \citealt{su10},\citealt{guo12a}). Alternatively, in the hadronic scenario, the gamma ray emission results from CR protons, which collide inelastically with the ambient gas and produce neutral pions, which decay into gamma rays (\citealt{crocker11}, \citealt{zubovas11}, \citealt{mou15}). With properly chosen CR spectrum, both the leptonic and hadronic scenarios fit gamma ray data quite well, while the latter seems to require an extra population of primary electrons to explain the observed microwave emission from the {\it Fermi} bubbles \citep{ackermann14}. The elusive origin of the {\it Fermi} bubbles remains a topic of active research. \citet{crocker11} suggested that the bubbles are powered by CR protons continuously injected by supernova explosions in the GC over the last few Gyrs. \citet{crocker14} and \citet{crocker15} further argue that the bubbles are inflated by a nuclear outflow driven by GC star formation over the last few 100 million years. On the other hand, Sgr A$^{*}$ may be a natural energy source for the {\it Fermi} bubbles. Black hole accretion events often release winds and jets, as observed in quasars and radio galaxies \citep{fabian12}. Observational evidence for recent AGN activity at the GC includes (1) there appear to be two young stellar disks within $0.5$ pc of Sgr A$^{*}$ with typical stellar ages of $6\pm 2$ Myr (\citealt{genzel03}, \citealt{paumard06}), which may be remnants of recent accretion flows onto Sgr A$^{*}$; (2) the H$\alpha$ emission of the Magellanic Stream peaks toward the south Galactic pole, which may be energized by ionizing photons from Sgr A$^{*}$ about $1 - 3$ Myrs ago \citep{bland13}. The GC AGN activity could potentially inflate bubbles through jets or winds. The AGN jet model for the {\it Fermi} bubbles was first studied by \citet{guo12a}, motivated by the morphological similarity between the {\it Fermi} bubbles and extragalactic radio lobes. The model is further studied by \citet{guo12b}, \citet{yang12}, and \citet{yang13}, arguing that the bubbles were produced by a recent AGN jet activity about few Myrs ago, and the origin of the gamma ray emission is leptonic. In contrast, the AGN wind model typically assumes that the gamma ray emission of the {\it Fermi} bubbles results from CR protons. \citet{zubovas11} proposed that the {\it Fermi} bubbles were inflated by wide-angle, ultrafast outflows from Sgr A$^{*}$ in its quasar phase around 6 Myr ago (also see \citealt{zubovas12}). Alternatively, motivated by recent numerical studies of hot accretion flows onto SMBHs \citep{yuan14}, \citet{mou14} and \citet{mou15} argue that the {\it Fermi} bubbles were continuously inflated by winds from hot accretion flows around Sgr A$^{*}$ during the past $\sim 10$ Myrs. | While the AGN jet model for the {\it Fermi} bubbles is promising, there are still some challenging issues specifically related to its current version. The total power of two jets in our fiducial run in \citet{guo12a} is $\sim 0.3$ the Sgr A$^{*}$ Eddington luminosity, which might correspond to an accretion rate too high for hot accretion flows typically hosting AGN jets. However, the jet power could be much less if the halo gas density is lower \citep{guo12b}, and the jet power of hot accretion flows could exceed the accretion rate of rest mass energy \citep{sadowski13}. The current age of the bubbles in our model is about $1 - 3$ Myr, which is constrained by the cooling time of CR electrons. However, several pieces of evidence seem to suggest that the GC AGN activity occurred a slightly longer time ago. The ages of young stars in the GC stellar disks are about $6\pm 2$ Myr (\citealt{paumard06}). Ultraviolet absorption-line spectra suggests the existence for a biconical outflow from the GC probably driven by the {\it Fermi} bubble event over the past $2.5 - 4$ Myr \citep{fox15}. Observations of soft X-ray emission lines toward the bubble regions also suggest an expansion age of about 4 Myr \citep{miller16}. If the real bubble age is around 4 Myr, to keep their hard spectra CR electrons in the {\it Fermi} bubbles should be continuously reaccelerated by the second order Fermi acceleration \citep{mertsch11} or other mechanisms, unless the gamma ray emission from the bubbles is dominated by CR protons. | 16 | 9 | 1609.07705 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.